% Encoding: UTF-8 @Article{AACI, Title = {Recycling of strange sets: {I. Cycle} expansions}, Author = {Artuso, R. and Aurell, E. and Cvitanovi{\'c}, P.}, Journal = {Nonlinearity}, Year = {1990}, Pages = {325--359}, Volume = {3}, DOI = {10.1088/0951-7715/3/2/005} } @Article{AACII, Title = {Recycling of strange sets: {II. Applications}}, Author = {Artuso, R. and Aurell, E. and Cvitanovi{\'c}, P.}, Journal = {Nonlinearity}, Year = {1990}, Pages = {361--386}, Volume = {3}, DOI = {10.1088/0951-7715/3/2/006} } @Article{ACHKW11, Title = {Revealing the state space of turbulent pipe flow by symmetry reduction}, Author = {Willis, A. P. and Cvitanovi{\'c}, P. and Avila, M.}, Journal = {J. Fluid Mech.}, Year = {2013}, Addendum = {\arXiv{1203.3701}}, Pages = {514--540}, Volume = {721}, DOI = {10.1017/jfm.2013.75} } @Book{adams2003sobolev, Title = {Sobolev Spaces}, Author = {Adams, R. A. and Fournier, J. J. F.}, Publisher = {Academic Press}, Year = {2003}, Address = {New York} } @Article{AGHO288, Title = {Heteroclinic cycles and modulated travelling waves in systems with {O(2)} symmetry}, Author = {D. Armbruster and J. Guckenheimer and P. Holmes}, Journal = {Physica D}, Year = {1988}, Pages = {257--282}, Volume = {29}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{agladze1987, Title = {An observation of resonance of spiral waves in distributed excitable medium}, Author = {Agladze, K. I. and Davydov, V. A. and Mikhailov, A. S.}, Journal = {JETP Lett}, Year = {1987}, Pages = {767--770}, Volume = {45} } @Article{AHA, Title = {Heart disease and stroke statistics-2008 update: a report from the {America}n Heart Association Statistics Committee and Stroke Statistics Subcommittee}, Author = {W. Rosamond and K. Flegal and K. Furie and A. Go and K. Greenlund and N. Haase and S. M. Hailpern and M. Ho and V. Howard and B. Kissela and S. Kittner and D. Lloyd-Jones and M. McDermott and J. Meigs and C. Moy and G. Nichol and C. O'Donnell and V. Roger and P. Sorlie and J. Steinberger and T. Thom and M. Wilson and Y. Hong}, Journal = {Circulation}, Year = {2008}, Pages = {e25}, Volume = {117}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Owner = {roman}, Timestamp = {2013.11.03} } @Article{ahuja_template-based_2007, Title = {Template-based stabilization of relative equilibria in systems with continuous symmetry}, Author = {S. Ahuja and I. G. Kevrekidis and C. W. Rowley}, Journal = {J. Nonlin. Sci.}, Year = {2007}, Pages = {109--143}, Volume = {17}, Abstract = {We present an approach to the design of feedback control laws that stabilize relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original systems are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. We present two different approaches of control design. The first approach assumes that the closed loop system is affine in the control and that the actuation is equivariant. We derive feedback laws for the reduced system that minimize a quadratic cost function. The second approach is more general; here the actuation need not be equivariant, but the actuators can be translated in the symmetry direction. The controller resulting from this approach leaves the dynamics associated with the symmetry variable unchanged. Both approaches are simple to implement, as they use standard tools available from linear control theory. We illustrate the approaches on three examples: a rotationally invariant planar {ODE,} an inverted pendulum on a cart, and the {Kuramoto-Sivashinsky} equation with periodic boundary conditions.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Akhmediev04, Title = {Strongly asymmetric soliton explosions}, Author = {Akhmediev, N. and Soto-Crespo, J. M.}, Journal = {Phys. Rev. E}, Year = {2004}, Volume = {70} } @article{Allessie1977, title={Circus movement in rabbit atrial muscle as a mechanism of tachycardia}, author={Allessie, Maurits A and Bonke, Felix Im and Schopman, Francien Jg}, journal={Circulation Research}, volume={41}, number={1}, pages={9--18}, year={1977} } @article{Allessie1985, title={Experimental evaluation of {M}oe's multiple wavelet hypothesis of atrial fibrillation}, author={Allessie, Maurits A}, journal={Cardiac arrhythmias}, pages={265--276}, year={1985}, publisher={Grune \& Stratton} } @Article{alkhadra2000, Title = {The role of electroporation in defibrillation}, Author = {A. Al-Khadra and V. Nikolski and I. R. Efimov}, Journal = {Circ. Res.}, Year = {2000}, Pages = {797--804}, Volume = {87}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{AllCro13, author = {Allen, J.-M. A. and Cross, M. C.}, title = {Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns}, journal = {Phys. Rev. E}, year = {2013}, volume = {87}, pages = {052902}, note = {\arXiv{1303.1548}}, doi = {10.1103/PhysRevE.87.052902}, } @article{Alonso2016, title={Nonlinear physics of electrical wave propagation in the heart: a review}, author={Alonso, Sergio and B{\"a}r, Markus and Echebarria, Blas}, journal={Reports on Progress in Physics}, volume={79}, number={9}, pages={096601}, year={2016}, publisher={IOP Publishing} } @Article{Alvarez:2009, Title = {{Global coupling in excitable media provides a simplified description of mechanoelectrical feedback in cardiac tissue}}, Author = {Alvarez-Lacalle, E. and Echebarria, B.}, Journal = {{Phys. Rev. E}}, Year = {{2009}}, Pages = {031921}, Volume = {{79}}, DOI = {{10.1103/PhysRevE.79.031921}}, Owner = {roman}, Timestamp = {2014.09.14} } @Misc{AMD_OpenCL_FFT, author = {{AMD.com}}, title = {{AMD OpenCL Fast {Fourier} Transform}}, howpublished = {\url{http://developer.amd.com/appsdk}}, year = {2012}, date-added = {2014-07-29 23:49:06 +0000}, date-modified = {2014-07-29 23:49:06 +0000}, } @Incollection{ampatt, Title = {Amplitude equations for pattern forming systems}, Author = {M. van Hecke and P. C. Hohenberg and W. van Saarloos}, Booktitle = {Fundamental Problems in Statistical Mechanics}, Publisher = {North-Holland}, Year = {1994}, Address = {Amsterdam}, Editor = {H. van Beijeren and M. H. Ernst}, Volume = {VIII} } @Book{AnAr88, Title = {Dynamical systems {I}: {Ordinary} Differential Equations and Smooth Dynamical Systems}, Author = {D. V. Anosov and V. I. Arnol'd}, Publisher = {Springer}, Year = {1988}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{anderson1990, Title = {Optimal control: linear quadratic methods}, Author = {B. D. O. Anderson and J. B. Moore}, Publisher = {Prentice Hall}, Year = {1990}, Address = {Englewood Cliffs, N.J.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Misc{Apple_OpenCL_FFT, Title = {{OpenCL\_FFT}}, Author = {{Apple Inc.}}, HowPublished = {\url{http://developer.apple.com/library/mac/\#samplecode/OpenCL_FFT}}, Year = {2012} } @Article{aranson1991interaction, Title = {On the interaction of spiral waves in non-equilibrium media}, Author = {Aranson, IS and Kramer, L and Weber, A}, Journal = {Physica D}, Year = {1991}, Number = {2}, Pages = {376--384}, Volume = {53}, Publisher = {Elsevier} } @Article{aranson1993interaction, Title = {Theory of interaction and bound states of spiral waves in oscillatory media}, Author = {Aranson, Igor S. and Kramer, Lorenz and Weber, Andreas}, Journal = {Phys. Rev. E}, Year = {1993}, Month = may, Pages = {3231--3241}, Volume = {47}, DOI = {10.1103/PhysRevE.47.3231}, Issue = {5}, Numpages = {0}, Publisher = {American Physical Society} } @Article{aranson1995drift, Title = {Drift of spiral waves in excitable media}, Author = {Aranson, Igor and Kessler, David and Mitkov, Igor}, Journal = {Physica D}, Year = {1995}, Pages = {142--155}, Volume = {85} } @Article{Aranson2002, Title = {The world of the complex {Ginzburg-Landau} equation}, Author = {I. S. Aranson and L. Kramer}, Journal = {Rev. Mod. Phys.}, Year = {2002}, Pages = {99--143}, Volume = {74} } @Book{ArKoNe88, title = {{Mathematical Aspects of Classical and Celestial Mechanics}}, publisher = {Springer}, year = {1988}, author = {V. I. Arnol'd and V. V. Kozlov and A. I. Neishtadt}, address = {New York}, } @Book{arnold89, Title = {Mathematical Methods for Classical Mechanics}, Author = {V. I. Arnol'd}, Publisher = {Springer}, Year = {1989}, Address = {New York} } @Article{arnold91k, Title = {Kolmogorov's hydrodynamic attractors}, Author = {V. I. Arnol'd}, Journal = {Proc. R. Soc. Lond. A}, Year = {1991}, Pages = {19--22}, Volume = {434}, Abstract = {A review of Kolmogorov's efforts relating the Navier-Stokes equation to the theory of dynamical system. Several interesting questions regarding the connection are exposed.} } @Book{arnold92, Title = {Ordinary Differential Equations}, Author = {V. I. Arnol'd}, Publisher = {Springer}, Year = {1992}, Address = {New York}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Arnoldi1951, Title = {The principle of minimized iterations in the solution of the matrix eigenvalue problem}, Author = {W. E. Arnoldi}, Journal = {Quart. Appl. Math.}, Year = {1951}, Pages = {17--29}, Volume = {9} } @Article{art03, Title = {Cycle expansions for intermittent maps}, Author = {R. Artuso and P. Cvitanovi{\'c} and G. Tanner}, Journal = {Proc. Theo. Phys. Supp.}, Year = {2003}, Pages = {1--21}, Volume = {150}, DOI = {10.1143/PTPS.150.1} } @Phdthesis{ashi2008numerical, Title = {Numerical methods for stiff systems}, Author = {H. Ashi}, School = {Univ. of Nottingham}, Year = {2008}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{AshMe97, Title = {Noncompact drift for relative equilibria and relative periodic orbits}, Author = {P. Ashwin and I. Melbourne}, Journal = {Nonlinearity}, Year = {1997}, Pages = {595}, Volume = {10}, Bdsk-url-1 = {http://stacks.iop.org/0951-7715/10/i=3/a=002}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, URL = {http://stacks.iop.org/0951-7715/10/i=3/a=002} } @Article{AshMeNi99, Title = {Drift bifurcations of relative equilibria and transitions of spiral waves}, Author = {P. Ashwin and I. Melbourne and M. Nicol}, Journal = {Nonlinearity}, Year = {1999}, Pages = {741}, Volume = {12}, Abstract = {We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems. In particular, we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a `drift bifurcation'. To do this, we use results of Arnold to analyse parametrized families of elements in the Lie algebra of the symmetry group. We examine effects in physical space of such drift bifurcations for planar reaction-diffusion systems and note that these effects can explain certain aspects of the transition from rigidly rotating spirals to rigidly propagating `retracting waves'. This is a bifurcation observed in numerical simulations of excitable media where the rotation rate of a family of spirals slows down and gives way to a semi-infinite translating wavefront.}, Bdsk-url-1 = {http://stacks.iop.org/0951-7715/12/i=4/a=301}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, URL = {http://stacks.iop.org/0951-7715/12/i=4/a=301} } @Article{Aslanidi2009, Title = {Optimal velocity and safety of discontinuous conduction through the heterogeneous {Purkinje}-ventricular junction}, Author = {O. V. Aslanidi and P. Stewart and M. R. Boyett and H. Zhang}, Journal = {Biophys. J.}, Year = {2009}, Pages = {20--39}, Volume = {97}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{atlas12, Title = {Cartography of high-dimensional flows: {A} visual guide to sections and slices}, Author = {Cvitanovi{\'c}, P. and Borrero-Echeverry, D. and Carroll, K. and Robbins, B. and Siminos, E.}, Journal = {Chaos}, Year = {2012}, Addendum = {\arXiv{1209.4915}}, Pages = {047506}, Volume = {22}, DOI = {10.1063/1.4758309} } @Article{Aubry88, Title = {The dynamics of coherent structures in the wall region of turbulent boundary layer}, Author = {N. Aubry and P. Holmes and J. L. Lumley and E. Stone}, Journal = {J. Fluid Mech.}, Year = {1988}, Pages = {115--173}, Volume = {192}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Incollection{aver_dasbuch, Author = {P. Cvitanovi{\'c}}, Booktitle = {{Chaos: Classical and Quantum}}, Publisher = {Niels Bohr Inst.}, Year = {2016}, Address = {Copenhagen}, Chapter = {{Averaging}}, URL = {http://ChaosBook.org/paper.shtml#average} } @Misc{award_04, Author = {E. M. Cherry and F. H. Fenton}, HowPublished = {One of five finalists for the Golden Polygon award in 2004 in the Simulation/Industry/e-learning/Science category}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Misc{award_05, Author = {E. M. Cherry and F. H. Fenton}, HowPublished = {One of five finalists for the Golden Polygon award in 2005 in the Simulation/Industry/e-learning/Science category}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Misc{award_06, Author = {E. M. Cherry and F. H. Fenton}, HowPublished = {An honorable mention in the 2006 NSF and Science Scientific Visualization Challenge in the Interactive Media category, available at\\ {\tt www.vet.cornell.edu/news/FentonCherry/Media/main.html}}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{BabSap16, Title = {A minimization principle for the description of modes associated with finite-time instabilities}, Author = {Babaee, H. and Sapsis, T. P.}, Journal = {Proc. R. Soc. Lond. A}, Year = {2016}, Pages = {20150779}, Volume = {472}, DOI = {10.1098/rspa.2015.0779} } @Article{Baer2007, Title = {Alternans and the influence of ionic channel modifications: Cardiac three-dimensional simulations and one-dimensional numerical bifurcation analysis}, Author = {S. Bauer and G. Roeder and M. Baer}, Journal = {Chaos}, Year = {2007}, Pages = {015104}, Volume = {17}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{BakasovAbraham93, Title = {Laser second threshold: {Its} exact analytical dependence on detuning and relaxation rates}, Author = {A. A. Bakasov and N. B. Abraham}, Journal = {Phys. Rev. A}, Year = {1993}, Pages = {1633--1660}, Volume = {48} } @Article{BaKnTu90, Title = {Spiral wave dynamics in a simple model of excitable media: {Transition} from simple to compound rotation}, Author = {D. Barkley and M. Kness and L. S. Tuckerman}, Journal = {Phys. Rev. A}, Year = {1990}, Pages = {2489--2492}, Volume = {42}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Bar:1993tu, Title = {Turbulence due to spiral breakup in a continuous excitable medium}, Author = {B{\"a}r, M. and Eiswirth, M.}, Journal = {Phys. Rev. E}, Year = {1993}, Pages = {1635--1637}, Volume = {48}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{bar1994spiral, title={Spiral waves in a surface reaction: model calculations}, author={B{\"a}r, Markus and Gottschalk, N and Eiswirth, Markus and Ertl, Gerhard}, journal={The Journal of chemical physics}, volume={100}, number={2}, pages={1202--1214}, year={1994}, publisher={AIP Publishing} } @Article{BarKev94, Title = {A dynamical systems approach to spiral wave dynamics}, Author = {Barkley, D. and Kevrekidis, I. G.}, Journal = {Chaos}, Year = {1994}, Pages = {453--460}, Volume = {4}, Bdsk-url-1 = {http://dx.doi.org/10.1063/1.166023}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1063/1.166023} } @Article{barkley1991model, Title = {A model for fast computer simulation of waves in excitable media}, Author = {Barkley, D.}, Journal = {Physica D}, Year = {1991}, Pages = {61--70}, Volume = {49}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{barkley1992, Title = {Linear stability analysis of rotating spiral waves in excitable media}, Author = {Barkley, D.}, Journal = {Phys. Rev. Lett.}, Year = {1992}, Pages = {2090--2093}, Volume = {68}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1103/PhysRevLett.68.2090}, Urldate = {2014-06-30} } @Article{Barkley94, Title = {{Euclid}ean symmetry and the dynamics of rotating spiral waves}, Author = {D. Barkley}, Journal = {Phys. Rev. Lett.}, Year = {1994}, Pages = {164--167}, Volume = {72}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @InProceedings{bartocci2011toward, Title = {Toward real-time simulation of cardiac dynamics}, Author = {E. Bartocci and E. M. Cherry and J. Glimm and R. Grosu and S. A. Smolka and F. H. Fenton}, Booktitle = {CMSB '11: Proceedings of the 9\textsuperscript{th} International Conference on Computational Methods in Systems Biology}, Year = {2011}, Address = {New York}, Editor = {F. Fages}, Pages = {103--112}, Publisher = {ACM}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{BaVo86, author = {N. L. Balasz and A. Voros}, title = {Chaos on the pseudosphere}, journal = {Phys. Rep.}, year = {1986}, volume = {143}, pages = {109--240}, doi = {10.1016/0370-1573(86)90159-6}, } @Article{Bayly1993, Title = {A quantitative measurement of spatial ordering ventricular fibrillation}, Author = {Bayly, P. V. And Johnson, E. E. And Wolf, P. D. And Greenside, H. S. And Smith, W. M. And Ideker, R. E.}, Journal = {J. Cardiovasc. Electrophysiol.}, Year = {1993}, Pages = {533--546}, Volume = {4}, Abstract = {Quantifying Spatial Order in Fibrillation. Introduction: The degree of organization in ventricular fibrillation (V F) is not known. As an objective measurement of spatial order, spatial correlation functions and their characteristic lengths were estimated from epicardial electrograms of pigs in VF.Methods and Results: VF was induced by premature stimulation in five pigs, EIectroj;raniswere simultaneously recorded with a 22 $\times$ 23 array of unipolar electrodes spaced 1.12 mmapart, Data were obtained by sampling the signals at 2000 Hz for 20 minutes immediately afterthe initiation of VF. Correlations between all pairs of signals were computed at various times.Correlation lengths were estimated from the decay of average correlation as a function of electrode separation. The correlation length of the VF in pigs was found to be approximately 4 to 10 mM. varying as fihrillation progressed. The degree of correlation decreased in the first 4 seconds after fibrillation then increased over the next minute.Conclusion: The correlation length is much smaller than the scale of the heart, suggestingthat many independent regions of activity exist on the epicardium at any one time. On theother hand, the correlation length is 4 to 10 times the interelectrode spacing, indicating thatsome coherence is present. These results imply that the heart behaves during VF as a highdimensional, but not random, system involving many spatial degrees of freedom, which mayexplain the lack of convergence of fractal dimension estimates reported in the literature.Changes in the correlation length also suggest that VF reorganizes slightly in the first minuteafter an initial breakdown in structure.}, DOI = {10.1111/j.1540-8167.1993.tb01242.x}, Keywords = {spatial correlation, correlation length, organization, dynamics, ventricular fibrillation, sudden death} } @InProceedings{BayOrt04, Title = {Lie algebra template tracking}, Author = {E. Bayro-Corrochano and J. Ortegon-Aguilar}, Booktitle = {International Conference on Pattern Recognition}, Year = {2004}, Pages = {56--59}, Volume = {2}, DOI = {10.1109/ICPR.2004.1334036} } @Article{BBBBF09, Title = {Computation of the response functions of spiral waves in active media}, Author = {I. V. Biktasheva and D. Barkley and V. N. Biktashev and G. V. Bordyugov and A. J. Foulkes}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {056702}, Volume = {79}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{BCISV93, Title = {Advection of vector fields by chaotic flows}, Author = {Balmforth, N. J. and Cvitanovi{\'c}, P. and Ierley, G. R. and Spiegel, E. A. and Vattay, G.}, Journal = {Ann. New York Acad. Sci.}, Year = {1993}, Pages = {148--160}, Volume = {706}, DOI = {10.1111/j.1749-6632.1993.tb24687.x} } @Misc{Bealto_FFT, Title = {Bealto {OpenCL} Fast {Fourier} Transform}, Author = {E. Bainville}, HowPublished = {\url{http://www.bealto.com/gpu-fft.html}}, Year = {2010} } @article{beaumont1998spiral, title={Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core}, author={Beaumont, Jacques and Davidenko, Nicolas and Davidenko, Jorge M and Jalife, Jos{\'e}}, journal={Biophysical Journal}, volume={75}, number={1}, pages={1--14}, year={1998}, publisher={Elsevier} } @Article{Beeler1977, Title = {Reconstruction of action potential of ventricular myocardial fibers}, Author = {G. W. Beeler and H. Reuter}, Journal = {J. Physiol.}, Year = {1977}, Pages = {177--210}, Volume = {268}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{bertozzi1997linear, title={Linear stability and transient growth in driven contact lines}, author={Bertozzi, Andrea L and Brenner, Michael P}, journal={Physics of Fluids}, volume={9}, number={3}, pages={530--539}, year={1997}, publisher={AIP} } @Article{BeLo08, Title = {Nonlinear stability of rotating patterns}, Author = {W.-J. Beyn and J. Lorenz}, Journal = {Dynamics of PDE}, Year = {2008}, Pages = {349--400}, Volume = {5} } @Incollection{BeOtRo14, Title = {Stability and computation of dynamic patterns in {PDEs}}, Author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.}, Booktitle = {Current Challenges in Stability Issues for Numerical Differential Equations}, Publisher = {Springer}, Year = {2014}, Pages = {89--172}, Series = {Lect. Notes Math.}, DOI = {10.1007/978-3-319-01300-8_3}, Editors = {Dieci, L. and Guglielmi, N.} } @Misc{BeOtRo16, Title = {Computation and stability of traveling waves in second order evolution equations}, Author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.}, Year = {2016}, URL = {http://arxiv.org/abs/1606.08844} } @Article{berger2007, Title = {Period-Doubling Bifurcation to Alternans in Paced Cardiac Tissue: Crossover from Smooth to Border-Collision Characteristics}, Author = {C. M. Berger and X. Zhao and D. G. Schaeffer and M. Dobrovolny and W. Krassowska and D. J. Gauthier}, Journal = {Phys. Rev. Lett.}, Year = {2007}, Pages = {058101}, Volume = {99} } @Article{bernus2003spiral, Title = {Spiral wave stability in cardiac tissue with biphasic restitution}, Author = {Bernus, O. and Verschelde, H. and Panfilov, A. V.}, Journal = {Phys. Rev. E}, Year = {2003}, Pages = {021917}, Volume = {68} } @Article{BeTh04, Title = {Freezing solutions of equivariant evolution equations}, Author = {W.-J. Beyn and V. Th{\"u}mmler}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2004}, Pages = {85--116}, Volume = {3}, DOI = {10.1137/030600515} } @Article{Bevans98, Title = {Isoform composition of connexin channels determines selectivity among second messengers and uncharged molecules}, Author = {Bevans, C. G. and Kordel, M. and Rhee, S. K. and Harris, A. L.}, Journal = {J. Biol. Chem.}, Year = {1998}, Pages = {2808--2816}, Volume = {273}, Abstract = {Intercellular connexin channels (gap junction channels) have long been thought to mediate molecular signaling between cells, but the nature of the signaling has been unclear. This study shows that connexin channels from native tissue have selective permeabilities, partially based on pore diameter, that discriminate among cytoplasmic second messenger molecules, Permeability was assessed by measurement of selective loss/retention of tracers from liposomes containing reconstituted connexin channels. The tracers employed were tritiated cyclic nucleotides and a series of oligomaltosaccharides derivatized with a small uncharged fluorescent moiety, The data define different size cut-off limits for permeability through homomeric connexin-32 channels and through heteromeric connexin-32/connexin-26 channels, Connexin-26 contributes to a narrowed pore, Both cAMP and cGMP were permeable through the homomeric connexin-32 channels. cAMP was permeable through only a fraction of the heteromeric channels, Surprisingly, cGMP was permeable through a substantially greater fraction of the heteromeric channels than was cAMP. The data suggest that isoform stoichiometry and/or arrangement within a connexin channel determines whether cyclic nucleotides can permeate, and which ones, This is the first evidence for connexin-specific selectivity among biological signaling molecules.}, DOI = {{10.1074/jbc.273.5.2808}} } @Article{BeyHuls14, Title = {Continuation and collapse of homoclinic tangles}, Author = {W.-J. Beyn and T. H{\"u}ls}, Journal = {J. Computat. Dynamics}, Year = {2014}, Pages = {71--109}, __markedentry = {[predrag:]}, DOI = {10.3934/jcd.2014.1.71} } @Article{Beyn12, Title = {An integral method for solving nonlinear eigenvalue problems}, Author = {W.-J. Beyn}, Journal = {Linear Algebra Appl.}, Year = {2012}, Pages = {3839--3863}, Volume = {436}, Abstract = {We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where k is much smaller than the matrix dimension.}, DOI = {10.1016/j.laa.2011.03.030} } @Article{beyn2008freezing, Title = {Freezing multipulses and multifronts}, Author = {Beyn, W.-J. and Selle, S. and Th{\"u}mmler, V.}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2008}, Pages = {577--608}, Volume = {7}, DOI = {10.1137/07070749X} } @Article{BeyOtt16, Title = {Spatial decay of rotating waves in reaction diffusion systems}, Author = {Beyn, W.-J. and Otten, D.}, Journal = {Dynami. Part. Differ. Eq.}, Year = {2016}, Pages = {191--240}, Volume = {13}, DOI = {10.4310/DPDE.2016.v13.n3.a2} } @Article{BiHoBi06, Title = {Localization of Response Functions of Spiral Waves in the {F}itz{H}ugh--{N}agumo System}, Author = {I. V. Biktasheva and A. V. Holden and V. N. Biktashev}, Journal = {Int. J. Bifur. 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Accuracy of the method is also considered.}, DOI = {10.1117/12.162683} } @Article{CvitaEckardt, Title = {Symmetry decomposition of chaotic dynamics}, Author = {Cvitanovi{\'c}, P. and Eckhardt, B.}, Journal = {Nonlinearity}, Year = {1993}, Addendum = {\arXiv{chao-dyn/9303016}}, Pages = {277--311}, Volume = {6}, DOI = {10.1088/0951-7715/6/2/008} } @Article{Cvitanovic1995109, Title = {Dynamical averaging in terms of periodic orbits}, Author = {Cvitanovi{\'c}, P.}, Journal = {Physica D}, Year = {1995}, Pages = {109--123}, Volume = {83}, DOI = {10.1016/0167-2789(94)00256-P} } @InProceedings{CvitLanCrete02, Title = {Turbulent fields and their recurrences}, Author = {P. Cvitanovi{\'c} and Y. Lan}, Booktitle = {Correlations and Fluctuations in QCD : Proceedings of 10\textsuperscript{th} International Workshop on Multiparticle Production}, Year = {2003}, Address = {Singapore}, Editor = {N. Antoniou}, Pages = {313--325}, Publisher = {World Scientific}, Addendum = {\arXiv{nlin.CD/0308006}}, DOI = {10.1142/9789812704641_0032}, ISBN = {978-981-238-455-3} } @Book{cvt89b, Title = {Universality in Chaos}, Author = {P. Cvitanovi{\'c}}, Publisher = {Adam Hilger}, Year = {1989}, Address = {Bristol}, ISBN = {9780852742600} } @Incollection{CVW96, Title = {Quantum fluids and classical determinants}, Author = {Cvitanovi{\'c}, P. and Vattay, G. and Wirzba, A.}, Booktitle = {Classical, Semiclassical and Quantum Dynamics in Atoms}, Publisher = {Springer}, Year = {1997}, Addendum = {\arXiv{chao-dyn/9608012}}, Address = {New York}, Editor = {H. Friedrich and B. Eckhardt}, Pages = {29--62}, DOI = {10.1007/BFb0105968} } @Article{Cytrynbaum2002, Title = {Stability conditions for the traveling pulse: Modifying the restitution hypothesis}, Author = {E. Cutrynbaum and J. P. Keener}, Journal = {Chaos}, Year = {2002}, Pages = {788--799}, Volume = {12}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Cytrynbaum2003, Title = {The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue}, Author = {J. P. Keener and E. Cutrynbaum}, Journal = {J. Theor. Biol.}, Year = {2003}, Pages = {233--248}, Volume = {223}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Dang86, Title = {Steady-state mode interactions in the presence of {0(2)}-symmetry}, Author = {Dangelmayr, G.}, Journal = {Dyn. Sys.}, Year = {1986}, Pages = {159--185}, Volume = {1}, Bdsk-url-1 = {http://dx.doi.org/10.1080/02681118608806011}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1080/02681118608806011} } @Article{DASB11, Title = {Optimal transfers between unstable periodic orbits using invariant manifolds}, Author = {Davis, K. E. and Anderson, R. L. and Scheeres, D. J. and Born, G. H.}, Journal = {Celestial Mech. Dynam. Astronom.}, Year = {2011}, Pages = {241--264}, Volume = {109}, Abstract = {This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between unstable periodic orbits in the Sun--Earth, Earth--Moon, and Jupiter-Europa three-body systems. Multiple solutions are found between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost is accompanied by an increase in transfer time of flight.}, DOI = {10.1007/s10569-010-9327-x} } @Book{DasBuch, Title = {Chaos: Classical and Quantum}, Author = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, Publisher = {Niels Bohr Inst.}, Year = {2016}, Address = {Copenhagen}, Note = {{\tt ChaosBook.org}}, URL = {http://ChaosBook.org/} } @Incollection{DasBuchMirror, Author = {P. Cvitanovi{\'c}}, Booktitle = {Chaos: Classical and Quantum}, Publisher = {Niels Bohr Inst.}, Year = {2016}, Address = {Copenhagen}, Chapter = {{World} in a mirror}, URL = {http://ChaosBook.org/paper.shtml#discrete} } @Article{davidenko1992, Title = {Stationary and drifting spiral waves of excitation in isolated muscle}, Author = {J. M. Davidenko and A. V. Pertsov and R. Salomonsz and W. Baxter and J. 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Mellibovsky and M. Avila and B. Hof}, Journal = {Phys. Rev. Lett.}, Year = {2012}, Pages = {214502}, Volume = {108} } @Book{Dennis96, Title = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations}, Author = {J. E. Dennis and R. B. Schnabel}, Publisher = {SIAM}, Year = {1996}, Addr = {Philadelphia}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Denz2004, Title = {Transverse pattern formation and its control in photorefractive optics}, Author = {Denz, C. and Jander, Ph. and Schwab, M. and Sandfuchs, O. and Beli\'{c}, M. and Kaiser, F.}, Journal = {Ann. Phys.}, Year = {2004}, Pages = {391--402}, Volume = {13} } @Article{DesBra13, Title = {Quasi-one-dimensional solutions and their interaction with two-dimensional dissipative solitons}, Author = {Descalzi, O. and Brand, H. R.}, Journal = {Phys. Rev. E}, Year = {2013}, Pages = {022915}, Volume = {87}, DOI = {10.1103/PhysRevE.87.022915} } @Article{Descalzi10, Title = {Transition from modulated to exploding dissipative solitons: {Hysteresis}, dynamics, and analytic aspects}, Author = {Descalzi, O. and Brand, H. R.}, Journal = {Phys. Rev. E}, Year = {2010}, Pages = {026203}, Volume = {82} } @Article{DFGHMS86, Title = {Chaotic streamlines in the {ABC} flows}, Author = {Dombre, T. and Frisch, U. and Greene, J. M. and H\'enon, M. and Mehr, A. and Soward, A. M.}, Journal = {J. Fluid Mech.}, Year = {1986}, Pages = {353--391}, Volume = {167}, DOI = {10.1017/S0022112086002859} } @Article{DhoPatZhi15, Title = {The action of the special orthogonal group on planar vectors: integrity bases via a generalization of the symbolic interpretation of Molien functions}, Author = {G. Dhont and F. Patra and B. I. Zhilinski\'is}, Journal = {J. Phys. A}, Year = {2015}, Pages = {035201}, Volume = {48}, DOI = {10.1088/1751-8113/48/3/035201} } @Article{DhoZhi13, Title = {The action of the orthogonal group on planar vectors: invariants, covariants and syzygies}, Author = {G. Dhont and B. I. Zhilinski\'i}, Journal = {J. Phys. A}, Year = {2013}, Pages = {455202}, Volume = {46}, DOI = {10.1088/1751-8113/46/45/455202} } @Article{diag_Fred, Title = {Spectrum of stochastic evolution operators: {Local} matrix representation approach}, Author = {Cvitanovi{\'c}, P. and S{\o}ndergaard, N. and Palla, G. and Vattay, G. and Dettmann, C. P.}, Journal = {Phys. Rev. E}, Year = {1999}, Addendum = {\arXiv{chao-dyn/9904027}}, Pages = {3936--3941}, Volume = {60}, DOI = {10.1103/PhysRevE.60.3936} } @Misc{DiBrVePa13, Title = {Drift laws for spiral waves on curved anisotropic surfaces}, Author = {H. Dierckx and E. Brisard and H. Verschelde and A. V. Panfilov}, Note = {\arXiv{1301.5469}} } @Unpublished{Dierckx2010, Title = {Detailed anatomical reconstruction of the whole canine heart including fiber and sheet architecture using {MRI} and DTMRI}, Author = {H. Dierckx and E. M. Cherry and O. Bernus and F. H. Fenton}, Note = {In preparation}, Year = {2010}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{dierckx2012buckling, Title = {Buckling of scroll waves}, Author = {Dierckx, Hans and Verschelde, Henri and Selsil, {\"O}zg{\"u}r and Biktashev, Vadim N}, Journal = {Physical review letters}, Year = {2012}, Number = {17}, Pages = {174102}, Volume = {109}, Publisher = {APS} } @Article{dierckx2013drift, Title = {Drift laws for spiral waves on curved anisotropic surfaces}, Author = {Dierckx, Hans and Brisard, Evelien and Verschelde, Henri and Panfilov, Alexander V}, Journal = {Phys. Rev. E}, Year = {2013}, Number = {1}, Pages = {012908}, Volume = {88}, Publisher = {APS} } @Article{DiFrancesco1985, Title = {A model of cardiac electrical activity incorporating ionic pumps and concentration changes}, Author = {D. DiFrancesco and D. Noble}, Journal = {Philos. Trans. R. Soc. Lond. B Biol. Sci.}, Year = {1985}, Pages = {353--398}, Volume = {307} } @Article{DingCvit14, Title = {Periodic eigendecomposition and its application in {Kuramoto-Sivashinsky} system}, Author = {Ding, X. and Cvitanovi{\'c}, P.}, Journal = {{SIAM} J. Appl. Dyn. Syst.}, Year = {2016}, Pages = {1434--1454}, Volume = {15}, DOI = {10.1137/15M1037299} } @Article{doelman89, Title = {Slow time-periodic solutions of the {Ginzburg-Landau} equation}, Author = {A. Doelman}, Journal = {Physica D}, Year = {1989}, Pages = {156--172}, Volume = {40} } @Article{doelman91n, Title = {Finite-dimensional models of the {Ginzburg-Landau} equation}, Author = {A. Doelman}, Journal = {Nonlinearity}, Year = {1991}, Pages = {231--250}, Volume = {4} } @Article{doercgl87, Title = {Exact {Lyapunov} dimension of the universal attractor for the complex {Ginzburg-Landau} equation}, Author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko}, Journal = {Phys. Rev. Lett.}, Year = {1987}, Pages = {2911--2914}, Volume = {59}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{doercgl88, Title = {Low-dimensional behaviour in the complex {Ginzburg-Landau} equation}, Author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko}, Journal = {Nonlinearity}, Year = {1988}, Pages = {279--309}, Volume = {1}, Abstract = {The stability of plane waves of the CGLe is analyzed in a periodic domain. The mass and energy integrals are estimated to give an upper bound of the magnitude of the field variable. After that, cone condition is established for the CGLe which indicates the existence of the inertial manifold and proves the existence of finite dimensionality of the attractor in this infinite-dimensional system. The Lyapunov dimension is estimated. Note the defition of Lyapunov exponents which is a little different from usual.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Dominguez1979, Title = {Effect of streach on conduction velocity and cable properties of cardiac {Purkinje} fibers}, Author = {G. Dominguez and H. A. Fozzard}, Journal = {Am. J. Physiol.}, Year = {1979}, Pages = {C119}, Volume = {237}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Dorato1994, Title = {Linear-Quadratic Control: An Introduction}, Author = {P. Dorato and V. Cerone and C. Abdallah}, Publisher = {Simon \& Schuster}, Year = {1994}, Address = {New York}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{dorato1995, Title = {Linear-Quadratic control: {An} Introduction}, Author = {P. Dorato and C. Abdallah and V. Cerone}, Publisher = {Prentice Hall}, Year = {1995}, Address = {Englewood Cliffs, N.J.} } @Book{Dorato2000, Title = {Linear-Quadratic Control}, Author = {P. Dorato and C. T. Abdallah and V. Cerone}, Publisher = {Krieger Publishing Company}, Year = {2000}, Address = {Melbourne} } @InProceedings{dosSantos2003, Title = {On the influence of a volume conductor on the orientation of currents in a thin cardiac tissue}, Author = {dos Santos, W. R. and Dickstein, F.}, Booktitle = {Functional Imaging and Modeling of the Heart}, Year = {2003}, Address = {Berlin}, Pages = {111--121}, Publisher = {Springer}, Series = {Lect. Notes Comp. Sci.}, Volume = {2674}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{DR04, Title = {Hydrodynamic Stability}, Author = {P. Drazin and W. H. Reid}, Publisher = {Cambridge Univ. Press}, Year = {2004}, Address = {Cambridge}, Edition = {Second}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{DR81, Title = {Hydrodynamic Stability}, Author = {P. Drazin and W. H. Reid}, Publisher = {Cambridge Univ. Press}, Year = {1981}, Address = {Cambridge}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Drazin02, Title = {Introduction to Hydrodynamic Stability}, Author = {P.G. Drazin}, Publisher = {Cambridge Univ.\ Press}, Year = {2002}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{DruCip00, Title = {Application of {Lie} algebras to visual servoing}, Author = {T. Drummond and R. Cipolla}, Journal = {Intern. J. Computer Vision}, Year = {2000}, Pages = {21--41}, Volume = {37} } @Article{dubljevic2008, Title = {Studies of feedback control of cardiac alternans}, Author = {S. Dubljevic and S.-F. Lin and P. D. Christofides}, Journal = {Comp. Chem. Eng.}, Year = {2008}, Pages = {2086}, Volume = {32}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{dubljevic2009, Title = {Optimal boundary control of cardiac alternans}, Author = {S. Dubljevic}, Journal = {Int. J. Robust Nonlinear Control}, Year = {2009}, Pages = {135}, Volume = {19} } @Article{duguet2008relative, Title = {Relative periodic orbits in transitional pipe flow}, Author = {Duguet, Y. and Pringle, C. C. T. and Kerswell, R. R.}, Journal = {Physics of Fluids (1994-present)}, Year = {2008}, Pages = {114102}, Volume = {20} } @Book{DuiKol00, Title = {Lie Groups}, Author = {J. J. Duistermaat and J. A. C. Kolk}, Publisher = {Springer}, Year = {2000}, Address = {New York}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Echebarria2002, Title = {Instability and spatiotemporal dynamics of alternans in paced cardiac tissue}, Author = {Echebarria, B. and Karma, A.}, Journal = {Phys. Rev. Lett.}, Year = {2002}, Pages = {208101}, Volume = {88} } @Article{echebarria2007, Title = {Amplitude equation approach to spatiotemporal dynamics of cardiac alternans}, Author = {Echebarria, B. and Karma, A.}, Journal = {Phys. Rev. E}, Year = {2007}, Pages = {051911}, Volume = {76}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{eck81, Title = {Roads to turbulence in dissipative dynamical systems}, Author = {J.-P. Eckmann}, Journal = {Rev. Mod. Phys.}, Year = {1981}, Pages = {643}, Volume = {53} } @Article{eckcgl, Title = {The {Eckhaus} instability for travelling waves}, Author = {B. Janiaud and A. Pumir and D. Bensimon and V. Croquette and H. Richter and L. Kramer}, Journal = {Physica D}, Year = {1992}, Pages = {269--286}, Volume = {55} } @Article{Eckhardt09, Title = {Basin boundary, edge of chaos and edge state in a two-dimensional model}, Author = {J. Vollmer and T. M. Schneider and B. Eckhardt}, Journal = {New J. Phys.}, Year = {2009}, Pages = {013040}, Volume = {11} } @Article{efimov2000, Title = {Virtual electrodes and deexcitation: new insights into fibrillation induction and defibrillation}, Author = {Efimov, I. R. and Gray, R. A. and Roth, B. J.}, Journal = {Journal of cardiovascular electrophysiology}, Year = {2000}, Pages = {339--353}, Volume = {11} } @Article{EGtran95, Title = {Characterization of the transition from defect to phase turbulence}, Author = {D. A. Egolf and H. S. Greenside}, Journal = {Phys. Rev. Lett.}, Year = {1995}, Pages = {1751}, Volume = {74}, Abtract = {For the CGLe on a large periodic interval, the transition from defect to phase turbulence is continuous. The conclusion is based on the calculation of the defect density, Lyapunov dimension density and correlation lengths.} } @Book{ellip, Title = {Elliptic Functions and Applications}, Author = {D. F. Lawden}, Publisher = {Springer}, Year = {1989}, Address = {New York} } @Article{enright1986interpolants, Title = {Interpolants for Runge-Kutta formulas}, Author = {Enright, Wayne H and Jackson, KR and N{\o}rsett, Syvert P and Thomsen, Per Grove}, Journal = {ACM Transactions on Mathematical Software (TOMS)}, Year = {1986}, Number = {3}, Pages = {193--218}, Volume = {12}, Publisher = {ACM} } @Article{Entch11, Title = {Stimulating Cardiac Muscle by Light: Cardiac Optogenetics by Cell Delivery}, Author = {Jia, Z. and Valiunas, V. and Lu, Z. and Bien, H. and Liu, H. and Wang, H. and Rosati, B. and Brink, P. R. and Cohen, I. S. and Entcheva, E.}, Journal = {Circ. Arrhythm. Electrophysiol.}, Year = {2011}, Pages = {753--267}, Volume = {4} } @Article{Ermentrout:1984fr, Title = {Frequency plateaus in a chain of weakly coupled oscillators, {I.}}, Author = {Ermentrout, G. B. and Kopell, N.}, Journal = {SIAM J. Math. Anal.}, Year = {1984}, Pages = {215--237}, Volume = {15}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Ermentrout:1995ah, Title = {A heuristic description of spiral wave instability in discrete media}, Author = {Ermentrout, B.}, Journal = {Physica D}, Year = {1995}, Pages = {154--164}, Volume = {82}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @InProceedings{etc12, Title = {Geometry of state space in plane {C}ouette flow}, Author = {Cvitanovi{\'c}, P. and Gibson, J. F.}, Booktitle = {Advances in Turbulence XII}, Year = {2009}, Address = {Berlin}, Editor = {B. Eckhardt}, Pages = {75--78}, Publisher = {Springer}, Series = {Proc. 12\textsuperscript{th} EUROMECH Eur. Turb. Conf., Marburg}, DOI = {10.1007/978-3-642-03085-7-17} } @Techreport{EZRide, Title = {{EZRide}: {A} code for simulating spiral waves in a comoving frame of reference}, Author = {D. Barkley and V. N. Biktashev and A. J. Foulkes}, Institution = {U. Liverpool}, Year = {2010}, Note = {www.maths.liv.ac.uk/$\sim$vadim/software/EZRide/}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Publisher = {V. N. Biktashev} } @Misc{Faraz15, Title = {An adjoint-based approach for finding invariant solutions of {Navier-Stokes} equations}, Author = {Farazmand, M.}, Note = {\arXiv{1508.06363}}, Year = {2015} } @Misc{FarCvi16, Title = {An adjoint-based approach for finding symmetry-invariant solutions of {Kuramoto-Sivashinsky} equation}, Author = {Farazmand, M. and Cvitanovi{\'c}, P.}, Note = {In preparation}, Year = {2016} } @Article{Farrell1996, Title = {Generalized stability theory part 1: {A}utonomous operators}, Author = {P. J. Ioannou and B. F. Farrell}, Journal = {J. Atmos. Sci.}, Year = {1996}, Pages = {2025--2040}, Volume = {53}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Farrell1996b, Title = {Generalized stability theory part 2: {N}onautonomous operators}, Author = {P. J. Ioannou and B. F. Farrell}, Journal = {J. Atmos. Sci.}, Year = {1996}, Pages = {2041--2053}, Volume = {53}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{farrell2013automated, Title = {Automated derivation of the adjoint of high-level transient finite element programs}, Author = {Farrell, Patrick E and Ham, David A and Funke, Simon W and Rognes, Marie E}, Journal = {SIAM Journal on Scientific Computing}, Year = {2013}, Number = {4}, Pages = {C369--C393}, Volume = {35}, Publisher = {SIAM} } @Article{fast1997role, Title = {Role of wavefront curvature in propagation of cardiac impulse}, Author = {Fast, V. G. and Kl{\'e}ber, A. G.}, Journal = {Cardiovascular research}, Year = {1997}, Pages = {258--271}, Volume = {33} } @Article{Fedorov2007, Title = {Application of blebbistatin as an excitation-contraction uncoupler for electrophysiological study of rat and rabbit hearts}, Author = {V. V. Fedorov and I. T. Lozinsky and E. A. Sosunov and E. P. Anyukhovsky and M. R. Rosen and W. C. Balke and I. R. Efimov}, Journal = {Heart Rhythm}, Year = {2007}, Pages = {619--626}, Volume = {4}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{FelsOlver98, Title = {Moving coframes: {I. A} practical algorithm}, Author = {M. Fels and P. J. Olver}, Journal = {Acta Appl. Math.}, Year = {1998}, Pages = {161--213}, Volume = {51}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{FelsOlver99, Title = {Moving coframes: {II. Regularization} and theoretical foundations}, Author = {M. Fels and P. J. Olver}, Journal = {Acta Appl. Math.}, Year = {1999}, Pages = {127--208}, Volume = {55}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Fenton1998, Title = {Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: {Filament} instability and fibrillation}, Author = {F. Fenton and A. Karma}, Journal = {Chaos}, Year = {1998}, Pages = {20--47}, Volume = {8}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{fenton1998e, Title = {Erratum:``Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: filament instability and fibrillation'' [Chaos 8, 20-47 (1998)]}, Author = {F. Fenton and A. Karma}, Journal = {Chaos}, Year = {1998}, Pages = {879}, Volume = {8}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Fenton1998prl, Title = {Fiber-rotation-induced vortex turbulence in thick myocardium}, Author = {F. Fenton and A. Karma}, Journal = {Phys. Rev. Lett.}, Year = {1998}, Pages = {481--484}, Volume = {81}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Fenton1999, Title = {Spatiotemporal control of wave instabilities in cardiac tissue}, Author = {W.-J. Rappel and F. Fenton and A. Karma}, Journal = {Phys. 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Evans}, Journal = {BioSystems}, Year = {2002}, Pages = {73--96}, Volume = {64}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Fenton2005, Title = {Modeling wave propagation in realistic heart geometries using the phase-field method}, Author = {F. H. Fenton and E. M. Cherry and A. Karma and W. J. Rappel}, Journal = {Chaos}, Year = {2005}, Pages = {13502}, Volume = {15} } @Article{Fenton2008jvc, Title = {Termination of equine atrial fibrillation by quinidine: an optical mapping study}, Author = {F. H. Fenton and E. M. Cherry and B. G. Kornreich}, Journal = {J. Vet. Cardiol.}, Year = {2008}, Pages = {87--102}, Volume = {10}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Fenton2009, Title = {Termination of atrial fibrillation using pulsed low-energy far-field stimulation}, Author = {F. H. Fenton and S. Luther and E. M. Cherry and N. F. Otani and V. Krinksy and A. Pumir and E. Bodenschatz and Gilmour, Jr., R. F.}, Journal = {Circulation}, Year = {2009}, Pages = {467--476}, Volume = {120}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Unpublished{Fenton2010, Title = {APD restitution curve splitting in cardiac tissue: theory and experiments}, Author = {F. H. Fenton and R. F. Gilmour Jr. and E. M. Cherry}, Note = {In preparation}, Year = {2010}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{FentonCherry08ca, Title = {Cardiac arrhythmia}, Author = {F. H. Fenton and E. M. Cherry and L. Glass}, Journal = {Scholarpedia}, Year = {2008}, Pages = {1665}, Volume = {3}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{FentonCherry08mcc, Title = {Models of cardiac cell}, Author = {F. H. Fenton and E. M. 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Cherry}, Note = {(unpublished)}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Timestamp = {2013.11.03} } @Book{fiedler2002handbook, Title = {Handbook of Dynamical Systems}, Author = {Fiedler, B.}, Publisher = {Elsevier}, Year = {2002}, Address = {Amsterdam}, Volume = {2} } @Article{Field:1980eq, Title = {Equivariant Dynamical Systems}, Author = {Field, M J}, Journal = {Transactions of the American Mathematical Society}, Year = {1980}, Pages = {185}, Volume = {259}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Field70, Title = {Equivariant dynamical systems}, Author = {M. Field}, Journal = {Bull. Amer. Math. Soc.}, Year = {1970}, Pages = {1314--1318}, Volume = {76}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Incollection{Field88, author = {M. Field}, title = {Local structure of equivariant dynamics}, booktitle = {Singularity Theory and its Applications: Warwick 1989, Part II: Singularities, Bifurcations and Dynamics}, publisher = {Springer}, year = {1996}, editor = {M. Roberts and I. Stewart}, isbn = {9783540470472}, pages = {142--166}, address = {New York}, doi = {10.1007/BFb0085422} } @Article{Field96, Title = {Symmetry breaking for compact {Lie} groups}, Author = {M. Field}, Journal = {Memoirs Amer. Math. Soc.}, Year = {{1996}}, Pages = {{R8}}, Volume = {{120}}, Abstract = {{This work comprises a general study of symmetry breaking for compact Lie groups in the context of equivariant bifurcation theory. We start by extending the theory developed by Field and Richardson {[}37] for absolutely irreducible representations of finite groups to general irreducible representations of compact Lie groups. In particular, we allow for branches of relative equilibria and phenomena such as the Hopf bifurcation. We also present a general theory of determinacy for irreducible Lie group actions along the lines previously described in Field {[}29]. In the main result of this work, we show that branching patterns for generic equivariant bifurcation problems defined on irreducible representations persist under perturbations by sufficiently high order non-equivariant terms. We give applications of this result to normal form computations yielding, for example, equivariant Hopf bifurcations and show how normal form computations of branching and stabilities are valid when we take account of the non-normalized tail.}}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Unpublished{Fink2010, Title = {Cardiac cell modelling: {Observations} from the heart of the cardiac physiome project}, Author = {M. Fink and S. A. Niederer and E. M. Cherry and F. H. Fenton and J. T. Koivumaki and G. Seemann and R. Thul and H. Zhang and F. B. Sachse and D. Beard and E. J. 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FitzHugh}, title = {Impulses and physiological states in theoretical models of nerve membrane}, journal = {Biophys. J.}, year = {445-466}, volume = {1}, pages = {445} } @Article{FKYY83, Title = {The {Liapunov} dimension of strange attractors}, Author = {P. Frederickson and J. L. Kaplan and E. D. Yorke and J. A. Yorke}, Journal = {J. Diff. Eqn.}, Year = {1983}, Pages = {185--207}, Volume = {49}, Abstract = {... the question of estimating the dimension of the attractor is addressed. While more general conjectures are made here, particular attention is paid to the idea that if the Jacobian determinant of a map is greater than one and a ball is mapped into itself, then generically, the attractor will have positive two-dimensional measure, and most of this paper is devoted to presenting cases with such Jacobians for which the attractors are proved to have non-empty interior. }, DOI = {10.1016/0022-0396(83)90011-6} } @Article{FoBaBiBi10, Title = {Alternative stable scroll waves and conversion of autowave turbulence}, Author = {A. J. Foulkes and D. Barkley and V. N. Biktashev and I. V. Biktasheva}, Journal = {Chaos}, Year = {2010}, Pages = {043136}, Volume = {20}, Bdsk-url-1 = {http://dx.doi.org/10.1063/1.3517079}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1063/1.3517079}, Numpages = {13} } @Article{focusPOT, Title = {Recurrent flows: {The} clockwork behind turbulence}, Author = {Cvitanovi{\'c}, P.}, Journal = {J. Fluid Mech. Focus on Fluids}, Year = {2013}, Pages = {1--4}, Volume = {726}, DOI = {10.1017/jfm.2013.198} } @Article{foerster1989critical, Title = {Critical size and curvature of wave formation in an excitable chemical medium}, Author = {Foerster, P and M{\"u}ller, SC and Hess, B}, Journal = {Proceedings of the National Academy of Sciences}, Year = {1989}, Number = {18}, Pages = {6831--6834}, Volume = {86}, Publisher = {National Acad Sciences} } @Article{FouBik10, Title = {Riding a spiral wave: {Numerical} simulation of spiral waves in a comoving frame of reference}, Author = {A. J. Foulkes and V. N. Biktashev}, Journal = {Phys. Rev. E}, Year = {2010}, Note = {{\arXiv{1001.4454}}}, Pages = {046702}, Volume = {81}, Abstract = {We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Phdthesis{Foulkes09thesis, Title = {Drift and Meander of Spiral Waves}, Author = {A. J. Foulkes}, School = {Univ. of Liverpool}, Year = {2009}, Address = {Liverpool, UK}, Note = {\arXiv{0912.4247}} } @Article{FowlerCLE82, Title = {The complex {Lorenz} equations}, Author = {Fowler, A. C. and Gibbon, J. D. and McGuinness, M. J.}, Journal = {Physica D}, Year = {1982}, Pages = {139--163}, Volume = {4}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{fox2002ionic, Title = {Ionic mechanism of electrical alternans}, Author = {Fox, J. J. and McHarg, J. L. and Gilmour Jr, R. 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H.}, Journal = {Chaos}, Year = {1993}, Addendum = {\arXiv{chao-dyn/9307014}}, Pages = {619--636}, Volume = {3}, DOI = {10.1063/1.165992} } @Article{Gall69, Title = {On a proof by {Petrov} of the stability of plane {Couette} flow and plane {Poiseuille} flow}, Author = {A. P. Gallagher}, Journal = {SIAM J. Appl. Math.}, Year = {1969}, Pages = {765--768}, Volume = {17}, Abstract = {A proof by Petrov \cite{Petr40} that plane {Couette} flow and plane Poiseuille flow are always stable with respect to infinitesimal disturbances is examined and found to be based on a set of incomplete functions, thus rendering the proof invalid.} } @Article{Garcia04, Title = {Gap junction-mediated spread of cell injury and death during myocardial ischemia-reperfusion}, Author = {Garcia-Dorado, D. and Rodriguez-Sinovas, A. and Ruiz-Meana, M.}, Journal = {Cardiovasc. Res.}, Year = {2004}, Pages = {386--401}, Volume = {61}, Abstract = {{Gap junction-mediated intercellular communication (GJMIC) has been known for a long time to be essential in propagation of electrical impulse in the heart, and the contribution of altered GJMIC to the genesis of arrhythmias has been extensively investigated. However, although it is well known that GJMIC allows the exchange of biologically important molecules between adjacent cells, the pathophysiological significance of such chemical coupling during myocardial ischemia and reperfusion is much less known. It has been solidly established that ischemia impairs GJMIC and eventually leads to electrical uncoupling, but recent studies suggest that GJMIC may still allow synchronization of the onset of ischemic rigor contracture and of the progression of ischemic injury beyond rigor onset. During reperfusion, GJMIC has been shown to mediate cell-to-cell propagation of hypercontracture and cell death, and there is evidence that this phenomenon explains the continuity of areas of contraction band necrosis and contributes to final infarct size. Finally, there is increasing evidence that GJ or their protein components are involved in the genesis of the protective effect of ischemic preconditioning, although probably through mechanisms independent from modulator of GJMIC. GJ play an important role in the pathphysiology of cell injury and death during myocardial ischemia-reperfusion and are potential targets for new cardioprotective therapeutic strategies. (C) 2004 European Society of Cardiology. Published by Elsevier B.V.. All rights reserved.}}, DOI = {{10.1016/j.cardiores.2003.11.039}} } @InProceedings{garciaadaptive, Title = {An adaptive step size {GPU ODE} solver for simulating the electric cardiac activity}, Author = {V. M. Garcia and A. Liberos and A. M. Climent and A. 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J.}, Year = {2007}, Pages = {448--460}, Volume = {92}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{garnier, Title = {Nonlinear dynamics of waves and modulated waves in 1{D} thermocapillary flows}, Author = {N. Garnier and A. Chiffaudel and F. Daviaud and A. Prigent}, Journal = {Physica D}, Year = {2003}, Pages = {1--29}, Volume = {174} } @Article{Garnier2006, Title = {{Spatiotemporal Chaos: The Microscopic Perspective}}, Author = {Garnier, N. and W\'{o}jcik, D.}, Journal = {Phys. Rev. Lett.}, Year = {2006}, Pages = {114101}, Volume = {96} } @Article{GaRuBa10, Title = {Complex networks and symmetry: {A} review}, Author = {Garlaschelli, D. and Ruzzenenti, F. and Basosi, R.}, Journal = {Symmetry}, Year = {2010}, Pages = {1683--1709}, Volume = {2}, DOI = {10.3390/sym2031683} } @InProceedings{GarzGrig11, Title = {Model-based control of cardiac alternans in a model of {Purkinje} fibers}, Author = {A. Garz{\'o}n and R. O. Grigoriev}, Booktitle = {5\textsuperscript{th} International Conference on Physics and Control (PhysCon 2011)}, Year = {2011}, Address = {Saint Petersburg, Russia}, Note = {lib.physcon.ru/doc?id=824ed8fb5a6a}, Publisher = {IPACS}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Unpublished{Garzon10, Title = {Controllability of cardiac alternans in {Purkinje} fibers}, Author = {A. Garz{\'o}n and and F. H. Fenton}, Note = {In preparation}, Year = {2010}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Garzon11, Title = {Model-based control of cardiac alternans in {Purkinje} fibers}, Author = {A. Garz{\'o}n and R. O. Grigoriev and F. H. Fenton}, Journal = {Phys. Rev. E}, Year = {2011}, Pages = {041927}, Volume = {84}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Garzon14, Title = {Continuous-time control of alternans in long Purkinje fibers}, Author = {A. Garz{\'o}n and R. O. Grigoriev and F. H. Fenton}, Journal = {Chaos}, Year = {2014}, Pages = {033124}, Volume = {24}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{garzon2009, Title = {Model-based control of cardiac alternans on a ring}, Author = {A. Garz\'{o}n and R. O. Grigoriev and F. H. Fenton}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {021932}, Volume = {80}, Timestamp = {2013.11.03} } @Article{gasp02, Title = {Trace formula for noisy flows}, Author = {P. Gaspard}, Journal = {J. Stat. Phys.}, Year = {2002}, Pages = {57}, Volume = {106}, Abstract = {A trace formula is derived for the FokkerPlanck equation associated with Ito stochastic differential equations describing noisy time-continuous nonlinear dynamical systems. In the weak-noise limit, the trace formula provides estimations of the eigenvalues of the Fokker-Planck operator on the basis of the Pollicott-Ruelle resonances of the noiseless deterministic system, which is assumed to be non-bifurcating. At first order in the noise amplitude, the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo-energy of the Onsager-Machlup-Freidlin-Wentzell scheme. }, DOI = {10.1023/A:1013167928166} } @Book{gatermannHab, Title = {Computer Algebra Methods for Equivariant Dynamical Systems}, Author = {Gatermann, K.}, Publisher = {Springer}, Year = {2000}, Address = {New York}, ISBN = {9783540671619} } @Article{Gauthier2002, Title = {Progress toward controlling in vivo fibrillating sheep atria using a nonlinear-dynamics-based closed-loop feedback method}, Author = {D. J. Gauthier and G. M. Hall and R. A. Oliver and E. G. Dixon-Tulloch and P. D. Wolf and S. Bahar}, Journal = {Chaos}, Year = {2002}, Pages = {952--961}, Volume = {12}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Gauthier2004, Title = {Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics}, Author = {E. G. Tolkacheva and M. M. Romeo and M. Guerraty and D. J. Gauthier}, Journal = {Phys Rev. E}, Year = {2004}, Pages = {031904}, Volume = {69}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Gauthier2005, Title = {Restitution in mapping models with an arbitrary amount of memory}, Author = {S. S. Kalb and E. G. Tolkacheva and D. G. Schaeffer and D. J. Gauthier and W. Krassowska}, Journal = {Chaos}, Year = {2005}, Pages = {023701}, Volume = {15}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Gauthier2007, Title = {Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization}, Author = {C. M. Berger and J. W. Cain and J. E. S. Socolar and D. J. Gauthier}, Journal = {PHYS. REV. E}, Year = {2007}, Pages = {041917}, Volume = {76}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Geerts2002, Title = {Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging}, Author = {L. Geerts and P. Bovendeerd and K. Nicolay and T. Arts}, Journal = {Am. J. Physiol. Heart Circ. 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Physiol.}, Year = {1952}, Pages = {500--544}, Volume = {117 (4):}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Owner = {roman}, Timestamp = {2014.06.27} } @Article{Holmes2000, Title = {Direct histological validation of diffusion tensor {MRI} in formaldehyde-fixed myocardium}, Author = {A. A. Holmes and D. F. Scollan and R. L. Winslow}, Journal = {Magn. Reson. Med.}, Year = {2000}, Pages = {157--161}, Volume = {44}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Holmes96, Title = {Turbulence, Coherent Structures, Dynamical Systems and Symmetry}, Author = {P. Holmes and J.L. Lumley and G. Berkooz}, Publisher = {Cambridge Univ. Press}, Year = {1996}, Address = {Cambridge}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{hopf48, Title = {A mathematical example displaying features of turbulence}, Author = {Hopf, E.}, Journal = {Comm. Pure Appl. Math.}, Year = {1948}, Pages = {303--322}, Volume = {1}, Copyright = {Copyright {\copyright} 1948 Wiley Periodicals, Inc., A Wiley Company}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1002/cpa.3160010401}, ISSN = {1097-0312}, Urldate = {2014-07-17} } @Book{horn1985, Title = {Matrix analysis}, Author = {R. A. Horn and C. R. Johnson}, Publisher = {Cambridge Univ. Press}, Year = {1985}, Address = {Cambridge, N.Y.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Misc{houtzager2008, Title = {Discrete-time periodic {R}iccati equation solver for periodic {LQ} state-feedback design}, Author = {I. Houtzager}, Note = {http://www.mathworks.com/matlabcentral/fileexchange/21379-dpre}, Year = {2008}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Howard1977, Title = {Slowly varying waves and shock structures in reaction-diffusion equations}, Author = {L. N. Howard and N. Kopell}, Journal = {Studies Appl. Math.}, Year = {1977}, Pages = {95--145}, Volume = {56} } @Book{hoyll06, Title = {Pattern Formation: An Introduction to Methods}, Author = {R. Hoyle}, Publisher = {Cambridge Univ. Press}, Year = {2006}, Address = {Cambridge}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Hsu1998, Title = {Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation}, Author = {E. W. Hsu and A. L. Muzikant and S. A. Matulevicius and R. C. Penland and C. S. Henriquez}, Journal = {Am. J. Physiol.}, Year = {1998}, Pages = {1627--1634}, Volume = {274}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Huikuri2001, Title = {Sudden death due to cardiac arrhythmias}, Author = {H. V. Huikuri and A. Castellanos and R. J. Myerburg}, Journal = {N. Engl. J. Med.}, Year = {2001}, Pages = {1473--1482}, Volume = {345}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{Hund2000, title={Determinants of excitability in cardiac myocytes: mechanistic investigation of memory effect}, author={Hund, T. J. and Rudy, Y.}, journal={Biophys. J.}, volume={79}, pages={3095--3104}, year={2000}, } @Article{Hund2004, Title = {Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model}, Author = {T. J. Hund and Y. Rudy}, Journal = {Circulation}, Year = {2004}, Pages = {3168--3174}, Volume = {110}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Hunter1998, Title = {Modelling the mechanical properties of cardiac muscle}, Author = {P. J. Hunter and A. D. McCulloch and H. E. ter Keurs}, Journal = {Prog. Biophys. Mol. Biol.}, Year = {1998}, Pages = {289--331}, Volume = {69} } @Article{HW90, Title = {Spectral properties of strongly perturbed {Coulomb} systems: {Fluctuation} properties}, Author = {H\"onig, A. and Wintgen, D.}, Journal = {Phys. Rev. A}, Year = {1989}, Pages = {5642--5657}, Volume = {39}, Bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevA.39.5642}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1103/PhysRevA.39.5642} } @Article{Ideker2006, Title = {Human ventricular fibrillation: wandering wavelets, mother rotors, or both?}, Author = {R. E. Ideker and J. M. Rogers}, Journal = {Circulation}, Year = {2006}, Pages = {530}, Volume = {114}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Timestamp = {2013.11.03} } @Article{IdZhKn95, Title = {Correlation Among Fibrillation, Defibrillation, and Cardiac Pacing}, Author = {Ideker, R. E. and Zhou, X. and Knisley, S. B.}, Journal = {Pacing and Clinical Electrophysiology}, Year = {1995}, Pages = {512--525}, Volume = {18}, Abstract = {An electrical stimulus must create an electric field of approximately 1 V/cm in the extracellular space to stimulate myocardium during diastole. To initiate fibrillation by premature stimulation during the vulnerable period or to defibrillate, an extracellular electric field of approximately 6 V/cm is required, a value approximately six times greater than that necessary for diastolic pacing. Yet, the current strength of the pulse given to the stimulating electrode to initiate fibrillation or to defibrillate is much greater than six times the diastolic pacing threshold. The ventricular fibrillation threshold is typically 40 times greater than the diastolic pacing threshold expressed in terms of current. The defibrillation threshold in terms of current is typically thousands of times greater than the diastolic pacing threshold. The reason that these thresholds vary so much more in terms of stimulus current than in terms of extracellular potential gradient is that each of the three thresholds requires creation of the required potential gradient at different distances from the stimulating electrode. Pacing requires a potential gradient of approximately 1 V/cm only in a small liminal volume of tissue immediately adjacent to the electrode. Initiation of ventricular fibrillation by premature stimulation during the vulnerable period requires a potential gradient of approximately 6 V/cm about 1 cm away from the stimulating electrode to allow sufficient space for the central common pathway of a figure-eight reentrant circuit to form. Since the potential gradient falls off rapidly with distance from the stimulating electrode, a stimulating current about 40 times greater than the diastolic pacing threshold is required to generate an electric field of 6 V/cm approximately 1 cm away from the stimulating electrode. Defibrillation requires an electric field of approximately 6 V/cm throughout all or almost all of the ventricular myocardium. Since some portions of the ventricles can be more than 10cm away from the defibrillation electrodes, a shock of several amps is required to create this field, a current thousands of times greater than the pacing threshold.}, Bdsk-url-1 = {http://dx.doi.org/10.1111/j.1540-8159.1995.tb02562.x}, DOI = {10.1111/j.1540-8159.1995.tb02562.x} } @Article{inv, Title = {Invariant measurement of strange sets in terms of cycles}, Author = {P. Cvitanovi{\'c}}, Journal = {Phys. Rev. Lett.}, Year = {1988}, Pages = {2729--2732}, Volume = {61}, DOI = {10.1103/PhysRevLett.61.2729} } @Incollection{ISI:000087624900005, Title = {Ion permeation through connexin gap junction channels: {Effects} on conductance and selectivity}, Author = {Veenstra, R. D.}, Booktitle = {Gap Junctions}, Year = {2000}, Pages = {95--129}, Series = {CURRENT TOPICS IN MEMBRANES}, Volume = {49}, ISSN = {{1063-5823}}, Owner = {roman}, Unique-id = {{ISI:000087624900005}} } @Incollection{ISI:000087624900010, Title = {Distinct behaviors of chemical and voltage sensitive gates of gap junction channel}, Author = {Bukauskas, F. F. and Peracchia, C.}, Booktitle = {Gap Juntions}, Year = {2000}, Pages = {207--221}, Series = {Current Topics in Membranes}, Volume = {49}, ISSN = {{1063-5823}}, Owner = {roman}, Timestamp = {2014.12.18}, Unique-id = {{ISI:000087624900010}} } @article{iyer2001experimentalist, title={An experimentalist's approach to accurate localization of phase singularities during reentry}, author={Iyer, Anand N and Gray, Richard A}, journal={Annals Biomed. Eng.}, volume={29}, number={1}, pages={47--59}, year={2001}, publisher={Springer} } @Article{izu2001evolution, author = {Izu, L. T. and Wier, W. G. and Balke, C. W.}, title = {Evolution of cardiac calcium waves from stochastic calcium sparks}, journal = {Biophys. J.}, year = {2001}, volume = {80}, pages = {103--120} } @Article{Jac97, Title = {{Laplace} and the origin of the {Ornstein-Uhlenbeck} process}, Author = {Jacobsen, M.}, Journal = {Bernoulli}, Year = {1997}, Pages = {271--286}, Volume = {2}, Annote = {a second-order partial differential equation, found by Laplace in 1810, is the Fokker-Planck equation for a one-dimensional Ornstein-Uhlenbeck process. It is argued that Laplace's reasoning, although not rigorous, can be entirely justified by using the modern theory of weak convergence of stochastic processes. The solutions to the differential equation found by Laplace and others, using expansions in terms of Hermite polynomials, are discussed. } } @Article{jacquemet2007, Title = {Steady-state solutions in mathematical models of atrial cell electrophysiology and their stability}, Author = {V. Jacquemet}, Journal = {Math. Biosci.}, Year = {2007}, Pages = {241}, Volume = {208}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{jahnke1989chemical, title={Chemical vortex dynamics in the {B}elousov-{Z}habotinskii reaction and in the two-variable Oregonator model}, author={Jahnke, W. and Skaggs, W. E. and Winfree, A. T.}, journal={J. Phys. Chem.}, volume={93}, number={2}, pages={740--749}, year={1989}, publisher={ACS Publications} } @article{jahnke1991survey, title={A survey of spiral-wave behaviors in the Oregonator model}, author={Jahnke, W. and Winfree, A. T.}, journal={International Journal of Bifurcation and Chaos}, volume={1}, number={02}, pages={445--466}, year={1991}, publisher={World Scientific} } @Article{Jaime2012, Title = {The transition to explosive solitons and the destruction of invariant tori}, Author = {Cisternas, J. and Descalzi, O. and Cartes, C.}, Journal = {Cent. Eur. J. Phys.}, Year = {2012}, Pages = {660--668}, Volume = {10}, DOI = {10.2478/s11534-012-0023-1} } @Article{Jaime2013, Title = {Intermittent explosions of dissipative solitons and noise-induced crisis}, Author = {Cisternas, J. and Descalzi, O.}, Journal = {Phys. Rev. E}, Year = {2013}, Pages = {022903}, Volume = {88}, DOI = {10.1103/PhysRevE.88.022903}, Numpages = {8} } @Article{Jalife2000, Title = {Ventricular fibrillation: mechanisms of initiation and maintenance}, Author = {J. Jalife}, Journal = {Annual Rev. Physiol.}, Year = {2000}, Pages = {25}, Volume = {62}, Timestamp = {2013.11.03} } @article{Jalife2002, title={Mother rotors and fibrillatory conduction: a mechanism of atrial fibrillation}, author={Jalife, Jos{\'e} and Berenfeld, Omer and Mansour, Moussa}, journal={Cardiovascular Research}, volume={54}, number={2}, pages={204--216}, year={2002}, publisher={The Oxford University Press} } @Book{jhos, Title = {Oscillations in Nonlinear Systems}, Author = {J. K. Hale}, Publisher = {McGraw-Hill}, Year = {1963}, Address = {New York} } @Article{Jiang2004, Title = {Three-dimensional diffusion tensor microscopy of fixed mouse hearts}, Author = {Y. Jiang and K. Pandya and O. Smithies and E. W. Hsu}, Journal = {Magn. Reson. Med.}, Year = {2004}, Pages = {453--460}, Volume = {52}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{JoPro87, Title = {Strong spatial resonance and travelling waves in {Benard} convection}, Author = {C. A. Jones and M. R. E. Proctor}, Journal = {Phys. Lett. A}, Year = {1987}, Pages = {224--228}, Volume = {121}, Bdsk-url-1 = {http://dx.doi.org/10.1016/0375-9601(87)90008-9}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1016/0375-9601(87)90008-9} } @Book{kailath, Title = {Linear Systems}, Author = {T. Kailath}, Publisher = {Prentice Hall}, Year = {1980}, Address = {Englewood Cliffs, N.J.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{KaMaPaa96, Title = {Spatial dynamics of time-periodic solutions for the {Ginzburg-Landau} equation}, Author = {T. Kapitula and S. Maier-Paape}, Journal = {Z. Angew. Math. Phys.}, Year = {1996}, Pages = {265--305}, Volume = {47}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{kantz04, Title = {Nonlinear Time Series Analysis}, Author = {Kantz, H.}, Publisher = {Cambridge Univ. Press}, Year = {2004}, Address = {Cambridge, {UK}}, Edition = {2 edition} } @Incollection{KapYor79, Title = {Numerical solution of a generalized eigenvalue problem for even mappings}, Author = {Kaplan, J. L. and Yorke, J. A.}, Booktitle = {Functional Differential Equations and Approximation of Fixed Points}, Publisher = {Springer}, Year = {1979}, Address = {New York}, Editor = {Peitgen, H.-O. and Walther, H.-O.}, Pages = {228--237}, Series = {Lect. Notes Math.}, Volume = {730}, DOI = {10.1007/BFb0064320} } @Incollection{KapYor79a, Title = {Chaotic behavior of multidimensional difference equations}, Author = {Kaplan, J. L. and Yorke, J. A.}, Booktitle = {Functional Differential Equations and Approximation of Fixed Points}, Publisher = {Springer}, Year = {1979}, Address = {Berlin}, Editor = {Peitgen, H.-O. and Walther, H.-O.}, Pages = {204--227}, Series = {Lect. Notes Math.}, Volume = {730}, DOI = {10.1007/BFb0064320} } @Article{Karma:1991un, author = {A. Karma}, title = {Universal limit of spiral wave propagation in excitable media}, journal = {Phys. Rev. Lett.}, year = {1991}, volume = {66}, pages = {2274--2277}, doi = {10.1103/physrevlett.66.2274}, } @Article{Karma1993, Title = {Spiral breakup in model equations of action-potential propagation in cardiac tissue}, Author = {A. Karma}, Journal = {Phys. Rev. Lett.}, Year = {1993}, Pages = {1103--1106}, Volume = {71} } @Article{Karma2002, Title = {Spatiotemporal control of cardiac alternans}, Author = {B. Echebarria and A. Karma}, Journal = {Chaos}, Year = {2002}, Pages = {923--930}, Volume = {12}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{karma94, Title = {Electrical alternans and spiral wave breakup in cardiac tissue}, Author = {A. Karma}, Journal = {Chaos}, Year = {1994}, Pages = {461--472}, Volume = {4}, DOI = {10.1063/1.166024} } @Article{kassam2005fourth, Title = {Fourth-order time stepping for stiff {PDEs}}, Author = {A. K. Kassam and L. N. Trefethen}, Journal = {SIAM J. Sci. Comput.}, Year = {2005}, Pages = {1214--1233}, Volume = {26}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{KawKida01, Title = {Periodic motion embedded in plane {Couette} turbulence: {Regeneration} cycle and burst}, Author = {G. Kawahara and S. Kida}, Journal = {J. Fluid Mech.}, Year = {2001}, Pages = {291--300}, Volume = {449}, Abstract = {Two time-periodic solutions are found in a 3-d constrained plane Couette flow, multishooting method being used. The turbulent state mainly follows the periodic orbit with strong variations. The gentle one is related to the bursting behavior of the system. Heteroclinic orbits between these two periodic orbits are found.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Keener:1986ag, Title = {A geometrical theory for spiral waves in excitable media}, Author = {Keener, J. P.}, Journal = {SIAM J. Appl. Math.}, Year = {1986}, Pages = {1039--1056}, Volume = {46}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Keener:1986sp, Title = {Spiral waves in the {Belousov-Zhabotinskii} reaction}, Author = {Keener, J. P. and Tyson, J. J.}, Journal = {Physica D}, Year = {1986}, Pages = {307--324}, Volume = {21}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{keener1988dynamics, Title = {The dynamics of three-dimensional scroll waves in excitable media}, Author = {Keener, James P}, Journal = {Physica D}, Year = {1988}, Number = {2}, Pages = {269--276}, Volume = {31}, Publisher = {Elsevier} } @Article{Kerswell05, Title = {Recent progress in understanding the transition to turbulence in a pipe}, Author = {R. R. Kerswell}, Journal = {Nonlinearity}, Year = {2005}, Pages = {17--44}, Volume = {18}, Abstract = {The problem of understanding the nature of fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. So far no explanation has been substantiated to rationalize the transition process by which the steady unidirectional laminar flow state gives way to a temporally and spatially disordered three-dimensional (turbulent) solution as the flow rate increases. Recently, new travelling wave solutions have been discovered which are saddle points in phase space. These plausibly represent the lowest level in a hierarchy of spatio-temporal periodic flow solutions which may be used to construct a cycle expansion theory of turbulent pipe flows. We summarize this success against the backdrop of past work and discuss its implications for future research.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{kilpatrick2012response, Title = {Response of traveling waves to transient inputs in neural fields}, Author = {Kilpatrick, Zachary P and Ermentrout, Bard}, Journal = {Phys. Rev. E}, Year = {2012}, Number = {2}, Pages = {021910}, Volume = {85}, Publisher = {APS} } @Article{knoll2004, Title = {Jacobian-free {N}ewton-{K}rylov methods: {A} survey of approaches and applications}, Author = {D. A. Knoll and D. E. Keyes}, Journal = {J. Comp. Phys.}, Year = {2004}, Pages = {357}, Volume = {193}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{KoEhlMo96, Title = {Problems and progress in microswimming}, Author = {Koiller, J. and Ehlers, K. and Montgomery, R.}, Journal = {J. Nonlin. Sci.}, Year = {1996}, Pages = {507--541}, Volume = {6}, Bdsk-url-1 = {http://dx.doi.org/10.1007/BF02434055}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1007/BF02434055} } @Article{Kohler2003, Title = {Investigation of the microstructure of the isolated rat heart: a comparison between T*2- and diffusion-weighted {MRI}}, Author = {S. Kohler and K. H. Hiller and C. Waller and W. R. Bauer and A. Haase and P. M. Jakob}, Journal = {Magn. Reson. Med.}, Year = {2003}, Pages = {1144--1150}, Volume = {50}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Koller1998, Title = {Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation}, Author = {M. L. Koller and M. L. Riccio and R. F. {Gilmour Jr.}}, Journal = {Am. J. Physiol.}, Year = {1998}, Pages = {H1635}, Volume = {275} } @Article{konta1990significance, Title = {Significance of discordant ST alternans in ventricular fibrillation.}, Author = {Konta, Tsuyoshi and Ikeda, Kozue and Yamaki, Michiyasu and Nakamura, Kazuharu and Honma, Kentarou and Kubota, Isao and Yasui, Shoji}, Journal = {Circulation}, Year = {1990}, Number = {6}, Pages = {2185--2189}, Volume = {82}, Publisher = {Am Heart Assoc} } @Incollection{koopmania, Author = {P. Cvitanovi{\'c}}, Booktitle = {Chaos: Classical and Quantum}, Publisher = {Niels Bohr Inst.}, Year = {2016}, Address = {Copenhagen}, Chapter = {{Implementing} evolution}, URL = {http://ChaosBook.org/paper.shtml#appendMeasure} } @Article{Kothe:2009se, Title = {Second universal limit of wave segment propagation in excitable media}, Author = {Kothe, A. and Zykov, V. S. and Engel, H.}, Journal = {Phys. Rev. Lett.}, Year = {2009}, Pages = {154102--154102}, Volume = {103}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{KreEck12, Title = {Periodic orbits near onset of chaos in plane {Couette} flow}, Author = {T. Kreilos and B. Eckhardt}, Journal = {Chaos}, Year = {2012}, Note = {\arXiv{1205.0347}}, Pages = {047505}, Volume = {22}, Bdsk-url-1 = {http://dx.doi.org/10.1063/1.4757227}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1063/1.4757227} } @Article{krinskii1966spread, Title = {Spread of excitation in an inhomogeneous medium (state similar to cardiac fibrillation)}, Author = {Krinskii, V. I.}, Journal = {Biophysics-USSR}, Year = {1966}, Pages = {776}, Volume = {11} } @Article{Krinsky1983, Title = {Interaction of rotating waves in an active chemical medium}, Author = {V. I. Krinsky and K. I. Agladze}, Journal = {Physica D}, Year = {1983}, Pages = {50--56}, Volume = {8} } @Article{KroghMadsen2007, author = {Krogh-Madsen, T. and Christini, D. J.}, title = {Action Potential Duration Dispersion and Alternans in Simulated Heterogeneous Cardiac Tissue with a Structural Barrier}, journal = {Biophys. J.}, year = {2007}, volume = {92}, pages = {1138--1149}, doi = {10.1529/biophysj.106.090845} } @Article{Krupa90, Title = {Bifurcations of relative equilibria}, Author = {M. Krupa}, Journal = {SIAM J. Math. Anal.}, Year = {1990}, Pages = {1453--1486}, Volume = {21}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{kskent92, Title = {Travelling-waves of the {Kuramoto-Sivashinsky} equation: {Period-multiplying} bifurcations}, Author = {P. Kent and J. Elgin}, Journal = {Nonlinearity}, Year = {1992}, Pages = {899--919}, Volume = {5}, Abstract = {Some properties of the KSe are discussed. A unified argument about the connections and periodic orbits is given. In particular, the K-bifurcation of the system is conjectured to arises in the 1:n resonances of a fixed point.} } @Article{kstroy89, Title = {The existence of steady solutions of the {Kuramoto-Sivashinsky} equation}, Author = {W. C. Troy}, Journal = {J. Diff. Eqn.}, Year = {1989}, Pages = {269--313}, Volume = {82}, Abstract = {For c=1, the existence of two periodic orbits and two heteroclinic orbits are proved and suggestions for proving the existence of more complicated orbits are given.} } @Article{ku, Title = {Persistent propagation of concentration waves in dissipative media far from thermal equilibrium}, Author = {Y. Kuramoto and T. Tsuzuki}, Journal = {Progr. Theor. Phys.}, Year = {1976}, Pages = {365--369}, Volume = {55}, Abstract = {The KSe is derived through the CGLe near the bifurcation point. Some scaling argument is used to sort out the domiant terms.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{KuPa12, Title = {Theory and computation of {Covariant {Lyapunov} Vectors}}, Author = {Kuptsov, P. V. and Parlitz, U.}, Journal = {J. Nonlin. Sci.}, Year = {2012}, Note = {\arXiv{1105.5228}}, Pages = {727--762}, Volume = {22}, DOI = {10.1007/s00332-012-9126-5} } @Book{kura84tur, Title = {Chemical Oscillations, Waves and Turbulence}, Author = {Y. Kuramoto}, Publisher = {Springer}, Year = {1984}, Address = {Berlin} } @Article{LaMi99, Title = {{Karhunen-Loeve} decomposition in the presence of symmetry. {I}}, Author = {B. Lahme and R. Miranda}, Journal = {IEEE Trans. Image Processing}, Year = {1999}, Pages = {1183--1190}, Volume = {8}, Abtract = {The Karhunen-Loeve (KL) decomposition is widely used for data which very often exhibit some symmetry, afforded by a group action. For a finite group, we derive an algorithm using group representation theory to reduce the cost of determining the KL basis. We demonstrate the technique on a Lorenz-type ODE system. For a compact group such as tori or SO(3,R) the method also applies, and we extend results to these cases. As a short example, we consider the circle group S1.} } @Article{LanBar13, Title = {Non-specular reflections in a macroscopic system with wave-particle duality: {Spiral} waves in bounded media}, Author = {J. Langham and D. Barkley}, Journal = {Chaos}, Year = {2013}, Note = {\arXiv{1304.0591}}, Pages = {013134}, Volume = {23}, Bdsk-url-1 = {http://dx.doi.org/10.1063/1.4793783}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1063/1.4793783} } @Article{LanBar14, Title = {Asymptotic dynamics of reflecting spiral waves}, Author = {Langham, Jacob and Biktasheva, Irina and Barkley, Dwight}, Journal = {Phys. Rev. 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We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.}}, DOI = {{10.1103/PhysRevLett.71.2026}}, Researcherid-numbers = {{Bodenschatz, Eberhard/C-6603-2009 Morris, Stephen/F-6778-2013}} } @Article{Mozaffarian2016, title = {{Heart disease and stroke statistics-2016 update a report from the American Heart Association}}, author = {Mozaffarian, Dariush and Benjamin, Emelia J. and Go, Alan S. and Arnett, Donna K. and others}, Journal = {Circulation}, number = {4}, pages = {e38--e360}, volume = {133}, year = {2016} } @Book{mpc, Title = {Model predictive control}, Author = {E. F. Camacho and C. 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D}, Year = {2013}, Pages = {34--45}, Volume = {252}, DOI = {10.1016/j.physd.2013.02.009} } @Article{SapMajPhysD13, Title = {Blending reduced subspace algorithms for uncertainty quantification of quadratic systems with a stable mean state}, Author = {Sapsis, T. P. and Majda, A. J.}, Journal = {Phys. D}, Year = {2013}, Pages = {61--76}, Volume = {258}, DOI = {10.1016/j.physd.2013.05.004} } @Article{Sapsis13, Title = {Attractor local dimensionality, nonlinear energy transfers and finite-time instabilities in unstable dynamical systems with applications to two-dimensional fluid flows}, Author = {Sapsis, T. P.}, Journal = {Proc. R. Soc. Lond. A}, Year = {2013}, Volume = {469}, DOI = {10.1098/rspa.2012.0550} } @Article{SaScWu97, Title = {Dynamics of spiral waves on unbounded domains using center-manifold reductions}, Author = {B. Sandstede and A. Scheel and C. Wulff}, Journal = {J. Diff. Eqn.}, Year = {1997}, Pages = {122--149}, Volume = {141}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{SaScWu97a, Title = {Center-manifold reduction for spiral waves}, Author = {Sandstede, B. and Scheel, A. and Wulff, C.}, Journal = {C. R. Acad. Sci. Paris, S\'er. I}, Year = {1997}, Pages = {153--158}, Volume = {324}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Incollection{SaScWu99, Title = {Dynamical behavior of patterns with {Euclidean} symmetry}, Author = {B. Sandstede and A. Scheel and C. Wulff}, Booktitle = {Pattern Formation in Continuous and Coupled Systems}, Publisher = {Springer}, Year = {1999}, Address = {New York}, Pages = {249--264}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{SaScWu99a, Title = {Bifurcations and dynamics of spiral waves}, Author = {B. Sandstede and A. Scheel and C. Wulff}, Journal = {J. Nonlin. Sci.}, Year = {1999}, Pages = {439--478}, Volume = {9}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{sato2009acceleration, Title = {Acceleration of cardiac tissue simulation with graphic processing units}, Author = {D. Sato and Y. Xie and J. N. Weiss and Z. Qu and A. Garfinkel and A. R. Sanderson}, Journal = {Medical and biological engineering and computing}, Year = {2009}, Pages = {1011--1015}, Volume = {47}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{scarle2009implications, Title = {Implications of the {Turing} completeness of reaction-diffusion models, informed by {GPGPU} simulations on an {XBox} 360: {Cardiac} arrhythmias, re-entry and the halting problem}, Author = {S. Scarle}, Journal = {Computational biology and chemistry}, Year = {2009}, Pages = {253--260}, Volume = {33} } @Article{SCD07, Title = {On the state space geometry of the {Kuramoto-Sivashinsky} flow in a periodic domain}, Author = {Cvitanovi{\'c}, P. and Davidchack, R. L. and Siminos, E.}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2010}, Addendum = {\arXiv{0709.2944}}, Pages = {1--33}, Volume = {9}, DOI = {10.1137/070705623} } @Unpublished{SCD09b, Title = {Recurrent spatio-temporal structures of translationally invariant {Kuramoto-Sivashinsky} flow}, Author = {E. Siminos and P. Cvitanovi{\'c} and R. L. Davidchack}, Note = {{In} preparation}, Year = {2012} } @article{schneider2007, title={Turbulence transition and the edge of chaos in pipe flow}, author={Schneider, T. M. and Eckhardt, B. and Yorke, J. A.}, journal={Phys. Rev. Lett.}, volume={99}, pages={034502}, year={2007}, } @Unpublished{SchlAvVa11, Title = {Numerical bifurcation study of superconducting patterns on a square}, Author = {Schl{\"o}mer, N. and Avitabile, D. and Vanroose, W.}, Note = {\arXiv{1102.1212}}, Year = {2011}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Schrlau2009, Title = {Cell Electrophysiology with Carbon Nanopipettes}, Author = {M. G. Schrlau and N. J. Dun and H. H. Bau}, Journal = {ACSNANO}, Year = {2009}, Pages = {563--568}, Volume = {3} } @Article{SchWri08, Title = {Colliding dissipative pulses -- {The} shooting manifold}, Author = {A. Scheel and J. D. Wright}, Journal = {J. Diff. Eqn.}, Year = {2008}, Pages = {59--79}, Volume = {245}, DOI = {10.1016/j.jde.2008.03.019} } @Article{science04, Title = {Experimental observation of nonlinear traveling waves in turbulent pipe flow}, Author = {B. Hof and C. W. H. van Doorne and J. Westerweel and F. T. M. Nieuwstadt and H. Faisst and B. Eckhardt and H. Wedin and R. R. Kerswell and F. Waleffe}, Journal = {Science}, Year = {2004}, Pages = {1594--1598}, Volume = {305}, Abstract = {Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable traveling waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these traveling waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Scollan1998, Title = {Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging}, Author = {D. F. Scollan and A. Holmes and R. Winslow and J. Forder}, Journal = {Am. J. Physiol.}, Year = {1998}, Pages = {2308--2318}, Volume = {275}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Scollan2000, Title = {Reconstruction of cardiac ventricular geometry and fiber orientation using magnetic resonance imaging}, Author = {D. F. Scollan and A. Holmes and J. Zhang and R. L. Winslow}, Journal = {Ann. Biomed. 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Siminos}, School = {School of Physics, Georgia Inst. of Technology}, Year = {2009}, Address = {Atlanta}, Note = {\\\wwwcb{/projects/theses.html}}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Simitev2006, author = {Simitev, R. D. and Biktashev, V. N.}, title = {Conditions for propagation and block of excitation in an asymptotic model of atrial tissue}, journal = {Biophys. J.}, year = {2006}, volume = {90}, pages = {2258--2269} } @Article{sinai, Title = {Gibbs measures in ergodic theory}, Author = {Ya. G. Sinai}, Journal = {Russian Math. Surveys}, Year = {1972}, Pages = {21}, Volume = {166} } @Article{SiRo87, Title = {Coherent structures and chaos: {A} model problem}, Author = {L. Sirovich and J. D. Rodriguez}, Journal = {Phys. Lett. A}, Year = {1987}, Pages = {211--214}, Volume = {120} } @Article{sirovcgl90, Title = {Low-dimensional dynamics for the complex {Ginzburg-Landau} equation}, Author = {J. D. Rodriguez and L. 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Sivashinsky}, Journal = {Acta Astronaut.}, Year = {1977}, Pages = {1177--1206}, Volume = {4}, Abstract = {A integro-differential equation (KSe) is derived directly from the flame propagation equations near the bifurcation point.} } @article{Skardal2014, title={Spatiotemporal dynamics of calcium-driven cardiac alternans}, author={Skardal, Per Sebastian and Karma, Alain and Restrepo, Juan G}, journal={Physical Review E}, volume={89}, number={5}, pages={052707}, year={2014}, publisher={APS} } @article{skardal2014coexisting, title={Coexisting chaotic and multi-periodic dynamics in a model of cardiac alternans}, author={Skardal, Per Sebastian and Restrepo, Juan G}, journal={Chaos}, volume={24}, number={4}, pages={043126}, year={2014}, publisher={AIP Publishing} } @Article{skeleton, Title = {Periodic orbits as the skeleton of classical and quantum chaos}, Author = {P. 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M. and Akhmediev, N. and Ankiewicz, A.}, Journal = {Phys. Rev. Lett.}, Year = {2000}, Pages = {2937--2940}, Volume = {85}, DOI = {10.1103/PhysRevLett.85.2937} } @Article{SoAkDeMe08, Title = {Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons}, Author = {J. M. Soto-Crespo and N. Akhmediev and N. Devine and C. Mej\'{i}a-Cort\'{e}s}, Journal = {Opt. Express}, Year = {2008}, Pages = {15388--15401}, Volume = {16}, Abstract = {Dissipative media admit the existence of two types of stationary self-organized beams: continuously self-focused and continuously self-defocused. Each beam is stable inside of a certain region of its existence.Beyond these two regions, beams loose their stability, and new dynamical behaviors appear. We present several types of instabilities related to each beam configuration and give examples of beam dynamics in the areas adjacent to the two regions. We observed that, in one case beams loose the radial symmetry while in the other one the radial symmetry is conserved during complicated beam transformations.}, DOI = {10.1364/OE.16.015388} } @Article{Socolar1994, Title = {Stabilizing unstable periodic orbits in fast dynamical-systems}, Author = {J. E. S. Socolar and D. W. Sukow and D. J. Gauthier}, Journal = {Phys. Rev. E}, Year = {1994}, Pages = {3245}, Volume = {50}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{solomon, Title = {Uniform resonant chaotic mixing in fluid flows}, Author = {T. H. Solomon and I. Mezi{\'c}}, Journal = {Nature}, Year = {2003}, Pages = {376}, Volume = {425}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{sparrow, Title = {The {Lorenz} Equations: {Bifurcations}, Chaos and Strange Attractors}, Author = {C. Sparrow}, Publisher = {Springer}, Year = {1982}, Address = {New York} } @Article{spercgl, Title = {Small-amplitude periodic and chaotic solutions of the complex {Ginzburg-Landau} equation for a subcritical bifurcation}, Author = {W. Sch{\"o}pf and L. Kramer}, Journal = {Phys. Rev. Lett.}, Year = {1991}, Pages = {2316}, Volume = {66} } @Article{SPScgl92, Title = {Spatiotemporal chaos in the one-dimensional complex {Ginzburg-Landau} equation}, Author = {B. I. Shraiman and A. Pumir and van Saarloos, W. and Hohenberg, P. C. and H. Chat\'{e} and M. Holen}, Journal = {Physica D}, Year = {1992}, Pages = {241--248}, Volume = {57} } @Article{Sq33, Title = {On the stability of three-dimensional distribution of viscous fluid between parallel walls}, Author = {H. B. Squire}, Journal = {Proc. R. Soc. Lond. A}, Year = {1933}, Pages = {621}, Volume = {142} } @article{Starmer1993, title={Vulnerability in an excitable medium: analytical and numerical studies of initiating unidirectional propagation.}, author={Starmer, C Frank and Biktashev, Vladimir N and Romashko, Dimitry N and Stepanov, Mikhael R and Makarova, Olga N and Krinsky, Valentin I}, journal={Biophysical journal}, volume={65}, number={5}, pages={1775}, year={1993}, publisher={The Biophysical Society} } @article{starmer1997cardiac, title={The Cardiac Vulnerable Period and Reentrant Arrhythmias: Targets of Anti-and Proarrhythmic Processes}, author={Starmer, C}, journal={Pacing and clinical electrophysiology}, volume={20}, number={2}, pages={445--454}, year={1997}, publisher={Wiley Online Library} } @article{Starobin1994, title={Vulnerability in one-dimensional excitable media}, author={Starobin, Joseph and Zilberter, Yuri I and Starmer, C Frank}, journal={Physica D}, volume={70}, number={4}, pages={321--341}, year={1994}, publisher={Elsevier} } @Article{stabpcgl, Title = {Stability of plane wave solutions of complex {Ginzburg-Landau} equations}, Author = {B. J. Matkowsky and V. Volpert}, Journal = {Quart. Appl. Math.}, Year = {1993}, Pages = {265--281}, Volume = {LI} } @Unpublished{stadium95, Title = {Symbolic dynamics and {Markov} partitions for the stadium billiard}, Author = {Hansen, K. T. and Cvitanovi{\'c}, P.}, Addendum = {\arXiv{chao-dyn/9502005}; {\em J. Stat. Phys.}, accepted 1996, revised version still not resubmitted}, Year = {1995} } @Article{Stevens2003, Title = {Ventricular mechanics in diastole: material parameter sensitivity}, Author = {C. Stevens and E. Remme and I. LeGrice and P. Hunter}, Journal = {J. Biomechanics}, Year = {2003}, Pages = {737--748}, Volume = {36}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Stewart2009, Title = {Mathematical models of the electrical action potential of {Purkinje} fibre cells}, Author = {P. Stewart and O. V. Aslanidi and D. Noble and P. J. Noble and M. R. Boyett and H. Zhang}, Journal = {Phil. Trans. Roy. Soc. Lond. A}, Year = {2009}, Pages = {2225--2255}, Volume = {367}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{StGo09, Title = {Mathematics for Physics: A Guided Tour for Graduate Students}, Author = {M. Stone and P. Goldbart}, Publisher = {Cambridge Univ. Press}, Year = {2009}, Address = {Cambridge}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{stoer1980, Title = {Introduction to numerical analysis}, Author = {J. Stoer and R. Bulirsch}, Publisher = {Springer}, Year = {1998}, Address = {New York}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Strain:1998si, Title = {Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable medium}, Author = {Strain, M. C. and Greenside, H. S.}, Journal = {Phys. Rev. Lett.}, Year = {1998}, Pages = {2306--2309}, Volume = {80}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{strogb, Title = {Nonlinear Dynamics and Chaos}, Author = {S. H. Strogatz}, Publisher = {Perseus Publishing}, Year = {2000}, Address = {Cambridge, Mass}, Series = {Studies in Nonlinearity}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{Chugh2014, author = {Chugh, Sumeet S and Havmoeller, Rasmus and Narayanan, Kumar and Singh, David and others}, journal = {Circulation}, number = {8}, pages = {837--847}, pmid = {24345399}, title = {{Worldwide epidemiology of atrial fibrillation: A global burden of disease 2010 study}}, volume = {129}, year = {2014} } @Article{SumRules, Title = {Beyond the periodic orbit theory}, Author = {Cvitanovi{\'c}, P. and Hansen, Kim and Rolf, J. and Vattay, G.}, Journal = {Nonlinearity}, Year = {1998}, Addendum = {\arXiv{chao-dyn/9712002}}, Pages = {1209--1232}, Volume = {11}, Abstract = {The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated {Fredholm} determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory approach for determining eigenspectra of transfer operators. AMS classification scheme numbers: 58F20}, DOI = {10.1088/0951-7715/11/5/003} } @InProceedings{sunil_ahuja_template-based_2006, Title = {Template-based stabilization of relative equilibria}, Author = {S. Ahuja and I. G. Kevrekidis and C. W. Rowley}, Booktitle = {2006 American Control Conference, 14-16 June 2006}, Year = {2006}, Address = {Piscataway, NJ}, Pages = {6}, Publisher = {{IEEE}}, Abstract = {We present an approach to the design of feedback control laws that stabilize the relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original system are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. Assuming equivariant actuation, we derive feedback laws for the reduced system that are optimal in the sense that they minimize a quadratic cost function. We illustrate the method by stabilizing unstable traveling waves of a dissipative {PDE} possessing translational invariance} } @article{Suri2017, title={Forecasting Fluid Flows Using the Geometry of Turbulence}, author={B. Suri and J. Tithof and RO Grigoriev and MF Schatz}, journal={Phys. Rev. Lett.}, volume={118}, pages={114501}, year={2017}, } @article{Surovyatkina2010, title={Multistability property in cardiac ionic models of mammalian and human ventricular cells}, author={Surovyatkina, Elena and Noble, Denis and Gavaghan, David and Sher, Anna}, journal={Progress in Biophysics and Molecular Biology}, volume={103}, number={1}, pages={131--141}, year={2010}, publisher={Elsevier} } @Article{SYE05, author = {J. D. Skufca and J. A. Yorke and B. Eckhardt}, title = {The {Edge of Chaos} in a parallel shear flow}, journal = {Phys. Rev. Lett.}, year = {2006}, volume = {96}, pages = {174101}, doi = {10.1103/PhysRevLett.96.174101} } @Incollection{symb_dyn, Author = {P. Cvitanovi{\'c}}, Booktitle = {Chaos: Classical and Quantum}, Publisher = {Niels Bohr Inst.}, Year = {2016}, Address = {Copenhagen}, Chapter = {{Charting} the state space}, URL = {http://ChaosBook.org/paper.shtml#knead} } @Article{symmcgl, Title = {Breaking the hidden symmetry in the {Ginzburg-Landau} equation}, Author = {A. Doelman}, Journal = {Physica D}, Year = {1996}, Pages = {398--428}, Volume = {97} } @Article{tachibana1998, Title = {Discordant S-T alternans contributes to formation of reentry: a possible mechanism of reperfusion arrhythmia}, Author = {H. Tachibana and I. Kubota and M. Yamaki and T. Watanabe and H. Tomoike}, Journal = {Am. J. Physiol.}, Year = {1998}, Pages = {H116}, Volume = {275}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Owner = {roman}, Timestamp = {2013.11.03} } @Article{takac98, Title = {Bifurcations to invariant 2-tori for the complex {Ginzburg-Landau} equation}, Author = {P. Tak\'{a}\v{c}}, Journal = {Appl. Math. Comput.}, Year = {1998}, Pages = {241--257}, Volume = {89}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{tao2011space, Title = {Space-time {FLAVORS}: finite difference, multisymlectic, and pseudospectral integrators for multiscale {PDEs}}, Author = {Tao, M. and Owhadi, H. and Marsden, J. E}, Journal = {arXiv preprint \arXiv1104.0272}, Year = {2011}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{tbohr, Title = {The diversity of steady state solutions of the complex {Ginzburg-Landau} equation}, Author = {M. Bazhenov and T. Bohr and K. Gorshkov and M. Rabinovich}, Journal = {Phys. Lett. A}, Year = {1996}, Pages = {104}, Volume = {217} } @Article{TeHaHe10, Title = {Spatial optimal growth in three-dimensional boundary layers}, Author = {D. Tempelmann and A. Hanifi and D. S. Henningson}, Journal = {J. Fluid Mech.}, Year = {2010}, Pages = {5--37}, Volume = {646}, Bdsk-url-1 = {http://dx.doi.org/10.1017/S0022112009993260}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1017/S0022112009993260} } @Article{ten2006alternans, Title = {Alternans and spiral breakup in a human ventricular tissue model}, Author = {ten Tusscher, Kirsten HWJ and Panfilov, Alexander V}, Journal = {American Journal of Physiology-Heart and Circulatory Physiology}, Year = {2006}, Number = {3}, Pages = {H1088--H1100}, Volume = {291}, Publisher = {Am Physiological Soc} } @Article{tenTusscher2008, Title = {Modelling of the ventricular conduction system}, Author = {K. H. Tusscher and A. V. Panfilov}, Journal = {Prog. Biophys. Mol. Biol.}, Year = {2008}, Pages = {152--170}, Volume = {96}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{teramura2014damping, Title = {Damping filter method for obtaining spatially localized solutions}, Author = {Teramura, Toshiki and Toh, Sadayoshi}, Journal = {Phys. Rev. E}, Year = {2014}, Pages = {052910}, Volume = {89} } @Misc{TerToh13, Title = {A dumping filter method for obtaining spatially localized exact solutions}, Author = {Teramura, T. and Toh, S.}, Note = {\arXiv{1311.2792}}, Year = {2013} } @Article{TFGphase97, Title = {Studies of phase turbulence in the one-dimensional complex {Ginzburg-Landau} equation}, Author = {A. Torcini and H. Frauenkron and P. Grassberger}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {5073}, Volume = {55}, Abstract = {The phase gradient is used as an order parameter. Different states are identified. In the PT region, a modified KSe rules the phase dynamics of the CGLe.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Misc{TheVirtualHeart, Title = {{The Virtual Heart}}, Author = {F. H. Fenton and E. M. Cherry}, HowPublished = {\url{TheVirtualHeart.org}}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{thiffeault2014braidlab, Title = {Braidlab: A software package for braids and loops}, Author = {Thiffeault, Jean-Luc and Budisic, Marko}, Journal = {arXiv preprint arXiv:1410.0849}, Year = {2014} } @Book{Thomas1995, Title = {Numerical Partial Differential Equations: Finite Difference Methods}, Author = {J. W. Thomas}, Publisher = {Springer}, Year = {1995}, Address = {New York}, Date-added = {2017-06-28 23:12:47 +0000}, } @article{budivsic2015finite, title={Finite-time braiding exponents}, author={Budi{\v{s}}i{\'c}, M. and Thiffeault, J.-L.}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume={25}, number={8}, pages={087407}, year={2015}, publisher={AIP Publishing} } @Article{ThuCoo10, Title = {Understanding cardiac alternans: {A} piecewise linear modeling framework}, Author = {R. Thul and S. Coombes}, Journal = {Chaos}, Year = {2010}, Pages = {045102}, Volume = {20}, Bdsk-url-1 = {http://dx.doi.org/10.1063/1.3518362}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1063/1.3518362}, Numpages = {13} } @Phdthesis{Thum05, Title = {Numerical Analysis of the Method of Freezing Traveling Waves}, Author = {V. Th{\"u}mmler}, School = {Bielefeld Univ.}, Year = {2005}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Tinkham, Title = {Group Theory and Quantum Mechanics}, Author = {M. Tinkham}, Publisher = {Dover}, Year = {2003}, Address = {New York}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{tolkacheva2002, Title = {Analysis of the Fenton-Karma model through an approximation by a one-dimensional map}, Author = {E. G. Tolkacheva and D. G. Schaeffer and D. J. Gauthier and C. C. Mitchell}, Journal = {Chaos}, Year = {2002}, Pages = {1034}, Volume = {12}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Owner = {roman}, Timestamp = {2013.11.03} } @Article{torc96, Title = {Order parameter for the transition from phase to amplitude turbulence}, Author = {A. Torcini}, Journal = {Phys. Rev. Lett.}, Year = {1996}, Pages = {1047}, Volume = {77}, Abstract = {The maximal consersed phase gradient is introduced as an order parameter to characterize the transition from phase to defect turbulence in the CGLe. It has a finite value in the PT regime and decreases to zero when the transition to defect turbulence is approached. A modified KSe is able to reproduce the main feature of the stable waves and to explain their origin.}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{toricgl, Title = {Invariant 2-tori in the time-dependent {Ginzburg-Landau} equation}, Author = {P. Tak\'{a}\v{c}}, Journal = {Nonlinearity}, Year = {1992}, Pages = {289--321}, Volume = {5}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Inbook{torino, Author = {P. Cvitanovi{\'c}}, Chapter = {Chaos for cyclists}, Editor = {E. Moss and L. A. Lugiato and W. Schleich}, Publisher = {Cambridge Univ. Press}, Year = {1989}, Address = {Cambridge}, Booktitle = {Noise and Chaos in Nonlinear Dynamical Systems}, ISBN = {9780521384179} } @Article{Tranquillo2004, Title = {Genesis of the monophasic action potential: role of interstitial resistance and boundary gradients}, Author = {J. V. Tranquillo and M. R. Franz and B. C. Knollmann and A. P. Henriquez and D. A. Taylor and C. S. Henriquez}, Journal = {Am. J. Physiol. Heart Circ. Physiol.}, Year = {2004}, Pages = {1370--1381}, Volume = {286}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Trefethen00, Title = {Spectral Methods in MATLAB}, Author = {L. N. Trefethen}, Publisher = {SIAM}, Year = {2000}, Addr = {Philadelphia}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Trefethen1993, Title = {Hydrodynamic stability without eigenvalues}, Author = {L. N. Trefethen and A. E. Trefethen and S.C. Reddy and T. A. Driscoll}, Journal = {Science}, Year = {1993}, Pages = {578--584}, Volume = {261}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Trefethen97, Title = {Numerical Linear Algebra}, Author = {L. N. Trefethen and D. Bau}, Publisher = {SIAM}, Year = {1997}, Addr = {Philadelphia}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{TreWei14, Title = {The exponentially convergent trapezoidal rule}, Author = {Trefethen, L. N. and Weideman, J.}, Journal = {SIAM Review}, Year = {2014}, Pages = {385--458}, Volume = {56}, DOI = {10.1137/130932132} } @Article{tsankov03, Title = {Strange Attractors are Classified by Bounding Tori}, Author = {Tsankov, T. D. and Gilmore, R.}, Journal = {Phys. Rev. Lett.}, Year = {2003}, Pages = {134104}, Volume = {91}, DOI = {10.1103/PhysRevLett.91.134104} } @Article{TSYTES15, Title = {Phase-lag synchronization in networks of coupled chemical oscillators}, Author = {Totz, J. F. and Snari, R. and Yengi, D. and Tinsley, M. R. and Engel, H. and Showalter, K.}, Journal = {Phys. Rev. E}, Year = {2015}, Pages = {022819}, Volume = {92}, DOI = {10.1103/PhysRevE.92.022819} } @article{Tyson1980, title={Target patterns in a realistic model of the Belousov--Zhabotinskii reaction}, author={Tyson, J. J. and Fife, P. C.}, journal={J. Chem. Phys.}, volume={73}, number={5}, pages={2224--2237}, year={1980}, publisher={AIP} } @article{Tyson1988, title={Singular perturbation theory of traveling waves in excitable media (a review)}, author={Tyson, J. J. and Keener, J. P.}, journal={Physica D}, volume={32}, number={3}, pages={327--361}, year={1988}, publisher={Elsevier} } @Inbook{UFOlund, Title = {Order and Chaos in Non-linear Physical System}, Author = {P. Cvitanovi{\'c}}, Chapter = {Renormalization description of transitions to chaos}, Editor = {S. Lundquist, N. H. March and E. Tosatti}, Pages = {73--97}, Publisher = {Plenum}, Year = {1988}, Address = {New York} } @InProceedings{Varga01, Title = {On balancing and order reduction of unstable periodic systems}, Author = {Varga, A.}, Booktitle = {Proc. of IFAC Workshop on Periodic Control Systems, Como, Italy}, Year = {2001}, Pages = {177--182} } @Article{varga2008, Title = {On solving periodic {Riccati} equations}, Author = {A. Varga}, Journal = {Numer. Linear Algebra Appl.}, Year = {2008}, Pages = {809--835}, Volume = {15} } @Article{Vasiev94, Title = {Simulation of {D}ictyostelium discoideum aggregation via reaction-diffusion model}, Author = {Vasiev, B. N. and Hogeweg, P. and Panfilov, A. V.}, Journal = {Phys. Rev. Lett.}, Year = {1994}, Pages = {3173--3176}, Volume = {73}, Bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.73.3173%7D}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {{10.1103/PhysRevLett.73.3173}} } @Article{VC08, Title = {Stable manifolds and the transition to turbulence in pipe flow}, Author = {Viswanath, D. and Cvitanovi{\'c}, P.}, Journal = {J. Fluid Mech.}, Year = {2009}, Addendum = {\arXiv{0801.1918}}, Pages = {215--233}, Volume = {627}, DOI = {10.1017/S0022112009006041} } @Article{Vetter1998, Title = {Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy}, Author = {F. J. Vetter and A. D. McCulloch}, Journal = {Prog. Biophys. Mol. Biol.}, Year = {1998}, Pages = {157--183}, Volume = {69}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Vigmond2008, Title = {Solvers for the cardiac biodomain equations}, Author = {E. J. Vigmond and R. Weber dos Santos and A. J. Prassl and M. Deo and G. Plank}, Journal = {Prog. Biophys. Mol. Biol.}, Year = {2008}, Pages = {3--18}, Volume = {96}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @InProceedings{vigmond2009near, Title = {Near-real-time simulations of biolelectric activity in small mammalian hearts using graphical processing units}, Author = {E. J. Vigmond and P. M. Boyle and L. J. Leon and G. Plank}, Booktitle = {Engineering in Medicine and Biology Society, 2009. EMBC 2009. Annual International Conference of the IEEE}, Year = {2009}, Organization = {IEEE}, Pages = {3290--3293} } @Article{Visw07b, Title = {Recurrent motions within plane {Couette} turbulence}, Author = {D. Viswanath}, Journal = {J. Fluid Mech.}, Year = {2007}, Note = {\arXiv{physics/0604062}}, Pages = {339--358}, Volume = {580} } @Article{Viswanath:2001, Title = {The {L}indstedt-{P}oincar{\'e} Technique as an Algorithm for Computing Periodic Orbits}, Author = {Viswanath, D.}, Journal = {SIAM Review}, Year = {2001}, Pages = {478--495}, Volume = {43}, Annote = {unpublished}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{vKampen92, Title = {Stochastic Processes in Physics and Chemistry}, Author = {N. G. van Kampen}, Publisher = {North-Holland}, Year = {1992}, Address = {Amsterdam} } @Article{VNM06, Title = {On passage through resonances in volume-preserving systems}, Author = {D. L. Vainchtein and A. I. Neishtadt and I. Mezi{\'c}}, Journal = {Chaos}, Year = {2006}, Pages = {043123}, Volume = {16}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{VWG:2007a, Title = {Mixing properties of steady flow in thermocapillary driven droplets}, Author = {D. L. Vainchtein and J. Widloski and R. O. Grigoriev}, Journal = {Phys. Fluids}, Year = {2007}, Pages = {067102}, Volume = {19}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{VWG:2007b, Title = {Resonant chaotic mixing in a cellular flow}, Author = {D. L. Vainchtein and J. Widloski and R. O. Grigoriev}, Journal = {Phys. Rev. Lett.}, Year = {2007}, Pages = {094501}, Volume = {99} } @Article{VWG:2008, Title = {Resonant mixing in perturbed action-action-angle flow}, Author = {D. L. Vainchtein and J. Widloski and R. O. Grigoriev}, Journal = {Phys. Rev. E}, Year = {2008}, Pages = {026302}, Volume = {78}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{Waktare1998, title={Acute treatment of atrial fibrillation: why and when to maintain sinus rhythm}, author={Waktare, Johan EP and Camm, A John}, journal={The American Journal of Cardiology}, volume={81}, number={5}, pages={3C--15C}, year={1998}, publisher={Elsevier} } @Article{W95a, Title = {Hydrodynamic Stability and Turbulence: Beyond transients to a self-sustaining process}, Author = {F. Waleffe}, Journal = {Stud.\ Applied Math.}, Year = {1995}, Pages = {319--343}, Volume = {95}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{W97, Title = {On a self-sustaining process in shear flows}, Author = {F. Waleffe}, Journal = {Phys. Fluids}, Year = {1997}, Pages = {883--900}, Volume = {9}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{WaKilIde03, Title = {Do clinically relevant transthoracic defibrillation energies cause myocardial damage and dysfunction?}, Author = {Walcott, G. P. and Killingsworth, C. R. and Ideker, R. E.}, Journal = {Resuscitation}, Year = {2003}, Pages = {59--70}, Volume = {59}, Abstract = {Sufficiently strong defibrillation shocks will cause temporary or permanent damage to the heart. Weak defibrillation shocks do not cause any damage to the heart but also do not defibrillate. A relevant and practical question is what range of shock energies is most likely to defibrillate while not causing damage to the heart. This question is most difficult to answer in the pre-hospital defibrillation setting where the patients' size and shape vary, placement of the defibrillation patches vary, and the etiology of their arrhythmia varies. Unlike internal defibrillators, which are tested at implantation, efficacy of an external defibrillator is determined only once, when it is most needed. This review discusses shock damage and dysfunction caused by monophasic waveforms as well as biphasic waveforms. Evidence is presented suggesting that for perfused hearts, the threshold for damage is well above any shock size delivered clinically. For non-perfused hearts, both in humans and animals, evidence is presented that monophasic shocks of up to 5 J/kg do not cause any more cardiac damage/dysfunction than that associated with smaller shocks and that much of this damage is caused by the ischemic period itself rather than the shock. Although many patients can be defibrillated with 150 J (2.2 J/kg) biphasic shocks, some patients may require biphasic shocks up to 360 J (5 J/kg) to be defibrillated. Studies still need to be performed comparing the efficacy and damaging effects of 360 J biphasic shocks to 150 J biphasic shocks. Until those studies are completed, it seems reasonable to use the same 360 J (5 J/kg) energy limit for biphasic shocks as for monophasic shocks.}, DOI = {10.1016/S0300-9572(03)00161-8} } @Article{waleffe01, Title = {Exact coherent structures in channel flow}, Author = {F. Waleffe}, Journal = {J. Fluid Mech.}, Year = {2001}, Pages = {93--102}, Volume = {435}, Bdsk-url-1 = {http://dx.doi.org/10.1017/S0022112001004189}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1017/S0022112001004189} } @Article{walker2003, Title = {Repolarization alternans: implications for the mechanism and prevention of sudden cardiac death}, Author = {M. L. Walker and D. S. Rosenbaum}, Journal = {Cardiovasc. Res.}, Year = {2003}, Pages = {599}, Volume = {57}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, Owner = {roman}, Timestamp = {2013.11.03} } @Article{walter1914nature, Title = {The nature of fibrillary contraction of the heart - its relation to tissue mass and form}, Author = {W. E. Garrey}, Journal = {American Journal of Physiology}, Year = {1914}, Pages = {397--414}, Volume = {33} } @Article{Wang2008, Title = {Mathematical model of the neonatal mouse ventricular action potential}, Author = {L. J. Wang and E. A. Sobie}, Journal = {Am. J. Physiol. Heart Circ. Physiol.}, Year = {2008}, Pages = {2565--2575}, Volume = {294}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @InProceedings{Wardetzky:2007:DLO:1281991.1281995, Title = {Discrete {Laplace} operators: no free lunch}, Author = {M. Wardetzky and S. Mathur and F. K{\"a}lberer and E. Grinspun}, Booktitle = {Proceedings of the fifth Eurographics symposium on Geometry processing}, Year = {2007}, Address = {Aire-la-Ville, Switzerland, Switzerland}, Pages = {33--37}, Publisher = {Eurographics Association}, Series = {SGP '07}, Acmid = {1281995}, ISBN = {978-3-905673-46-3}, Location = {Barcelona, Spain}, Numpages = {5}, URL = {http://dl.acm.org/citation.cfm?id=1281991.1281995} } @Book{Wat07, Title = {The Matrix Eigenvalue Problem: {GR} and {Krylov} Subspace Methods}, Author = {Watkins, D. S.}, Publisher = {SIAM}, Year = {2007}, Address = {Philadelphia}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Watanabe2001, Title = {Mechanisms for discordant alternans}, Author = {M. A. Watanabe and F. H. Fenton and S. J. Evans and H. M. Hastings and A. Karma}, Journal = {J. Cardiovasc. Electrophysiol.}, Year = {2001}, Pages = {196--206}, Volume = {12} } @Article{wedin04, Title = {Exact coherent structures in pipe flow: travelling wave solutions}, Author = {Wedin, H. and Kerswell, R. R.}, Journal = {Journal of Fluid Mechanics}, Year = {2004}, Pages = {333--371}, Volume = {508}, Bdsk-url-1 = {http://dx.doi.org/10.1017/S0022112004009346}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000}, DOI = {10.1017/S0022112004009346}, Shorttitle = {Exact coherent structures in pipe flow} } @article{Weiss2006, abstract = {Computer simulations and nonlinear dynamics have provided invaluable tools for illuminating the underlying mechanisms of cardiac arrhythmias. Here, we review how this approach has led to major insights into the mechanisms of spatially discordant alternans, a key arrhythmogenic factor predisposing the heart to re-entry and lethal arrhythmias. During spatially discordant alternans, the action potential duration (APD) alternates out of phase in different regions of the heart, markedly enhancing dispersion of refractoriness so that ectopic beats have a high probability of inducing reentry. We show how, at the cellular level, instabilities in membrane voltage (ie, steep APD restitution slope) and intracellular Ca (Cai) cycling dynamics cause APD and the Cai transient to alternate and how the characteristics of alternans are affected by different "modes" of the bidirectional coupling between voltage and Cai. We illustrate how, at the tissue level, additional factors, such as conduction velocity restitution and ectopic beats, promote spatially discordant alternans. These insights have illuminated the mechanistic basis underlying the clinical association of cardiac alternans (eg, T wave alternans) with arrhythmia risk, which may lead to novel therapeutic approaches to avert sudden cardiac death.}, author = {Weiss, James N. and Karma, Alain and Shiferaw, Yohannes and Chen, Peng Sheng and Garfinkel, Alan and Qu, Zhilin}, doi = {10.1161/01.RES.0000224540.97431.f0}, file = {:C$\backslash$:/Users/alejandro.garzon/Documents/Downloads/weiss2006.pdf:pdf}, isbn = {1524-4571 (Electronic)$\backslash$r0009-7330 (Linking)}, issn = {00097330}, journal = {Circulation Research}, keywords = {Alternans,Arrhythmias,Electrical restitution,Heart failure,Intracellular Ca cycling}, number = {10}, pages = {1244--1253}, pmid = {16728670}, title = {{From pulsus to pulseless: The saga of cardiac alternans}}, volume = {98}, year = {2006} } @Book{Weyl39, Title = {The Classical Groups: Their Invariants and Representations}, Author = {Weyl, H.}, Publisher = {Princeton Univ. Press}, Year = {1939}, Address = {Princeton, NJ}, ISBN = {9780691057569} } @Misc{WFSBC15, author = {Budanur, N. B. and Short, K. Y. and Farazmand, M. and Willis, A. P. and Cvitanovi{\'c}, P.}, title = {Relative periodic orbits form the backbone of turbulent pipe flow}, year = {2017}, note = {Submitted to J. Fluid. Mech.}, url = {https://arxiv.org/abs/1705.03720}, } @Article{Wheeler:2006co, Title = {Computation of spiral spectra}, Author = {Wheeler, P. and Barkley, D.}, Journal = {SIAM J. Appl. Dyn. Syst.}, Volume = {5}, Number = {1}, pages = {157--177}, Year = {2006}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Article{Wikswo1995, Title = {Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation}, Author = {J. P. Wikswo Jr. and S. F. Lin and R. A. Abbas}, Journal = {Biophys. J.}, Year = {1995}, Pages = {2195--2210}, Volume = {69}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Unpublished{Wilczak09, Title = {Reducing the state-space of the complex {L}orenz flow}, Author = {R. Wilczak}, Note = {{NSF REU} summer 2009 project, {U. of Chicago}, \\ \wwwcb{/projects/Wilczak/blog.pdf}}, Year = {2009}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @Book{Winfree1980, Title = {The Geometry of Biological Time}, Author = {A. T. Winfree}, Publisher = {Springer}, Year = {1980}, Address = {New York}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @book{Winfree1987, title={When Time Breaks Down. The 3-dimensional Dynamics of Electrochemical Waves and Cardiac Arrhytmias}, author={Winfree, Arthur T}, year={1987}, publisher={Princeton University Press} } @Article{Winfree1988, Title = {When time breaks down: The three-dimensional dynamics of electrochemical waves and cardiac arrhythmias}, Author = {A. T. Winfree and J. J. Tyson}, Journal = {Physics Today}, Year = {1988}, Pages = {107}, Volume = {41}, Date-added = {2014-07-29 23:49:06 +0000}, Date-modified = {2014-07-29 23:49:06 +0000} } @article{Winfree1989, title={Electrical instability in cardiac muscle: phase singularities and rotors}, author={Winfree, Arthur T}, journal={J. Theor. Biol.}, volume={138}, number={3}, pages={353--405}, year={1989}, publisher={Elsevier} } @Article{winfree1994electrical, Title = {Electrical turbulence in three-dimensional heart muscle}, Author = {Winfree, A. 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