Spatial confinement causes lifetime enhancement and expansion of vortex rings with positive filament tension

We study the impact of spatial confinement on the dynamics of three-dimensional (3D) excitation vortices with circular filaments. In a chemically active medium we observe a decreased contraction rate of such scroll rings and even expanding ones, despite their positive filament tension. All experimentally observed regimes of spatially confined scroll ring evolution are reproduced by full 3D numerical integration of the underlying reaction–diffusion equations. Additionally, we propose a kinematical model that takes into account the interaction of the scroll ring with a no-flux boundary. Its predictions agree quantitatively with data obtained from simulations of the reaction–diffusion model.

[1]  Weber,et al.  Theory of interaction and bound states of spiral waves in oscillatory media. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Stefan Müller,et al.  Three dimensional reconstruction of organizing centers in excitable chemical media , 1993 .

[3]  M. Bär,et al.  Scroll wave instabilities in an excitable chemical medium. , 2008, Physical review letters.

[4]  Hydrodynamically enforced entropic trapping of Brownian particles. , 2012, Physical review letters.

[5]  A. Mikhailov,et al.  Negative-tension instability of scroll waves and winfree turbulence in the oregonator model. , 2006, The journal of physical chemistry. A.

[6]  I. Aranson,et al.  On the interaction of spiral waves in non-equilibrium media , 1991 .

[7]  C J Weijer,et al.  Three-dimensional waves of excitation during Dictyostelium morphogenesis. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Hartmann,et al.  Rotating chemical waves in small circular domains. , 1996, Physical review letters.

[9]  Alexander V. Panfilov,et al.  Turbulent rings in 3-dimensional active media with diffusion by 2 components , 1986 .

[10]  Mark-Anthony Bray,et al.  Interaction dynamics of a pair of vortex filament rings. , 2003, Physical review letters.

[11]  John J. Tyson,et al.  The Dynamics of Scroll Waves in Excitable Media , 1992, SIAM Rev..

[12]  C. R. Smith,et al.  Vortex Interactions with Walls , 1994 .

[13]  O. Steinbock,et al.  Negative filament tension of scroll rings in an excitable system. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  G. Kastberger,et al.  Social Waves in Giant Honeybees Repel Hornets , 2008, PloS one.

[15]  E. Bodenschatz,et al.  Selection of spiral waves in excitable media with a phase wave at the wave back. , 2011, Physical review letters.

[16]  Jan Frederik Totz,et al.  Three-dimensional autonomous pacemaker in the photosensitive Belousov-Zhabotinsky medium , 2014, 1406.5964.

[17]  B. Hess,et al.  Two-dimensional spectrophotometry of spiral wave propagation in the belousov—Zhabotinskii reaction. II. Geometric and kinematic parameters , 1987 .

[18]  H. Engel,et al.  Experimental study of the dynamics of spiral pairs in light-sensitive Belousov–Zhabotinskii media using an open-gel reactor , 2000 .

[19]  H. Engel,et al.  Autowave propagation in heterogeneous active media , 1991 .

[20]  S. Alonso,et al.  Twists of opposite handedness on a scroll wave. , 2013, Physical review letters.

[21]  Elizabeth M Cherry,et al.  Effects of boundaries and geometry on the spatial distribution of action potential duration in cardiac tissue. , 2011, Journal of theoretical biology.

[22]  R. Aliev,et al.  Spiral waves in the homogeneous and inhomogeneous Belousov-Zhabotinskii reaction , 1992 .

[23]  U. Keyser,et al.  Local characterization of hindered Brownian motion by using digital video microscopy and 3D particle tracking. , 2014, The Review of scientific instruments.

[24]  E. A. Ermakova,et al.  On the interaction of vortices in two-dimensional active media , 1989 .

[25]  U. Keyser,et al.  Anisotropic diffusion of spherical particles in closely confining microchannels. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  A. M. Zhabotinskii,et al.  Mechanism and mathematical model of the oscillating bromate-ferroin-bromomalonic acid reaction , 1984 .

[27]  Zulma A. Jiménez,et al.  Scroll wave filaments self-wrap around unexcitable heterogeneities. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  A. Winfree,et al.  Scroll-Shaped Waves of Chemical Activity in Three Dimensions , 1973, Science.

[29]  The investigation of the minimum size of the domain supporting a spiral wave in oscillatory media , 2006 .

[30]  V N Biktashev,et al.  Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations. , 2015, Physical review letters.

[31]  Oliver Steinbock,et al.  Waves and vortices of rust on the surface of corroding steel , 2000 .

[32]  Jeremy M. V. Rayner,et al.  On the Vortex Wake of an Animal Flying in a Confined Volume , 1991 .

[33]  K. Showalter,et al.  Formation and evolution of scroll waves in photosensitive excitable media. , 1998, Chaos.

[34]  R. M. Noyes,et al.  Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system , 1972 .

[35]  Stephen K. Scott,et al.  Scroll waves in the Belousov–Zhabotinsky reaction: exploitation of O2-effect on the ferroin-catalysed system , 1999 .

[36]  A. Pertsov,et al.  Asymmetric bound states of spiral pairs in excitable media. , 2005, Physical review letters.

[37]  O. Steinbock,et al.  Nucleation and collapse of scroll rings in excitable media. , 2006, Physical review letters.

[38]  C. R. Neto,et al.  A tomographic study of desynchronization and complex dynamics of scroll waves in an excitable chemical reaction with a gradient , 2003 .

[39]  P. Hänggi,et al.  Entropic particle transport: higher-order corrections to the Fick-Jacobs diffusion equation. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[41]  Francesc Sagués,et al.  Taming Winfree Turbulence of Scroll Waves in Excitable Media , 2003, Science.

[42]  A. Winfree,et al.  Dynamical stability of untwisted scroll rings in excitable media , 1989 .

[43]  K. Gubbins,et al.  Phase separation in confined systems , 1999 .

[44]  A. V. Panfilopv.  Two regimes of the scroll ring drift in the three-dimensional active media , 1987 .

[45]  Arun V. Holden,et al.  Tension of organizing filaments of scroll waves , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[46]  F. Fenton,et al.  Visualization of spiral and scroll waves in simulated and experimental cardiac tissue , 2008 .