scholarly journals Existence of pulses in excitable media with nonlocal coupling

2015 ◽  
Vol 270 ◽  
pp. 400-456 ◽  
Author(s):  
Grégory Faye ◽  
Arnd Scheel
Keyword(s):  
Excitable Media ◽  
Nonlocal Coupling

The need of electron microscopy in the study of domains and domain walls in ferroelectrics

1994 ◽  
Vol 52 ◽  
pp. 550-551
Author(s):  
Wenwu Cao
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
High Mobility ◽  
Continuum Theory ◽  
Polarization Vector ◽  
Ferroelectric Materials ◽  
Dielectric Constants ◽  
Nonlocal Coupling ◽  
Cubic Symmetry ◽  
Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

Entrainment and Annihilation of Reentrant Excitation in a Periodically Stimulated Ring of Excitable Media

1997 ◽  
Vol 36 (04/05) ◽  
pp. 290-293
Author(s):  
L. Glass ◽  
T. Nomura
Keyword(s):  
Cardiac Arrhythmias ◽  
Initial Phase ◽  
Human Heart ◽  
Periodic Wave ◽  
Excitable Media ◽  
One Dimensional ◽  
Clinical Observations ◽  
Periodic Stimulation ◽  
Reentrant Excitation ◽  
Stimulation Of

Abstract:Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.

scholarly journals Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

2014 ◽  
Vol 11 (97) ◽  
pp. 20140352 ◽  
Author(s):  
Alfonso Bueno-Orovio ◽  
David Kay ◽  
Vicente Grau ◽  
Blanca Rodriguez ◽  
Kevin Burrage
Keyword(s):  
Structural Heterogeneity ◽  
Biological Tissues ◽  
Tissue Level ◽  
Fractional Diffusion ◽  
Diffusion Models ◽  
Excitable Media ◽  
Research Fields ◽  
Dispersion Of Repolarization ◽  
Electrical Propagation

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

scholarly journals Stable and unstable vortex knots in excitable media

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Jack Binysh ◽  
Carl A. Whitfield ◽  
Gareth P. Alexander
Keyword(s):  
Excitable Media

Refraction of waves in excitable media

1998 ◽  
Vol 58 (3) ◽  
pp. 2910-2917 ◽  
Author(s):  
Leonid Pechenik ◽  
Herbert Levine
Keyword(s):  
Excitable Media

SUPPRESSING SPIRAL WAVES IN EXCITABLE MEDIA VIA UNIDIRECTIONAL COUPLING

2008 ◽  
Vol 22 (24) ◽  
pp. 4153-4161 ◽  
Author(s):  
YU QIAN ◽  
YU XUE ◽  
GUANG-ZHI CHEN
Keyword(s):  
Co Oxidation ◽  
Power Law ◽  
Coupling Strength ◽  
Control Method ◽  
Spiral Waves ◽  
Coupling Method ◽  
Excitable Media ◽  
Catalytic Co Oxidation ◽  
Unidirectional Coupling ◽  
High Control

A unidirectional coupling method to successfully suppress spiral waves in excitable media is proposed. It is shown that this control method has high control efficiency and is robust. It adapts to control of spiral waves for catalytic CO oxidation on platinum as well as for the FHN model. The power law n ~ c-k of control time steps n versus the coupling strength c for different models has been obtained.

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