SUPEREXCITABILITY INDUCED SPIRAL BREAKUP IN EXCITABLE SYSTEMS

1996 ◽  
Vol 06 (09) ◽  
pp. 1753-1759 ◽  
Author(s):  
A. GIAQUINTA ◽  
S. BOCCALETTI ◽  
F.T. ARECCHI
Keyword(s):  
Wave Propagation ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Cardiac Cells ◽  
Excitable Media ◽  
Threshold Dynamics ◽  
Cardiac Tissues ◽  
Breakup Mechanism ◽  
Excitable Systems

We introduce a 2D coupled map lattice model which, besides simulating the two variable FitzHugh–Nagumo reaction diffusion mechanism, accounts also for a superexcitable period. Superexcitability in the threshold dynamics of excitable media has been recently observed in experiments on cardiac tissues. By this model, we can reproduce the transition from normal cardiac behavior toward fibrillating processes in a 2D assembly of cardiac cells. The role of superexcitability results in producing two states of wave propagation and a spiral breakup mechanism in qualitative agreement with the experimental evidence of coarse and fine fibrillation in human hearts.

scholarly journals Weak and Strong Interaction of Excitation Kinks in Scalar Parabolic Equations

2021 ◽  
Author(s):  
Antoine Pauthier ◽  
Jens D. M. Rademacher ◽  
Dennis Ulbrich
Keyword(s):  
Parabolic Equations ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Excitable Media ◽  
Diffusion Type ◽  
Phase Dynamics ◽  
Pde Model ◽  
Excitable Systems ◽  
Carry Over ◽  
The One

AbstractMotivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest PDE model of excitable media given by the scalar reaction diffusion-type $$\theta $$ θ -equations for excitable angular phase dynamics. On the one hand, we qualitatively study geometric kink positions using the comparison principle and the theory of terraces. This yields the minimal initial distance as a global lower bound, a well-defined sequence of collision data for kinks- and antikinks, and implies that periodic pure kink sequences are asymptotically equidistant. On the other hand, we study metastable dynamics of finitely many kinks using weak interaction theory for certain analytic kink positions, which admits a rigorous reduction to ODE. By blow-up type singular rescaling we show that distances become ordered in finite time, and eventually diverge. We conclude that diffusion implies a loss of information on kink distances so that the entropic complexity based on positions and collisions in the GHCA does not simply carry over to the PDE model.

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue

2006 ◽  
Vol 364 (1842) ◽  
pp. 1299-1311 ◽  
Author(s):  
Benjamin E Steinberg ◽  
Leon Glass ◽  
Alvin Shrier ◽  
Gil Bub
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Cardiac Tissue ◽  
Dimensionless Parameter ◽  
Spiral Waves ◽  
Excitable Media ◽  
Intercellular Coupling ◽  
Pathological Conditions ◽  
Linear Decrease

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.

Information Transmission Concept Based Model of Wave Propagation in Discrete Excitable Media

2004 ◽  
Vol 9 (3) ◽  
pp. 271-289 ◽  
Author(s):  
Š. Raudys
Keyword(s):  
Wave Propagation ◽  
Information Transmission ◽  
Propagation Speed ◽  
Excitable Media ◽  
New Approach ◽  
Breakup Mechanism ◽  
New Information ◽  
Excitation Time ◽  
Continuous Character ◽  
Wave Breakdown

A new information transmission concept based model of excitable media with continuous outputs of the model’s cells and variable excitation time is proposed. Continuous character of the outputs instigates infinitesimal inaccuracies in calculations. It generates countless number of the cells’ excitation variants that occur in front of the wave even in the homogenous and isotropic grid. New approach allows obtain many wave propagation patterns observed in real world experiments and known simulation studies. The model suggests a new spiral breakup mechanism based on tensions and gradually deepening clefts that appear in front of the wave caused by uneven propagation speed of curved and planar segments of the wave. The analysis hints that the wave breakdown and daughter wavelet bursting behavior possibly is inherent peculiarity of excitable media with weak ties between the cells, short refractory period and granular structure. The model suggested is located between cellular automaton with discrete outputs and differential equation based models and gives a new tool to simulate wave propagation patterns in applied disciplines. It is also a new line of attack aimed to understand wave bursting, propagation and annihilation processes in isotropic homogenous media.

scholarly journals The Diffusion Mechanism of Megaproject Citizenship Behavior: The Role of Institutional Isomorphism

2021 ◽  
Vol 13 (15) ◽  
pp. 8123
Author(s):  
Delei Yang ◽  
Jun Zhu ◽  
Qingbin Cui ◽  
Qinghua He ◽  
Xian Zheng
Keyword(s):  
Structural Equation ◽  
Diffusion Mechanism ◽  
Vital Role ◽  
Citizenship Behavior ◽  
Equation Modeling ◽  
Positive Effects ◽  
Diffusion Limited ◽  
The Relationship ◽  
Mimetic Isomorphism

Megaproject citizenship behavior (MCB) has been confirmed to a play vital role on megaproject performance. Although current research has argued that institution elements have had an impact on MCB diffusion, limited studies have empirically investigated the distinct effectiveness of various institution elements on driving MCB’s widespread diffusion in construction megaprojects. Based on institution theory, this study proposes a theoretical model comprising institutional elements (i.e., normative and mimetic isomorphism), owner’s support, relationship-based trust, and their effect or impact on MCB’s diffusion. Based on 171 industrial questionnaires collected from managers of contractors and designers in megaprojects. Partial least squares structural equation modeling (PLS-SEM) was used to validate the established model. The results indicated that both normative and mimetic isomorphism have positive effects on facilitating MCB diffusion, and owner’s support has shown partial mediation in promoting MCB diffusion through normative isomorphism, as well as full mediation in the promoting of MCB diffusion through mimetic isomorphism. Meanwhile, relationship-based trust exerts a positive moderating effect on the relationship between mimetic isomorphism and MCB. This study extends current literature on driving MCB diffusion from the perspective of institutional theory, contributing by providing four implications for megaprojects managers to “buy in” more extensive MCB.

scholarly journals Travelling colourful patterns in self-organized cellulose-based liquid crystalline structures

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Pedro E. S. Silva ◽  
Ricardo Chagas ◽  
Susete N. Fernandes ◽  
Pawel Pieranski ◽  
Robin L. B. Selinger ◽  
...  
Keyword(s):  
Simple Model ◽  
Temporal Variation ◽  
Liquid Crystalline ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Self Organization ◽  
Spatial And Temporal Variation ◽  
Living Matter ◽  
Equilibrium Conditions ◽  
Self Organized

AbstractCellulose-based systems are useful for many applications. However, the issue of self-organization under non-equilibrium conditions, which is ubiquitous in living matter, has scarcely been addressed in cellulose-based materials. Here, we show that quasi-2D preparations of a lyotropic cellulose-based cholesteric mesophase display travelling colourful patterns, which are generated by a chemical reaction-diffusion mechanism being simultaneous with the evaporation of solvents at the boundaries. These patterns involve spatial and temporal variation in the amplitude and sign of the helix´s pitch. We propose a simple model, based on a reaction-diffusion mechanism, which simulates the observed spatiotemporal colour behaviour.

scholarly journals From Loschmidt daemons to time-reversed waves

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150156 ◽  
Author(s):  
Mathias Fink
Keyword(s):  
Wave Propagation ◽  
Time Reversal ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Propagation Time ◽  
Reversal Invariance ◽  
Spatial Boundary ◽  
Dual Approaches ◽  
Spatio Temporal

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses ‘time-reversal mirrors’ with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that ‘instantaneous time mirrors’, mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

Role of Nuclei in Liesegang Pattern Formation: Insights from Experiment and Reaction-Diffusion Simulation

2018 ◽  
Vol 122 (6) ◽  
pp. 3669-3676 ◽  
Author(s):  
Masaki Itatani ◽  
Qing Fang ◽  
Kei Unoura ◽  
Hideki Nabika
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Diffusion Simulation
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