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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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The Diffusion of Passive Tracers in Laminar Shear Flow
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Oscillatory pulse-front waves in a reaction-diffusion system with cross diffusion.

Evgeny P Zemskov1, Mikhail A Tsyganov2, Werner Horsthemke3

  • 1Federal Research Center for Computer Science and Control, Russian Academy of Sciences, Vavilova 40, 119333 Moscow, Russia.

Physical Review. E
|July 18, 2018
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Summary
This summary is machine-generated.

We discovered novel traveling waves with complex pulse-front patterns in a FitzHugh-Nagumo model. These waves exhibit unique speed dynamics, differing from standard kink-type fronts.

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Area of Science:

  • * Nonlinear Dynamics
  • * Mathematical Biology
  • * Chemical Kinetics

Background:

  • * Reaction-diffusion systems model complex phenomena.
  • * FitzHugh-Nagumo models neural activity and other biological processes.
  • * Bistable systems exhibit multiple stable states, leading to complex wave dynamics.

Purpose of the Study:

  • * To investigate traveling waves with oscillatory tails in a bistable piecewise linear reaction-diffusion system.
  • * To characterize the unique pulse-front wave profiles and their dynamics.
  • * To analyze the hybrid speed diagram and compare with standard kink-type fronts.

Main Methods:

  • * Analytical description of wave profiles and heteroclinic trajectories in the phase plane.
  • * Numerical simulations of the partial differential equations governing the system.
  • * Investigation of wave formation and propagation phenomena.

Main Results:

  • * Identified novel traveling waves with a front-back-front (pulse-front) pattern.
  • * Characterized a hybrid speed diagram reflecting both FitzHugh-Nagumo dynamics and solitary pulse behavior.
  • * Demonstrated that pulse-front waves are composed of distinct fronts and pulses.

Conclusions:

  • * Pulse-front waves represent a distinct class of traveling waves in reaction-diffusion systems.
  • * The hybrid speed diagram offers new insights into wave propagation dynamics.
  • * Analytical and numerical methods confirm the complex structure and behavior of these waves.