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Results for Nonlinear Diffusion Equations with Stochastic Resetting.

Ervin K Lenzi1,2, Rafael S Zola3, Michely P Rosseto1

  • 1Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil.

Entropy (Basel, Switzerland)
|December 23, 2023
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Summary
This summary is machine-generated.

This study explores particle diffusion with random resets, revealing non-Gaussian distributions and transient anomalous diffusion. Results depend on nonlinearity and resetting rate.

Keywords:
Lévy distributionsTsallis entropyanomalous diffusionq-exponentials

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Nonlinear diffusion processes are crucial in various scientific fields.
  • Stochastic resetting introduces unique dynamics to particle transport.
  • Porous media equations model complex diffusion phenomena.

Purpose of the Study:

  • To investigate a nonlinear diffusion process with stochastic resetting.
  • To analyze the probability distribution and mean square displacement of particles.
  • To understand the influence of nonlinearity and resetting rate on system behavior.

Main Methods:

  • Modeling the nonlinear diffusion process using porous media equations and extensions.
  • Employing analytical and numerical calculations.
  • Comparing theoretical results with numerical simulations.

Main Results:

  • Observed non-Gaussian probability distributions for particle positions.
  • Identified transient anomalous diffusion, including subdiffusion and superdiffusion.
  • Characterized stationary states dependent on nonlinearity and resetting rate.

Conclusions:

  • Stochastic resetting in nonlinear diffusion leads to complex, non-equilibrium behaviors.
  • The interplay between nonlinearity and resetting rate dictates system dynamics.
  • Findings provide insights into anomalous transport phenomena.