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