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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Microscopic dynamics of nonlinear Fokker-Planck equations
1Departamento de Física-Matemática, Instituto de Física, Universidade de São Paulo, São Paulo 05508-090, São Paulo, Brazil.
Physical Review. E
|April 17, 2021
Summary
We introduce a novel method for analyzing nonlinear Fokker-Planck equations using a generalized Wiener process. This approach simplifies obtaining analytical solutions and explains anomalous diffusion via memory effects.
Area of Science:
- Statistical Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Nonlinear Fokker-Planck equations are crucial for modeling systems with complex dynamics.
- Understanding anomalous diffusion and memory effects is essential in various scientific fields.
Purpose of the Study:
- To develop a simplified formalism for describing the microscopic dynamics of nonlinear Fokker-Planck equations.
- To provide analytical solutions for nonextensive processes and explain anomalous diffusion.
Main Methods:
- Utilizing a nonextensive generalization of the Wiener process.
- Deriving analytical solutions for nonextensive Brownian free-particle and Ornstein-Uhlenbeck processes.
- Modeling anomalous diffusion through memory effects in generalized Gaussian white noise.
Main Results:
- Analytical solutions were obtained for nonextensive Brownian motion and Ornstein-Uhlenbeck processes.
- Anomalous diffusion was explained by memory effects in a generalized nonextensive noise.
- The formalism was successfully applied to model thermal noise in electric circuits.
Conclusions:
- The proposed formalism offers a powerful and simple approach to analyze nonlinear Fokker-Planck equations.
- The framework provides physical insights into anomalous diffusion and memory effects.
- This method has practical applications in modeling physical systems like electric circuits.
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