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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Nonlinear driven diffusive systems with dissipation: fluctuating hydrodynamics.

A Prados1, A Lasanta, Pablo I Hurtado

  • 1Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, Sevilla 41080, Spain. prados@us.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

This study derives a hydrodynamic description for nonlinear diffusive models, revealing a fluctuating energy balance equation. Key transport coefficients were calculated, showing an Einstein relation in nonequilibrium systems.

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Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Understanding macroscopic behavior from microscopic dynamics is crucial in complex systems.
  • Nonlinear diffusive models with dissipation and boundary driving present unique theoretical challenges.

Purpose of the Study:

  • To derive a hydrodynamic description for a general class of nonlinear diffusive models in the large size limit.
  • To analyze both average macroscopic behavior and fluctuating properties of hydrodynamic fields.
  • To investigate the interplay between diffusion and dissipation in nonequilibrium systems.

Main Methods:

  • Derivation of a fluctuating balance equation for local energy density from microscopic dynamics.
  • Analysis of diffusive and dissipation terms, including nonlinear Fourier's law.
  • Calculation of transport coefficients (diffusivity, mobility, dissipation) within a local equilibrium approximation.

Main Results:

  • A mesoscopic fluctuating balance equation for energy density was obtained.
  • Dissipation fluctuations were found to be enslaved to density fluctuations.
  • Diffusivity and mobility coefficients were shown to obey an Einstein relation, even in a nonequilibrium context.
  • Theoretical predictions were validated against numerical simulations of a nonlinear heat transport model.

Conclusions:

  • The study provides a general framework for the hydrodynamic description of nonlinear diffusive systems.
  • The derived model successfully captures the complex interplay of diffusion and dissipation.
  • The findings offer insights into nonequilibrium statistical mechanics and transport phenomena.