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Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
Saikat Sarkar1, Shubhankar Roy Chowdhury1, Debasish Roy1
1Computational Mechanics Laboratory, Indian Institute of Science, Bangalore 560012, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
Summary
Researchers derived a generalized Langevin equation (GLE) incorporating memory-dependent noise. This new model explains particle motion fluctuations in materials, matching experimental data and offering insights into nonlocal interactions.
Area of Science:
- Continuum mechanics
- Statistical physics
- Materials science
Background:
- Micropolar formulations account for nonlocal microstructural effects.
- Classical Langevin equations do not fully capture complex material behaviors.
Purpose of the Study:
- To derive a generalized Langevin equation (GLE) that includes memory-dependent noise.
- To model particle motion with nonlocal interactions in materials.
- To explain experimental observations of fluctuations in mean square displacement.
Main Methods:
- Utilized a micropolar continuum formulation.
- Derived a generalized Langevin equation (GLE) for particle displacement.
- Incorporated randomness in microrotation variables due to an uncertainty principle.
- Introduced memory-dependent multiplicative or internal noise.
Main Results:
- The derived GLE qualitatively reproduces experimentally measured fluctuations.
- Demonstrated agreement with steady-state mean square displacement data in polyvinyl alcohol.
- Identified nonlocal spatial interactions within the continuum as the source of fluctuations.
Conclusions:
- The proposed GLE offers a more accurate model for particle motion in materials with nonlocal interactions.
- The model is applicable to a broad range of solids and fluids exhibiting complex response regimes.
- This work provides a novel framework for understanding fluctuations in material dynamics.
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