Internal noise driven generalized Langevin equation from a nonlocal continuum model
Abstract
Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree-of-freedom (DOF), is derived. The GLE features a memory dependent multiplicative or internal noise, which appears upon recognising that the micro-rotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the new GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum. A constraint equation, similar to a fluctuation dissipation theorem (FDT), is shown to statistically relate the internal noise to the other parameters in the GLE.
Keywords
Cite
@article{arxiv.1503.02772,
title = {Internal noise driven generalized Langevin equation from a nonlocal continuum model},
author = {Saikat Sarkar and Shubhankar Roy Chowdhury and Debasish Roy and Ram Mohan Vasu},
journal= {arXiv preprint arXiv:1503.02772},
year = {2015}
}