%0 Journal Article
%T Internal noise driven generalized Langevin equation from a nonlocal continuum model
%A Saikat Sarkar
%A Shubhankar Roy Chowdhury
%A Debasish Roy
%A Ram Mohan Vasu
%J Physics
%D 2015
%I arXiv
%R 10.1103/PhysRevE.92.022150
%X 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.
%U http://arxiv.org/abs/1503.02772v1