arXiv subjects

G. George

Publications and source records attributed to G. George.

4 recordsLinked to original sources

arXiv2021

Simple models for strictly non-ergodic stochastic processes of macroscopic systems

We investigate simple models for strictly non-ergodic stochastic processes $x_t$ ($t$ being the discrete time step) focusing on the expectation value $v$ and the standard deviation $δv$ of the empirical variance $v[x]$ of finite time series $x$. $x_t$ is averaged over a fluctuating field $σ_{r}$ ($r$ being the microcell position) characterized by a quenched spatially correlated Gaussian field. Due to the quenched field $δv(Δt)$ becomes a finite constant, $Δ_{ne} > 0$, for large sampling times $Δt$. The volume dependence of the non-ergodicity parameter $Δ_{ne}$ is investigated for different spatial correlations. Models with marginally long-ranged $\fr$-correlations are successfully mapped on shear-stress data from simulated amorphous glasses of polydisperse beads.

cond-mat.dis-nn↗

arXiv2021

Fluctuations of non-ergodic stochastic processes

We investigate the standard deviation $δv(\tsamp)$ of the variance $v[\xbf]$ of time series $\xbf$ measured over a finite sampling time $\tsamp$ focusing on non-ergodic systems where independent "configurations" $c$ get trapped in meta-basins of a generalized phase space. It is thus relevant in which order averages over the configurations $c$ and over time series $k$ of a configuration $c$ are performed. Three variances of $v[\xbf_{ck}]$ must be distinguished: the total variance $\dvtot = \dvint + \dvext$ and its contributions $\dvint$, the typical internal variance within the meta-basins, and $\dvext$, characterizing the dispersion between the different basins. We discuss simplifications for physical systems where the stochastic variable $x(t)$ is due to a density field averaged over a large system volume $V$. The relations are illustrated for the shear-stress fluctuations in quenched elastic networks and low-temperature glasses formed by polydisperse particles and free-standing polymer films. The different statistics of $\svint$ and $\svext$ are manifested by their different system-size dependence

cond-mat.stat-mech↗

arXiv2020

Ensemble fluctuations matter for variances of macroscopic variables

Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average $v(Δt)$ and the standard deviation $δv(Δt)$ of the variance $v[\mathbf{x}]$ of time series $\mathbf{x}$ of a stochastic process $x(t)$ measured over a finite sampling time $Δt$. Assuming a stationary, Gaussian and ergodic process, $δv$ is given by a functional $δv_G[h]$ of the autocorrelation function $h(t)$. $δv(Δt)$ is shown to become large and similar to $v(Δt)$ if $Δt$ corresponds to a fast relaxation process. Albeit $δv = δv_G[h]$ does not hold in general for non-ergodic systems, the deviations for common systems with many microstates are merely finite-size corrections. Various issues are illustrated for shear-stress fluctuations in simple coarse-grained model systems.

cond-mat.stat-mech↗

arXiv2018

Shear-stress fluctuations in free-standing polymer films

Using molecular dynamics simulation of a polymer glass model we investigate free-standing polymer films focusing on the in-plane shear modulus $μ$ and the corresponding shear-stress relaxation modulus $G(t)$ as functions of temperature $T$, film thickness $H$ (tuned by means of the lateral box size $L$) and sampling time $Δt$. Various observables are seen to vary linearly with $1/H$ demonstrating thus the (to leading order) linear superposition of bulk and surface properties. In agreement with recent studies on three-dimensional polymer glass-formers, $μ$ and $G(t)$ are found to decrease continuously with $T$. A jump-singularity is not observed. Confirming the time-translational invariance of our systems, the $Δt$-dependence of $μ$ is traced back to $G(t)$.

cond-mat.soft↗