Simple models for strictly non-ergodic stochastic processes of macroscopic systems
| Autor: | J. P. Wittmer, G. George, Alexander N. Semenov, J. Baschnagel, L. Klochko |
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| Přispěvatelé: | Semenov, Alexander, Institut Charles Sadron (ICS), Université de Strasbourg (UNISTRA)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2021 |
| Předmět: |
Physics
[PHYS]Physics [physics] Series (mathematics) Stochastic process Gaussian Biophysics FOS: Physical sciences Field (mathematics) Surfaces and Interfaces General Chemistry Expectation value Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Delta-v (physics) [PHYS] Physics [physics] Combinatorics symbols.namesake Position (vector) symbols Ergodic theory General Materials Science Biotechnology |
| Zdroj: | European Physical Journal E: Soft matter and biological physics European Physical Journal E: Soft matter and biological physics, 2021, 44 (10), pp.125. ⟨10.1140/epje/s10189-021-00129-3⟩ |
| ISSN: | 1292-8941 1292-895X |
| DOI: | 10.48550/arxiv.2111.11115 |
| Popis: | 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 $\delta v$ of the empirical variance $v[x]$ of finite time series $x$. $x_t$ is averaged over a fluctuating field $\sigma_{r}$ ($r$ being the microcell position) characterized by a quenched spatially correlated Gaussian field. Due to the quenched field $\delta v(\Delta t)$ becomes a finite constant, $\Delta_{ne} > 0$, for large sampling times $\Delta t$. The volume dependence of the non-ergodicity parameter $\Delta_{ne}$ 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. Comment: 11 pages, 8 figures |
| Databáze: | OpenAIRE |
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