Long range correlations and slow time scales in a boundary driven granular model

Abstract

We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the system’s equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.

Анализ Кооперативной Динамики Нелинейных Систем На Основе Совместного Спектра Сингулярностей

“…DOI: 10.21883/PJTF.2023. 10.55425.19505 Мультифрактальный анализ широко используется для количественного описания сложного скейлинга, который характерен для динамики различных систем в природе [1][2][3][4]. К числу мультифрактальных объектов относятся многие экспериментально регистрируемые сигналы, структура которых очень сложна, и привлечение представлений мультифрактального формализма является одним из способов их статистического анализа, особенно в применении к сильно неоднородным и нестационарным процессам [5].…”

Analysis of the cooperative dynamics of nonlinear systems based on joint singularity spectrum

“…Multifractal analysis is used widely to quantitatively characterize complex scaling, which is typical of the dynamics of various systems in nature [1][2][3][4]. A considerable number of experimentally recorded signals with a very complex structure belong to the class of multifractal objects.…”

Collective drifts in vibrated granular packings: the interplay of friction and structure

“…This may be expected, since both normal pressure and compenetration affect the tangential component of the force exerted by the vibrating plate (see SM): what is remarkable in our opinion is its global dynamical consequence. Recent analytical results [27] for an idealized model of vibrofluidized dense granular material suggest long-range spatial correlations that may justify the global influence of defects. A deeper insight is provided by the external tangential force provided by the plate F T x (x-component), which directly affects the CM:…”