Conserved mass models with stickiness and chipping

Abstract

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass sticks to the site. In the asymmetric version, the chipped off mass is distributed among the site and the right neighbour, whereas in the symmetric version the redistribution occurs among the two neighbours. The steady state mass distribution of the model is obtained using a perturbation method for both parallel and random sequential updates. In most cases, this perturbation theory provides a steady state distribution with reasonable accuracy.

Zeroth law and nonequilibrium thermodynamics for steady states in contact

“…There are numerous examples [28][29][30][31][32], where nonequilibrium processes with a conserved mass show short-ranged spatial correlations, but the exact steady-state structures are not known. How does one find a contact dynamics which ensures Eq.…”

Gammalike Mass Distributions and Mass Fluctuations in Conserved-Mass Transport Processes

“…Next we consider a generic variant of paradigmatic mass transport processes, called mass chipping models (MCM) [7,8,[12][13][14]. These models are based on mass conserving dynamics with linear mixing of masses at neighboring sites which ensures that σ 2 v ≃ hmi 2 =vη when the two-point correlations are negligible.…”

“…For generic λ and p and for a uniform ϕðrÞ ¼ 1 with r ∈ ½0; 1, the steady state is not factorized [14] and the spatial correlations, in general, are nonzero. Consequently, no closed form expression of the mass distribution is known, except in a mean-field approximation for λ ¼ 1=2 and p ¼ 0 [14].…”

“…Consequently, no closed form expression of the mass distribution is known, except in a mean-field approximation for λ ¼ 1=2 and p ¼ 0 [14]. However, the spatial correlations are small and gamma distribution provides, in general, a good approximation of P v ðmÞ.…”

“…In symmetric MCMs, with parallel update rules, a fraction λ of continuous mass variable m i at site i is retained at the site and a fraction (1 − λ) of the mass is randomly and symmetrically distributed to the two nearest-neighbor sites [14]: m i ðt þ 1Þ ¼ λm i ðtÞ þ ð1 − λÞr i−1 m i−1 ðtÞ þ ð1 − λÞð1 − r iþ1 Þm iþ1 ðtÞ where r i uniformly distributed in [0,1]. For λ ¼ 0, the steady state is factorized [14] and P 1 ðmÞ is exactly given by Eq.…”