Dynamic bond percolation theory for diffusion of interacting particles: Tracer diffusion in a binary mixture lattice gas

1990 ◽  
Vol 93 (8) ◽  
pp. 5918-5934 ◽  
Author(s):  
Rony Granek ◽  
Abraham Nitzan
Keyword(s):  
Binary Mixture ◽  
Percolation Theory ◽  
Lattice Gas ◽  
Tracer Diffusion ◽  
Bond Percolation ◽  
Interacting Particles

scholarly journals Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

2020 ◽  
Vol 75 (5) ◽  
pp. 449-463
Author(s):  
Dominik Lips ◽  
Artem Ryabov ◽  
Philipp Maass
Keyword(s):  
Current Density ◽  
Lattice Gas ◽  
Yukawa Potential ◽  
Exclusion Process ◽  
Quantum Spin ◽  
Nonequilibrium Steady States ◽  
Interacting Particles ◽  
Driven Diffusive Systems ◽  
Periodic Potentials ◽  
Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

Critical sponge dimensions in percolation theory

1981 ◽  
Vol 13 (02) ◽  
pp. 314-324 ◽  
Author(s):  
G. R. Grimmett
Keyword(s):  
Positive Constant ◽  
Percolation Theory ◽  
Square Lattice ◽  
Bond Percolation ◽  
Critical Probability ◽  
Percolation Process ◽  
Open Path ◽  
Image Position

In the bond percolation process on the square lattice, with let S(k) be the probability that some open path joins the longer sides of a sponge with dimensions k by a log k. There exists a positive constant α = αp such that Consequently, the subset of the square lattice {(x, y):0 ≦ y ≦ f(x)} which lies between the curve y = f(x) and the x-axis has the same critical probability as the square lattice itself if and only if f(x)/log x → ∞ as x → ∞.

Velocity enhancement of slow particles in lattice–gas binary mixture

2007 ◽  
Vol 383 (2) ◽  
pp. 425-434 ◽  
Author(s):  
Masahiro Fukamachi ◽  
Ryota Kuwajima ◽  
Yasuhito Imanishi ◽  
Takashi Nagatani
Keyword(s):  
Binary Mixture ◽  
Lattice Gas ◽  
Velocity Enhancement
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