A kinetic lattice-gas model for the triangular lattice with strong dynamic correlations. I. Self-diffusion

Abstract

AbsvaeL Self-diffusion in a lattice-gas model with two-vacancy assisted hopping on the eiangular lattice is investigated, by both Monte Carlo simulation and analythd calculation. A very rapid decrease of the tracerarrelation factor and marked size effece in finite laltica give evidence for Swng dynamic correlations in both space and time at high particle concentration. Although the decrease of the self-dihion coefficient over 3.5 decades for concentrations up to c = 0.77 is best fitted by a power law (0.835c)3,54, it is w e d that the model dces not have a sharp dynamical phase transition with a critical concentration lower than one. The argument is based on a p m f of absence of permanently blocked panicles in infinite lattices at all concentrations Mow one. The self-diffusion coefficient is calculated analytically within a pair approximation which gives good results for lower wncenwtims, but fails at Lhe highex concentrations. The approximation is in qualitative agreement with the Monte Carlo data far the hater-correlation factor at all concentrations for a variant of the model with one-vacancy assisted hopping, in which the dynamic conelations are less pronounced.

Rotational correlation and dynamic heterogeneity in a kinetically constrained lattice gas

“…These rules coincide with a physical interpretation of steric constraints on the movement of hard core particles in a dense fluid [10].…”

“…Translation of particles obeys the kinetic constraints of the two vacancy assisted triangular lattice gas, or the (2)-TLG [10,11]: a particle at site r is allowed to move to a nearest neighbor site, r ′ , if (1) r ′ is not occupied and (2) the two mutual nearest neighbor sites of r and r ′ are also empty. These rules coincide with a physical interpretation of steric constraints on the movement of hard core particles in a dense fluid [10].…”

“…The self-diffusion coefficient, D s , is defined as D s = lim t→∞ |∆r i (t)| 2 /4t. We omit further discussion of these quantities as they have been presented at length elsewhere for this [6,10] and other models [8].…”

Heterogeneities in aging models of granular compaction

“…Close to dynamical arrest, the density of connected holes decreases with the density of particles and is related with the inverse of the bootstrap length [45,46], the average distance between two connected holes, in bootstrap percolation. In turn, this length is associated with the transport properties of the system [47][48][49].…”

Geometry of dynamically available empty space is the key to near-arrest dynamics

“…In our previous work we deemed disconnected holes irrelevant for the long length and time scale transport coefficients, and the connected holes (of density ν c ) become the natural order parameter [2]. Subsequently [3] it has become apparent that, asymptotically close to final arrest (in the lattice models, for ρ = 1) this is equivalent, via the relation ν c = 1/ξ d , to relating the transport coefficients to the bootstrap length ξ [21,22].…”