Showing papers by "Ramakrishna Ramaswamy published in 1986"
TL;DR: In this paper, the chemical lengths of minimal backbend paths on the Bethe lattice were calculated on all lattices and shown to diverge as (p-pc)-12/.
Abstract: Just above the percolation concentration, a path on the backbone which leads from one side of the lattice to the other is not direct by zigzags through the lattice. Backbends are the portions of the zigzags which go backwards. They are important in the problem of particle transport in strong external fields, as they act as traps and limit the current. The threshold concentration for the proliferation of paths with backbends no longer than a given length L is defined as pb(L), with the limits pb(0)=pd (directed percolation) and pb( infinity )=pc (ordinary percolation). The inverse function zeta (p) is the smallest integer such that, for given p between pc and pd, there are paths to infinity on which every backbend is smaller than zeta (p). This minimal backbend length is computed on a Bethe lattice and shown to diverge as (p-pc)-12/. It is argued heuristically that on all lattices zeta (p) is proportional to the correlation length in the limit p to pc. The chemical lengths of minimal backbend paths on the Bethe lattice are calculated.
8 citations
TL;DR: In this paper, the dynamics of particles with hard core exclusion performing biased random walks on a one-dimensional lattice with a reflecting wall were studied, where the bias is toward the wall and the particles are placed initially on the sites of the lattice closest to the wall.
Abstract: The dynamics ofN particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on theN sites of the lattice closest to the wall. ForN=1 the leading behavior of the first passage timeT
FP to a distant sitel is known to follow the Kramers escape time formulaT
FP∼λ
l whereλ is the ratio of hopping rates toward and away from the wall. ForN > 1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes toT
FR∼λ
IN. First passage times for the other particles are studied as well. A second question that is studied pertains to survival timesT
s in the presence of an absorbing barrier placed at sitel. In contrast to the first passage time, it is found thatT
s follows the leading behaviorλ′ independent ofN.
6 citations
TL;DR: In this paper, an explanation for sum-rules observed in gas-surface scattering is offered via a classical scaling theory for inelastic collisions, which is based on the classical scaling model of the scaling process.
Abstract: An explanation for sum-rules observed in gas-surface scattering is offered via a classical scaling theory for inelastic collisions.