David P. Sanders

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We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor λ , of the incident angle. These pinball billiards interpolate between a one-dimensional map when λ = 0 and the classical Hamiltonian case of elastic collisions when λ = 1. For all λ < 1, the dynamics is(More)
In systems that exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random-walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the(More)
From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e., when no particle can travel arbitrarily far without colliding. For the infinite horizon case we(More)
We develop an analytical method to calculate encounter times of two random walkers in one dimension when each individual is segregated in its own spatial domain and shares with its neighbor only a fraction of the available space, finding very good agreement with numerically exact calculations. We model a population of susceptible and infected territorial(More)
We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to(More)
The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for independent walkers, where any number of walkers can occupy the same site, and for walkers with an exclusion interaction,(More)
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers(More)
We introduce a construction to "periodize" a quasiperiodic lattice of obstacles, i.e., embed it into a unit cell in a higher-dimensional space, reversing the projection method used to form quasilattices. This gives an algorithm for simulating dynamics, as well as a natural notion of uniform distribution, in quasiperiodic structures. It also shows the(More)
We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different(More)
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with two-step memory on different(More)