A+A→∅model with a bias towards nearest neighbor

Abstract

We have studied the A+A→∅ reaction-diffusion model on a ring, with a bias ε(0≤ε≤0.5) of the random walkers A to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The z exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at ε=0 to the mean-field value of unity for any nonzero ε. We study the problem analytically using independent interval approximation and compare the scaling results with those obtained from simulation. The distribution P(k,t) (per site) of the spacing between two walkers is given by t(-2/z)f(k/t(1/z)) and is obtained both analytically and numerically. We also obtain the result that εt becomes the new time scale for ε≠0.

Branching annihilating random walks with long-range attraction in one dimension

“…The asymptotic behavior of the density ρ of the AWLA was first reported in Ref. [30] for σ = 0 and later in Ref. [33] for any σ, which is…”

“…Recently, another form of bias that cannot be removed by the Galilean transformation was introduced [30], initially motivated from opinion dynamics [31,32]. This hopping bias is implemented in such a way that a particle prefers hopping toward its nearest particle.…”

“…In the original setting [30], the strength of the bias does not depend on how far a walker's nearest particle is located. Then, the bias is generalized in Ref.…”

Genetic Drift and Selection in Many-Allele Range Expansions

“…Equation (S1.1) reduces to standard equations in the literature [1] when 32 describing with two competing strains. Unfortunately, equation (S1.1) becomes analytically 33 intractable when multiple strains and selective advantages are present because of the closure Neutral correlation functions 37 Much is known about equation (S1.1) in the neutral case where all s i = 0 as discussed in the main 38 text [1]. Unsurprisingly, it can be shown that the average fraction F i = f i equals the initial…”

“…To control for this fact, we grew the colonies used to 29 determine u i and u j on the same plate as the colony used for evaluating v ij w directly from the 30 motion of domain walls, i.e., on one plate we inoculated a colony of a fast growing strain i, a 31 colony of a slower growing strain j, and a mixed colony composed of 10% of strain i and 90% of 32 strain j. The mixed colony's ratio of strains was chosen so that single sectors of the more fit 33 strain would form. 34 Using the radial expansion velocities of the i and j expansions (u i and u j ) in eq.…”