We present a numerical study of classical particles obeying a Langevin equation moving on a solid bcc(110) surface. The particles are subject to a two dimensional periodic and symmetric potential of rectangular symmetry and to an external dc field along one of the diagonals of the structure. One observes a bias current with a component orthogonal to the dc field. The drift velocity (magnitude and direction) and diffusion of the particle depend on the surface potential and external field parameters, the temperature, and the friction coefficient. We numerically explore these dependences. Because the potential perceived by a particle as well as its friction coefficient depend on the nature of the particle, so might the angle between the particle velocity and the dc field. This scenario may thus provide a useful particle sorting technique.
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. Under some reasonable assumptions we find rigorous results for the asymptotic survival probability of the particle in most cases, but have not succeeded in doing so for a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.
We present a comprehensive study of phase transitions in single-field extended systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift but is instead similar to the one associated with noise-induced transitions a la Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Ito vs Stratonovich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems.
KEYWORDS: Stochastic processes, Monte Carlo methods, Data modeling, Climatology, Solids, Switching, Time metrology, Mathematical modeling, Differential equations, Correlation function
We present an analysis of two features that generalize the original
model for the spread of the Hantavirus introduced by Abramson and Kenkre [Phys. Rev. E Vol. 66, 011912 (2002)]. One, the effect of seasonal alternations, may cause the virus to spread under conditions that do not lead to an epidemic under the action of either season alone. The other, the effect of internal fluctuations, modifies
the distribution of infected mice and may lead to extinction of the infected population even when the mean population is above epidemic conditions.
We revisit the issue of directed motion induced by zero average forces in extended systems driven by ac forces. It has been shown recently that a directed energy current appears if the ac external force, f(t), breaks the symmetry f(t) = -f(t+T/2), T being the period, if topological solitons (kinks) existed in the system. In this work, a collective coordinate approach allows us to identify the mechanism through which the width oscillation drives the kink and its relation
with the mathematical symmetry conditions. Furthermore, our theory predicts, and numerical simulations confirm, that the direction of motion depends on the initial phase of the driving, while the system behaves in a ratchet-like fashion if averaging over initial conditions. Finally, the presence of noise overimposed to the ac driving does not destroy the directed motion; on the contrary, it gives rise to an activation process that increases the velocity of the motion. We conjecture that this could be a signature of resonant phenomena at larger noises.
We study the reaction front for the process A + B → C in which the reagents move subdiffusively. We propose a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. Scaling solutions to these equations are presented and compared with those of a direct numerical integration of the equations. We find that for reactants whose mean square displacement varies sublinearly with time as (r2) ~ tγ, the scaling behaviors of the reaction front can be recovered from those of the corresponding diffusive problem with the substitution t → tγ.
We review the critical patch size problem, already classic in the mathematical biology literature. We consider a logistic population
living in a finite patch of length L and undergoing random dispersal. The patch presents good conditions for life, while the conditions are so harsh outside that they lead to certain extinction. The usual mean field approach leads to a critical patch size Lc, such that if the actual length of the patch is smaller than Lc the population becomes extinct with certainty, whereas a longer patch leads to certain survival. We study the fluctuations in the population due to its low density near extinction and analyze their effects on the probability of extinction. We find that there is no patch size that can be considered absolutely safe for the population and that, under certain circumstances, the population is under risk of extinction for any patch size.
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