Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation

A simple example of a non-equilibrium system for which fluctuations are important is a system of particles which diffuse and may annihilate in pairs on contact. The renormalization group can be used to calculate the time dependence of the density of particles, and provides both an exact value for the exponent governing the decay of particles and an epsilon-expansion for the amplitude of this power law. When the diffusion is anomalous, as when the particles perform Levy flights, the critical dimension depends continuously on the control parameter for the Levy distribution. The epsilon-expansion can then become an expansion in a small parameter. We present a renormalization group calculation and compare these results with those of a simulation.Comment: As-published version; two significant errors fixed, two references adde

Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: i) the Stokes time, accounting for the inertia of the particles, ii) the mean collision time among the grains, iii) the typical time scale of the flow, and iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or not appear.Comment: 4 pages, 3 figure

The iron limitation mosaic in the California Current System: Factors governing Fe availability in the shelf/near-shelf region

The California Current System is a productive eastern boundary region off the coasts of Washington, Oregon, and California. There is strong seasonality to the region, with high levels of rainfall and river input to the coastal ocean during the winter season, and coastal and Ekman upwelling during the spring and summer. Iron (Fe) input to the coastal ocean during the winter months can be stored in the continental shelf mud belts and then be delivered to the surface ocean by upwelling in the spring and summer. There have been a number of studies providing strong evidence of Fe-limitation of diatom growth occurring in regions of the California Current System off of California, and the occurrence of Fe-limitation has been linked with narrow continental shelf mud belt width and low river input. We provide evidence for potential Fe-limitation of diatoms off the southern coast of Oregon in July 2014, just off the shelf break near Cape Blanco in a region with moderate shelf width and river input. Since eastern boundary regions account for a disproportionally large amount of global primary production, this observation of potential Fe-limitation in an unexpected near-shore region of the California Current System has implications for global models of primary productivity. In order to re-evaluate the factors impacting Fe availability, we utilize satellite imagery to compare with historical datasets, and show that unexpected levels of Fe can often be explained by eddies, plumes of upwelled water moving offshore, or lack of recent upwelling

Fractional Langevin equation

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion which enables to distinguish these two non-Markovian processes.Comment: 4 page

Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions

A N-sized inertial classical Heisenberg ferromagnet, which consists in a modification of the well-known standard model, where the spins are replaced by classical rotators, is studied in the limit of infinite-range interactions. The usual canonical-ensemble mean-field solution of the inertial classical $n$-vector ferromagnet (for which $n=3$ recovers the particular Heisenberg model considered herein) is briefly reviewed, showing the well-known second-order phase transition. This Heisenberg model is studied numerically within the microcanonical ensemble, through molecular dynamics.Comment: 18 pages text, and 7 EPS figure

Exponential Ergodicity of stochastic Burgers equations driven by α\alpha-stable processes

In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by $\alpha/2$-subordinated cylindrical Brownian motions with $\alpha\in(1,2)$. To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by $\alpha$-stable noises established in Zhang (arXiv:1204.2630v2).Comment: 17p