Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension $d_H$ =1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. The topological effects become evident from the emergence of a logarithmic periodic oscillation superimposed to a power law in the decay of the magnetization and its logarithmic derivative and also from the dependence of the critical exponents on the segmentation step. These oscillations are discussed in the framework of the discrete scale invariance of the substrate and carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The exponent $\theta$ of the initial increase in the magnetization was also obtained and the results suggest that it would be almost independent of the fractal dimension of the susbstrate, provided that $d_H$ is close enough to d=2.Comment: 9 figures, 3 tables, 10 page

The fractal nature of a diffusion front and the relation to percolation

International audienceUsing a two dimensional simulation, a diffusion front is shown to have a fractal geometry in a range increasing with the diffusion length. The number of particles on the front, and the width measuring its spread, follow power laws as a function of the diffusion length. The associated exponents and the fractal dimension can be expressed as simple functions of the critical exponents of the two dimensional percolation problem

A mean-field kinetic lattice gas model of electrochemical cells

We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the electrode surfaces to allow for growth and dissolution. We confirm the viability of our approach by simulating (i) the electrochemical equilibrium at flat electrodes, which displays the correct charged double-layer, (ii) the growth kinetics of one-dimensional electrochemical cells during growth and dissolution, and (iii) electrochemical dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure

Black Holes, Space-Filling Chains and Random Walks

Many approaches to a semiclassical description of gravity lead to an integer black hole entropy. In four dimensions this implies that the Schwarzschild radius obeys a formula which describes the distance covered by a Brownian random walk. For the higher-dimensional Schwarzschild-Tangherlini black hole, its radius relates similarly to a fractional Brownian walk. We propose a possible microscopic explanation for these random walk structures based on microscopic chains which fill the interior of the black hole.Comment: 18 pages, 4 figures, 2 tables; v2 and v3: minor changes and refs. adde