Statistical Analysis of Precipitation Events

In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential distributions based on the information-theoretical entropy reasoning. The proposed models can be also treated as the result of following the popular Bayesian approach.Comment: 5 pages, 4 figures; ICNAAM 201

Electrochemical behavior of a titanium electrode in hydrazine solutions

The kinetics of the establishment of the oxidation-reduction potential of a titanium electrode upon contact with hydrazine was studied in different media: H2SO4, NaOH, and Na2SO4. It was found that the nature of the potential shift depends little on the medium. The initial potential determines the rate of potential displacement upon contact with hydrazine, which is explained by the different condition of the electrode's surface

On the kinetic equation approach to pair production by time-dependent electric field

We investigate the quantum kinetic approach to pair production from vacuum by time-dependent electric field. Equivalence between this approach and the more familiar S-matrix approach is explicitly established for both scalar and fermion cases. For the particular case of a constant electric field exact solution for kinetic equations is provided and the accuracy of low-density approximation is estimated.Comment: 8 pages, 4 figure

On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes

Defect-Mediated Emulsification in Two Dimensions

We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a single droplet and a pair of droplets are calculated and a universal droplet-droplet pair potential is obtained. The interaction of dispersed droplets via the ordered phase is attractive at large distances and repulsive at short distances, which results in a well defined preferred separation for two droplets and topological stabilization of the emulsion. This interaction also drives self-assembly into chains. Preferred separations and energy barriers to coalescence are calculated, and effects of thermal fluctuations and film thickness are discussed.Comment: revtex4, 13 pages, 12 figure

Fisher waves in the strong noise limit

We investigate the effects of strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute the wave velocity in one and two spatial dimensions, for which we find a linear and a square-root dependence of the speed on the particle density. Instead of smooth sigmoidal wave profiles, we observe fronts composed of a few rugged kinks that diffuse, annihilate, and rarely branch; this dynamics leads to power-law tails in the distribution of the front sizes.Comment: 4 pages, 2 figures, updat