Analysis of patterns formed by two-component diffusion limited aggregation

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial patter can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.Comment: Accepted for publication in Physical Review

Survival of interacting Brownian particles in crowded 1D environment

We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle interaction. Due to the absorbing boundary the number of particles in the pore gradually decreases. We present the exact analytical solution of the problem. Our procedure merely requires the knowledge of the corresponding single-particle problem. First, we calculate the simultaneous probability density of having still a definite number $N-k$ of surviving particles at definite coordinates. Focusing on an arbitrary tagged particle, we derive the exact probability density of its coordinate. Secondly, we present a complete probabilistic description of the emerging escape process. The survival probabilities for the individual particles are calculated, the first and the second moments of the exit times are discussed. Generally speaking, although the original inter-particle interaction possesses a point-like character, it induces entropic repulsive forces which, e.g., push the leftmost (rightmost) particle towards (opposite) the absorbing boundary thereby accelerating (decelerating) its escape. More importantly, as compared to the reference problem for the non-interacting particles, the interaction changes the dynamical exponents which characterize the long-time asymptotic dynamics. Interesting new insights emerge after we interpret our model in terms of a) diffusion of a single particle in a $N$-dimensional space, and b) order statistics defined on a system of $N$ independent, identically distributed random variables

Oxidation of n-С5-С8 hydrocarbons and cyclohexane in a reactor with barrier discharge. P. 2. Simulating cyclohexane oxidation reaction

Numerical model of hydrocarbon oxidation kinetics in a reactor with barrier discharge has been proposed by the example of cyclohexane oxidation reaction. The results of calculations with the use of barrier discharge surface model showed that electron energy and other discharge characteristics in pure oxygen and in the mixture of oxygen with cyclohexane vapors slightly differ that allowed using a simplified model of homogeneous discharge for simulating cyclohexane oxidation reaction. The results of calculation showed good fit with the experimental dat

Determining selection across heterogeneous landscapes: a perturbation-based method and its application to modeling evolution in space

Spatial structure can decisively influence the way evolutionary processes unfold. Several methods have thus far been used to study evolution in spatial systems, including population genetics, quantitative genetics, momentclosure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply in both continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very effi- cient, and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations

The "Horizon-T" Experiment: Extensive Air Showers Detection

Horizon-T is an innovative detector system constructed to study Extensive Air Showers (EAS) in the energy range above 10^16 eV coming from a wide range of zenith angles (0 - 85 degrees). The system is located at Tien Shan high-altitude Science Station of Lebedev Physical Institute of the Russian Academy of Sciences at approximately 3340 meters above the sea level. It consists of eight charged particle detection points separated by the distance up to one kilometer as well as optical detector subsystem to view the Vavilov-Cerenkov light from the EAS. The time resolution of charged particles and Vavilov-Cerenkov light photons passage of the detector system is a few ns. This level of resolution allows conducting research of atmospheric development of individual EAS.Comment: Initial technical note for Horizon-T experiment, updated with recent detector upgrades, 11/2016. Updated 12/2017 with minor edits. Large upgrade will be in another articl