Mean-field solution of the parity-conserving kinetic phase transition in one dimension

A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class embracing systems that possess two symmetric absorbing states, which in one-dimensional systems, is in many cases equivalent to parity conservation. The phase transition is studied analytically through a mean-field like modification of the so-called {\it parity interval method}. The original method of parity intervals allows for an exact analysis of the diffusion-controlled limit of infinite reaction rate, where there is no active phase and hence no phase transition. For finite rates, we obtain a surprisingly good description of the transition which compares favorably with the outcome of Monte Carlo simulations. This provides one of the first analytical attempts to deal with the broadly studied DP2 universality class.Comment: 4 Figures. 9 Pages. revtex4. Some comments have been improve

Исследование динамики интервальных систем автоматического управления с использованием корневых портретов

Automation control systems with polynomial dynamics description are considered in the paper. Characteristic equation coefficients of these systems are changeable in infinite intervals of actual values. A root portrait concept of an interval control system has been introduced. Root portraits have been used to investigate dynamics of interval automation control systems described by characteristic equations of the third power. Some regularities in change of system behavior and characteristics due to application of various parameters have been observed. These regularities may be applied for development of synthesis and analysis methods on automation control systems by various technical objects.Рассмотрены системы автоматического управления (САУ) с полиномиальным описанием динамики. Коэффициенты характеристических уравнений этих систем изменяются на бесконечных интервалах действительных значений. Введено понятие корневого портрета интервальной динамической системы. С использованием корневых портретов проведено исследование динамики интервальных САУ, описываемых характеристическими уравнениями третьей степени. Установлены некоторые закономерности изменения характера поведения и свойств систем в зависимости от изменяющихся параметров, которые могут использоваться как для разработки методов синтеза, так и анализа САУ всевозможными техническими объектами

Interpreting Quantum Mechanics in Terms of Random Discontinuous Motion of Particles

This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity