Electron Kinetics with Attachment and Ionization from Higher Order Solutions of Boltzmann's Equation

An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF₆. The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation.     

Quantum-hydrodynamic approach to the problem of electron exchange between atomic particles and nanosystems

The application of quantum-hydrodynamic methods for solving the problem of electron exchange between atomic particles and solid surfaces, and nanosystems has been examined. The derivation of a system of equations that is alternative to the nonstationary Schrödinger equation is given to describe the dynamics of electronic processes with variable charge and current densities. A comparison of results of solving the nonstationary Schrödinger equation and the quantum-hydrodynamic system of equations shows that both approaches give a good coincidence. The numerical solution to the system of quantum-hydrodynamic equations has a number of advantages, because it does not lead to oscillations at the boundary of the computational mesh and nor to the problem of exponential growth in numerical complexity for many-electron systems.     

Transformation-matrix method for tunnel-effect simulation

The problem of numerically simulating steady-state scattering and the tunneling transfer of electrons was considered for a 1D potential barrier with an arbitrary shape. An effective numerical approach to solving this problem was developed on the basis of the transformation-matrix method. To test this approach, a computer program was written and applied to calculations of the tunneling processes. The convergence of the method proposed was further investigated in numerical experiments.     

Estimating the ionization time of a hydrogen atom during its motion in a carbon nanotube

The processes in a hydrogen atom moving at a certain velocity along a row of atoms in a carbon nanotube are considered. The change in the atomic state is calculated by numerically solving the nonstationary Schr?dinger equation. The ionization time of the atom is estimated.     

Kinetics of ions in a neutral gas upon abrupt application of an electric field. I. CEM model

A new method for calculating matrix elements of the collision integral is used for solving problems of the mobility of ions against the background of atoms and for constructing the distribution functions for ions upon an abrupt application of an electric field. It is shown how the stationary distribution function can be constructed using the nonstationary moments method in the case when the stationary moments method is completely inapplicable. The solution to the nonstationary problem for the CEM model corresponding to resonant charge exchange with a constant collision frequency, which is constructed analytically, is used for analyzing the limits of applicability of the nonstationary moments method.     

Correlated random walks

We present a new approach to the calculation of first passage statistics for correlated random walks on one-dimensional discrete systems. The processes may be non-Markovian and also nonstationary. A number of examples are used to demonstrate the theory.     

Interval-stochastic thermal processes in electronic systems: Modeling in practice

Mathematical and computer modeling of thermal processes, applied presently in thermal design of electronic systems, is based on the assumption that the factors determining the thermal processes are completely known and uniquely determined, that is, they are deterministic. Meanwhile, practice shows that the determining factors are of indeterminate interval-stochastic character. Moreover, thermal processes in electronic systems are nonstationary and nonlinearly depend on both the stochastic determining factors and the temperatures of electronics elements and environment. At present, the literature does not present methods of mathematical modeling of nonstationary, stochastic, nonlinear, interval-stochastic thermal processes in electronic systems to model thermal processes, which satisfy all the above-listed requirements to modeling adequacy. The present paper develops a method of mathematical and computer modeling of the nonstationary interval-stochastic nonlinear thermal processes in electronic systems. The method is based on obtaining equations describing the dynamics of time variation of statistical measures (expectations, variances, covariances) of temperature of electronic systemelements with given statistical measures of the initial interval-stochastic determining factors. A practical example of applying the developed approach to a the real electronic system is given.     

Wavelet correlations of nonstationary signals

Two approaches to the analysis of nonstationary random signals are proposed and studied. The first approach is based on the adaptive Morlet wavelet that allows variations in time and frequency resolution of signals using an auxiliary control parameter. The second approach is related to the application of double correlation function that represents correlation of continuous wavelet transforms of two signals calculated in time and frequency domains. The advantages of the proposed correlation function in comparison with alternative correlation functions, in particular, analysis of both time and frequency correlations of nonstationary signals are outlined. Applications of the proposed approaches in the analysis of various transient processes in physics are discussed.     

The influence of different factors on the shape of pressure pulse at the liquid-vapor contact

The process of formation and propagation of the depression wave at spontaneous contact of cold liquid and saturated vapor is investigated in a gas dynamics approach. Modeling of wave processes was performed using Godunov’s method based on solving the Riemann problem on arbitrary discontinuity decomposition. The influence of various factors, namely, the kinetics of condensation and intensification of heat-transfer processes, on the pressure pulse form is investigated. Results of the investigation are in good agreement with results of modeling based on numerical solving the Boltzmann kinetic equation.     

Phenomenological diffusion laws in solids

A method is considered for study of diffusion in the solid phase, free of the shortcomings of Fick's equations. For the stationary case analytical expressions are obtained for the probability of transmission, reflection, and absorption of diffusing particles by a layer of specified thickness. Principles are formulated for reduction of the nonstationary problem to the stationary case. The results obtained are applied to a study of the kinetics of oxidation processes. A generalization of Fick's first law to the nonstationary case is presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 31–36, April, 1979.     

Analysis of Fokker-Planck type stochastic equations with variable boundary conditions in an elementary process of collisional ionization

The diffusion model of ionization of Rydberg atoms in single collisions is formulated. The solution of kinetic equations describing nonstationary diffusion processes is discussed. Methods of analytical calculation of the effective times for the development of ionization in phase regions with moving boundaries are presented. An analytical method, going back to Weisskopf, for determining the corresponding cross sections for impact ionization in the adiabatic approximation is described. A numerical scheme for solving problems of stochastic movement of a Rydberg electron inside a Coulomb condensation of levels under conditions of time-variable ionization boundaries and region of development of stochastic instability is developed.     

The inverse problem of the theory of nonstationary powder combustion

The inverse problem for nonstationary powder combustion in a half-closed volume is considered. A transient was initiated by the abrupt change of the nozzle section. Experiments measured the time dependence of the pressure in a combustion chamber at various ratios of the initial and final nozzle sections. Comparison of the experimental data and the results from solving the direct problem allows one to solve the inverse problem, in other words, to obtain defined information of the characteristics of a combustion chamber, i.e., the characteristic time of chamber evacuation and the powder, i.e., the effective thermal diffusivity.     

Hopfield networks for solving Tower of Hanoi problems

In this paper, Hopfield neural networks have been considered in solving the Tower of Hanoi test which is used in the determining of deficit of planning capability of the human prefrontal cortex. The main difference between this paper and the ones in the literature which use neural networks is that the Tower of Hanoi problem has been formulated here as a special shortest-path problem. In the literature, some Hopfield networks are developed for solving the shortest path problem which is a combinatorial optimization problem having a diverse field of application. The approach given in this paper gives the possibility of solving the Tower of Hanoi problem using these Hopfield networks. Also, the paper proposes new Hopfield network models for the shortest path and hence the Tower of Hanoi problems and compares them to the available ones in terms of the memory and time (number of steps) needed in the simulations.     

Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges

We consider a set of examples describing the behavior of linear nonstationary waves on the shallow water generated by time-instantaneous spatially-localized sources and propagating over underwater banks and ridges. To this end, we use an asymptotic approach developed by the authors of the present paper and their collaborators. The approach uses the generalized Maslov canonical operator. We establish the occurrence and dynamics of wave trains travelling over underwater ridges (which are nonstationary waves trapped by ridges) with wave-front singularities, moving focal (turning) points, cascades of space-time caustics, etc.     

Evolution of disperse phases with microparticle generation taken into account

A solution is presented of the problem of evolution of a disperse system in which the total number of particles is slowly supplemented because of generation or decreases additionally because of annihilation. An expression is obtained for the disperse particle size distribution function in a nonstationary approximation and for the resulting limit function. By solving the inverse problem, a dependence of the growth rate and the microparticle dissolution on their relative size is obtained. Application of the general formulas and expressions is illustrated by examples.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–77, June, 1984.     

Analysis of the Spectral Composition of Fluorescence from Laser-Excited Cold Atomic Clouds

A consistent quantum approach is used to calculate the signal of fluorescence from a laser-excited cold atomic ensemble. The possibility of analyzing the spectral composition of this nonstationary signal is investigated. Application of wavelet transforms is shown to be a very efficient method that allows achieving a good spectral or temporal resolution, depending on specific problem. On the basis of this approach, the spectral composition of fluorescence and its dynamics after excitation are studied. The spectral properties of the secondary emission of the ensemble are compared for different directions and polarizations.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.