Longitudinal acceptance computation for A 50 MeV race track microtron

The algorithm for analysing of longitudinal motion and for calculating phase trajectory in race track microtron (RTM) with small injection energy and small energy gain per turn is described. A longitudinal acceptance is calculated.We are indebted to E. A. Perelshtein and N. Ju. Kazarinov and A. Ju. Molodozhencev for stimulating advices. We thank M. Slodika for work with program coding.     

Single-cavity 8 MeV race-track microtron

This paper describes the operational details of the single-cavity race track microtron of this laboratory. The machine is capable of providing electrons of 8 MeV energy at 1 mA peak current. Important parameters of the machine and beam handling system are studied and the results are reported.     

Mathematical modeling of a satellite communications network

A dynamic multiple-access protocol with notification of clashes is proposed for operation with a satellite communications network. Mathematical modeling is used to find some basic probabilistic and temporal characteristics of the network: the throughput, the wait time, etc. It thus becomes possible to determine the region of initial parameter values in which this protocol is more effective than the ALOHA network protocol.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 120–127, September, 1992.     

Mathematical modeling the formation of a histone octamer

A physical model of the interaction of protein molecules and their ability to form complex biological systems for the in vitro case in a solution of monovalent salt has been developed. Their reactive abilities using the methods of electrostatics based on the example of the step-by-step formation of the histone octamer from the H2A, H2B, H3, and H4 proteins have been studied. To analyze the ability of protein molecules to form compounds the matrix of potential energy of interactions between protein molecules in solutions with different concentrations of monovalent salt has been examined.     

Mathematical modeling of contact thermocouple

The contact thermocouples introduce method errors into the thermal test results. The influence of the parameters, like the density of the incident thermal flux, the inaccuracy of the thermocouple position in the investigated construction element groove, and thermal characteristics of the groove materials, on the method error is given. The obtained results allow the increase of the precision of temperature measurement at the construction unit thermal tests. The text was submitted by the authors in English.     

Mathematical modeling of bacterial metabolism

A variant of mathematical model construction for the anaerobic metabolism of a purple nonsulfur bacterium based on a flux balance analysis is presented in this paper. The model includes all the central metabolic pathways of the bacterial cell, as well as pathways for biosynthesis of amino acids and bacteriochlorophyll. It is shown that the results of modeling of bacterial photoheterotrophic growth on acetate agree with experimental values for the known metabolite pathways, which shows that the constructed model adequately describes actual cellular processes.     

Mathematical modeling of a cylindrical waveguide with a deformed lateral surface

A mathematical model of a waveguide with re-entrant corners in its variable cross section is considered. The influence of the re-entrant corner on the waveguide field mode structure is investigated.     

Mathematical modeling of a diode system based on a field emitter

A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.     

Mathematical modeling of sedimentation of a rarefied cloud of particles

In the present paper a mathematical model of sedimentation of a rarefied cloud of particles with account of the feedback effect of particles on the fluid is suggested. The calculations have shown that this effect changes significantly the pattern of particle motion. The results of model calculations agree fairly well with the experimental data on the sedimentation of coal dust particles in a settler. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 109–113, March, 1999.     

Mathematical modeling of laser sublimation cutting

The mathematical modeling of the laser cutting of steel plates is considered here by implementing the model proposed by Niziev and Nesterov, as formulated in [1]. The 3D-cutting front is described, according to this model, by a highly nonlinear partial differential equation. A number of simplifying assumptions can be formulated, however, so that this complex equation can be handled more easily. This enables us to concentrate on the physics of the model, rather than having to struggle with its mathematical manipulations. This simple model confirms in a capturing way the conjecture originally launched in [1] that cutting speed can be increased with a factor of about 1.5 to 2 by switching over from circular to radial polarization. As a further consequence, the model predicts that a similar improvement is also found regarding the plate thickness at a constant cutting speed.     

Mathematical modeling of ceramics metallization technology

Metallization of ceramics by an incoherent light beam has been simulated. A ceramic substrate with a metal-containing paste deposited on its surface is considered as an infinite planar two-layer medium. The Stefan problem with phase transitions is formulated and solved by the quasi-stationary Leibenzon method.     

Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems.     

Three-body calculation of neutron-deuteron elastic scattering in the energy region from 2.5 MeV up to 50 MeV

The three-body Faddeev equations for neutron-deuteron scattering are solved in the energy region from 2.5 MeV to 50 MeV of the incident neutron energy with small energy steps. Higher-rank separable potentials are used in the¹ s ₀ wave and in the³ s ₁—³ d ₁ waves, while rank-1 separable potentials are used in¹ p ₁,³ p _0,1,2 ¹ d ₂ ³ d _2,3 waves. The calculation is compared with experiments for the total cross section, the total break-up cross section, the differential cross section and the analyzing power of neutron-deuteron scattering. The improvements in the agreement as compared to previous calculations are impressive in many cases. Especially, the calculated total cross section agrees with the experiment below 30 MeV within the error bars, which are as small as 1%. A discussion on the numerical accuracy is given. General aspects of the calculated cross section are discussed. It is pointed out that thes-wave asymptotic normalization of the deuteron wave function (A _s ) is important.     

Excitation of wake-field waves in plasma by a microtron beam

The experimental study of excitation of wake-field waves in plasma by a sequence of electron bunches of a microtron beam has been carried out. Results of measurement of the spectrum of electrons after their passage through plasma confirm the effect of adding of waves from a sequence of about 100 bunches which leads to the increase in the amplitude from 1 V/cm up to 100 V/cm.     

Mathematical modeling of the dynamics of photoreactions of a five-level molecule

A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.     

Mathematical modeling of aluminum electrolysis over a long interval of time

A new approach is proposed to the modeling of magnetohydrodynamic and chemical processes involved in aluminum electrolysis. In this approach a medium under study is presented as a mixture of reagents in unknown concentrations, making it possible to describe mixing and the chemical interaction of the electrolyte and the metal melt. Therefore, all stages of the electrolysis process can be modeled over a long interval of time.