Choosing an adequate mathematical model in problems with high pulsed energy deposition

The problems of choosing the optimal mathematical model for a prescribed range of parameters of a pulsed action are discussed. A preliminary analysis performed by similarity and dimensional-analysis methods using interpolation equations of state of the matter shows that the complete system of equations of gasdynamics can be simplified by dropping individual terms which are not important in a given parameter range. The results of an analysis are presented in the form of nomograms, which also make it possible to identify the class of fast and energy-intensive gasdynamic processes more accurately than at an intuitive level. Zh. Tekh. Fiz. 68, 44–47 (May 1998)     

Lattices of processes for graphs

The structure of the lattice of processes of a finite digraph with entries is investigated. Necessary and sufficient conditions for the isomorphism of a given lattice to the lattice of processes of a certain digraph are obtained. Bibliography: 5 titles. Translated by K. V. Shakhbazyan. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 135–153.     

Calculation of the dynamic temperature characteristics of a heated graphite tube used in electrothermal atomic absorption measurements

A method and computer program were developed for calculating the temperature of any part of a graphite furnace tube at any instant of time after onset of the heating cycle. Results for tubes of the Massman design show large differences in spatial temperature distributions during and at the end of the heating cycle when equilibrium is reached. When constant current is applied to contoured tubes, greater heating rates at the tube centres are obtained than with standard tubes.     

Violation of isotopic invariance in strong interactions and mass spectrum of the 1/2+ baryon octet

The ideas developed by Gell-Mann and Okubo in studying violation of unitary symmetry are used to describe violation of isototic invariance in strong interactions. The present consideration is performed for the example of the mass spectrum of the octet formed by baryons of spin-parity 1/2⁺: only for this family are the widths of its particles much less than the scale of the effects being investigated, their masses being known from experiments to a fairly high precision. The Gell-Mann-Okubo formula is generalized in such a way that relations both for the splitting between the isomultiplets of the octet and for the mass splitting within these isomultiplets follow from the new formula. Moreover, a relation between masses that describes their electromagnetic splitting and which coincides in form with the Coleman-Glashow relation also follows from this formula. The relations obtained for the masses of the baryons belonging to the octet in question are satisfied to a precision not poorer than 3%.     

Multi-layer structure in the strongly coupled 5D abelian Higgs model

We explore the phase diagram of the five-dimensional anisotropic Abelian Higgs model by Monte Carlo simulations. In particular, we study the transition between the confining phase and the four-dimensional layered Higgs phase. We find that, in a certain region of the lattice parameter space, this transition can be first order, and that each layer moves into the Higgs phase independently of the others (decoupling of layers). As the Higgs couplings vary, we find, using mean field techniques, that this transition may probably become second order. Received: 21 December 2001 / Published online: 12 April 2002     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

Technical Stability of Nonlinear Spatial Dynamic States of Continuous Systems in the Case of Their Interaction with a Flow of a Liquid

Nonlinear Oscillations -