## My life in the quantum fields (the report at the General Meeting of RAS on March 27, 2014)

Published in category «Uncategorized»

No abstract.

## Finite element modeling of bone deformation at the submicroscopic scale

Published in category «Simulation of physical processes»

By means of the direct finite element simulation and homogenization the analysis of variation influence in the morphological characteristics (hydroxyapatite crystals disorientation, sizes and orientation of mineral bridges, mineralization) on mechanical properties of the representative volume element of bone at the nanoscale (at the collagen fibrils level) is carried out. The morphological model of bone with an account of the mineral bridges between the associations of the hydroxyapatite crystals is used in the computations. The purpose of the paper is to analyze the influence of the nanostructure parameters of bone on its elastic and strength properties. Such studies are important for the creation of artificial bone-substitute materials. The analysis of the stress-strain state of the RVE of bone tissue has been performed in order to determine the location of the most critical points and deformation mechanisms of bridges. The most loaded elements are the corners of conglomerates and corners of bridges. Taking account of the bridges leads to the decrease of the von Mises stresses in the corner of the conglomerate and to the increase of the effective elastic moduli in the vertical and horizontal directions. The effects of orientation of conglomerates and bridges on the stress state of the representative volume were analyzed. The influence of the bone mineralization on the effective elastic moduli and stress state were investigated. The comparison of obtained results with experimental data was performed and discussed.

## Finite element modeling and an analysis of the stress-strain state of reinforced concrete structures

Published in category «Simulation of physical processes»

One of the tasks for engineers in the field of feasibility of strength of designs and constructions of nuclear power plants is the analysis of reactor buildings safety under dynamic loads such as earthquakes, fall aftereffects of a heavy passenger plane, etc. An application of linear-elastic material models and equations of the linear theory of elasticity results in excessively conservative outcomes, designs and constructions parameters being non-optimal economically and technologically. Reinforced concrete bearing elements of the reactor building of the nuclear power plant with wall thicknesses of up to two meters, according to requirements of standard documentation, offers a clear example. This work considers the present-day methods of computational mechanics and uses them for the analysis of stress-strain state of reinforced concrete designs taking into account nonlinear physical and mechanical properties of concrete and the cracking phenomenon.

## Boundary problems for the Crocco equation in the transport theory

Published in category «Mathematical physics»

The Crocco boundary problem is more convenient than the Fourier limit problem when either is applied to the transfer problem of passive and conservative tracers for a number of advantages given below. Firstly, the concentration density distribution is generally sought on the standard compact interval from 0 to 1 in the distribution class of the limited growth instead of a semi-infinite interval. Secondly, the dual variational formulation of the problem being equivalent to the marginal one is admitted, and it reduces the solutions topology from C(2)(0, 1) to W2 (1)(0, 1). Thirdly, there are simple invariants of the solution which are convenient for estimating the solution norms and have a simple interpretation for moments of the density distribution. And finally, the Crocco boundary problem is “insensitive” to the nonlinearity of the equation coefficients. In this problem with piecewise-constant coefficients boundary conditions on the contact within the (0, 1) interval of variation in the density distribution are equivalent to the transversality conditions. The paper presents the demonstration of these arguments and the solution examples of the limiting problem for the Crocco equation with a power variation in the transfer coefficient.

## Stationary solution of the Tang – Statz – Demars system of equations for YAG:Nd-laser

Published in category «Physical optics»

## The software system for real-time investigation of autocontrol mechanisms of transcranial blood circulation

Published in category «Biophysics and medical physics»

The paper presents architecture and details of software implementation of a client-server system developed to investigate the hemodynamics in the brain in real-time mode. That is our own implementation of distributed registering, recording, an analysis of blood flow velocity (BFV), arterial blood pressure (BP). Input signals (BFV, BP) are treated as quasiperiodic stochastic processes. The analysis is performed by spectral methods of stochastic processes theory. FFT algorithm is in use to get spectra estimates. Modified Welch estimator is applied to evaluate consistent estimates of harmonics amplitudes. GUI is implemented in client software to display input signals and their estimates. The results of the software clinical testing in which course we studied the M-wave phenomenon are given.

## Additive and multiplicative doubling variables in autonomous equations

Published in category «Mathematics»

The paper analyzes the Cauchy problem for a dynamic equation or for a dynamic system (1) of equations. In doing so, we take a flow and a tangential space Tx, the flow being the dynamic system or mapping X basis of segregation of Em subset on the Tx layer or a trivial tangential segregation. The segregation is given by diffeomorphism from X on E1, of Crr(T) class, r ≥ 1. The aim of this work is to elucidate the possibility of embedding this segregation into the field of extremals. A necessary and a sufficient condition for a trivial embedding is formulated as the intensification of Liouville’s condition in order to keep the phase volume or a condition of existence of invariant measure. The application of this condition allows to construct the dynamic system energy. The distribution which is a dual of Hamiltonian gives the Lagrangian density. In this manner a variational problem is obtained, in which the initial system plays the role of an intermediate integral and of coordination conditions for LaGrange’s system of equations. Procedures of different types of doubling variables (additive and multiplicative, external and internal) have been used in non-trivial embedding of the initial Cauchy problem characteristic into the field of extremals. Multiplicative doubling is analogous to the application of the integrating factor, and the additive one is identical to the addition of equations in variations to the initial system.

## The group problem of minimization

Published in category «Mathematics»

This problem was shown previously. The algorithm for reduction of an integer basic matrix to a normal form was used in the process. The speedup of calculations in this algorithm is gained due to the Euclidian algorithm. The following questions are considered in this article: (i) the statement of the group problem of minimization for a finite Abelian group; (ii) the numerical solution of this problem; (iii) the representation of the group elements is given for a cyclic group and for a direct sum of cyclic groups; (iiii) recurrence relations for the value function and the index function; (iiiii) calculation of the coefficients of the inequation, giving the facet of the polytope of the group equation; (iiiiii) a statement and a proof of the theorem on the steps number estimation. The recurrence relations and the theorem mentioned are the theoretical basis for the validation of the computational schemes.

## The algorithm for completing the standard table

Published in category «Mathematics»

The present article describes the computational scheme for numerical solving practical and theoretical problems. This scheme realizes the algorithm for completing the standard table (from top to bottom and from left to right). Among the computation features of this scheme are computer memory saving, the possibility to estimate the number of executed operations, parallelization of computations. The calculating formulae used in the scheme are given and the work of the algorithm for completing the standard table is illustrated with three numerical examples. The first example describes the simplest case when every coefficient of the group equation induces the whole finite group. The second example describes the general case. There could be some group elements among the coefficients of the group equation, which order is smaller than the finite group one. The third example shows that not all the points defining the hyperplane are the vertices of the polytope of the group equation. Note that in the applications the coefficients of the inequation, which defines the face of the polytope, are calculated with the filling of the standard table (this inequation is called the cut or the valid inequation in discrete optimization).

## Phan models of electric field of nucleons and electrons

Published in category «Theoretical physics»

In this article, we construct a model which describes the potential of electric charges distribution using degenerate partial differential equations. It has been proved that the potential of the electron cloud in the hydrogen atom being in the ground state and a hydrogen atom itself can be described by such equations. This description obviates the need to use the notion of a point charge. The medium properties are modeled by the equation coefficients, which can turn into infinity, solutions being sought in a certain class of functions. We name the constructed models “phan models”. We put forward a construction technique of phan models for different media containing divided charges, such as colloids and biological media. The models may be used in suprachemistry to calculate force interactions between the particles. Phan models are close to the Maxwell ones. Their applications are promising for cases when the quantum-mechanical calculations are too complex and conventional electromechanical models are not able to reflect accurately the medium properties. The examples given show the possibilities for the further development of phan theory.

## XXVII Всероссийская научная конференция студентов-радиофизиков

Published in category «Chronicle»

The paper discusses the 17th All-Russian scientific conference of undergraduates specializing in radiophysics, which took place on April, 22–23, 2014 in Petrodvoretz in the educational center of Saint Petersburg State University (SPbSU). About forty undergraduates and postgraduates and lecturers from Saint Petersburg’s institutions of higher education took part in the conference. The most number of reports were presented by SPbSU (9) and SPbSPU (5), and their total number was 35. The reports presented were written on a diverse range of subject matter, such as vibration theory, radiation and propagation of electromagnetic waves, electronic devices and systems, quantum radiophysics, and physical phenomena studied by radiophysical methods. Two reports from SPbSU got the 1st degree awards: (i) I.V. Ageev's “The short review of results of high-temperature measurements of electromagnetic radiation scattering intensity in glasses and their melts”; (ii) E.A. Danilogorskaya's “On the horizontal gradients contribution in errors of object positions establishment with global navigation satellite systems”.