Physics, mathematics, and technology

The work is devoted to the problem of determining small sound speed fluctuations in glandular tissue for specific breast model (2D). Our approach is based on visualization of acoustical medium (inclusions and unknown in­ner boundary between fat and glandular tissues) and determination of sound speeds in inclusions using kinematic argument. The results of numerical sim­ulation (2D) of the problem are presented in the paper.

The problem of 1D acoustic wave initiation by a rise of water masses is formulated as a boundary problem at half space . The atmosphere is modeled as a multi-layer gas with an exponential structure of density in each layer. The boundary conditions at determine the direction of propaga­tion, by link between dynamic variables (pressure, density, and velocity) of the wave. It defines the dynamic projection operators on the subspaces of z-evolution for each layer. The universal formulas for the perturbation of atmos­pheric variables in an arbitrary layer are derived in frequency and time do­mains. The explicit expressions for vertical velocity are built by the stationary phase method considering z as large parameter. The resulting formulas can be used to calculate the ionospheric effect by the explicit formula for electron den­sity evolution. This set of explicit relations form a base for a quick algorithm for early diagnostics of tsunami waves.

The paper presents the results of observations the ionospheric parameters in Kaliningrad (54° N, 20° E) during a meteorological storm in the Baltic sea on October 2018. The analysis of ionospheric variations showed the increase in the total electron content reached 20 % relative to the averaged values, and the increase in the critical frequency of the F2 layer was 19 % during the storm. The increase in the amplitudes of ionospheric variations with periods of 6—20 min over the area of a meteorological storm was also revealed. The re­sults of the numerical experiment on the disturbance of the upper atmosphere due to the observed variations in surface pressure also showed an increase in wave activity with periods of ~ 15 min and the formation of a large-scale dis­turbance at the heights of the thermosphere.

In this work the problem of electron bound to 3d linear atom chain scattering on impurity atoms is considered. In order to describe zone electrons the Bloch functions are constructed with respect to symmetry consideration. In addition, zero range potential approximation is used to model both atoms in chain and impurity atoms.

In a framework of Heisenberg theory, that link quantum-statistical des­crip­tion taking Gauss distribution into account, explicit form is obtained by per­mutations group theory, the division paramagnetic/ferromagnetic is stu­died. The magnetization curves are built for a given set of parameters, such as exchange integral, number of closest neighbours and temperature. In a special ran­ge of the parameters a transition from unique solution of the resulting Hei­senberg equation to multi-valued is observed. For this case exemplary hys­te­resis loops are built. The expression for Curie temperature allows to evaluate the exchange integral and proceed into temperature range above the critical temperature.

In this note we study the problem of a function reconstruction in a con­text of a Laplace method application. We use a unitary space of splines with a double dimension of one, that approximate the set of points, representing the results of observation. The conventional scalar product allows to project the approximation onto the subspace of observations. The use of the same scalar product yields the norm that we use to estimate error deviations within the model under consideration. Its minimum defines both a function reconstruc­tion and its error, which also include the measurements errors. The results we apply to the problems of reconstruction of initial or boundary conditions for 1D wave equation, that imply the procedure of directed waves division.

We investigate the properties of spin states in the electronic ground state of a single nitrogen-vacancy center (NV–) in 13C-enriched diamond. The anal­ysis is based on application of a method that uses a complete set of commuting operators (CSCO). Each state is characterized by a single set of values of CSCO. The properties of the spin states change at the level anti-crossing (LAC). This change leads to an increase in the spin-lattice relaxation rate and to a change in the ODMR spectrum. The LAC can occur during implantation and thus influence the observed yield of NV- centers of a certain type. We as­sume that during cascade transitions between the states of some NV- centers obtained by implantation, an intense 13C NMR signal can be observed. It is important to note that optical pumping of such NV- centers can be carried out in an arbitrary magnetic field.

The anthropic explanation of the smallness of the observed amount of dark energy implies the presence of a variable component compensating for the mag­nitude of the vacuum energy. According to Garriga and Vilenkin, this com­ponent should decrease slowly, leading to a change in the accelerated ex­pansion regime to the collapse phase, but not earlier than in a trillion years. Ho­wever, a decreasing scalar field can lead to unexpected singularities with a fi­nite value of the scale factor. We analyze this situation using the example of SFS and get an unexpected result: the time of appearance of such features of the same order as the lifetime of the observed universe.

An algorithm for realizing the algebra of two-dimensional supersymmet­ric quantum mechanics is described. The cases N = 2 and N = 3 are described in detail. The procedure for iterating Darboux transformations is considered separately. In contrast to the one-dimensional case, in which the problem is completely solved by Krum's formulas, iterations of two-dimensional Dar­boux transformations remain insufficiently understood.

This article is devoted to construction of a mathematical theory capable of explaining those experimentally observable periodic magnetic oscillations in the synthetic antiferromagnet Pt/Co/Ir/Co/Pt that take place after a switch in the direction of an external magnetic field. In particular, we demonstrate that in order to understand the aforementioned phenomenon it is essential to first properly model the collisions between the magnetic domains of different spin orientations (  and ). The resulting model comprised of a system of nonlinear differential equations is closely examined, after which we propose a simple analytical method of construction of its exact solutions. This method is shown to generate an infinite family of solutions associated with the degener­ate hypergeometric functions, parameterized by a natural number N. One of those solutions with N = 2 produces the magnetization function which perfect­ly fits the experimental data.

A new numerical method that unify finite-difference and the method of steepest descent paradigms is suggested. It allows to avoid the wavefuncions spa­ce and spin variables division, that leads to superposition in spin projec­tion stacionary states. The approach is verified by comparison with conven­tio­nal methods.

The formula for the emf Faraday induction from a domain wall moving in a microwire is derived. The time derivative of the magnetic flux in the measuring coil is expressed through a five-fold integral over the wall volume and over the coil section surface. The resulting expression is compared with those obtained previously with a simplified description of the measurement objects.