Darboux transformation for classical acoustic spectral problem

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two, by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows the steps, similar to those for the Schr\"{o}dinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a non-linear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing chain approach, we build a modified Harry Dym equation together with its LA-pair. As an application, we construct some singular and non-singular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.Comment: 16 pages; keywords Darboux (Moutard) transformation, Classical acoustic spectral problem, Reflexionless potentials, Soliton

Effect of an electric field on nucleation and growth of crystals

The effect of the electric field strength on nucleation and growth of the crystals of ammonium halides and alkali metal sulfates has been studied. The optimal electric field strength for NH[4]Cl and NH[4]Br crystals was found to be 15 kV/cm, and for NH[4]I, it equaled 10 kV/cm. No effect of the electric field strength on the crystal growth was found for alkali metal sulfates. This difference is analyzed in terms of the crystal growth thermodynamics. In case, when the electric field is small and the Gibbs energy is of a significant value, the influence of the electric field at the crystal growth is negligible. A method to estimate the critical radius of homogeneous nucleation of the crystal is suggested

The linearization method and new classes of exact solutions in cosmology

We develop a method for constructing exact cosmological solutions of the Einstein equations based on representing them as a second-order linear differential equation. In particular, the method allows using an arbitrary known solution to construct a more general solution parameterized by a set of 3\textit{N} constants, where \textit{N} is an arbitrary natural number. The large number of free parameters may prove useful for constructing a theoretical model that agrees satisfactorily with the results of astronomical observations. Cosmological solutions on the Randall-Sundrum brane have similar properties. We show that three-parameter solutions in the general case already exhibit inflationary regimes. In contrast to previously studied two-parameter solutions, these three-parameter solutions can describe an exit from inflation without a fine tuning of the parameters and also several consecutive inflationary regimes.Comment: 7 page

The Big Trip and Wheeler-DeWitt equation

Of all the possible ways to describe the behavior of the universe that has undergone a big trip the Wheeler-DeWitt equation should be the most accurate -- provided, of course, that we employ the correct formulation. In this article we start by discussing the standard formulation introduced by Gonz\'alez-D\'iaz and Jimenez-Madrid, and show that it allows for a simple yet efficient method of the solution's generation, which is based on the Moutard transformation. Next, by shedding the unnecessary restrictions, imposed on aforementioned standard formulation we introduce a more general form of the Wheeler-DeWitt equation. One immediate prediction of this new formula is that for the universe the probability to emerge right after the big trip in a state with $w=w_0$ will be maximal if and only if $w_0=-1/3$.Comment: accepted in Astrophysics and Space Scienc

ENVIRONMENTAL MANAGEMENT IN JOINT STREAMS REGULATION BY TWO HYDROELECTRIC COMPLEXES

Lowland river water power developments are usually built to solve complex tasks on the basis of the requirements of rational use of water resources. First of all, operating conditions of hydroelectric complex structures should provide safety and economic efficiency in their work. Besides, they are aimed to satisfy various demands of water consumers. It is particularly important that behaviour of hydroelectric complex structures should satisfy contemporary requirements of environmental security. The most important task here is to create favourable ecological conditions of life for people who live in settlements located in the zone of influence of two hydroelectric complexes located on different rivers. Here, to achieve environmental targets it is necessary to interlink modes of operation of these water storage control structures. There are two water power developments built in the Republic of Bashkortostan, Russia, in the middle flow of the Belaya River. Both of them have considerable impact on the formation of level mode and different consumers’ water supply. They are Umaguzinskiy and Nugushskiy water power developments. Both hydroelectric complexes and their water reservoirs together satisfy the following generally accepted requirements of water consumers: - they prevent the lowering of the water level in the river Belaya (during low streamflow period) below the minimum values required to ensure proper water supply for industrial enterprises; - they generate electric power and provide industries and cities with electricity. To do that each water-economic complex has its own water reservoir and a set of retaining structures and required culvert installations. In addition, the following environmental requirements are imposed on co-regulation of water runoff: - protection of waterfronts of the towns Meleuz, Salavat, Ishimbay and Sterlitamak from flooding in flood season; -protection of the territories of refineries in flood season (during water rise). Umaguzinskiy water power development has the following water sluices to control water stream: 1) submerged flood-discharge outlet; 2) shore flood spillway; 3) aggregates of powerhouse. General water carrying capacity of hydroelectric complex structures is 3915 м3/c. Nugushskiy hydroelectric complex consists of hydraulic engineering structure power room (1) and left shore spillway (2). Combined water carrying capacity of all hydroelectric complex structures here is 1250 м3/c. The authors investigated operation modes of Nugushskiy and Umaguzinskiy water power developments when linked into one water-economic complex and came to the conclusion that modes of operation of these water storage control structures should be adjusted in accordance with the operational condition of the main pressure installations and of downstream flood-control facilities. In particular, it is necessary to take into account the unfinished state of flood prevention measures in the middle reaches of the river Belaya

Effect of an electric field on nucleation and growth of crystals

The effect of the electric field strength on nucleation and growth of the crystals of ammonium halides and alkali metal sulfates has been studied. The optimal electric field strength for NH[4]Cl and NH[4]Br crystals was found to be 15 kV/cm, and for NH[4]I, it equaled 10 kV/cm. No effect of the electric field strength on the crystal growth was found for alkali metal sulfates. This difference is analyzed in terms of the crystal growth thermodynamics. In case, when the electric field is small and the Gibbs energy is of a significant value, the influence of the electric field at the crystal growth is negligible. A method to estimate the critical radius of homogeneous nucleation of the crystal is suggested

Similarities and differences in curricula of a bachelor’s degree in oceanology at the universities in St Petersburg, Klaipeda, and Kaliningrad

Conducting a multi-aspect comparative analysis of curricula of bachelor’s degree programmes in oceanology offered at universities in St Petersburg, Klaipeda and Kaliningrad, the authors trace similarities between the existing variants of oceanologist training in the context of competence modules, disciplines, the so-called academic practices, and the number of hours and credits stipulated in the existing curricula. A formal comparison of generalised quantitative indicators without analysing the content of curriculum components demonstrated certain similarities in all indicators in terms of workload, the number of disciplines (50, 56 and 45) and academic practices. The clustering of competence modules and disciplines at each university within generalised academic areas - physics and mathematics, philosophy, informatics and computers, geoecology, measurement disciplines, etc. - made a more detailed comparison possible. The results of research demonstrate considerable similarities in the curricula used at the given universities in terms of all variants of comparison. The strongest similarity is observed in the areas of basic and professional disciplines