Vol 21, No 10 (2015)

The article concerns a numerical investigation of nonlinear diffusion mod- el in the circle. Nonlinear diffusion equation simulates the change of potential concentration of viscoelastic fluid, which is filtered in a porous media. This equa- tion is a semilinear Sobolev type equation. Sobolev type equations constitute a vast area of non-classical equations of mathematical physics. Theorem of exis- tence and uniqueness of a weak generalized solution to the Showalter - Sidorov problem for nonlinear diffusion equation is stated. The algorithm of numerical solution to the problem in a circle was developed using the modified Galerkin method. There is a result of computational experiment in this article.

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

The paper is devoted to analytical determination of coefficients of the Williams asymptotic expansion of the stress field in the neighborhood of two collinear crack tips in an infinite plate under mixed mode loading. On the basis of the Kolosof-Muskhelishvili approach the complete asymptotic expansion of the stress field in the vicinity of the crack tips of two collinear cracks of equal lengths under mixed mode loading is derived. The analysis of the higher order terms in the asymptotic expansion series is performed. It is clear that it is necessary to take into account the higher order terms.

In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconserva- tive force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

Self-oscillations in the system oscillating in discrete time and being under the influence of an external harmonious signal are investigated. As an object of researches the option of discrete map of the oscillator of Van der Pol offered earlier by authors is brought to attention. The modes of synchronous self-oscillations are analysed by means of methods of numerical experiment and harmonic balance. It is established that the effect of subharmonic synchronization in discrete time can be realized at any relation of frequencies of synchronized self-oscillations and the synchronizing signal.

The process of hydrogenation of unsaturated hydrocarbons is one of the main processes of the petrochemical industry. Unsaturated hydrocarbons are practi- cally inseparable from alkanes, which have the same mass, and to obtain high--quality gasoline unsaturated hydrocarbons are to be eliminated. Furthermore, acetylenic hydrocarbons must be removed from an olefinic feedstock, which is intended for the production of polymers. These problems can be solved by using catalysts with different selectivities. The article studied the copper nanoparti- cles in the hydrogenation reaction hexyne-1. The nanoparticles were obtained by means of levitation blasting and mixed with inerton. Analysis of the reaction mixture was performed by means of gas chromatography. We calculated the rate constants at different temperatures and measured the activation energy of the reaction. It is shown that the first hexyne-1 is converted to hexene-1, followed by hexane. Thus, the catalyst shows the analyzed selective properties, which enables selection of the conditions for obtaining the priority of a particular product.

Due to the continuous reduction of the areas for crops and increase of urban
population, the increase in productivity of crops is especially important
aspect in production of food today. One of problems of agriculture is creation
of conditions for receiving a crop. Quality of a crop of various crops depends on
efficiency of preseeding processing of seeds. This research investigated a method
of impact of preseeding processing of seeds of flax by a complex of physical
factors: ultra-violet radiation, ozone and the magnetic field (MF) with induktion
of 100, 200, 250 and 300 Gs on growth and activity of a catalase and
peroxidase of a plant, and also the maintenance of photosynthetic pigments in
flax sprouts.

In this paper the construction of the graph model, structuring multivariate analytical reports on the interaction of natural and anthropogenic factors in the ecosystem, which were presented in the form of a set of related concepts is presented. In the signed directed graph in the computing environment a propa- gation of pulses from the vertices within the context the study the situation of degradation of sturgeon stocks of the Caspian Sea was analyzed. These species are included in the Red Book since 2010 despite efforts in organizing an ar- tificial breeding of fish. Method of cognitive structurization allowed to reveal hidden feedback loop on the basis of the graph, weakens the reproduction of fish populations and become the cause of overestimation acceptable exploitation of bioresources. An approach of functional iteration for describing the dynamics of population processes with nonlinear function of the efficiency of reproduc- tion was discussed. It is shown that the discrete iteration have contradictory qualitative behavior of the trajectory in terms of biological interpretation of bi- furcations. It is proposed to use the predicative redefined computing structure based on the chart of behaviors for the description chain of regime changes of the simulated process. For this type of structural changes is promising to allocate substantial fluctuations of growth rate in the early ontogenesis of fish.