In the mathematical modeling of the crystallization process, the results of a numerical experiment were used, in which a banded structure of the initial stage of the process was discovered, the mechanism of which is diffusion stratification. Qualitatively, this is consistent with the natural experiment. In the terminology of G.I. Barenblatt, the process is related to flow of the transformed state in the initial stage of crystallization before the formation of the dendritic structure. The universality of the principles of mathematical modeling and the relationship between critical processes of destruction, sintering of materials, and crystallization of binary alloys based on their physical commonality is shown.

We study the stabilization rate of periodic perturbations of the equilibrium position for discrete kinetic equations in the model case of the two-dimensional Broadwell system. We propose a method for identifying a subset of periodic initial data for which the solution to the Cauchy problem for the Broadwell system with the corresponding periodic initial data (periodicperturbationsoftheequilibriumposition) exponentially stabilizes to equilibrium state. Bibliography : 9 titles. Illustrations : 1 figure.

В статье дается обзор коллекции позднеантичных изделий из кости в собрании отдела Древнего Востока ГМИИ им. А. С. Пушкина (168 предметов), большая часть которых не опубликована. Затрагивается проблема провенанса па мятников и предлагается их первичная систематизация – рассматриваются основные типы изделий и изобразительные мотивы на них; углубленный физический, типологический и стилистический анализы в рамках данной статьи не представ ляются возможными. Поэтому во многом это предварительное и описательное знакомство с частью музейной коллекции, имеющей по преимуществу археологический характер. The paper provides an overview of the collection consisting of bone objects from the late Antiquity kept in Department of the Ancient Orient in the Pushkin 216 О. А. Васильева State Museum of Fine Arts (168 items), a greater part of which has not been published. The paper touches upon the provenance of these objects and proposes their initial systematization. It reviews main types of the objects and visual motifs they exhibit. It does not appear possible to conduct in-depth physical, typological and stylistical analyses in one paper. For this reason, this paper is basically a preliminary and descriptive introduction into this part of the museum collection which is largely archaeological in nature.

We consider the regularities in critical phenomena including fracture of materials, crystallization, combustion, and explosion, as well as sintering of materials as a thermal process. Sintering is widely used for consolidation of particles in machine building articles in such as ceramics, metals, polymers, and cemented carbides. We outline the complex of problems that must be solved for fundamental and applied investigations of processes in the theory of classical phenomena and propose their physical analogs. We propose a model of the process as an important supplement to experiments, which is required for understanding sintering mechanisms as well as for optimization and designing of the process. Basic hypotheses and boundary conditions for the application of models are formulated. We consider the problems of the theory of the laminar–turbulent transition, which require detailed understanding of processes and quantitative models on different scales.

New mathematical models of combustion process (thermal theory combustion process and vibration combustion) are developed based on thermodynamic analysis. The global inhomogeneity of the system can be characterized as an inhomogeneous distribution of the enthalpy over the flow (mixture). In this case, the combustion process in the phase space (ϱ , P, T, n, S, E) , the increment of the enthalpy is not a total differential, but it is a total differential on the local equilibrium manifold. These two assertions allow one to single out in the phase space the state equations for the pressure and entropy. The resulting pressure and entropy close the classical model of hydrodynamics and kinetics, which describes the laminar stage of the combustion process. Our numerical experiments shows that the two combustion regimes (deflagration and detonation) depend on the structure of the standard value of the chemical potential. In addition, if the passive component velocity is controlled at the inlet, then, depending on the structure, there appear high-frequency acoustic oscillations described by Raushenbakh. Moreover, for critical values of the chemical potential, such oscillations cause a blow-up.

In mathematical modeling of crystallization process, we have used the results of numerical experiment, in which a striated structure of the initial stage of the process governed by diffusive foliation mechanism has been detected. This is in qualitative agreement with a natural experiment. In G.I. Barenblatt’s terminology, the process is associated with the converted state flux at the initial stage of crystallization up to the formation of a dendrite structure. The universality of mathematical modeling principles and the relation with the critical processes of destruction, sintering of materials, and crystallization of binary alloys has been demonstrated based on their physical generality.

The research works on the modeling and numerical algorithmization of combustion processes, the formation of secondary structures and the mechanisms of associated transient processes revealed that resonance can be avoided due to skip from local equilibrium manifold by turbulization of the laminar process during thermal pumping. In the case of a single active component, the global heterogeneity of a system can be characterized as a nonuniform enthalpy distribution over the flow (mixture). The results of numerical experiment show that the turbulization of combustion process during thermal pumping, as well as for vibrational combustion, leads to the formation of a vast .time zone of detonation combustion in the vicinity of thermal explosion resonance.

Статья посвящена системе внутренних коммуникаций, как части корпоративной культуры, которая необходима не только для полноценной работы организации, но и для поддержания конкурентоспособности на рынке всего предприятия. Целью является улучшение внутренней составляющей крупных предприятий промышленного сектора. Фокус внимания будет уделен описанию ситуации на примере АО «Машиностроительный завод «ЗиО-Подольск». Результатами работы станут рекомендации по улучшению системы внутренних коммуникаций, как части корпоративной культуры, и возможные инструменты для их реализации.

В статье рассматривается роль графического дизайна в маркетинге, приводятся основные задачи и методы графического дизайна. Сравнивается международный и российский опыт кампаний в использовании визуального оформления. В статье анализируются успешные кейсы, на основе которых выявляются шаги на пути к созданию эффективного графического дизайна.

We consider the simplified building material production process based on autocatalytic reaction of two reagents in a finite cylinder. We investigate the effect of uneven heating of the mixture on the duration of the production process. To describe the process, we used a new recently proposed model taking into account the terms of the second order. The mathematical model under consideration is an initial boundary value problem for a nonlinear system of second-order partial differential equations with variable coefficients. We have obtained analytical stationary solutions to the problem, one of which is the equilibrium position, the achievement of which means the end of the process The influence of the uneven distribution of the mixture temperature is studied by numerical investigation of the specified mathematical model. For the numerical solution of the initial boundary value problem for a system of second-order equations with variable coefficients, a second-order finite-difference method is used. To study the obtained solution, quadrature formulas of the second order of accuracy and spline approximation methods are used. The results of the study of the effect of uneven heating of the mixture on the duration of the production process are presented. The obtained results are compared with the results obtained using other mathematical models of autocatalytic reactions. Based on the comparison of the results, it is concluded that taking into account the uneven heating of the mixture makes it possible to more accurately estimate the time of the production process for different criteria of its completion.

Based on thermodynamic analysis of combustion processes, we build a new model of laminar combustion process of vibration combustion. If the passive component velocity for the two-component mixture is controlled at the inlet (the interior energy is pumped at the inlet of the combustion chamber), high-frequency resonance oscillations of vibration combustion are shown to develop depending on the structure of the standard chemical potential. The resonance is driven by hydrodynamic instability. Numerical experiment models the regimes of resonance with pumped internal energy, the nature of their nucleation depending on the structure of the standard chemical potential is revealed. For low temperatures, the appearance of detonation combustion with substantial pressure increase is established near resonance.

On the basis of thermodynamic analysis, new mathematical models of the combus- tion process (thermal theory) and vibrational combustion are constructed. A global inhomo- geneity of the system can be described as an inhomogeneous distribution of the enthalpy over a two-component mixture. In this case, for the combustion process in the phase space of the variables (%, P, T, n, S, E), an increase in the enthalpy is not a total differential. An increase in the enthalpy is a total differential on the local equilibrium manifold (a laminar combustion process). These two assertions, which allow one to single out in the phase space the corre- sponding adiabatic of the combustion process (the Hugoniot adiabatic) and the equation for the entropy, close the classical mathematical model of the combustion process. The above numerical experiments show that two regimes of the combustion process (deflagration and detonation) depend on the structure of the standard chemical potential Moreover, a control of the passive component velocity at the inlet results in (depending on the structure of the standard chemical potential) high-frequency oscillations, which are responsible for a blow-up.

We consider a mathematical model of the laminar process of vibration combustion proposed recently. It allows us to simulate detonation and deflagration modes, the occurrence of which occurs depending on the structure of the standard chemical potential. For simplicity of presentation and analysis, we consider a one-dimensional mathematical model formulated for the reduced dimensionless variables for the case of a two-component mixture. The obtained numerical results are presented and discussed.

Processes that accompany propagation of time-limited pulsed signals in a relaxing medium are investigated for the case of a nonlinear medium with power-law (quadratic or cubic) nonlinearity or nonanalytic nonlinearity (modular or quadratically cubic one). Instead of ordinary integro-differential equations with exponential or fractional-power kernels, a simplified model of a medium with finite “memory time” is used. Such a medium “remembers” its prehistory within a limited time interval, and the corresponding kernel of the integral term is nonzero only within a finite interval. For this model, the problem is reduced to solving a difference-differential equation, which considerably reduces the amount of calculations, as compared to the initial integral equation. The processes that accompany evolution of pulses, namely, the formation of compression and rarefaction shock fronts and the appearance of triangular and trapezoidal nonlinear structures, are described. Effect of relaxation time on these processes is revealed.

For the laminar–turbulent transition, a model of reconstructing the initial stage of an instability treated as a nonequilibrium phase transition is developed. Its mechanism is based on diffusion stratification. It is shown that the Gibbs free energy of the deviation from the homogeneous state (with respect to the instability under consideration) is an analogue of the Ginzburg–Landau potentials. Numerical experiments concerning the self-excitation of a homogeneous state by applying a boundary control condition in the form of an increasing velocity were performed. Under an external influence (an increase in the velocity as input), the system exhibits a transition to chaos through period-doubling bifurcations similar to the Feigenbaum period-doubling cascade.

A computer study of the technological processes for the production of building materials based on the use of reversible autocatalysis reactions is carried out. For the mathematical description of the process of autocatalytic reactions, mathematical models are used, described by a initial-boundary problems for the Carleman system. The considered mathematical model describes the autocatalysis reaction under the following assumptions: the rate of decrease in the density of positive ions is proportional to the square of the deviation of the density of positive ions from the equilibrium state, the rate of decrease in the density of negative ions is proportional to the square of the deviation of the density of negative ions from the equilibrium position and the law of conservation of the total charge of the system including liquid solution. This mathematical model is non-linear, therefore numerical methods are used for its study. For a numerical solution of the initial-boundary value problem for the Carleman system, a finite-difference method of the second order of accuracy is used. For the numerical investigation of the solution obtained, linear interpolation and spline interpolation are used. A numerical study is made on the dependence of the chemical reaction time from the parameters of the model and various initial conditions.