All issues

It is known that the internal mobility of DNA molecules plays an important role in the functioning of these molecules. This explains the great interest of researchers in studying the internal dynamics of DNA. Complexity, laboriousness and high cost of research in this field stimulate the search and creation of simpler physical analogues, convenient for simulating the various dynamic regimes possible in DNA. One of the directions of such a search is connected with the use of a mechanical analogue of DNA — a chain of coupled pendulums. In this model, pendulums imitate nitrous bases, horizontal thread on which pendulums are suspended, simulates a sugarphosphate chain, and gravitational field simulates a field induced by a second strand of DNA. Simplicity and visibility are the main advantages of the mechanical analogue. However, the model becomes too cumbersome in cases where it is necessary to simulate long (more than a thousand base pairs) DNA sequences. Another direction is associated with the use of an electronic analogue of the DNA molecule, which has no shortcomings of the mechanical model. In this paper, we investigate the possibility of using the Josephson line as an electronic analogue. We calculated the coefficients of the direct and indirect transformations for the simple case of a homogeneous, synthetic DNA, the sequence of which contains only adenines. The internal mobility of the DNA molecule was modeled by the sine-Gordon equation for angular vibrations of nitrous bases belonging to one of the two polynucleotide chains of DNA. The second polynucleotide chain was modeled as a certain average field in which these oscillations occur. We obtained the transformation, allowing the transition from DNA to an electronic analog in two ways. The first includes two stages: (1) the transition from DNA to the mechanical analogue (a chain of coupled pendulums) and (2) the transition from the mechanical analogue to the electronic one (the Josephson line). The second way is direct. It includes only one stage — a direct transition from DNA to the electronic analogue.

Base long-term modern scenarios of hydrochemical and temperature regimes of the Sea of Azov were considered. New schemes of modeling mechanisms of algal adaptation to changes in the hydrochemical regime and temperature were proposed. In comparison to the traditional ecological-evolutionary schemes, these models have a relatively small dimension, high speed and allow carrying out various calculations on long-term perspective (evolutionally significant times). Based on the ecology-evolutionary model of the lower trophic levels the impact of these environmental factors on the dynamics and microevolution of algae in the Sea of Azov was estimated. In each scenario, the calculations were made for 100 years, with the final values of the variables and parameters not depending on the choice of the initial values. In the process of such asymptotic computer analysis, it was found that as a result of climate warming and temperature adaptation of organisms, the average annual biomass of thermophilic algae (Pyrrophyta and Cyanophyta) naturally increases. However, for a number of diatom algae (Bacillariophyta), even with their temperature adaptation, the average annual biomass may unexpectedly decrease. Probably, this phenomenon is associated with a toughening of competition between species with close temperature parameters of existence. The influence of the variation in the chemical composition of the Don River’s flow on the dynamics of nutrients and algae of the Sea of Azov was also investigated. It turned out that the ratio of organic forms of nitrogen and phosphorus in sea waters varies little. This stabilization phenomenon will take place for all high-productive reservoirs with low flow, due to autochthonous origin of larger part of organic matter in water bodies of this type.

A dynamic game theoretic model of struggle against corruption in resource allocation is considered. It is supposed that the system of resource allocation includes one principal, one or several supervisors, and several agents. The relations between them are hierarchical: the principal influences to the supervisors, and they in turn exert influence on the agents. It is assumed that the supervisor can be corrupted. The agents propose bribes to the supervisor who in exchange allocates additional resources to them. It is also supposed that the principal is not corrupted and does not have her own purposes. The model is investigated from the point of view of the supervisor and the agents. From the point of view of agents a non-cooperative game arises with a set of Nash equilibria as a solution. The set is found analytically on the base of Pontryagin maximum principle for the specific class of model functions. From the point of view of the supervisor a hierarchical Germeyer game of the type Г_2t is built, and the respective algorithm of its solution is proposed. The punishment strategy is found analytically, and the reward strategy is built numerically on the base of a discrete analogue of the initial continuous- time model. It is supposed that all agents can change their strategies in the same time instants only a finite number of times. Thus, the supervisor can maximize his objective function of many variables instead of maximization of the objective functional. A method of qualitatively representative scenarios is used for the solution. The idea of this method consists in that it is possible to choose a very small number of scenarios among all potential ones that represent all qualitatively different trajectories of the system dynamics. These scenarios differ in principle while all other scenarios yield no essentially new results. Then a complete enumeration of the qualitatively representative scenarios becomes possible. After that, the supervisor reports to the agents the rewardpunishment control mechanism.

In the conditions of the development of modern economy, human capital is one of the main factors of economic growth. The formation of human capital begins with the birth of a person and continues throughout life, so the value of human capital is inseparable from its carriers, which in turn makes it difficult to account for this factor. This has led to the fact that currently there are no generally accepted methods of calculating the value of human capital. There are only a few approaches to the measurement of human capital: the cost approach (by income or investment) and the index approach, of which the most well-known approach developed under the auspices of the UN.

This paper presents the assigned task in conjunction with the task of demographic dynamics solved in the time-age plane, which allows to more fully take into account the temporary changes in the demographic structure on the dynamics of human capital.

The task of demographic dynamics is posed within the framework of the Mac-Kendrick – von Foerster model on the basis of the equation of age structure dynamics. The form of distribution functions for births, deaths and migration of the population is determined on the basis of the available statistical information. The numerical solution of the problem is given. The analysis and forecast of demographic indicators are presented. The economic and mathematical model of human capital dynamics is formulated on the basis of the demographic dynamics problem. The problem of modeling the human capital dynamics considers three components of capital: educational, health and cultural (spiritual). Description of the evolution of human capital components uses an equation of the transfer equation type. Investments in human capital components are determined on the basis of budget expenditures and private expenditures, taking into account the characteristic time life cycle of demographic elements. A one-dimensional kinetic equation is used to predict the dynamics of the total human capital. The method of calculating the dynamics of this factor is given as a time function. The calculated data on the human capital dynamics are presented for the Russian Federation. As studies have shown, the value of human capital increased rapidly until 2008, in the future there was a period of stabilization, but after 2014 there is a negative dynamics of this value.

Theoretical and experimental investigations of water vapor interaction with porous materials are carried out both at the macro level and at the micro level. At the macro level, the influence of the arrangement structure of individual pores on the processes of water vapor interaction with porous material as a continuous medium is studied. At the micro level, it is very interesting to investigate the dependence of the characteristics of the water vapor interaction with porous media on the geometry and dimensions of the individual pore.

In this paper, a study was carried out by means of mathematical modelling of the processes of water vapor interaction with suffering pore of the cylindrical type. The calculations were performed using a model of a hybrid type combining a molecular-dynamic and a macro-diffusion approach for describing water vapor interaction with an individual pore. The processes of evolution to the state of thermodynamic equilibrium of macroscopic characteristics of the system such as temperature, density, and pressure, depending on external conditions with respect to pore, were explored. The dependence of the evolution parameters on the distribution of the diffusion coefficient in the pore, obtained as a result of molecular dynamics modelling, is examined. The relevance of these studies is due to the fact that all methods and programs used for the modelling of the moisture and heat conductivity are based on the use of transport equations in a porous material as a continuous medium with known values of the transport coefficients, which are usually obtained experimentally.

In the present paper the application of the kinetic methods to the blood flow problems in elastic vessels is studied. The Lattice Boltzmann (LB) kinetic equation is applied. This model describes the discretized in space and time dynamics of particles traveling in a one-dimensional Cartesian lattice. At the limit of the small times between collisions LB models describe hydrodynamic equations which are equivalent to the Navier – Stokes for compressible if the considered flow is slow (small Mach number). If one formally changes in the resulting hydrodynamic equations the variables corresponding to density and sound wave velocity by luminal area and pulse wave velocity then a well-known 1D equations for the blood flow motion in elastic vessels are obtained for a particular case of constant pulse wave speed.

In reality the pulse wave velocity is a function of luminal area. Here an interesting analogy is observed: the equation of state (which defines sound wave velocity) becomes pressure-area relation. Thus, a generalization of the equation of state is needed. This procedure popular in the modeling of non-ideal gas and is performed using an introduction of a virtual force. This allows to model arbitrary pressure-area dependence in the resulting hemodynamic equations.

Two test case problems are considered. In the first problem a propagation of a sole nonlinear pulse wave is studied in the case of the Laplace pressure-area response. In the second problem the pulse wave dynamics is considered for a vessel bifurcation. The results show good precision in comparison with the data from literature.

The article describes the modes with the exacerbation of social and biological history. The analysis of the possible causes of the sharp acceleration of biological and social processes in certain historical periods is carried out. Using mathematical modeling shows that hyperbolic trends in social and biological evolution may be the result of transitional processes in periods of expansion of ecological niches. Accelerating biological speciation due to the fact that its earlier life change inhabitancy, making it more diverse, saturating the organic, thus creating favourable conditions for the emergence of new species. In the social history of the expansion of ecological niches associated with technological revolutions, of which the most important were: Neolithic revolution — the transition from appropriating economy to producing economy (10 thousand years ago), “urban revolution” — a shift from the Neolithic epoch to the bronze epoch (5 thousand years ago), the “axial age” — transition to the development of iron tools (2.5 thousand years ago), the industrial revolution — the transition from manual labor to machine production (200 years ago). All of these technological revolutions have been accompanied by dramatic population growth, changes in social and political spheres. So, observed in the last century, hyperbolic nature of some demographic, economic growth and other indicators of world dynamics is a consequence of the transition process, which began as a result of the industrial revolution and to prepare for the transition of the society to a new stage of its development. Singularity point of hyperbolic trend shows the end of the initial phase of the process and marks the transition to the final stage. The mathematical model describing the demographic and economic changes in the era of change is proposed. It is shown that a direct analogue of the contemporary situation in this sense is the “axial age” (since 8 century BC to the beginning of our era). The existence of this analogy allows you to see into the future by studying the past.

The paper proposes a new mathematical model to study the interaction dynamics of the longitudinal wall of a narrow channel with its end seal. The end seal was considered as the edge wall on a spring, i.e. spring-mass system. These walls interaction occurs via a viscous liquid filling the narrow channel; thus required the formulation and solution of the hydroelasticity problem. However, this problem has not been previously studied. The problem consists of the Navier–Stokes equations, the continuity equation, the edge wall dynamics equation, and the corresponding boundary conditions. Two cases of fluid motion in a narrow channel with parallel walls were studied. In the first case, we assumed the liquid motion as the creeping one, and in the second case as the laminar, taking into account the motion inertia. The hydroelasticty problem solution made it possible to determine the distribution laws of velocities and pressure in the liquid layer, as well as the motion law of the edge wall. It is shown that during creeping flow, the liquid physical properties and the channel geometric dimensions completely determine the damping in the considered oscillatory system. Both the end wall velocity and the longitudinal wall velocity affect the damping properties of the liquid layer. If the fluid motion inertia forces were taken into account, their influence on the edge wall vibrations was revealed, which manifested itself in the form of two added masses in the equation of its motion. The added masses and damping coefficients of the liquid layer due to the joint consideration of the liquid layer inertia and its viscosity were determined. The frequency and phase responses of the edge wall were constructed for the regime of steady-state harmonic oscillations. The simulation showed that taking into account the fluid layer inertia and its damping properties leads to a shift in the resonant frequencies to the low-frequency region and an increase in the oscillation amplitudes of the edge wall.

In this paper, we address the mathematical modeling of robots based on tensegrity structures. The pivotal property of such structures is the forming elements working only for compression or tension, which allows the use of materials and structural solutions that minimize the weight of the structure while maintaining its strength.

Tensegrity structures hold several properties important for collaborative robotics, exploration and motion tasks in non-deterministic environments: natural compliance, compactness for transportation, low weight with significant impact resistance and rigidity. The control of such structures remains an open research problem, which is associated with the complexity of describing the dynamics of such structures.

We formulate an approach for describing the dynamics of such structures, based on second-order dynamics of the Cartesian coordinates of structure elements (rods), first-order dynamics for angular velocities of rods, and first-order dynamics for quaternions that are used to describe the orientation of rods. We propose a numerical method for solving these dynamic equations. The proposed methods are implemented in the form of a freely distributed mathematical package with open source code.

Further, we show how the provided software package can be used for modeling the dynamics and determining the operating modes of tensegrity structures. We present an example of a tensegrity structure moving in zero gravity with three rigid rods and nine elastic elements working in tension (cables), showing the features of the dynamics of the structure in reaching the equilibrium position. The range of initial conditions for which the structure operates in the normal mode is determined. The results can be directly used to analyze the nature of passive dynamic movements of the robots based on a three-link tensegrity structure, considered in the paper; the proposed modeling methods and the developed software are suitable for modeling a significant variety of tensegrity robots.

Despite numerous achievements of modern science the problem of lightning initiation in an electrodeless thundercloud, the maximum electric field strength inside which is approximately an order of magnitude lower than the dielectric strength of air, remains unsolved. Although there is no doubt that discharge activity begins with the appearance of positive streamers, which can develop under approximately half the threshold electric field as compared to negative ones, it remains unexplored how cold weakly conducting streamer systems unite in a joint hot well-conducting leader channel capable of self-propagation due to effective polarization in a relatively small external field. In this study, we present a self-organizing transport model which is applied to the case of electric discharge tree formation in a thundercloud. So, the model is aimed at numerical simulation of the initial stage of lightning discharge development. Among the innovative features of the model are the absence of grid spacing, high spatiotemporal resolution, and consideration of temporal evolution of electrical parameters of transport channels. The model takes into account the widely known asymmetry between threshold fields needed for positive and negative streamers development. In our model, the resulting well-conducting leader channel forms due to collective effect of combining the currents of tens of thousands of interacting streamer channels each of which initially has negligible conductivity and temperature that does not differ from the ambient one. The model bipolar tree is a directed graph (it has both positive and negative parts). It has morphological and electrodynamic characteristics which are intermediate between laboratory long spark and developed lightning. The model has universal character which allows to use it in other tasks related to the study of transport (in the broad sense of the word) networks.