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We consider a model of spontaneous formation of a computational structure in the human brain for solving a given class of tasks in the process of performing a series of similar tasks. The model is based on a special definition of a numerical measure of the complexity of the solution algorithm. This measure has an informational property: the complexity of a computational structure consisting of two independent structures is equal to the sum of the complexities of these structures. Then the probability of spontaneous occurrence of the structure depends exponentially on the complexity of the structure. The exponential coefficient requires experimental determination for each type of problem. It may depend on the form of presentation of the source data and the procedure for issuing the result. This estimation method was applied to the results of a series of experiments that determined the strategy for solving a series of similar problems with a growing number of initial data. These experiments were described in previously published papers. Two main strategies were considered: sequential execution of the computational algorithm, or the use of parallel computing in those tasks where it is effective. These strategies differ in how calculations are performed. Using an estimate of the complexity of schemes, you can use the empirical probability of one of the strategies to calculate the probability of the other. The calculations performed showed a good match between the calculated and empirical probabilities. This confirms the hypothesis about the spontaneous formation of structures that solve the problem during the initial training of a person. The paper contains a brief description of experiments, detailed computational schemes and a strict definition of the complexity measure of computational structures and the conclusion of the dependence of the probability of structure formation on its complexity.

The paper deals with a heat wave motion problem for a degenerate second-order nonlinear parabolic equation with power nonlinearity. The considered boundary condition specifies in a plane the motion equation of the circular zero front of the heat wave. A new numerical-analytical algorithm for solving the problem is proposed. A solution is constructed stepby- step in time using difference time discretization. At each time step, a boundary value problem for the Poisson equation corresponding to the original equation at a fixed time is considered. This problem is, in fact, an inverse Cauchy problem in the domain whose initial boundary is free of boundary conditions and two boundary conditions (Neumann and Dirichlet) are specified on a current boundary (heat wave). A solution of this problem is constructed as the sum of a particular solution to the nonhomogeneous Poisson equation and a solution to the corresponding Laplace equation satisfying the boundary conditions. Since the inhomogeneity depends on the desired function and its derivatives, an iterative solution procedure is used. The particular solution is sought by the collocation method using inhomogeneity expansion in radial basis functions. The inverse Cauchy problem for the Laplace equation is solved by the null field method as applied to a circular domain with a circular hole. This method is used for the first time to solve such problem. The calculation algorithm is optimized by parallelizing the computations. The parallelization of the computations allows us to realize effectively the algorithm on high performance computing servers. The algorithm is implemented as a program, which is parallelized by using the OpenMP standard for the C++ language, suitable for calculations with parallel cycles. The effectiveness of the algorithm and the robustness of the program are tested by the comparison of the calculation results with the known exact solution as well as with the numerical solution obtained earlier by the authors with the use of the boundary element method. The implemented computational experiment shows good convergence of the iteration processes and higher calculation accuracy of the proposed new algorithm than of the previously developed one. The solution analysis allows us to select the radial basis functions which are most suitable for the proposed algorithm.

The work investigates the search for inefficient edges in the model of stable dynamics by Nestrov – de Palma (2003). For this purpose, we prove several general theorems about equilibrium properties, including the condition of equal costs for all used routes that can be extended to all paths involving edges from equilibrium routes. The study demonstrates that the standard problem formulation of finding edges whose removal reduces the cost of travel for all participants has no practical significance because the same edge can be both efficient and inefficient depending on the network’s load. In the work, we introduce the concept of an inefficient edge based on the sensitivity of total driver costs to the costs on the edge. The paper provides an algorithm for finding inefficient edges and presents the results of numerical experiments for the transportation network of the city of Anaheim.

The article presents an analytical-numerical method to simulate $p$-dimentional heat transfer processes on complex geometry domains when conventional methods are not applicable. The model is converted by the proposed method so that conventional numerical analysis methods is applied to the numerical research. The results of numerical experiments are given to demonstrate the effectiveness of the proposed method. The obtained results, other authors’ numerical results and exact analytical solutions, known for a class of problems, is compared.

The goal of this work is to generalize second order mathematical models for automotive flow using algorithm for building state equation — the dependency of pressure on traffic density — which is adequate with regard to real world data. The form of state equation, which closes the system of model equations, is obtained from experimental form of fundamental diagram — the dependency of traffic flow intensity on its density, and completely defines all properties of any phenomenological model. The proposed approach was verified using numerical experiments on typical traffic data, obtained from PeMS system (http://pems.dot.ca.gov/), using segment of I-507 highway in California, USA as model system.

In the last decades, the development of methods for increasing the efficiency of hydrocarbon extraction in fields with unconventional reserves containing large amounts of gas condensate is of great importance. This makes important the development of methods of mathematical modeling that realistically describe physical processes in a gas-condensate mixture in a porous medium.

In the paper, a mathematical model which describes the dynamics of the pressure, velocity and concentration of the components of a two-component two-phase mixture entering a laboratory model of plast filled with a porous substance with known physicochemical properties is considered. The mathematical model is based on a system of nonlinear spatially one-dimensional partial differential equations with the corresponding initial and boundary conditions. Laboratory experiments show that during a finite time the system stabilizes, what gives a basis to proceed to the stationary formulation of the problem.

The numerical solution of the formulated system of ordinary differential equations is realized in the Maple environment on the basis of the Runge–Kutta procedure. It is shown that the physical parameters of the gascondensate mixture, which characterize the modeled system in the stabilization regime, obtained on this basis, are in good agreement with the available experimental data. This confirms the correctness of the chosen approach and the validity of its further application and development for computer modeling of physical processes in gas-condensate mixtures in a porous medium. The paper presents a mathematical formulation of the system of partial differential equations and of respective system stationary equations, describes the numerical approach, and discusses the numerical results obtained in comparison with experimental data.

A variant of import into ANSYS Mechanical APDL system of the model of behavior of flexible woven composite materials with reinforcing weaving cloth of linen at static stretching along the reinforcement yarns is offered. The import was carried out using an integration module based on the use of an analytical model of deformation of the material under study. The model is presented in the articles published earlier and takes into account the changes in the geometric structure occurring in the reinforcing layer of the material during the deformation process, the formation of irreversible deformations and the interaction of cross-lying reinforcing fabric threads. In the introduction input characteristics of the plain weave of the reinforcing fabric and the analytical model imported into ANSYS are briefly described. The input parameters of the module are the mechanical characteristics of the materials that make up the composite (binder and material of reinforcement yarns), the geometric characteristics of the interlacing of the reinforcing fabric. The algorithm for importing the model is based on the calculation and transfer in ANSYS of the calculated points of the material stress-strain diagram for uniaxial stretching along the reinforcement direction and using the Multilinear Kinematich Hardening model material embedded in the ANSYS. The analytical model imported with the help of the presented module allows to model a composite material with reinforcing fabric without a detailed description of the geometry of the interlacing of threads during modeling of the material as a whole. The imported model was verified. For verification full-scale experimental studies and numerical simulation of the stretching of samples from flexible woven composites were carried out. The analysis of the obtained results showed good qualitative and quantitative agreement of calculations.

In this article, a meshfree-spectral method for numerical investigation of dynamics of planar geophysical flows is proposed. We investigate inviscid incompressible fluid flows with the presence of planetary rotation. Mathematically this problem is described by the non-steady system of two partial differential equations in terms of stream and vorticity functions with different boundary conditions (closed flow region and periodic conditions). The proposed method is based on several assumptions. First of all, the vorticity field is given by its values on the set of particles. The function of vorticity distribution is approximated by piecewise cubic polynomials. Coefficients of polynomials are found by least squares method. The stream function is calculated by using the spectral global Bubnov –Galerkin method at each time step.

The dynamics of fluid particles is calculated by pseudo-symplectic Runge –Kutta method. A detailed version of the method for periodic boundary conditions is described in this article for the first time. The adequacy of numerical scheme was examined on test examples. The dynamics of the configuration of four identical circular vortex patches with constant vorticity located at the vertices of a square with a center at the pole is investigated by numerical experiments. The effect of planetary rotation and the radius of patches on the dynamics and formation of vortex structures is studied. It is shown that, depending on the direction of rotation, the Coriolis force can enhance or slow down the processes of interaction and mixing of the distributed vortices. At large radii the vortex structure does not stabilize.

The paper presents the results of numerical simulation of the effect of a long spark discharge on the mixing dynamics of an injected gas jet with supersonic air flow. The calculations were performed using the CFD software package FlowVision. The fuel was supplied using an injector located on the channel wall, and the discharge was organized near the wall downstream of the injector. Simulation of electrical spark discharge was performed using a volumetric heat source. In order to describe the principal specifications of a plasma actuator to accelerate mixing in a supersonic flow (Mach number M = 2), the research involved varying the energy impact to the discharge in the range of 100–500 mJ per pulse, determining the influence of the shape and location of the discharge. A study of the fuel injection modes in a supersonic air flow has been carried out and an optimal gas jet outflow regime has been found to study the effect of a spark discharge. A method has been developed for analyzing the disturbance pattern of the fuel-oxidant interface caused by the operation of a pulsed spark discharge. A program was prepared in the LabView software environment for obtaining quantitative characteristics for further comparison with the results obtained in the experiment.

The simulation results allow us to conclude that the long spark discharge located along the flow downstream of the injector provides the maximum increase in the interface between the jet of fuel and the main flow. A typical repetition frequency of discharge pulses in a pulse-periodic mode should be more than 6 kHz with a discharge length of ~10 mm to ensure a continuous effect on the mixing at a flow velocity of 500 m/s.

As part of the paper, a physical and theoretical analysis of the impact processes of various factors of a highaltitude and high-energy nuclear explosion on the asteroid in extra-atmospheric conditions of open space is done. It is shown that, in accordance with the energy and permeability of the plasma of explosion products, X-ray and gamma-neutron radiation, a layered structure with a different energy density depending on angular coordinates is formed on the surface of the asteroid. The temporal patterns of the energy transformation for each layer is clarified and the roles of various photo- and collision processes are determined. The effect of a high-speed plasma flow is erosive in nature, and the plasma pulse is transmitted to the asteroid. The paper presents that in a thin layer of x-ray absorption, the asteroid substance is heated to high temperatures and as a result of its expansion, a recoil impulse is formed, which is not decisive due to the small mass of the expanding high-temperature plasma. Calculations shows that the main impulse received by an asteroid is associated with the entrainment of a heated layer of a substance formed by a neutron flux (7.5 E 10¹⁴ g E cm/s). It is shown that an asteroid with a radius of ~100 m acquires a velocity of . 100 cm/s. The calculations were performed taking into account the explosion energy spent on the destruction of the amorphous structure of the asteroid material (~1 eV/atom = 3.8 E 10¹⁰ erg/g) and ionization in the region of the high-temperature layer. Based on a similar analysis, an approximation is obtained for estimating the average size of fragments in the event of the possible destruction of the asteroid by shock waves generated inside it under the influence of pressure impulses. A physical experiment was conducted in laboratory conditions, simulating the fragmentation of a stone asteroid and confirming the validity of the obtained dependence on the selected values of certain parameters. As a result of numerical studies of the effects of the explosion, carried out at different distances from the surface of the asteroid, it is shown that taking into account the real geometry of the spallation layer gives the optimal height for the formation of the maximum asteroid momentum by a factor of 1.5 greater than similar estimates according to the simplified model. A two-stage concept of the impact of nuclear explosions on an asteroid using radar guidance tools is proposed. The paper analyzes the possible impact of the emerging ionization interference on the radar tracking of the movement of large fragments of the asteroid in the space-time evolution of all elements of the studied dynamic system.