Home – Home – Jornals – Advanced Search

For a 3-dimensional dynamical system considered as a model of a gene network with nonlinear degradation of its components, the uniqueness of an equilibrium point is proved. Using approaches of qualitative theory of ordinary differential equations, we find conditions of existence of a cycle of this system and describe an invariant domain which contains all such cycles in the phase portrait. Numerical experiments with trajectories of this system are conducted.

The main focus of this paper is an analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator. The findings contribute to the theoretical understanding of TSNTS in B.S. and have practical implications in various applications, such as integral equations further validating our results.

A three-dimensional (3D) matching operator is proposed for a fourth-order accurate solution of a Dirichlet problem of Laplace's equation in a rectangular parallelepiped. The operator is constructed based on homogeneous, orthogonal-harmonic polynomials in three variables, and employs a cubic grid difference solution of the problem for the approximate solution inbetween the grid nodes. The difference solution on the nodes used by the interpolation operator is calculated by a novel formula, developed on the basis of the discrete Fourier transform. This formula can be applied on the required nodes directly, without requiring the solution of the whole system of difference equations. The fourth-order accuracy of the constructed numerical tools is demonstrated further through a numerical example.

The results of modeling the propagation of seismoacoustic waves based on the numerical solution of a direct dynamic problem for a porous medium are considered. The propagation of seismic waves in a porous medium saturated with fluid in the absence of energy loss is described by a system of differential equations of the first order in the Cartesian coordinate system. The initial system is written as a hyperbolic system in terms of the velocities of the elastic host medium, the velocity of the saturating fluid, the components of the stress tensor, and the pressure of the fluid. For the numerical solution of the problem posed, the method of complexing the integral Laguerre transform in time with a finite-difference approximation in spatial coordinates is used. The solution algorithm used makes it possible to efficiently carry out calculations when modeling in a complexly constructed porous medium and to investigate the wave effects that arise in such media.

A study of the influence of unbalancing the processor load in parallelization of solutions of 3D boundary value problems on quasi-structured parallelepiped grids is carried out. Estimates of the influence of the unbalance on the time of solving the problems depending on the number of processors and the number of grid nodes used are given. The results of numerical experiments confirm the theoretical conclusions.

The relationship between the critical detonation thickness in transverse wedges made of plasticized TATB and the acoustic rigidity of the adjacent material and the speed of sound in it was determined by streak photography. The wedge-shaped charge was initiated over the entire lateral surface of the detonation wave propagating in a steady mode.

The process of detonation propagation in a charge made of a plasticized explosive composition based on TATB in the form of a hollow cylinder with a steel shell inside is studied when normal detonation is initiated along a line on the outer surface of the charge. In experiments, the shape of the detonation wave (DW) front at certain points in time was determined using the X-ray method. Using electric contact sensors, the speed of propagation of the DW front along the outer surface of the charge was measured. The original setup of the experiments made it possible to study the propagation of detonation at angles greater than 180 °C from the initiation line. It is shown that in the initiation plane the front velocity of the diverging DW is ≈7.3 km/s. In the region of the “shadow” of the initiation point, the speed of the front of the diverging DW decreases depending on the distance traveled both along the outer surface of the charge - up to ≈6 km/s, and along the inner - up to ≈5.6 km/s. At the same time, near the steel shell in the region of rotation angles of the DW front from approximately 150 to 210 °C, a zone of unreacted TATB was recorded, which may indicate the disruption of detonation and its transformation into a shock wave. A numerical simulation of the process was carried out using the SURF detonation kinetics implemented in the MIMOSA technique. The calculation results are in good agreement with experimental data both at the early stage of the detonation initiation process and in the region of the “shadow” of the initiation point, where the velocity of the DW front decreases.

A semi-empirical equation of state for bismuth has been constructed taking into account five solid phases, liquid, evaporation, and thermal ionization. The results of model calculations are in satisfactory agreement with data from static and dynamic experiments in the pressure range from atmospheric to ≈1 TPa and temperatures from room to ≈10⁵ K.

Periclase (MgO) is one of the important materials that make up the mantles of the terrestrial planets. In this regard, its properties at high temperatures and pressures reflect the nature of the planetary interior. Numerical modeling of shock wave loading of MgO taking into account the polymorphic phase transition in a pressure range of 325 ÷ 400 GPa was carried out using a thermodynamic equilibrium model. The parameters of the consistent equation of state for the high and low pressure phases of periclase (MgO I and MgO II) are determined. The thermodynamic parameters of these phases were modeled. Shock adiabats of single and double compression were constructed in the range 1 ÷ 1000 GPa, the values of heat capacity along the normal isobar, entropy as a function of temperature, and temperature along the shock adiabat were calculated. The modeling results were verified based on the results of experiments and calculations of other authors.

The paper is a summаry of experimental studies of water droplet breakup in the flow behind the shock wave in the range of gas flow velocities 40 ≤ U ≤ 175 m/s. A change between two different mechanisms of stalling breakup of the droplet occurs in this range of velocities, with domination of the inertia force in the case of droplet deformation and viscous friction force in the case of boundary layer shedding. The analysis of the change in the breakup mechanisms is based on a vast pool of observations and quantitative data on droplet dynamics and delays of its breakup obtained by a high-speed method of visualization with a stroboscopic laser source of light. A physical model of the process is constructed on the basis of experimental data and results of the parametric analysis, and criteria of the change in stalling mechanisms of droplet breakup are derived.