Abstract: The article briefly reviews two promising directions in the development of relativistic optics, presents simulation results for the interaction of super-high-power laser radiation with cluster plasma, and proposes a particle acceleration method that may provide a promising and unique tool for laser physics research. PubDate: 2020-04-04

Abstract: Solving nonlinear differential equation of a circular sector oscillator is of a scientific importance. Thus, to solve such equations, a single- step implicit block method involving one hybrid point with the introduction of a third derivative is proposed. To derive this method, the approximate basis solution is interpolated at {xn, xn + 3/5} while its second and third derivatives are collocated at all points {xn, xn + 3/5, xn + 1}on the integrated interval of approximation. Numerical results are presented in the form of table and graphs for the variation of different physical parameters. The study reveals that the proposed hybrid block method is zero stable, which proves that it is convergent beside a significant interval of absolute stability, thus making it suitable for solving stiff ODEs. PubDate: 2020-04-04

Abstract: To the article “Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis,” by N. L. Grigorenko, É. V. Grigorieva, P. K. Roi, and E. N. Khailov, Vol. 30, No. 4, pp. 352–363, October, 2019. PubDate: 2020-04-03

Abstract: The article considers a numerical method for the inverse problem of determining the boundaries of nonhomogeneities from probe data. A nonlinear system of integral equations in a three-dimensional region is solved and numerical results are reported. PubDate: 2020-04-01

Abstract: We consider the escape of a photon from a single-mode optical cavity with a controlled variable intensity. The source of the photon is a relaxing two-level atom. The quantum bottleneck effect involves a counterintuitive decrease of the probability of photon escape from the cavity with the increase of its escape intensity. Numerical simulations of the process were carried out using the basic Lindblad quantum equation for the Jaynes-Cummings model with thermal relaxation. A quasi-classical description of the bottleneck mechanism is presented, similar to the Zeno effect. The counterintuitive behavior described plays an important role in the description of the exchange of single photons in nanosystems and in molecular complexes converting solar energy in bacteria. PubDate: 2020-04-01

Abstract: The article presents a numerical scheme for solving the spatially nonhomogeneous coagulation problem. The problem is solved in a two-dimensional spatial region using unstructured grids. The finite-volume method is used with monotonicity-preserving limiters. The coagulation kernel in the Smoluchowski collision integrals is approximated by a low-rank decomposition, which reduces the machine time requirement. Reflection is reduced by introducing a perfectly matched layer on the spatial boundary. PubDate: 2020-04-01

Abstract: For a mathematical model with internal-diffusion kinetics and an oxidation-reduction reaction, we consider two inverse problems of determining the sorption isotherm or the redox reaction rate constant from the output dynamic curve. A numerical method for the solution of these inverse problems is proposed, computational results are reported, and its potential is investigated. PubDate: 2020-04-01

Abstract: Noble metals are commonly used as plasmon materials because of their high density of free electrons, but semiconductor materials are also becoming of interesting in this field because its electron density can be varied by doping. Metal nitrides can be an alternative to noble metals because of their low absorption loss and high electron density. Among others, TiN and ZrN seem to be most suitable as alternative plasmonic materials because their optical properties are dominated by conduction electrons near the plasmon frequency. There is the flame spray pyrolysis process, which is currently developed to produce such kind of nanoparticles. In this paper, based on an extension of the discrete sources method, the effect of the hydrodynamic Drude model of the quantum nonlocal effect on the optical characteristics of semiconductor nanoparticles is analyzed. The influence of accounting for the nonlocal effect (NLE) on the optical properties under spherical particles deformation has been investigated. It has been shown that accounting for the NLE leads to a plasmon resonance blue shift and a damping similar to noble metals. It was found that smaller particles demonstrate larger NLE influence than larger ones. Besides, the influence of polarization on the local and nonlocal responses of 3D nonspherical semiconductor particles has been investigated as well. Using simulation accounting for the nonlocal effect, it is shown that the extinction of a nonspherical ZrN particles exceeds that of a gold particle. PubDate: 2020-04-01

Abstract: The article describes the application of an original quasi-acoustic scheme for numerical solution of two-dimensional shallow-water equations with an uneven bottom. The numerical scheme partitions the linear reconstruction of the solution into small-perturbation blocks. The main advantage of the quasi-acoustic scheme is that it constructs the solution without using limiters, artificial regularizers, or any tuning parameters. The scheme is verified on a number of test and prototype problems. PubDate: 2020-04-01

Abstract: A nonhomogeneous generalization of the “attack–defense” game is considered. A linearization method is proposed to determine the best guaranteed outcome (BGO) of defense. The linearization utilizes a decomposition of the solution in a small parameter in the neighborhood of the trivial uniform distribution of defense resources. We show that the determination of correcting perturbations to the trivial uniform allocation of defense resources is reducible to a linear program. A prototype example to construct the correcting perturbations is considered. PubDate: 2020-04-01

Abstract: The article examines a mathematical model linking changes in GDP and in national debt. The model is based on a system of two linear ordinary differential equations (ODE) with variable coefficients. The model is approximate, but it describes the statistical data with good accuracy. The model coefficients are unknown. An algorithm is proposed to find the linear system coefficients from an approximate solution. A stable solution is obtained by the Tikhonov regularization method. Solving the forward and the inverse problem on prototype examples, we show that the time-dependent coefficients are reconstructed with good accuracy. The algorithm is applied to find and analyze the coefficients of a linear (ODE) system describing the dynamics of the national debt and GDP. The statistical data of several developed countries are applied to estimate the model coefficients and to analyze the dynamics of economic growth. PubDate: 2020-04-01

Abstract: We derive asymptotic Green’s functions for the Helmholtz equations describing the radiation from electric and magnetic dipoles located at an interface. The directional diagram of a distributed magnetic antenna is analyzed, formulas are derived for the phase shifts between different radiators intended for controlling the peak direction, an approximate formula is obtained for the angular width of the antenna main lobes. PubDate: 2020-04-01

Abstract: In this paper, we consider a time-fractional inverse problem in which the nonlinear boundary conditions contain an unknown function. A finite difference scheme will be proposed to solve numerically the inverse problem. This inverse problem is generally ill-posed. For this reason, we will employ the mollification regularization method with the generalized cross-validation criterion to find a stable solution. The stability and convergence of numerical solutions are investigated. Finally, some numerical examples are presented to illustrate the validity and effectiveness of the proposed method. PubDate: 2019-11-14

Abstract: A mathematical model is constructed for the first-wall cooling system in the tokamak reactor. A numerical analysis is carried out for the existing first-wall design for the future FNS (Fusion Neutron Source) reactor. PubDate: 2019-11-01

Abstract: We consider a problem that describes the biorthogonal adjoint system for the classical system of root functions for a loaded string with one free end in the presence of a multiple eigenvalue. We show that the complete and minimal subsystems isolated from the system of root functions constitute a basis in the presence of one or two associated functions. PubDate: 2019-11-01

Abstract: The article examines the kinetic equations of irreversible coagulation with a source of monomers and a sink of particles that exceed the maximum allowed size. Time-periodic solutions are known for the class of Brownian kernels. In this study, we analyze the effect of the monomer source intensity on the period and the amplitude of the particle concentration oscillations over time. The numerical results suggest that as the source intensity is increased, the oscillation amplitude increases while the oscillation period decreases, so that no qualitative changes are observed in the solution structure. A change in source intensity does not produce scaling of the model time and model concentrations of the particles per unit volume of the medium. PubDate: 2019-11-01

Abstract: The inverse problem of the determination of the unknown coefficient in an integro-differential equation is considered. Existence and uniqueness theorems are proved for the inverse problem. A numerical method for the determination of the unknown coefficient is proposed and substantiated. Numerical results illustrating the convergence of the method are reported. PubDate: 2019-11-01

Abstract: The development of cervical cancer cells from normal cells is caused by the human papilloma virus (HPV), and the progression can be described using a population model of the cells and free virus. We develop a mathematical model consisting of five compartments to describe the interactions between the human papilloma virus and four classes of epithelial and basal cells (susceptible, infected, precancerous, and cancerous) of cervix. In our mathematical model, we consider that the disease transmission rate from precancerous to cancerous cells is governed by a response function f(P) according to the risk and our cell immunity power which is dependent on the antibody genes p53 and pRb. So we have considered f(P) as three types of functions linear, Holling type II, and Holling type III. We analyze the local stability of the equilibrium points of each of the types in a comparative way and investigate analytically and numerically the parameters that play an important role in the progression towards the cervical cancer. Furthermore, we have taken some control strategies on the Holling type III functional response based on two types of drugs to eradicate the infected and cancer cell populations. PubDate: 2019-11-01

Abstract: A mathematical model is developed for the blood flow in the vessels connected with the hepatic portal vein. A satisfactory anatomical model of the venous vessels of unpaired organs in the abdominal cavity and in the portal vein basin is constructed and integrated into the general systemic circulation model. Computer experiments are carried out modeling redistribution of venous and arterial blood flows in the presence of portal hypertension in liver fibrosis. The hydrodynamic properties of the blood flow are investigated allowing for anatomical and artificial shuts and their effect on pressure reduction in the portal vein. The calculation results are consistent with clinical data. PubDate: 2019-11-01

Abstract: We consider the maximization of the welfare function in the process of expansion of the energy transmission network. Production and transportation costs as well as the utility of consumption are taken into consideration. The article presents previously developed methods for the calculation of optimal (or nearly optimal) transmission capacities, flows, and production volumes with a model of a network energy market. We also examine the dynamic problem of optimal expansion of the transmission system given that the demand and cost functions are exogenous for each time interval during the planning period, PubDate: 2019-11-01