Open Repository of Keldysh Institute of Applied Mathematics of RAS
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Mathematical modelling of the cluster targets for femtosecondlaser-cluster-driven experiments
No full textAbstract:
The interaction of femtosecond ultra-intense laser pulses with clusters increases absorption of the incident laser light compared to the interaction with solid targets and leads to enhanced generation of different quantum beams with unique parameters. Future investigations of such interaction urgently need detailed modeling and optimization of cluster parameters, for instance, in order to obtain the clusters with desired size, or some specific spatial configuration of the target etc. A numerical model of gas-cluster targets production by the nozzle flows of gases and binary mixtures is presented. Some previous results of the model utilization are summarized, and some new results are given. Techniques of experimental verification of the numerical results are discussed.Note:
Research direction:Mathematical modelling in actual problems of science and technic
On the software development using “client-server” technology for models of flows in porous media containing gas-hydrate depositions
No full textAbstract:
The work concerns with algorithms and data structures put on the basis of the code, intended for modeling flows in porous media containing gas hydrates, i.e. low-molecular compounds of natural gas (methane et al.) and water. At low temperature and certain pressure conditions gashydrates exist in a solid phase occupying part of the pore space. The сode «HYDRAT1D» solves the fluid dynamics equations in the thawed zone and piezoconductivity medium with gas hydrate inclusions. It accounts for a complete set of essential physical effects and implements calculations in 1D planar and cylindrical geometries. The code is written in JavaScript (JS) on the basis of the JS interpreter (the V8 'engine»). Work with the code 'HYDRAT1D' is organized according to the principles of computer architecture 'client-server' which makes the code convenient in remote calculations, cloud technologies etc.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Dependence on Ionization Degree and Relativistic Effects in Electron Binding Energies in Free Atoms and Ions
No full textAbstract:
The electron binding energy analysis proposed before for atoms is applied to positive free ions. As a result the binding energy self-similar dependence on atomic number and ionization degree of ions is shown up. The revealed scaling enables to compare electron binding energies in a large number of atoms and ions, manifests the relativistic spin-orbit interaction effect in heavy atoms and can be used for the new data verification. Оne can represent the orbital energies in filled shells of arbitrary many-electron atom or ion through two universal functions. The polynomial fit approximation of the last ones is constructed to estimate the binding energies in ions. The estimation can be used as initial value in more perfect computation and for rough calculation of the ionization cross section of many-electron atoms and ions by other particles.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Сells’ bypassing algorithm for characteristic methods of transport equation solving
No full textAbstract:
When solving the transport equation by the interpolation-characteristic method on an unstructured grid, the problem of an economical algorithm for queuing solvable cells arises. This paper describes the implementation of this algorithm based on the topological sorting of the oriented graph. Therefore, the proposed algorithm is the most economical of all possible ones. A parallel implementation of the bypass algorithm is presented in the case when the computational grid is divided into separate areas stored on different nodes of the computational cluster. There are grids for which the interpolation-characteristic method leads to an unsolvable problem. Proposed method makes it possible to diagnose such grids.Note:
Research direction:Programming, parallel computing, multimedi
Compressible plasma flows in the QSPA in the presence of strong longitudinal magnetic field
No full textAbstract:
Compressible plasma flows in the quasi-stationary plasma accelerator are considered in the presence of strong longitudinal magnetic field on the basis of model of radiation magnetic gas dynamics. Formation of compressible flows occurs in the accelerator channel with specific geometry of electrodes on condition that the internal electrode is shorter than the external one. Strong longitudinal magnetic field leads to a number of features in stream, which should be taken into account for development of new approach to solve the problem of the controlled thermonuclear fusion on the basis of plasma accelerator as an injector for perspective thermonuclear installations.Note:
Research direction:Mathematical modelling in actual problems of science and technic
On the Vlasov-Maxwell-Einstein equation and its non-relativistic and weakly relativistic analogues
No full textAbstract:
In the present paper we consider the Lagrangian of gravity of general theory of relativity together with
Lagrangian electromagnetism. From it derived equations of Vlasov type in general, non-relativistic and weakly relativistic limits. Expressions for the resulting corrections in the Poisson equation are proposed, which can contribute to the effective action of dark matter and dark energy.Note:
Research direction:Mathematical problems and theory of numerical method
Safety issues in the exploitation of sedimentary basins of hydrocarbon deposits
No full textAbstract:
Numerical simulation of fluid motion in the formation of hydrocarbon deposits allowed us to investigate complex self-oscillating regimes of this process. This paper presents the results of computational experiments for these models, conducted on the basis of empirical data for a number of regions, and made on this basis the conclusion about their characteristic properties.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Analysis of the contribution of the ISON network in solving problems of monitoring space debris on geosynchronous orbits
No full textAbstract:
The article describes the current state of the scientific network of optical instruments for astrometric and photometric observations. The analysis of results of observational network in 2017, including the comparison with other Russian observing cooperation, is given. We demonstrate that the ISON network continues to make a notable contribution to the task of maintaining the catalog of the precise orbits of large GEO-objects.Note:
Research direction:Mathematical modelling in actual problems of science and technic
On limit points of Bernoulli distribution algebras
No full textAbstract:
We consider algebras of Bernoulli distributions, i. e. sets of distributions that are closed under transformations defined by substituting independent random variables for variables of a Boolean function from a given system. We establish that unless the transforming functions are unary the set of algebra’s limits point is either empty, one-element, or at least countable.Note:
Research direction:Mathematical problems and theory of numerical method
An approach to modeling of the secondary radiation-induced effects in complex technical objects
No full textAbstract:
The technique of the calculation of initial data for computing the secondary radiation-induced effects in complex technical objects being under radiation is developed. The method is based on the multidimensional approximation of the results of the statistical modeling of the interaction between radiation end matter to a difference grid destined for numerical solving the thermodynamic equations. Various types of the approximation and methods of their implementation are formulated. Applicability of the types is determined by the available a priori information on the function to be approximated and geometrical properties of an object. Examples of the multidimensional approximation in discussed problems by use of the neural networks are given.Note:
Research direction:Mathematical modelling in actual problems of science and technic