A new analytical approach for calculation of white dwarfs characteristics that accounts for two important competing factors — axial rotation and Coulomb interparticle interactions, is proposed. The feature of our approach is simultaneous usage of differential and integral forms of equilibrium equation. In dimensionless form the differential equilibrium equation is strongly nonlinear inhomogeneous equation of the second order in partial derivatives with two dimensionless parameters — the relativistic parameter in stellar center $x_0$ and dimensionless angular velocity
The aim of this work is to study an inverse problem for a frictional contact model for locking material. The deformable body consists of electro-elastic-locking materials. Here, the locking character makes the solution belong to a convex set, the contact is presented in the form of multivalued normal compliance, and frictions are described with a sub-gradient of a locally Lipschitz mapping. We develop the variational formulation of the model by combining two hemivariational inequalities in a linked system. The existence and uniqueness of the solution are demonstrated utilizing recent co
Thermal processes of new technological methods of heat treatment (thermocyclic, electropulse) of metals and alloys are considered in the paper. Mathematical models of the temperature field in a moving tape and a wire with cyclically acting pulsed heat sources are considered. Based on these models, the formulation of inverse problems for homogeneous and inhomogeneous thermal conductivity equations is proposed. For each case (internal, external heat source or a combination), the appropriate method for solving the inverse problem is proposed. The integral condition of heat balance is used
A generalized spatial mathematical model of the multicomponent pollutant removal for a liquid treatment is proposed. Under the assumption of domination of convective processes over diffusive ones, the model considers an inverse influence of the determining factor (pollution concentration in water and sludge) on the media characteristics (porosity, diffusion) and takes into account the specified additional condition (overridden condition) for estimation of the unknown mass transfer coefficient of a small value.
Algorithms for the mathematical modeling of the direct current electrical prospecting in the 3D complex boundary geomedia are presented. Methods of normalization VES data for the interpretation accounting any surface relief are suggested. Effective algorithms of the direct problem solution for a horizontal layered halfspace are chosen. On the basis of the above the software for electrical prospecting modeling and VES data interpretation is developed.
In the paper the implementation of energy wave field analysis approach for developed informational model of the geological medium is considered. The solutions of seismic inverse problem are presented, which involves geophysical parameters obtaining of geological medium with the use of field seismic data. In order to obtain geological and geophysical environmental parameters the number of wave field transformations are being carried out, conventionally divided into primary and final part (interpretation).
The paper establishes existence and unique conditions for an inverse problem with an unknown source. The unknown source is a polynomial for а spatial variable with unknown coefficients depending on time.
A modeling problem of the process of liquid multi component decontamination by a spatial filter is considered, it takes into account the reverse influence of decisive factors (contamination concentrations of liquid and sediment) on characteristics (coefficient of porosity, diffusion) of the medium and gives us the possibility to determine small mass transfer coefficient under the conditions of prevailing of convective constituents over diffusive ones.
Purpose. The aim of the research is to develop a methodology for determining local earthquake mechanisms which are registered by a limited number of stations, using real records. Methodology. Methods of the inverse problem solving for determining earthquake parameters are based on the results obtained by direct problem of seismic wave propagation in an anisotropic media using the method of Thomson-Haskell.