Global weak solutions to the cometary flow equation with a self-generated electric field

We study the Cauchy problem of a cometary flow equation with a self-generated electric field. This kinetic model originates from the theory of astrophysical plasmas and can be viewed as a perturbation, by a wave-particle collision operator, of the classical Vlasov-Poisson system. By asymptotic methods in kinetic theory, global existence of nonnegative weak solutions to the Cauchy problem in three space variables is established for bounded initial data having finite second order velocity moments.     

Substantiation of the field functional method as applied to scattering by a doubly periodic magnetodielectric structure

A new method based on volume integro-differential equations is examined as applied to scattering by doubly periodic magnetodielectric structures. The uniqueness and boundedness of the solution to the problem is proved.     

The propagation of weak concentration discontinuities in the isothermal flow of a multicomponent mixture in a porous medium with phase transitions

It is shown that for the general case of a system of non-linear equations, describing multicomponent isothermal flow in a porous medium with phase transitions, as in hyperbolic systems, weak concentration discontinuities propagate with finite velocities, which are determined by solving an eigenvalue problem. If the seeping phases are incompressible and there are no phase transitions, the results obtained for weak discontinuities transfer into the well-known formulae for the Buckley – Leverett model. The results are demonstrated for the case of two-component seepage with phase transitions.     

A self-consistent field method applied to the dynamics of viscous suspensions

A method for the approximate solution of the problem of many bodies of spherical form in a viscous fluid is developed in the Stokes approximation. Using a purely hydrodynamic approach, based on the use of the concept of a self-consistent field, the classical boundary value problem is reduced to a formal procedure for solving a linear system of algebraic equations in the tensor coefficients, which occur in the solution obtained for the velocity field and pressure of the liquid. A procedure for the approximate solution of this system of equations is constructed for the case of dilute suspensions, when the ratio of the size of the dispersed particles to the characteristic distance between them is a small parameter. Finally, the initial boundary value problem is reduced to solving a recurrent system of equations, in which each subsequent approximation for all the required quantities depends solely on the previous approximations. The system of recurrent equations obtained can be solved analytically in any specified approximation with respect to a small parameter. It is shown that this system of equations contains in itself all possible physical formulations of the problems, and, within the frameworks of the mathematical procedure constructed, they are distinguished solely by a set of specified and required functions. The practical possibilities of the method are in no way limited by the number of dispersed particles in the fluid.     

A difference scheme with anti-diffusion terms to improve the computation of contact discontinuities and the study of weak discontinuities in compressible flow

The investigation of Mach reflection formed after the impingement of a weak plane shock wave on a wedge with shock Mach number M_s near 1, is still an open problem[12]. It's difficult for shock tube experiments with interferometer to detect contact discontinuities if it is too weak; also difficult to catch with due accuracy the transition condition between Mach reflection and regular reflection. The interest to this phenomenon is continuing, especially for weak shocks, because there was systematic discrepancy between simplified three shock theory of von Neumann [8] and shock tube results [15] which was named by G. Birkhoff as “von Neumann Paradox on three shock theory” [18].In 1972, K.O.Friedrichs called for more computational efforts on this problem. Recently it is known that for weak impinging shocks it's still difficult to get contact discontinuities and curved Mach stem with satisfactory accuracy. Recent numerical computation sometimes even fails to show reflected shock wave[6]. These explain why von Neumann paradox of the three shock theory in case of weak discontinuities is still a problem of interesting [9,12,14]. In this paper, on one hand, we investigate the numerical methods for Euler's equation for compressible inviscid flow, aiming at improving the computation of contact discontinuities, on the other hand, a methodology is suggested to correctly plot flow data from the massive information in storage. On this basis, all the reflected shock wave , contact discontinuities and the curved Mach stem are determined. We get Mach reflection under the condition when over-simplified shock theory predicts no such configuration[5].     

Conformal transformation method as applied to finding the current density distribution and induced magnetic field in a strip conductor with a rectangular cut

Given a conductor with a rectangular cut, the problem of determining the direct current distribution and the induced magnetic field in the conductor is solved with applications to the testing of chip conductors. An analytical expression for the current distribution is found assuming that the corners are rounded. The magnetic field induced by the given current is calculated.     

Existence and uniqueness of weak solutions for a system applied to image decomposition

In this paper, we prove the existence and uniqueness of weak solutions for a singular evolutionary system, which is deduced from a model for image decomposition combining staircase reduction and texture extraction. The main method we used is p-Laplace regularization. The numerical experimental result shows the efficiency of this kind of model.     

Error estimates for the Galerkin method as applied to time-dependent equations

A projection method is studied as applied to the Cauchy problem for an operator-differential equation with a non-self-adjoint operator. The operator is assumed to be sufficiently smooth. The linear spans of eigenelements of a self-adjoint operator are used as projection subspaces. New asymptotic estimates for the convergence rate of approximate solutions and their derivatives are obtained. The method is applied to initial-boundary value problems for parabolic equations.     

Electric field near the surface of a plasma with an arbitrary degree of degeneracy as a response to an external alternating electric field

Theoretical and Mathematical Physics - We analytically solve a boundary value problem for the behavior $$($$ oscillation $$)$$ of an electron plasma with an arbitrary degree of degeneracy of the...     

An iterative method for computing the anomalous electric field in a conducting medium

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 162–171, Izd. Moskovskogo Universiteta, Moscow, 1990.     

Mortar method for matching grids in a mixed scheme as applied to the biharmonic equation

Nitsche’s mortar method for matching grids in the Hermann-Miyoshi mixed scheme for the biharmonic equation is considered. A two-parameter mortar problem is constructed and analyzed. Existence and uniqueness theorems are proved under certain constraints on the parameters. The norm of the difference between the solutions to the mortar and original problems is estimated. The convergence rates are the same as in the Hermann-Miyoshi scheme on matching grids.     

The smoothing effect of a simultaneous directions parallel method as applied to Poisson problems

By using local Fourier analysis, a simultaneous directions parallel method, which is a particular instance of the parallel fractional step algorithm, is shown to possess smoothing effects when applied to Poisson problems. The specific smoothing factor is determined and the expected factor values are found to be consistent with those obtained. The simultaneous directions approach is an advantageous alternative to other existing smoothers in the multigrid environment. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Assessment of errors in the averaging method as applied to linear viscoelastic dynamics

Errors of the averaging method are assessed as applied to the oscillations of a undimensional, linear viscoelastic oscillator.M. V. Lomonosov State University, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 943–944, September–October, 1972.     

Modified discrete source method as applied to the simulation of flows over a periodically irregular surface and a body of revolution

The incompressible flow over a stationary periodically irregular surface and a compact body of revolution is computed by applying a modified discrete source method. The method is tested as applied to the flow over a stationary sphere. Numerical results are presented for flows over a sinusoidal surface, a cycloidal surface, a spheroid, a Chebyshev particle, an “analytical” cylinder, and a half ball.     

On the applicability of the Adomian method to initial value problems with discontinuities

In this paper we extend our results of L. Casasús, W. Al-Hayani [The decomposition method for ordinary differential equations with discontinuities, Appl. Math. Comput. 131 (2002) 245–251] to initial value problems with several types of discontinuities, giving relevant examples of linear and nonlinear cases.     

A perturbation method applied to the buckling of a compressed elastica

We consider the problem of carrying out an asymptotic analysis for the phenomenon of bifurcation which occurs at critical values of an axial force applied to an elastic column. In the present setting a discontinuous coefficient precludes the possibility of carrying out the usual asymptotic analysis. The problem is overcome via a nonlinear change of independent variables.