The large-particle method in arbitrary nets and its application to the solution of problems in the aeroelasticity of a parachute

Modifications are introduced into the large-particle method to make it possible to use the method in arbitrary nonrectangular computing nets in the study of the flow of an ideal compressible gas over mobile thin permeable membranes. A problem in the aeroelasticity of a parachute is stated. An example is given of the solution of a problem in the stationary formulation for an axially symmetric parachute in the wake of a cylindrical leading body for supersonic flow.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 16–22     

Molecular orbital momentum distributions and binding energies for nitric oxide

Binding energy spectra of the valence electrons of the open shell molecule NO have been obtained up to 55 eV at azimuthal angles of 0° and 7° using binary (e, 2e) spectroscopy at an impact energy of 1200 eV. The momentum distribution has been obtained for the least tightly bound (unpaired) electron, removal of which leads to formation of the X ¹Σ⁺ ground state of NO⁺. Momentum distributions have also been measured at 21.0 and 40.5 eV. The measured momentum distributions are compared with several literature wavefunctions of varying complexity. They are found to be in excellent agreement with those calculated using the natural spin orbital wavefunctions of Kouba and Ohrn.     

Estimate for the Gradient of the Solution to the Neumann Problem for (p,q)-Nonlinear Equations

We consider the Neumann boundary value problem for the class of (p,q)-nonlinear elliptic equations. The numbers p and q, 2 ⩽ p < q, characterize the power growth with respect to the gradient of eigenvalues of the leading matrix of the equation. An a priori estimate for the maximum of the modulus of the gradient of the solution is obtained in a neighborhood of the boundary of the domain for some interval of p and q. Bibliography: 5 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 47–57.     

Cusp catastrophe in slowly varying equilibriums

Solutions of the equations v _x+v ³?tv+x=0 and v _xx=v ³? tv+x, which describe the nucleation of domain walls occurring in the neighborhood of cusps of slowly varying equilibriums, are analyzed. Examples related to the diffusion in smoothly inhomogeneous media are considered.     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.