The Interference Slow Wave in a Poroacoustic Biot Layer

It is shown that in a poroacoustic Biot layer placed inside an elastic medium, for any parameters of the model an interference slow wave exists. For low frequencies, the wave has very weak attenuation and the polarization of it coincides with the direction of the layer. This is evidence for the possibility of mapping subtle collectors inside an elastic medium in crosshole measurements. Bibliography: 7 titles.     

Winning controllers and regions in competitive nonlinear dynamic games with two qualitative objectives and uncertain information

The Liapunov technique has been introduced in differential games in a sequence of works over the last decade. We discuss application of this technique to the interface between two competitive semi-games, each with different qualitative objective. The feedback information for controllers is provided from designed, analytically integrable state predictors with reduced dynamics, which considerably shortens the computing time. The case is illustrated on the scenario of target reaching before being intercepted, and intercepting before target is reached.Deceased.     

A problem with free boundary for the Navier-Stokes equations. II

Institute of Mathematics and Cybernetics, Lithuanian Academy of Sciences. Vilnius University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 2, pp. 337–350, April–June, 1991.     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Fluorides of ruthenium and chromium: Theoretical studies

The electronic and structural characteristics of CrF₅, CrF₄, RuF₅ and RuF₄ were studied. Ab initio (SCF-CI) calculations were performed with different structures and spin states for each complex. The favored conformation always corresponds to the highest multiplicity: doublet for CrF₅ in D_3h, triplet for CrF₄ in T_d, quadruplet for RuF₅ in C_4v and quintuplet for RuF₄ in D_4h symmetry.     

The Kosterlitz-Thouless model in Perovskite superconductors

Il Nuovo Cimento D - The applicability of the Kosterlitz-Thouless theory to HTSC is examined. The model initially presented in its general lines for bidimensional systems is then applied to...     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

A Parabolic Spline on a Nonuniform Grid

We obtain estimates for errors of interpolation on a nonuniform grid for a parabolic nonperiodic spline of defect 1.     

Elasticity in nanocrystalline Nd2Fe14B+αFe magnetic composites

The dynamic Young modulus (E) of magnetic Nd₂Fe₁₄B+αFe nanocomposites is investigated with mechanical spectroscopy techniques (vibrating reed configuration, f≈1.5 kHz <10⁻⁶). Reduced values of E are obtained (88–152 GPa) as compared with that predicted by the rule of mixtures for the composite (164 GPa). Three contributions to this reduction are briefly discussed: a large volume fraction of the specimen with grain boundary like structure; internal pores, resulting from the high cooling rate during processing (10⁶ K/min) and magneto-mechanical effects. Even when porosity is identified as the principal cause of modulus reduction, magnetic effects are also detected.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.