Filtration in inhomogeneous curved strata with a certain class permeability

Two-dimensional steady filtration flows of a homogeneous incompressible liquid (obeying D'Arcy's law) in inhomogeneous curved strata with variable permeability is studied. A novel extensive class of permeabilities for which the pressure head function is written in explicit form is obtained and studied. The pressure head function is given in explicit form for flows from sources situated at any point of the stratum.     

Characteristic matrix of a periodically inhomogeneous layer

We propose an analytic representation of the characteristic matrix of a periodically inhomogeneous layer; the characteristic matrix of the homogenized medium is defined and it is shown that the structure of characteristic matrix of transversely isotropic media coincides with the structure of the characteristic matrix of a layered inhomogeneous isotropic medium.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 177–181, 1987.     

Positively curved surfaces with no tangent support plane

We discuss a characterization of positively curved surfaces with the property that, at each point, the tangent plane to is not a support plane for the entire surface. Such positively curved surfaces with no tangent support plane necessarily have non-empty boundary, and any portion which has convex hull equal to the convex hull of we call a generating set. This set plays a key role in constructing examples. We give various examples among which there is an embedded topological disk with smallest possible generating set.

     

Ricci flow of negatively curved incomplete surfaces

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.     

Indentation of an incompressible inhomogeneous layer by a rigid circular indenter

This work deals with an incompressible inhomogeneous layer bondedto a rigid substrate and indented without friction by a rigidcircular indenter. The corresponding mixed boundary-value problemof elasticity is reduced to equivalent dual integral equations.It is shown that the pliability function in these equationsmay be found from a system of nonlinear differential equationsand that its behaviour is peculiar when the elastic medium isincompressible. A novel technique taking into account this peculiarityis developed in order to reduce the dual integral equationsto Fredholm integral equations of the second kind with symmetricstrictly coercive operators. For a homogeneous layer and a flatindenter, the structure of the Fredholm integral equations permitsan approximate analytical solution which is very accurate forany layer thickness. For an indenter of three-dimensional profile,leading asymptotic terms of the solution are derived in thecase of a thin inhomogeneous layer.     

Unsteady spreading of a thin layer of viscous liquid over a curved surface

The unsteady spreading of a thin layer of an incompressible viscous liquid over an impermeable curved surface, which occurs under the action of the gravity force, is considered. The solution of the boundary-value problem which arises reduces to solving a Cauchy problem for equations with a small number of independent variables.     

Ends of negatively curved surfaces in Euclidean space

We examine the geometry of a complete, negatively curved surface isometrically embedded in ${\mathbb{R}^3}$ . We are especially interested in the behavior of the ends of the surface and its limit set at infinity. Various constructions are developed, and a classification theorem is obtained, showing that every possible end type for a topologically finite surface with at least one bowl end arises, as well as all infinite type surfaces with a single nonannular end. Some other examples are given with oddly behaved bowl ends.     

Sound field of a source moving in an inhomogeneous layer on a homogeneous halfspace

Equations are suggested in the present paper for the amplitudes and instantaneous frequencies of sound waves generated by a moving source. The equations are derived by means of the Space-Time Ray (STR) method and by the two-scale expansion method (the method of horizontal rays and vertical modes).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 35–48, 1986.     

Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces

In this paper we obtain the equivalence of the Gromov hyperbolicity between an extensive class of complete Riemannian surfaces with pinched negative curvature and certain kind of simple graphs, whose edges have length 1, constructed following an easy triangular design of geodesics in the surface.     

A mathematical model of mechanical contact of bodies across a thin inhomogeneous layer

We obtain the generalized conditions of mechanical contact of bodies that model a thin inhomogeneous isotropic layer situated between them. The technique is based on the application of averaging of the equilibrium equations for the layer and the assumption of a cubic distribution of displacements over its thickness. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 107–109.     

Solutions with transition layer and spike in an inhomogeneous phase transition model

We consider the following singularly perturbed elliptic problem

     

Thermoelasticity of a Thermosensitive Hollow Anisotropic Sphere with a Thin Foreign Inclusion

By using generalized functions, we obtain the set of thermoelasticity equations for a hollow thermosensitive, transversally isotropic sphere with a thin foreign inclusion. By approximating the thermoelastic characteristics of the basic material and the material of the inclusion by piecewise-constant functions, we deduce a differential equation with coefficients of the type of impulse functions to determine a radial displacement. We carry out the numerical analysis of the temperature and level of thermal stresses in a system made of graphites.     

Propagation of sound pulses in a homogeneous layer under an inhomogeneous half space

We consider the propagation of two-dimensional sound pulses in a homogeneous layer ?y ₁?y?0. It is bounded by a plane stratified inhomogeneous half spacey?0 on one side and a perfectly reflecting boundary on the other. A line source is situated in the layer. The boundary condition isφ=0 or?φ/?y=0 aty=?y ₁, whereφ is the acoustic velocity potential. We suppose that the velocity of wave propagationc is given byc ^?2=p?qe ^?αy iny>0, wherep, q, α are real and positive andp>q. It is equal to C′ in the layer where C′ is a constant. The method of dual integral transformation is used and the velocity potentialφ is obtained after using asymptotic expressions for some of the functions which are in the integrand. We obtain the incident, reflected, multiply-reflected and diffracted pulses in the layer.     

Scattering of sound by an inhomogeneous thermoelastic spherical layer

The diffraction of sound by a radially layered isotropic thermoelastic spherical shell is considered. The system of equations for small perturbations of a hollow thermoelastic sphere is reduced to a system of ordinary differential equations, the boundary-value problem for which is solved by a spline-collocation method. Expressions are obtained which describe the wave fields outside the spherical layer. The results of calculations of the frequency and angular dependences of the amplitude of the scattered sound field in the far zone are presented.     

Stability of laminar boundary layer along longitudinally curved walls

Summary To a former work [1] the perturbations are determined in the whole flow field. This also yields more exact eigenvalues.

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Zusammenfassung Zu einer früheren Arbeit [1] werden die Störungen im ganzen Strömungsbereich errechnet. Damit ergaben sich auch genauere Eigenwerte.