Related papers: Nonlinear Two-Dimensional Green's Function in Smec…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
The equilibrium texture of nematic shells is studied as a function of their thickness. For ultrathin shells the ground state has four short 1/2 disclination lines but, as the thickness of the film increases, a three dimensional escaped…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…
In a disordered medium with Kerr-type nonlinearity, the transmitted speckle pattern was predicted to become unstable, as a result of the positive feedback between the intensity fluctuations and the nonlinear dependence of the local…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We have calculated the phase diagrams of one--component fluids made of five types of biaxial particles differing in their cross sections. The orientation of the principal particle axis is fixed in space, while the second axis is allowed to…
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect…
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity…
In this paper we derive a line tension model for dislocations in 3d starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the amplitude of the Burgers vectors (proportional to the…
The capture of a soft spherical particle by a rectangular slit leads to a non-monotonic pressure-flow rate relation at low Reynolds number. In the presence of the trapped particle the flow-induced deformations focus the streamlines and…
The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with model integral of collisions in the form $…
In this paper the inverse scattering problem for the nonstationary Dirac-type system on the whole plane was considered. A nonlinear evolution sytem of equation related to nonstationary Dirac-type system is introduced and the solviblity of…
We compile a list of 2-D and axisymmetric Green's functions for isotropic full and half spaces, to complement our letter "Linear elasticity of incompressible solids". We also extend the isotropic exactly incompressible linear theory from…
In the present work the mathematical apparatus necessary for solving of second Stokes problem is developed. Second Stokes problem is the problem about behavior of rarefied gas filling half-space. A plane, limiting half-space, makes…
A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such…
The forced time harmonic response of a spatiotemporally-modulated elastic beam of finite length with light damping is derived using a novel Green's function approach. Closed-form solutions are found that highlight unique mode coupling…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…