Possible Alterations of Local Gravitational Field Inside a Superconductor

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high–Tc and classical low–Tc superconductors with respect to the gravity/superfluid interplay.     

Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes

We present a novel idea for a coupling of solutions of stochastic differential equations driven by Lévy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential contractivity of the semigroups associated with these solutions with respect to an appropriately chosen Kantorovich distance. As a corollary, we obtain exponential convergence rates in the total variation and standard $L^1$-Wasserstein distances.     

Lp solutions of backward stochastic differential equations with jumps

Given $p\in (1,2)$, we study ${\mathbb{L}}^p$ solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z)$-variables. We show that such a BSDEJ with $p$-integrable terminal data admits a unique ${\mathbb{L}}^p$ solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.     

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｒｄｅｒｔｏｇｅｔｒｉｄｏｆｔｈｅｒｅｓｔｒｉｃｔｉｏｎｔｏｄｉｓｃｒｅｔｅＢａｂｕｓｋａ＿Ｂｒｅｚｚｉ’ｓｃｏｎｄｉｔｉｏｎｓｉｎｒｅｓｅａｒｃｈｅｓｏｆｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔ (ＭＦＥ)ｍｅｔｈｏｄｓ,ｏｎｅｕｓｕａｌｌｙｕｓｅｓｔｈｅｓｔａｂｉｌｉｚｅｄＭＦＥｍｅｔｈｏｄｓｆｏｒｍａｔ[1] .Ｔｈｅｒｅａｒｅａｎｕｍｂｅｒｏｆｓｔａｂｉｌｉｚｅｄｍｅｔｈｏｄｓ (ｓｅｅ ,ｅ.ｇ .,Ｒｅｆｓ.[1- 7]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ) ,ｗｈｉｃｈｈ…     

Stability of the equilibrium of rotating drillstrings

The quasistatic stability of a rotating drillstring under longitudinal force and torque is analyzed. Constitutive equations are derived, and a technique to solve them is proposed. It is shown that the buckling mode of the drillstring is helical within a section subjected to compressive forces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 101–109, June 2006.     

On the application of the Wiener–Hopf technique to problems in dynamic elasticity

Many problems in linear elastodynamics, or dynamic fracture mechanics, can be reduced to Wiener–Hopf functional equations defined in a strip in a complex transform plane. Apart from a few special cases, the inherent coupling between shear and compressional body motions gives rise to coupled systems of equations, and so the resulting Wiener–Hopf kernels are of matrix form. The key step in the solution of a Wiener–Hopf equation, which is to decompose the kernel into a product of two factors with particular analyticity properties, can be accomplished explicitly for scalar kernels. However, apart from special matrices which yield commutative factorizations, no procedure has yet been devised to factorize exactly general matrix kernels.

This paper shall demonstrate, by way of example, that the Wiener–Hopf approximant matrix (WHAM) procedure for obtaining approximate factors of matrix kernels (recently introduced by the author in [SIAM J. Appl. Math. 57 (2) (1997) 541]) is applicable to the class of matrix kernels found in elasticity, and in particular to problems in QNDE. First, as a motivating example, the kernel arising in the model of diffraction of skew incident elastic waves on a semi-infinite crack in an isotropic elastic space is studied. This was first examined in a seminal work by Achenbach and Gautesen [J. Acoust. Soc. Am. 61 (2) (1977) 413] and here three methods are offered for deriving distinct non-commutative factorizations of the kernel. Second, the WHAM method is employed to factorize the matrix kernel arising in the problem of radiation into an elastic half-space with mixed boundary conditions on its face. Third, brief mention is made of kernel factorization related to the problems of flexural wave diffraction by a crack in a thin (Mindlin) plate, and body wave scattering by an interfacial crack.     

On the Solution of Mixed Problems in Linear Anti-plane Piezoelectricity

In the present paper we consider interior and exterior mixed boundary value problems of anti-plane shear in the static theory of linear piezoelectricity. Using the boundary integral equation method we reduce the problems to systems of singular integral equations with discontinuous coefficients to which the classical Nöether’s theorems on existence of the solution can be applied. This allows us to establish well-posedness results and to obtain integral solutions of the corresponding mixed boundary value problems for a rather general class of piezoelectric materials. Mathematics Subject Classifications (2000) 45E05, 45F15, 74F15.     

Dichotomy Spectrum for Nonautonomous Differential Equations

For nonautonomous linear differential equations x=A(t) x with locally integrable A: RR ^N×N the so-called dichotomy spectrum is investigated in this paper. As the closely related dichotomy spectrum for skew product flows with compact base (Sacker–Sell spectrum) our dichotomy spectrum for nonautonomous differential equations consists of at most N closed intervals, which in contrast to the Sacker–Sell spectrum may be unbounded. In the constant coefficients case these intervals reduce to the real parts of the eigenvalues of A. In any case the spectral intervals are associated with spectral manifolds comprising solutions with a common exponential growth rate. The main result of this paper is a spectral theorem which describes all possible forms of the dichotomy spectrum.     

Equations of motion for mechanical systems: A unified approach

This paper presents a unified framework from which emerge the Lagrange equations, the Gibbs-Appell Equations and the Generalized Inverse Equations for describing the motion of constrained mechanical systems. The unified approach extends the applicability of the first two approaches to systems where the constraints are non-linear functions of the generalized velocities and are not necessarily independent. Furthermore, the approach leads to the Explicit Gibbs-Appell Equations.