2,248 research outputs found
APPROXIMATE METHODS OF SOLUTION OF SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS OF DIFFRACTION
В работе для численного решения сингулярного интегро-дифференциального уравне-
ния задачи дифракции используется метод механических квадратур. Доказано, что
этот метод устойчив относительно малых возмущений элементов аппроксимирую-
щих уравнений.For numerical solution of singular integro-differential equations of diffraction it is used the method of
mechanical quadratures. It is proved that this method is stable under small perturbations of approximating
equations.55-5
Non-Local Boundary Conditions in Euclidean Quantum Gravity
Non-local boundary conditions for Euclidean quantum gravity are proposed,
consisting of an integro-differential boundary operator acting on metric
perturbations. In this case, the operator P on metric perturbations is of
Laplace type, subject to non-local boundary conditions; by contrast, its
adjoint is the sum of a Laplacian and of a singular Green operator, subject to
local boundary conditions. Self-adjointness of the boundary-value problem is
correctly formulated by looking at Dirichlet-type and Neumann-type realizations
of the operator P, following recent results in the literature. The set of
non-local boundary conditions for perturbative modes of the gravitational field
is written in general form on the Euclidean four-ball. For a particular choice
of the non-local boundary operator, explicit formulae for the boundary-value
problem are obtained in terms of a finite number of unknown functions, but
subject to some consistency conditions. Among the related issues, the problem
arises of whether non-local symmetries exist in Euclidean quantum gravity.Comment: 23 pages, plain Tex. The revised version is much longer, and new
original calculations are presented in section
Stability of a vacuum nonsingular black hole
This is the first of series of papers in which we investigate stability of
the spherically symmetric space-time with de Sitter center. Geometry,
asymptotically Schwarzschild for large and asymptotically de Sitter as
, describes a vacuum nonsingular black hole for and
particle-like self-gravitating structure for where a critical
value depends on the scale of the symmetry restoration to de Sitter
group in the origin. In this paper we address the question of stability of a
vacuum non-singular black hole with de Sitter center to external perturbations.
We specify first two types of geometries with and without changes of topology.
Then we derive the general equations for an arbitrary density profile and show
that in the whole range of the mass parameter objects described by
geometries with de Sitter center remain stable under axial perturbations. In
the case of the polar perturbations we find criteria of stability and study in
detail the case of the density profile
where is the density of de Sitter vacuum at the center, is de
Sitter radius and is the Schwarzschild radius.Comment: 18 pages, 8 figures, submitted to "Classical and Quantum Gravity
Formation of singularities on the surface of a liquid metal in a strong electric field
The nonlinear dynamics of the free surface of an ideal conducting liquid in a
strong external electric field is studied. It is establish that the equations
of motion for such a liquid can be solved in the approximation in which the
surface deviates from a plane by small angles. This makes it possible to show
that on an initially smooth surface for almost any initial conditions points
with an infinite curvature corresponding to branch points of the root type can
form in a finite time.Comment: 14 page
Kinetic vs. Thermal-Field-Theory Approach to Cosmological Perturbations
A closed set of equations for the evolution of linear perturbations of
homogeneous, isotropic cosmological models can be obtained in various ways. The
simplest approach is to assume a macroscopic equation of state, e.g.\ that of a
perfect fluid. For a more refined description of the early universe, a
microscopic treatment is required. The purpose of this paper is to compare the
approach based on classical kinetic theory to the more recent
thermal-field-theory approach. It is shown that in the high-temperature limit
the latter describes cosmological perturbations supported by collisionless,
massless matter, wherein it is equivalent to the kinetic theory approach. The
dependence of the perturbations in a system of a collisionless gas and a
perfect fluid on the initial data is discussed in some detail. All singular and
regular solutions are found analytically.Comment: 31 pages, 10 figures (uu encoded ps-file appended), REVTEX 3.0, DESY
94-040 / TUW-93-2
New Results in Heat-Kernel Asymptotics on Manifolds with Boundary
A review is presented of some recent progress in spectral geometry on
manifolds with boundary: local boundary-value problems where the boundary
operator includes the effect of tangential derivatives; application of
conformal variations and other functorial methods to the evaluation of
heat-kernel coefficients; conditions for strong ellipticity of the
boundary-value problem; fourth-order operators on manifolds with boundary;
non-local boundary conditions in Euclidean quantum gravity. Many deep
developments in physics and mathematics are therefore in sight.Comment: 31 pages, plain Tex. Paper prepared for the Fourth Workshop on
Quantum Field Theory under the Influence of External Conditions, Leipzig,
September 199
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Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body
A static mixed boundary value problem (BVP) of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off function approach, the corresponding localized parametrix is constructed to reduce the nonlinear BVP to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations
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