424 research outputs found
Nonclassical spectral asymptotics and Dixmier traces: From circles to contact manifolds
We consider the spectral behavior and noncommutative geometry of commutators
, where is an operator of order with geometric origin and a
multiplication operator by a function. When is H\"{o}lder continuous, the
spectral asymptotics is governed by singularities. We study precise spectral
asymptotics through the computation of Dixmier traces; such computations have
only been considered in less singular settings. Even though a Weyl law fails
for these operators, and no pseudo-differential calculus is available,
variations of Connes' residue trace theorem and related integral formulas
continue to hold. On the circle, a large class of non-measurable Hankel
operators is obtained from H\"older continuous functions , displaying a wide
range of nonclassical spectral asymptotics beyond the Weyl law. The results
extend from Riemannian manifolds to contact manifolds and noncommutative tori.Comment: 40 page
An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates
The paper is devoted to the numerical solution of elastoplastic constitutive
initial value problems. An improved form of the implicit return-mapping scheme
for nonsmooth yield surfaces is proposed that systematically builds on a
subdifferential formulation of the flow rule. The main advantage of this
approach is that the treatment of singular points, such as apices or edges at
which the flow direction is multivalued involves only a uniquely defined set of
non-linear equations, similarly to smooth yield surfaces. This paper (PART I)
is focused on isotropic models containing: yield surfaces with one or two
apices (singular points) laying on the hydrostatic axis; plastic
pseudo-potentials that are independent of the Lode angle; nonlinear
isotropic hardening (optionally). It is shown that for some models the improved
integration scheme also enables to a priori decide about a type of the return
and investigate existence, uniqueness and semismoothness of discretized
constitutive operators in implicit form. Further, the semismooth Newton method
is introduced to solve incremental boundary-value problems. The paper also
contains numerical examples related to slope stability with available Matlab
implementation.Comment: 25 pages, 10 figure
Radiation from accelerated black holes in an anti-de Sitter universe
We study gravitational and electromagnetic radiation generated by uniformly
accelerated charged black holes in anti-de Sitter spacetime. This is described
by the C-metric exact solution of the Einstein-Maxwell equations with a
negative cosmological constant Lambda. We explicitly find and interpret the
pattern of radiation that characterizes the dependence of the fields on a null
direction from which the (timelike) conformal infinity is approached. This
directional pattern exhibits specific properties which are more complicated if
compared with recent analogous results obtained for asymptotic behavior of
fields near a de Sitter-like infinity. In particular, for large acceleration
the anti-de Sitter-like infinity is divided by Killing horizons into several
distinct domains with a different structure of principal null directions, in
which the patterns of radiation differ.Comment: 19 pages, 11 colour figures, submitted to Phys. Rev. D [Low quality
figures are included in this version because of arXive size restrictions. The
version with the standard quality figures is available at
http://utf.mff.cuni.cz/~podolsky/jppubl.htm.
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