1,699 research outputs found
On the structure of Finsler and areal spaces
We study underlying geometric structures for integral variational
functionals, depending on submanifolds of a given manifold. Applications
include (first order) variational functionals of Finsler and areal geometries
with integrand the Hilbert 1-form, and admit immediate extensions to
higher-order functionals.Comment: 8 pages, Proceedings for AGMP-8, to be published in the special issue
of Miskolc Mathematical Note
A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
We discuss a deformation of Sasakian structure in the presence of totally
skew-symmetric torsion by introducing odd dimensional manifolds whose metric
cones are K\"ahler with torsion. It is shown that such a geometry inherits
similar properties to those of Sasakian geometry. As an example of them, we
present an explicit expression of local metrics and see how Sasakian structure
is deformed by the presence of torsion. We also demonstrate that our example of
the metrics admits the existence of hidden symmetries described by non-trivial
odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using
these metrics as an {\it ansatz}, we construct exact solutions in five
dimensional minimal (un-)gauged supergravity and eleven dimensional
supergravity. Finally, we discuss the global structures of the solutions and
obtain regular metrics on compact manifolds in five dimensions, which give
natural generalizations of Sasaki--Einstein manifolds and
. We also discuss regular metrics on non-compact manifolds in eleven
dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra
Dynamic Procedure for Filtered Gyrokinetic Simulations
Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are
investigated as interesting candidates to decrease the computational cost. A
dynamic procedure is implemented in the GENE code, allowing for dynamic
optimization of the free parameters of the LES models (setting the amplitudes
of dissipative terms). Employing such LES methods, one recovers the free energy
and heat flux spectra obtained from highly resolved Direct Numerical
Simulations (DNS). Systematic comparisons are performed for different values of
the temperature gradient and magnetic shear, parameters which are of prime
importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the
degree of anisotropy of the problem, that can vary with parameters, can be
adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation
(GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic
solvers.Comment: 10 pages, 10 figures, submitted to Physics of Plasma
Generalized hidden symmetries and the Kerr-Sen black hole
We elaborate on basic properties of generalized Killing-Yano tensors which
naturally extend Killing-Yano symmetry in the presence of skew-symmetric
torsion. In particular, we discuss their relationship to Killing tensors and
the separability of various field equations. We further demonstrate that the
Kerr-Sen black hole spacetime of heterotic string theory, as well as its
generalization to all dimensions, possesses a generalized closed conformal
Killing-Yano 2-form with respect to a torsion identified with the 3-form
occuring naturally in the theory. Such a 2-form is responsible for complete
integrability of geodesic motion as well as for separability of the scalar and
Dirac equations in these spacetimes.Comment: 33 pages, no figure
Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs
We describe and analyse the parallel implementation of a novel domain decomposition preconditioner for the fast iterative solution of linear systems of algebraic equations arising from the discretization of elliptic partial differential equations (PDEs) in three dimensions. In previous theoretical work, this preconditioner has been proved to be optimal for symmetric positive-definite (SPD) linear systems.
In this paper, we provide details of our three-dimensional parallel implementation and demonstrate that the technique may be generalized to the solution of non-symmetric algebraic systems, such as those arising when convection-diffusion problems are discretized using either Galerkin or stabilized finite-element methods (FEMs). Furthermore, we illustrate the potential of the preconditioner for use within an adaptive finite-element framework by successfully solving convection-dominated problems on locally, rather than globally, refined meshes
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