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 $Y^{p,q}$ and $L^{a,b,c}$. 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