196 research outputs found
Nonlinear focusing of Terahertz laser beam using layered superconductor
We theoretically study the propagation of a Terahertz (THz) Gaussian beam
through a thin sample of layered superconductor. We consider the beam axis and
the superconducting layers to be perpendicular to the sample interface, while
the electric field in the beam is perpendicular to the layers. We show that, in
such a geometry, the Josephson current between the superconducting layers
supports lensing of the beam instead of divergence on the Rayleigh range.
Moreover, due to the nonlinearity, the focal length and waist of the
transmitted beam depend on the incident beam intensity. These dependences
demonstrate nontrivial hysteresis behavior that can be observed in experiments
with THz lasers
Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability
This paper concerns the explicit construction of extremal Kaehler metrics on
total spaces of projective bundles, which have been studied in many places. We
present a unified approach, motivated by the theory of hamiltonian 2-forms (as
introduced and studied in previous papers in the series) but this paper is
largely independent of that theory.
We obtain a characterization, on a large family of projective bundles, of
those `admissible' Kaehler classes (i.e., the ones compatible with the bundle
structure in a way we make precise) which contain an extremal Kaehler metric.
In many cases, such as on geometrically ruled surfaces, every Kaehler class is
admissible. In particular, our results complete the classification of extremal
Kaehler metrics on geometrically ruled surfaces, answering several
long-standing questions.
We also find that our characterization agrees with a notion of K-stability
for admissible Kaehler classes. Our examples and nonexistence results therefore
provide a fertile testing ground for the rapidly developing theory of stability
for projective varieties, and we discuss some of the ramifications. In
particular we obtain examples of projective varieties which are destabilized by
a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely
self-contained; partially replaces and extends math.DG/050151
Modeling Framework for Integrated, Model-based Development of Product-Service Systems
Product-service systems (PSS) are seen as the 21st-century solution for direct delivery of value to customers under the requirements of high availability, quality, and reduced risks. With mutual benefits for customers, manufacturers, service providers and often the environment, PSS represent a promising approach to sustainable development. This paper addresses the integrated development of product-service systems consisting of physical products/systems and services and proposes an integrated modeling framework that utilizes the Systems Modeling Language. A use case from Lenze, a German automation company, demonstrates the applicability of the integrated modeling framework in practice
K\"ahlerian Twistor Spinors
On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural
analogue of twistor spinors on Riemannian spin manifolds. They are defined as
sections in the kernel of a first order differential operator adapted to the
K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study
K\"ahlerian twistor spinors and give a complete description of compact K\"ahler
manifolds of constant scalar curvature admitting such spinors. As in the
Riemannian case, the existence of K\"ahlerian twistor spinors is related to the
lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.
A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues
It is proved that a compact Kahler manifold whose Ricci tensor has two
distinct, constant, non-negative eigenvalues is locally the product of two
Kahler-Einstein manifolds. A stronger result is established for the case of
Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant
eigenvalues of the Ricci tensor are shown to exist in various situations: there
are homogeneous examples of any complex dimension n > 1, if one eigenvalue is
negative and the other positive or zero, and of any complex dimension n > 2, if
the both eigenvalues are negative; there are non-homogeneous examples of
complex dimension 2, if one of the eigenvalues is zero. The problem of
existence of Kahler metrics whose Ricci tensor has two distinct, constant
eigenvalues is related to the celebrated (still open) Goldberg conjecture.
Consequently, the irreducible homogeneous examples with negative eigenvalues
give rise to complete, Einstein, strictly almost Kahler metrics of any even
real dimension greater than 4.Comment: 18 pages; final version; accepted for publication in International
Journal of Mathematic
Scaling of the GROMACS 4.6 molecular dynamics code on SuperMUC.
Here we report on the performance of GROMACS 4.6 on the SuperMUC cluster at the Leibniz Rechenzentrum in Garching. We carried out benchmarks with three biomolecular systems consisting of eighty thousand to twelve million atoms in a strong scaling test each. The twelve million atom simulation system reached a performance of 49 nanoseconds per day on 32,768 cores
Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples
Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a
hyper-Kahler space are discussed. These are one parameter deformations of the
metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191.
Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the
Eguchi-Hanson gravitational instantons are found, together with other examples.
By considering the Apostolov-Salamon theorem math.DG/0303197, we construct a
new example that, still being a T^2 bundle over hyper-Kahler, represents a non
trivial two parameter deformation of the metrics studied in hep-th/0108191. We
then review the Spin(7) metrics arising from a T^3 bundle over a hyper-Kahler
and we find two parameter deformation of such spaces as well. We show that if
the hyper-Kahler base satisfies certain properties, a non trivial three
parameter deformations is also possible. The relation between these spaces with
the half-flat structures and almost G_2 holonomy spaces is briefly discussed.Comment: 27 pages. Typos corrected. Accepted for publication in
Commun.Math.Phy
Memory functions and Correlations in Additive Binary Markov Chains
A theory of additive Markov chains with long-range memory, proposed earlier
in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical
properties of long-range correlated systems. The convenient characteristics of
such systems, a memory function, and its relation to the correlation properties
of the systems are examined. Various methods for finding the memory function
via the correlation function are proposed. The inverse problem (calculation of
the correlation function by means of the prescribed memory function) is also
solved. This is demonstrated for the analytically solvable model of the system
with a step-wise memory function.Comment: 11 pages, 5 figure
Stable bundles on hypercomplex surfaces
A hypercomplex manifold is a manifold equipped with three complex structures
I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact
smooth manifold equipped with a hypercomplex structure, and E be a vector
bundle on M. We show that the moduli space of anti-self-dual connections on E
is also hypercomplex, and admits a strong HKT metric. We also study manifolds
with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of
strong HKT-structures that have opposite torsion. In the language of Hitchin's
and Gualtieri's generalized complex geometry, (4,4)-manifolds are called
``generalized hyperkaehler manifolds''. We show that the moduli space of
anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a
(4,4)-structure.Comment: 17 pages. Version 3.0: reference adde
Symmetries of supergravity black holes
We investigate Killing tensors for various black hole solutions of
supergravity theories. Rotating black holes of an ungauged theory, toroidally
compactified heterotic supergravity, with NUT parameters and two U(1) gauge
fields are constructed. If both charges are set equal, then the solutions
simplify, and then there are concise expressions for rank-2 conformal
Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of
a conformally related metric that possesses a separability structure. We
directly verify the separation of the Hamilton-Jacobi equation on this
conformally related metric, and of the null Hamilton-Jacobi and massless
Klein-Gordon equations on the "physical" metric. Similar results are found for
more general solutions; we mainly focus on those with certain charge
combinations equal in gauged supergravity, but also consider some other
solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte
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