11,114 research outputs found
Killing spinors in supergravity with 4-fluxes
We study the spinorial Killing equation of supergravity involving a torsion
3-form \T as well as a flux 4-form \F. In dimension seven, we construct
explicit families of compact solutions out of 3-Sasakian geometries, nearly
parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The
constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We
investigate the constraint \T \cdot \Psi = 0, too, and show that it singles
out a very special choice of numerical parameters in the Killing equation,
which can also be justified geometrically
Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets
Arguably the most important problem in quantitative finance is to understand
the nature of stochastic processes that underlie market dynamics. One aspect of
the solution to this problem involves determining characteristics of the
distribution of fluctuations in returns. Empirical studies conducted over the
last decade have reported that they arenon-Gaussian, scale in time, and have
power-law(or fat) tails. However, because they use sliding interval methods of
analysis, these studies implicitly assume that the underlying process has
stationary increments. We explicitly show that this assumption is not valid for
the Euro-Dollar exchange rate between 1999-2004. In addition, we find that
fluctuations in returns of the exchange rate are uncorrelated and scale as
power-laws for certain time intervals during each day. This behavior is
consistent with a diffusive process with a diffusion coefficient that depends
both on the time and the price change. Within scaling regions, we find that
sliding interval methods can generate fat-tailed distributions as an artifact,
and that the type of scaling reported in many previous studies does not exist.Comment: 12 pages, 4 figure
Generalized vortex-model for the inverse cascade of two-dimensional turbulence
We generalize Kirchhoff's point vortex model of two-dimensional fluid motion
to a rotor model which exhibits an inverse cascade by the formation of rotor
clusters. A rotor is composed of two vortices with like-signed circulations
glued together by an overdamped spring. The model is motivated by a treatment
of the vorticity equation representing the vorticity field as a superposition
of vortices with elliptic Gaussian shapes of variable widths, augmented by a
suitable forcing mechanism. The rotor model opens up the way to discuss the
energy transport in the inverse cascade on the basis of dynamical systems
theory.Comment: 14 pages, 21 figure
On the existence of Killing vector fields
In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra
High resolution frequency selective photochemistry of phycobilisomes at cryogenic temperatures
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
This is the first in a series of articles on the numerical solution of
Friedrich's conformal field equations for Einstein's theory of gravity. We will
discuss in this paper why one should be interested in applying the conformal
method to physical problems and why there is good hope that this might even be
a good idea from the numerical point of view. We describe in detail the
derivation of the conformal field equations in the spinor formalism which we
use for the implementation of the equations, and present all the equations as a
reference for future work. Finally, we discuss the implications of the
assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2
Three-Dimensional MOS Process Development
A novel MOS technology for three-dimensional integration of electronic circuits on silicon substrates was developed. Selective epitaxial growth and epitaxial lateral overgrowth of monocrystalline silicon over oxidized silicon were employed to create locally restricted silicon-on-insulator device islands. Thin gate oxides were discovered to deteriorate in ambients typically used for selective epitaxial growth. Conditions of general applicability to silicon epitaxy systems were determined under which this deterioration was greatly reduced. Selective epitaxial growth needed to be carried out at low temperatures. However, crystalline defects increase as deposition temperatures are decreased. An exact dependence between the residual moisture content in epitaxial growth ambients, deposition pressure, and deposition temperature was determined which is also generally applicable to silicon epitaxy systems. The dependences of growth rates and growth rate uniformity on loading, temperature, flow rates, gas composition, and masking oxide thickness were investigated for a pancake type epitaxy reactor. A conceptual model was discussed attempting to describe the effects peculiar to selective epitaxial growth. The newly developed processing steps were assembled to fabricate three dimensional silicon-on-insulator capacitors. These capacitors were electrically evaluated. Surface state densities were in the order of 1O11cm-2 eV-1 and therefore within the range of applicability for a practical CMOS process. Oxidized polysilicon gates were overgrown with silicon by epitaxial lateral overgrowth. The epitaxial silicon was planarized and source and drain regions were formed above the polysilicon gates in Silicon-on-insulator material. The modulation of the source-drain current by bias changes of the buried gate was demonstrated
Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators
We present a matrix technique to obtain the spectrum and the analytical index
of some elliptic operators defined on compact Riemannian manifolds. The method
uses matrix representations of the derivative which yield exact values for the
derivative of a trigonometric polynomial. These matrices can be used to find
the exact spectrum of an elliptic operator in particular cases and in general,
to give insight into the properties of the solution of the spectral problem. As
examples, the analytical index and the eigenvalues of the Dirac operator on the
torus and on the sphere are obtained and as an application of this technique,
the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page
3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints
We present three-dimensional simulations of Einstein equations implementing a
symmetric hyperbolic system of equations with dynamical lapse. The numerical
implementation makes use of techniques that guarantee linear numerical
stability for the associated initial-boundary value problem. The code is first
tested with a gauge wave solution, where rather larger amplitudes and for
significantly longer times are obtained with respect to other state of the art
implementations. Additionally, by minimizing a suitably defined energy for the
constraints in terms of free constraint-functions in the formulation one can
dynamically single out preferred values of these functions for the problem at
hand. We apply the technique to fully three-dimensional simulations of a
stationary black hole spacetime with excision of the singularity, considerably
extending the lifetime of the simulations.Comment: 21 pages. To appear in PR
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