14,452 research outputs found
Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we
derive inequalities that involve a real parameter and join the eigenvalues of
the Dirac operator with curvature terms. The discussion of these inequalities
yields vanishing theorems for the kernel of the Dirac operator and lower
bounds for the spectrum of if the curvature satisfies certain conditions.Comment: Latex2e, 14p
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
General Relativistic Scalar Field Models in the Large
For a class of scalar fields including the massless Klein-Gordon field the
general relativistic hyperboloidal initial value problems are equivalent in a
certain sense. By using this equivalence and conformal techniques it is proven
that the hyperboloidal initial value problem for those scalar fields has an
unique solution which is weakly asymptotically flat. For data sufficiently
close to data for flat spacetime there exist a smooth future null infinity and
a regular future timelike infinity.Comment: 22 pages, latex, AGG 1
Do Magnetic Fields Prevent Hydrogen from Accreting onto Cool Metal-line White Dwarf Stars?
It is generally assumed that metals detected in the spectra of a few cool
white dwarfs cannot be of primordial origin and must be accreted from the
interstellar medium. However, the observed abundances of hydrogen, which should
also be accreted from the interstellar medium, are lower than expected from
metal accretion. Magnetic fields are thought to be the reason for this
discrepancy. We have therefore obtained circular polarization spectra of the
helium-rich white dwarfs GD40 and L745-46A, which both show strong metal lines
as well as hydrogen. Whereas L745-46A might have a magnetic field of about
-6900 G, which is about two times the field strength of 3000G necessary to
repell hydrogen at the Alfen radius, only an upper limit for the field strength
of GD40 of 4000G (with 99% confidence) can be set which is far off the minimum
field strength of 144000G to repell hydrogen.Comment: 4 LaTeX pages, 4 eps figures, to appear in the proceedings of the
14th European Workshop on White Dwarfs, eds. D. Koester and S. Moehler, ASP
Conf. Serie
Quasi-geostrophic approximation of anelastic convection
The onset of convection in a rotating cylindrical annulus with parallel ends filled with a compressible fluid is studied in the anelastic approximation. Thermal Rossby waves propagating in the azimuthal direction are found as solutions. The analogy to the case of Boussinesq convection in the presence of conical end surfaces of the annular region is emphasised. As in the latter case, the results can be applied as an approximation for the description of the onset of anelastic convection in rotating spherical fluid shells. Reasonable agreement with three-dimensional numerical results published by Jones, Kuzanyan & Mitchell (J. Fluid Mech., vol. 634, 2009, pp. 291–319) for the latter problem is found. As in those results, the location of the onset of convection shifts outwards from the tangent cylinder with increasing number Nρof density scale heights until it reaches the equatorial boundary. A new result is that at a much higher number Nρ the onset location returns to the interior of the fluid shell
Baroclinically-driven flows and dynamo action in rotating spherical fluid shells
The dynamics of stably stratified stellar radiative zones is of considerable interest due to the availability of increasingly detailed observations of Solar and stellar interiors. This article reports the first non-axisymmetric and time-dependent simulations of flows of anelastic fluids driven by baroclinic torques in stably stratified rotating spherical shells – a system serving as an elemental model of a stellar radiative zone. With increasing baroclinicity a sequence of bifurcations from simpler to more complex flows is found in which some of the available symmetries of the problem are broken subsequently. The poloidal component of the flow grows relative to the dominant toroidal component with increasing baroclinicity. The possibility of magnetic field generation thus arises and this paper proceeds to provide some indications for self-sustained dynamo action in baroclinically-driven flows. We speculate that magnetic fields in stably stratified stellar interiors are thus not necessarily of fossil origin as it is often assumed
An Iterative Procedure for the Estimation of Drift and Diffusion Coefficients of Langevin Processes
A general method is proposed which allows one to estimate drift and diffusion
coefficients of a stochastic process governed by a Langevin equation. It
extends a previously devised approach [R. Friedrich et al., Physics Letters A
271, 217 (2000)], which requires sufficiently high sampling rates. The analysis
is based on an iterative procedure minimizing the Kullback-Leibler distance
between measured and estimated two time joint probability distributions of the
process.Comment: 4 pages, 5 figure
Gaussian Subordination for the Beurling-Selberg Extremal Problem
We determine extremal entire functions for the problem of majorizing,
minorizing, and approximating the Gaussian function by
entire functions of exponential type. This leads to the solution of analogous
extremal problems for a wide class of even functions that includes most of the
previously known examples (for instance \cite{CV2}, \cite{CV3}, \cite{GV} and
\cite{Lit}), plus a variety of new interesting functions such as
for ; \,, for
;\, ; and \,, for . Further applications to number theory include optimal
approximations of theta functions by trigonometric polynomials and optimal
bounds for certain Hilbert-type inequalities related to the discrete
Hardy-Littlewood-Sobolev inequality in dimension one
- …