2,164 research outputs found
Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
We consider the problem of the renormalization of the vacuum polarization in
a symmetry space-time with axial but not spherical symmetry, Schwarzschild
space-time threaded by an infinite straight cosmic string. Unlike previous
calculations, our framework to compute the renormalized vacuum polarization
does not rely on special properties of Legendre functions, but rather has been
developed in a way that we expect to be applicable to Kerr space-time
On some geometric features of the Kramer interior solution for a rotating perfect fluid
Geometric features (including convexity properties) of an exact interior
gravitational field due to a self-gravitating axisymmetric body of perfect
fluid in stationary, rigid rotation are studied. In spite of the seemingly
non-Newtonian features of the bounding surface for some rotation rates, we
show, by means of a detailed analysis of the three-dimensional spatial
geodesics, that the standard Newtonian convexity properties do hold. A central
role is played by a family of geodesics that are introduced here, and provide a
generalization of the Newtonian straight lines parallel to the axis of
rotation.Comment: LaTeX, 15 pages with 4 Poscript figures. To be published in Classical
and Quantum Gravit
Quasi-local contribution to the scalar self-force: Non-geodesic Motion
We extend our previous calculation of the quasi-local contribution to the
self-force on a scalar particle to general (not necessarily geodesic) motion in
a general spacetime. In addition to the general case and the case of a particle
at rest in a stationary spacetime, we consider as examples a particle held at
rest in Reissner-Nordstrom and Kerr-Newman space-times. This allows us to most
easily analyse the effect of non-geodesic motion on our previous results and
also allows for comparison to existing results for Schwarzschild spacetime.Comment: 11 pages, 1 figure, corrected typo in Eq. 2.
Bounds on minors of binary matrices
We prove an upper bound on sums of squares of minors of {+1, -1} matrices.
The bound is sharp for Hadamard matrices, a result due to de Launey and Levin
(2009), but our proof is simpler. We give several corollaries relevant to
minors of Hadamard matrices, and generalise a result of Turan on determinants
of random {+1,-1} matrices.Comment: 9 pages, 1 table. Typo corrected in v2. Two references and Theorem 2
added in v
On the ill-posed character of the Lorentz integral transform
An exact inversion formula for the Lorentz integral transform (LIT) is
provided together with the spectrum of the LIT kernel. The exponential increase
of the inverse Fourier transform of the LIT kernel entering the inversion
formula explains the ill-posed character of the LIT approach. Also the
continuous spectrum of the LIT kernel, which approaches zero points necessarily
to the same defect. A possible cure is discussed and numerically illustrated.Comment: 13 pages, 3 figure
MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems
CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric
systems of linear equations. When these methods are applied to an incompatible
system (that is, a singular symmetric least-squares problem), CG could break
down and SYMMLQ's solution could explode, while MINRES would give a
least-squares solution but not necessarily the minimum-length (pseudoinverse)
solution. This understanding motivates us to design a MINRES-like algorithm to
compute minimum-length solutions to singular symmetric systems.
MINRES uses QR factors of the tridiagonal matrix from the Lanczos process
(where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where
rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned
systems (singular or not), MINRES-QLP can give more accurate solutions than
MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better
estimates of the solution and residual norms, the matrix norm, and the
condition number.Comment: 26 pages, 6 figure
Features of gravitational waves in higher dimensions
There are several fundamental differences between four-dimensional and
higher-dimensional gravitational waves, namely in the so called braneworld
set-up. One of them is their asymptotic behavior within the Cauchy problem.
This study is connected with the so called Hadamard problem, which aims at the
question of Huygens principle validity. We investigate the effect of braneworld
scenarios on the character of propagation of gravitational waves on FRW
background.Comment: to appear in ERE09 proceeding
Transport in Transitory, Three-Dimensional, Liouville Flows
We derive an action-flux formula to compute the volumes of lobes quantifying
transport between past- and future-invariant Lagrangian coherent structures of
n-dimensional, transitory, globally Liouville flows. A transitory system is one
that is nonautonomous only on a compact time interval. This method requires
relatively little Lagrangian information about the codimension-one surfaces
bounding the lobes, relying only on the generalized actions of loops on the
lobe boundaries. These are easily computed since the vector fields are
autonomous before and after the time-dependent transition. Two examples in
three-dimensions are studied: a transitory ABC flow and a model of a
microdroplet moving through a microfluidic channel mixer. In both cases the
action-flux computations of transport are compared to those obtained using
Monte Carlo methods.Comment: 30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sy
Sommerfeld's image method in the calculation of van der Waals forces
We show how the image method can be used together with a recent method
developed by C. Eberlein and R. Zietal to obtain the dispersive van der Waals
interaction between an atom and a perfectly conducting surface of arbitrary
shape. We discuss in detail the case of an atom and a semi- infinite conducting
plane. In order to employ the above procedure to this problem it is necessary
to use the ingenious image method introduced by Sommerfeld more than one
century ago, which is a generalization of the standard procedure. Finally, we
briefly discuss other interesting situations that can also be treated by the
joint use of Sommerfeld's image technique and Eberlein-Zietal method.Comment: To appear in the proceedings of Conference on Quantum Field Theory
under the Influence of External Conditions (QFEXT11
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