61 research outputs found

### Progressive internal gravity waves with bounded upper surface climbing a triangular obstacle

In this paper we discuss a theoretical model for the interfacial profiles of
progressive non-linear waves which result from introducing a triangular
obstacle, of finite height, attached to the bottom below the flow of a
stratified, ideal, two layer fluid, bounded from above by a rigid boundary. The
derived equations are solved by using a nonlinear perturbation method. The
dependence of the interfacial profile on the triangular obstacle size, as well
as its dependence on some flow parameters, such as the ratios of depths and
densities of the two fluids, have been studied

### Numerical computation of real or complex elliptic integrals

Algorithms for numerical computation of symmetric elliptic integrals of all
three kinds are improved in several ways and extended to complex values of the
variables (with some restrictions in the case of the integral of the third
kind). Numerical check values, consistency checks, and relations to Legendre's
integrals and Bulirsch's integrals are included

### Bianchi type II,III and V diagonal Einstein metrics re-visited

We present, for both minkowskian and euclidean signatures, short derivations
of the diagonal Einstein metrics for Bianchi type II, III and V. For the first
two cases we show the integrability of the geodesic flow while for the third
case a somewhat unusual bifurcation phenomenon takes place: for minkowskian
signature elliptic functions are essential in the metric while for euclidean
signature only elementary functions appear

### Photon Spectrum Produced by the Late Decay of a Cosmic Neutrino Background

We obtain the photon spectrum induced by a cosmic background of unstable
neutrinos. We study the spectrum in a variety of cosmological scenarios and
also we allow for the neutrinos having a momentum distribution (only a critical
matter dominated universe and neutrinos at rest have been considered until
now). Our results can be helpful when extracting bounds on neutrino electric
and magnetic moments from cosmic photon background observations.Comment: RevTex, 14 pages, 3 figures; minor changes, references added. To
appear in Phys. Rev.

### Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity

The bending angle of light is a central quantity in the theory of
gravitational lensing. We develop an analytical perturbation framework for
calculating the bending angle of light rays lensed by a Schwarzschild black
hole. Using a perturbation parameter given in terms of the gravitational radius
of the black hole and the light ray's impact parameter, we determine an
invariant series for the strong-deflection bending angle that extends beyond
the standard logarithmic deflection term used in the literature. In the
process, we discovered an improvement to the standard logarithmic deflection
term. Our perturbation framework is also used to derive as a consistency check,
the recently found weak deflection bending angle series. We also reformulate
the latter series in terms of a more natural invariant perturbation parameter,
one that smoothly transitions between the weak and strong deflection series. We
then compare our invariant strong deflection bending-angle series with the
numerically integrated exact formal bending angle expression, and find less
than 1% discrepancy for light rays as far out as twice the critical impact
parameter. The paper concludes by showing that the strong and weak deflection
bending angle series together provide an approximation that is within 1% of the
exact bending angle value for light rays traversing anywhere between the photon
sphere and infinity.Comment: 22 pages, 5 figure

### Exact time-dependent correlation functions for the symmetric exclusion process with open boundary

As a simple model for single-file diffusion of hard core particles we
investigate the one-dimensional symmetric exclusion process. We consider an
open semi-infinite system where one end is coupled to an external reservoir of
constant density $\rho^\ast$ and which initially is in an non-equilibrium state
with bulk density $\rho_0$. We calculate the exact time-dependent two-point
density correlation function $C_{k,l}(t)\equiv -$ and the mean and variance of the integrated average net flux
of particles $N(t)-N(0)$ that have entered (or left) the system up to time $t$.
We find that the boundary region of the semi-infinite relaxing system is in a
state similar to the bulk state of a finite stationary system driven by a
boundary gradient. The symmetric exclusion model provides a rare example where
such behavior can be proved rigorously on the level of equal-time two-point
correlation functions. Some implications for the relaxational dynamics of
entangled polymers and for single-file diffusion in colloidal systems are
discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference
17 adde

### Spectral curves and the mass of hyperbolic monopoles

The moduli spaces of hyperbolic monopoles are naturally fibred by the
monopole mass, and this leads to a nontrivial mass dependence of the
holomorphic data (spectral curves, rational maps, holomorphic spheres)
associated to hyperbolic multi-monopoles. In this paper, we obtain an explicit
description of this dependence for general hyperbolic monopoles of magnetic
charge two. In addition, we show how to compute the monopole mass of higher
charge spectral curves with tetrahedral and octahedral symmetries. Spectral
curves of euclidean monopoles are recovered from our results via an
infinite-mass limit.Comment: 43 pages, LaTeX, 3 figure

### Gravitational corrections in supersymmetric gauge theory and matrix models

Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are
obtained from topological string amplitudes. We show how they are recovered in
matrix model computations. This provides a test of the proposal by Dijkgraaf
and Vafa beyond the planar limit. Both, matrix model and topological string
theory, are used to check a conjecture of Nekrasov concerning these
gravitational couplings in Seiberg-Witten theory. Our analysis is performed for
those gauge theories which are related to the cubic matrix model, i.e. pure
SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic
superpotential. We outline the computation of the topological amplitudes for
the local Calabi-Yau manifolds which are relevant for these two cases.Comment: 27 pages, one eps figur

### Holomorphic Anomaly in Gauge Theories and Matrix Models

We use the holomorphic anomaly equation to solve the gravitational
corrections to Seiberg-Witten theory and a two-cut matrix model, which is
related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local
Calabi-Yau manifold. In both cases we construct propagators that give a
recursive solution in the genus modulo a holomorphic ambiguity. In the case of
Seiberg-Witten theory the gravitational corrections can be expressed in closed
form as quasimodular functions of Gamma(2). In the matrix model we fix the
holomorphic ambiguity up to genus two. The latter result establishes the
Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the
matrix model at fixed genus in closed form in terms of generalized
hypergeometric functions.Comment: 34 pages, 2 eps figures, expansion at the monopole point corrected
and interpreted, and references adde

### Corrections to the apparent value of the cosmological constant due to local inhomogeneities

Supernovae observations strongly support the presence of a cosmological
constant, but its value, which we will call apparent, is normally determined
assuming that the Universe can be accurately described by a homogeneous model.
Even in the presence of a cosmological constant we cannot exclude nevertheless
the presence of a small local inhomogeneity which could affect the apparent
value of the cosmological constant. Neglecting the presence of the
inhomogeneity can in fact introduce a systematic misinterpretation of
cosmological data, leading to the distinction between an apparent and true
value of the cosmological constant. We establish the theoretical framework to
calculate the corrections to the apparent value of the cosmological constant by
modeling the local inhomogeneity with a $\Lambda LTB$ solution. Our assumption
to be at the center of a spherically symmetric inhomogeneous matter
distribution correspond to effectively calculate the monopole contribution of
the large scale inhomogeneities surrounding us, which we expect to be the
dominant one, because of other observations supporting a high level of isotropy
of the Universe around us.
By performing a local Taylor expansion we analyze the number of independent
degrees of freedom which determine the local shape of the inhomogeneity, and
consider the issue of central smoothness, showing how the same correction can
correspond to different inhomogeneity profiles. Contrary to previous attempts
to fit data using large void models our approach is quite general. The
correction to the apparent value of the cosmological constant is in fact
present for local inhomogeneities of any size, and should always be taken
appropriately into account both theoretically and observationally.Comment: 16 pages,new sections added analyzing central smoothness and accuracy
of the Taylor expansion approach, Accepted for publication by JCAP. An essay
based on this paper received honorable mention in the 2011 Essay Context of
the Gravity Research Foundatio

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