33,307 research outputs found
Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum
The purpose of this work is to return, with a new observation and rather
unconventional point of view, to the study of asymptotically flat solutions of
Einstein equations. The essential observation is that from a given
asymptotically flat space-time with a given Bondi shear, one can find (by
integrating a partial differential equation) a class of asymptotically
shear-free (but, in general, twistiing) null geodesic congruences. The class is
uniquely given up to the arbitrary choice of a complex analytic world-line in a
four-parameter complex space. Surprisingly this parameter space turns out to be
the H-space that is associated with the real physical space-time under
consideration. The main development in this work is the demonstration of how
this complex world-line can be made both unique and also given a physical
meaning. More specifically by forcing or requiring a certain term in the
asymptotic Weyl tensor to vanish, the world-line is uniquely determined and
becomes (by several arguments) identified as the `complex center-of-mass'.
Roughly, its imaginary part becomes identified with the intrinsic spin-angular
momentum while the real part yields the orbital angular momentum.Comment: 26 pages, authors were relisted alphabeticall
The Large Footprints of H-Space on Asymptotically Flat Space-Times
We show that certain structures defined on the complex four dimensional space
known as H-Space have considerable relevance for its closely associated
asymptotically flat real physical space-time. More specifically for every
complex analytic curve on the H-space there is an asymptotically shear-free
null geodesic congruence in the physical space-time. There are specific
geometric structures that allow this world-line to be chosen in a unique
canonical fashion giving it physical meaning and significance.Comment: 7 page
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Shear-free Null Quasi-Spherical Spacetimes
The residual gauge freedom within the null quasi-spherical coordinate
condition is studied, for spacetimes admitting an expanding, shear-free null
foliation. The freedom consists of a boost and rotation at each coordinate
sphere, corresponding to a specification of inertial frame at each sphere.
Explicit formulae involving arbitrary functions of two variables are obtained
for the accelerated Minkowski, Schwarzschild, and Robinson-Trautman spacetimes.
These examples will be useful as test metrics in numerical relativity.Comment: 20 pages, revte
Error estimation in the histogram Monte Carlo method
We examine the sources of error in the histogram reweighting method for Monte
Carlo data analysis. We demonstrate that, in addition to the standard
statistical error which has been studied elsewhere, there are two other sources
of error, one arising through correlations in the reweighted samples, and one
arising from the finite range of energies sampled by a simulation of finite
length. We demonstrate that while the former correction is usually negligible
by comparison with statistical fluctuations, the latter may not be, and give
criteria for judging the range of validity of histogram extrapolations based on
the size of this latter correction.Comment: 7 pages including 3 postscript figures, typeset in LaTeX using the
RevTeX macro packag
Interacting epidemics and coinfection on contact networks
The spread of certain diseases can be promoted, in some cases substantially,
by prior infection with another disease. One example is that of HIV, whose
immunosuppressant effects significantly increase the chances of infection with
other pathogens. Such coinfection processes, when combined with nontrivial
structure in the contact networks over which diseases spread, can lead to
complex patterns of epidemiological behavior. Here we consider a mathematical
model of two diseases spreading through a single population, where infection
with one disease is dependent on prior infection with the other. We solve
exactly for the sizes of the outbreaks of both diseases in the limit of large
population size, along with the complete phase diagram of the system. Among
other things, we use our model to demonstrate how diseases can be controlled
not only by reducing the rate of their spread, but also by reducing the spread
of other infections upon which they depend.Comment: 9 pages, 3 figure
A user's manual for the Electromagnetic Surface Patch code: ESP version 3
This report serves as a user's manual for Version III of the Electromagnetic Surface Patch Code or ESP code. ESP is user-oriented, based on the method of moments (MM) for treating geometries consisting of an interconnection of thin wires and perfectly conducting polygonal plates. Wire/plate junctions must be about 0.1 lambda or more from any plate edge. Several plates may intersect along a common edge. Excitation may be by either a delta-gap voltage generator or by a plane wave. The thin wires may have finite conductivity and also may contain lumped loads. The code computes most of the usual quantities of interest such as current distribution, input impedance, radiation efficiency, mutual coupling, far zone gain patterns (both polarizations) and radar-cross-section (both/cross polarizations)
Characterizing the structure of small-world networks
We give exact relations which are valid for small-world networks (SWN's) with
a general `degree distribution', i.e the distribution of nearest-neighbor
connections. For the original SWN model, we illustrate how these exact
relations can be used to obtain approximations for the corresponding basic
probability distribution. In the limit of large system sizes and small
disorder, we use numerical studies to obtain a functional fit for this
distribution. Finally, we obtain the scaling properties for the mean-square
displacement of a random walker, which are determined by the scaling behavior
of the underlying SWN
Statistics of Certain Models of Evolution
In a recent paper, Newman surveys the literature on power law spectra in
evolution, self-organised criticality and presents a model of his own to arrive
at a conclusion that self-organised criticality is not necessary for evolution.
Not only did he miss a key model (Ecolab) that has a clear self-organised
critical mechanism, but also Newman's model exhibits the same mechanism that
gives rise to power law behaviour as does Ecolab. Newman's model is, in fact, a
``mean field'' approximation of a self-organised critical system. In this
paper, I have also implemented Newman's model using the Ecolab software,
removing the restriction that the number of species remains constant. It turns
out that the requirement of constant species number is non-trivial, leading to
a global coupling between species that is similar in effect to the species
interactions seen in Ecolab. In fact, the model must self-organise to a state
where the long time average of speciations balances that of the extinctions,
otherwise the system either collapses or explodes. In view of this, Newman's
model does not provide the hoped-for counter example to the presence of
self-organised criticality in evolution, but does provide a simple, almost
analytic model that can used to understand more intricate models such as
Ecolab.Comment: accepted in Phys Rev E.; RevTeX; See
http://parallel.hpc.unsw.edu.au/rks/ecolab.html for more informatio
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