36,194 research outputs found
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
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
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
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
CR Structures and Asymptotically Flat Space-Times
We discuss the unique existence, arising by analogy to that in algebraically
special space-times, of a CR structure realized on null infinity for any
asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page
Two-Dimensional Scaling Limits via Marked Nonsimple Loops
We postulate the existence of a natural Poissonian marking of the double
(touching) points of SLE(6) and hence of the related continuum nonsimple loop
process that describes macroscopic cluster boundaries in 2D critical
percolation. We explain how these marked loops should yield continuum versions
of near-critical percolation, dynamical percolation, minimal spanning trees and
related plane filling curves, and invasion percolation. We show that this
yields for some of the continuum objects a conformal covariance property that
generalizes the conformal invariance of critical systems. It is an open problem
to rigorously construct the continuum objects and to prove that they are indeed
the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure
A study of defect structures with the field ion microscope Semiannual report, Sep. 1, 1966 - Feb. 28, 1967
Defect structures in ion emission images of metals and stress distributions under imaging conditions studied with field ion microscop
Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences
In classical electromagnetic theory, one formally defines the complex dipole
moment (the electric plus 'i' magnetic dipole) and then computes (and defines)
the complex center of charge by transforming to a complex frame where the
complex dipole moment vanishes. Analogously in asymptotically flat space-times
it has been shown that one can determine the complex center of mass by
transforming the complex gravitational dipole (mass dipole plus 'i' angular
momentum) (via an asymptotic tetrad trasnformation) to a frame where the
complex dipole vanishes. We apply this procedure to such space-times which are
asymptotically stationary or static, and observe that the calculations can be
performed exactly, without any use of the approximation schemes which must be
employed in general. In particular, we are able to exactly calculate complex
center of mass and charge world-lines for such space-times, and - as a special
case - when these two complex world-lines coincide, we recover the Dirac value
of the gyromagnetic ratio.Comment: 11 page
Realistic spin glasses below eight dimensions: a highly disordered view
By connecting realistic spin glass models at low temperature to the highly
disordered model at zero temperature, we argue that ordinary Edwards-Anderson
spin glasses below eight dimensions have at most a single pair of physically
relevant pure states at nonzero low temperature. Less likely scenarios that
evade this conclusion are also discussed.Comment: 18 pages (RevTeX; 1 figure; to appear in Physical Review E
- …