31,827 research outputs found

### The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space,
we investigate the real geometric effects in real Minkowski space that are
induced by and associated with complex world-lines in complex Minkowski space.
It was already known, in a formal manner, that complex analytic curves in
complex Minkowski space induce shear-free null geodesic congruences. Here we
look at the direct geometric connections of the complex line and the real
structures. Among other items, we show, in particular, how a complex world-line
projects into the real Minkowski space in the form of a real shear-free null
geodesic congruence.Comment: 16 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

### 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

### Rotational correlation and dynamic heterogeneity in a kinetically constrained lattice gas

We study dynamical heterogeneity and glassy dynamics in a kinetically
constrained lattice gas model which has both translational and rotational
degrees of freedom. We find that the rotational diffusion constant tracks the
structural relaxation time as density is increased whereas the translational
diffusion constant exhibits a strong decoupling. We investigate distributions
of exchange and persistence times for both the rotational and translational
degrees of freedom and compare our results on the distributions of rotational
exchange times to recent single molecule studies.Comment: 7 pages, 5 figure

### Marking (1,2) Points of the Brownian Web and Applications

The Brownian web (BW), which developed from the work of Arratia and then
T\'{o}th and Werner, is a random collection of paths (with specified starting
points) in one plus one dimensional space-time that arises as the scaling limit
of the discrete web (DW) of coalescing simple random walks. Two recently
introduced extensions of the BW, the Brownian net (BN) constructed by Sun and
Swart, and the dynamical Brownian web (DyBW) proposed by Howitt and Warren, are
(or should be) scaling limits of corresponding discrete extensions of the DW --
the discrete net (DN) and the dynamical discrete web (DyDW). These discrete
extensions have a natural geometric structure in which the underlying Bernoulli
left or right "arrow" structure of the DW is extended by means of branching
(i.e., allowing left and right simultaneously) to construct the DN or by means
of switching (i.e., from left to right and vice-versa) to construct the DyDW.
In this paper we show that there is a similar structure in the continuum where
arrow direction is replaced by the left or right parity of the (1,2) space-time
points of the BW (points with one incoming path from the past and two outgoing
paths to the future, only one of which is a continuation of the incoming path).
We then provide a complete construction of the DyBW and an alternate
construction of the BN to that of Sun and Swart by proving that the switching
or branching can be implemented by a Poissonian marking of the (1,2) points.Comment: added 3 references to Sections 1, 2, 3; expanded explanations in
Subsections 7.3, 7.4, 7.

### 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

### Numerical design of streamlined tunnel walls for a two-dimensional transonic test

An analytical procedure is discussed for designing wall shapes for streamlined, nonporous, two-dimensional, transonic wind tunnels. It is based upon currently available 2-D inviscid transonic and boundary layer analysis computer programs. Predicted wall shapes are compared with experimental data obtained from the NASA Langley 6 by 19 inch Transonic Tunnel where the slotted walls were replaced by flexible nonporous walls. Comparisons are presented for the empty tunnel operating at a Mach number of 0.9 and for a supercritical test of an NACA 0012 airfoil at zero lift. Satisfactory agreement is obtained between the analytically and experimentally determined wall shapes

### The electrical conductivity of a collisionless magnetoplasma in a weakly turbulent magnetic field

Electrical conductivity of collisionless magnetoplasma in nearly turbulent magnetic fiel

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