1,687 research outputs found
Can one detect a non-smooth null infinity?
It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order is
proposed. By contrast, in the smooth version the effects are of order .
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra
Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input
We investigate with the help of analytical and numerical methods the reaction
A+A->A on a one-dimensional lattice opened at one end and with an input of
particles at the other end. We show that if the diffusion rates to the left and
to the right are equal, for large x, the particle concentration c(x) behaves
like As/x (x measures the distance to the input end). If the diffusion rate in
the direction pointing away from the source is larger than the one
corresponding to the opposite direction the particle concentration behaves like
Aa/sqrt(x). The constants As and Aa are independent of the input and the two
coagulation rates. The universality of Aa comes as a surprise since in the
asymmetric case the system has a massive spectrum.Comment: 27 pages, LaTeX, including three postscript figures, to appear in J.
Stat. Phy
Ісламський фактор в міжнародних економічних відносинах: приклад ЄС і Турції
В роботі представлена спроба цілісного вивчення впливу культурних, соціальних, економічних і політичних факторів на процеси взаємовідносин Туреччини і ЄС, що дозволяє надати більш об'ємне й глибоке уявлення про соціально-політичні процеси в Туреччині і ЄС в контексті їх еволюції. Дана оцінка сучасного стану мусульманської діаспори в країнах ЄС з подальшою систематизацією даних. Зроблена авторська порівняльна характеристика процесів євроінтеграції України (у якої є свій «ісламський» фактор) і Туреччини і її систематизаці
Generalized Painleve-Gullstrand descriptions of Kerr-Newman black holes
Generalized Painleve-Gullstrand metrics are explicitly constructed for the
Kerr-Newman family of charged rotating black holes. These descriptions are free
of all coordinate singularities; moreover, unlike the Doran and other proposed
metrics, an extra tunable function is introduced to ensure all variables in the
metrics remain real for all values of the mass M, charge Q, angular momentum
aM, and cosmological constant \Lambda > - 3/(a^2). To describe fermions in
Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein
one-forms at the horizon(s) is imposed and coordinate singularities are
eliminated by local Lorentz boosts. Other known vierbein fields of Kerr-Newman
black holes are analysed and discussed; and it is revealed that some of these
descriptions are actually not related by physical Lorentz transformations to
the original Kerr-Newman expression in Boyer-Lindquist coordinates - which is
the reason complex components appear (for certain ranges of the radial
coordinate) in these metrics. As an application of our constructions the
correct effective Hawking temperature for Kerr black holes is derived with the
method of Parikh and Wilczek.Comment: 5 pages; extended to include application to derivation of Hawking
radiation for Kerr black holes with Parikh-Wilczek metho
Symmetry and species segregation in diffusion-limited pair annihilation
We consider a system of q diffusing particle species A_1,A_2,...,A_q that are
all equivalent under a symmetry operation. Pairs of particles may annihilate
according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the
symmetry, and without self-annihilation (k_{ii} = 0). In spatial dimensions d >
2 mean-field theory predicts that the total particle density decays as n(t) ~
1/t, provided the system remains spatially uniform. We determine the conditions
on the matrix k under which there exists a critical segregation dimension
d_{seg} below which this uniformity condition is violated; the symmetry between
the species is then locally broken. We argue that in those cases the density
decay slows down to n(t) ~ t^{-d/d_{seg}} for 2 < d < d_{seg}. We show that
when d_{seg} exists, its value can be expressed in terms of the ratio of the
smallest to the largest eigenvalue of k. The existence of a conservation law
(as in the special two-species annihilation A + B -> 0), although sufficient
for segregation, is shown not to be a necessary condition for this phenomenon
to occur. We work out specific examples and present Monte Carlo simulations
compatible with our analytical results.Comment: latex, 19 pages, 3 eps figures include
Phase Synchronization in Railway Timetables
Timetable construction belongs to the most important optimization problems in
public transport. Finding optimal or near-optimal timetables under the
subsidiary conditions of minimizing travel times and other criteria is a
targeted contribution to the functioning of public transport. In addition to
efficiency (given, e.g., by minimal average travel times), a significant
feature of a timetable is its robustness against delay propagation. Here we
study the balance of efficiency and robustness in long-distance railway
timetables (in particular the current long-distance railway timetable in
Germany) from the perspective of synchronization, exploiting the fact that a
major part of the trains run nearly periodically. We find that synchronization
is highest at intermediate-sized stations. We argue that this synchronization
perspective opens a new avenue towards an understanding of railway timetables
by representing them as spatio-temporal phase patterns. Robustness and
efficiency can then be viewed as properties of this phase pattern
Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model
The persistence properties of a set of random walkers obeying the A+B -> 0
reaction, with equal initial density of particles and homogeneous initial
conditions, is studied using two definitions of persistence. The probability,
P(t), that an annihilation process has not occurred at a given site has the
asymptotic form , where is the
persistence exponent (``type I persistence''). We argue that, for a density of
particles , this non-trivial exponent is identical to that governing
the persistence properties of the one-dimensional diffusion equation, where
. In the case of an initially low density, , we find asymptotically. The probability that a site
remains unvisited by any random walker (``type II persistence'') is also
investigated and found to decay with a stretched exponential form, , provided . A heuristic argument
for this behavior, based on an exactly solvable toy model, is presented.Comment: 11 RevTeX pages, 19 EPS figure
Soluble two-species diffusion-limited Models in arbitrary dimensions
A class of two-species ({\it three-states}) bimolecular diffusion-limited
models of classical particles with hard-core reacting and diffusing in a
hypercubic lattice of arbitrary dimension is investigated. The manifolds on
which the equations of motion of the correlation functions close, are
determined explicitly. This property allows to solve for the density and the
two-point (two-time) correlation functions in arbitrary dimension for both, a
translation invariant class and another one where translation invariance is
broken. Systems with correlated as well as uncorrelated, yet random initial
states can also be treated exactly by this approach. We discuss the asymptotic
behavior of density and correlation functions in the various cases. The
dynamics studied is very rich.Comment: 28 pages, 0 figure. To appear in Physical Review E (February 2001
Multiparticle Reactions with Spatial Anisotropy
We study the effect of anisotropic diffusion on the one-dimensional
annihilation reaction kA->inert with partial reaction probabilities when
hard-core particles meet in groups of k nearest neighbors. Based on scaling
arguments, mean field approaches and random walk considerations we argue that
the spatial anisotropy introduces no appreciable changes as compared to the
isotropic case. Our conjectures are supported by numerical simulations for slow
reaction rates, for k=2 and 4.Comment: nine pages, plain Te
Segregation in diffusion-limited multispecies pair annihilation
The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for
1 <= i < j <= q) in d dimensions is studied by means of analytical
considerations and Monte Carlo simulations. In the long-time regime the total
particle density decays as rho(t) ~ t^{- alpha}. For d = 1 the system
segregates into single species domains, yielding a different value of alpha for
each q; for a simplified version of the model in one dimension we derive
alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2,
segregation occurs only for q < 1 + (4/d). The only physical realisation of
this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed
by an extra local conservation law. For d >= 2 and q >= 1 + (4/d) the system
remains disordered and its density is shown to decay universally with the
mean-field power law (alpha = 1) that also characterises the single-species
annihilation process A + A -> 0.Comment: 35 pages (IOP style files included), 10 figures included (as eps
files
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