33,208 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
Speciational view of macroevolution: are micro and macroevolution decoupled?
We introduce a simple computational model that, with a microscopic dynamics
driven by natural selection and mutation alone, allows the description of true
speciation events. A statistical analysis of the so generated evolutionary tree
captures realistic features showing power laws for frequency distributions in
time and size. Albeit these successful predictions, the difficulty in obtaining
punctuated dynamics with mass extinctions suggests the necessity of decoupling
micro and macro-evolutionary mechanisms in agreement with some ideas of Gould's
and Eldredge's theory of punctuated equilibrium.Comment: Europhys. Lett. 75:342--34
An explanation of the Newman-Janis Algorithm
After the original discovery of the Kerr metric, Newman and Janis showed that
this solution could be ``derived'' by making an elementary complex
transformation to the Schwarzschild solution. The same method was then used to
obtain a new stationary axisymmetric solution to Einstein's field equations now
known as the Kerr-newman metric, representing a rotating massive charged black
hole. However no clear reason has ever been given as to why the Newman-Janis
algorithm works, many physicist considering it to be an ad hoc procedure or
``fluke'' and not worthy of further investigation. Contrary to this belief this
paper shows why the Newman-Janis algorithm is successful in obtaining the
Kerr-Newman metric by removing some of the ambiguities present in the original
derivation. Finally we show that the only perfect fluid generated by the
Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov
typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra
Fitness-dependent topological properties of the World Trade Web
Among the proposed network models, the hidden variable (or good get richer)
one is particularly interesting, even if an explicit empirical test of its
hypotheses has not yet been performed on a real network. Here we provide the
first empirical test of this mechanism on the world trade web, the network
defined by the trade relationships between world countries. We find that the
power-law distributed gross domestic product can be successfully identified
with the hidden variable (or fitness) determining the topology of the world
trade web: all previously studied properties up to third-order correlation
structure (degree distribution, degree correlations and hierarchy) are found to
be in excellent agreement with the predictions of the model. The choice of the
connection probability is such that all realizations of the network with the
same degree sequence are equiprobable.Comment: 4 Pages, 4 Figures. Final version accepted for publication on
Physical Review Letter
Behaviour of spin-1/2 particle around a charged black hole
Dirac equation is separable in curved space-time and its solution was found
for both spherically and axially symmetric geometry. But most of the works were
done without considering the charge of the black hole. Here we consider the
spherically symmetric charged black hole background namely Reissner-Nordstrom
black hole. Due to presence of the charge of black-hole charge-charge
interaction will be important for the cases of incoming charged particle (e.g.
electron, proton etc.). Therefore both gravitational and electromagnetic gauge
fields should be introduced. Naturally behaviour of the particle will be
changed from that in Schwarzschild geometry. We compare both the solutions. In
the case of Reissner-Nordstrom black hole there is a possibility of
super-radiance unlike Schwarzschild case. We also check this branch of the
solution.Comment: 8 Latex pages and 4 Figures; RevTex.style; Accepted for Publication
in Classical and Quantum Gravit
Mean-field solution of the small-world network model
The small-world network model is a simple model of the structure of social
networks, which simultaneously possesses characteristics of both regular
lattices and random graphs. The model consists of a one-dimensional lattice
with a low density of shortcuts added between randomly selected pairs of
points. These shortcuts greatly reduce the typical path length between any two
points on the lattice. We present a mean-field solution for the average path
length and for the distribution of path lengths in the model. This solution is
exact in the limit of large system size and either large or small number of
shortcuts.Comment: 14 pages, 2 postscript figure
Clustering and preferential attachment in growing networks
We study empirically the time evolution of scientific collaboration networks
in physics and biology. In these networks, two scientists are considered
connected if they have coauthored one or more papers together. We show that the
probability of scientists collaborating increases with the number of other
collaborators they have in common, and that the probability of a particular
scientist acquiring new collaborators increases with the number of his or her
past collaborators. These results provide experimental evidence in favor of
previously conjectured mechanisms for clustering and power-law degree
distributions in networks.Comment: 13 pages, 2 figure
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
Identity and Search in Social Networks
Social networks have the surprising property of being "searchable": Ordinary
people are capable of directing messages through their network of acquaintances
to reach a specific but distant target person in only a few steps. We present a
model that offers an explanation of social network searchability in terms of
recognizable personal identities: sets of characteristics measured along a
number of social dimensions. Our model defines a class of searchable networks
and a method for searching them that may be applicable to many network search
problems, including the location of data files in peer-to-peer networks, pages
on the World Wide Web, and information in distributed databases.Comment: 4 page, 3 figures, revte
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
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