1,897 research outputs found
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
Asymmetric Swiss-cheese brane-worlds
We study a brane-world cosmological scenario with local inhomogeneities
represented by black holes. The brane is asymmetrically embedded into the bulk.
The black strings/cigars penetrating the Friedmann brane generate a
Swiss-cheese type structure. This universe forever expands and decelerates, as
its general relativistic analogue. The evolution of the cosmological fluid
however can proceed along four branches, two allowed to have positive energy
density, one of them having the symmetric embedding limit. On this branch a
future pressure singularity can arise for either (a) a difference in the
cosmological constants of the cosmological and black hole brane regions (b) a
difference in the left and right bulk cosmological constants. While the
behaviour (a) can be avoided by a redefinition of the fluid variables, (b)
establishes a critical value of the asymmetry over which the pressure
singularity occurs. We introduce the pressure singularity censorship which
bounds the degree of asymmetry in the bulk cosmological constant. We also show
as a model independent generic feature that the asymmetry source term due to
the bulk cosmological constant increases in the early universe. In order to
obey the nucleosynthesis constraints, the brane tension should be constrained
therefore both from below and from above. With the maximal degree of asymmetry
obeying the pressure singularity censorship, the higher limit is 10 times the
lower limit. The degree of asymmetry allowed by present cosmological
observations is however much less, pushing the upper limit to infinity.Comment: v2: considerably expanded, 19 pages, 8 figures, many new references.
Pressure singularity censorship introduced, strict limits on the possible
degree of asymmetry derived. v3: model independent analysis shows that the
asymmetry bounds the brane tension from above. Limits on the maximal tension
set. Version published in JCA
Spin-spin effects in radiating compact binaries
The dynamics of a binary system with two spinning components on an eccentric
orbit is studied, with the inclusion of the spin-spin interaction terms
appearing at the second post-Newtonian order. A generalized true anomaly
parametrization properly describes the radial component of the motion. The
average over one radial period of the magnitude of the orbital angular momentum
is found to have no nonradiative secular change. All spin-spin terms
in the secular radiative loss of the energy and magnitude of orbital angular
momentum are given in terms of and other constants of the motion.
Among them, self-interaction spin effects are found, representing the second
post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring
approximation.Comment: 12 pages, to appear in Phys. Rev.
Spin effects in gravitational radiation backreaction III. Compact binaries with two spinning components
The secular evolution of a spinning, massive binary system in eccentric orbit
is analyzed, expanding and generalizing our previous treatments of the
Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin
effects up to the 3/2 post-Newtonian order are considered, both in the
equations of motion and in the radiative losses. The description of the orbit
in terms of the true anomaly parametrization provides a simple averaging
technique, based on the residue theorem, over eccentric orbits. The evolution
equations of the angle variables characterizing the relative orientation of the
spin and orbital angular momenta reveal a speed-up effect due to the
eccentricity. The dissipative evolutions of the relevant dynamical and angular
variables is presented in the form of a closed system of differential
equations.Comment: 10 pages, 1 figur
Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model
We study hysteretic phenomena in random ferromagnets. We argue that the angle
dependent magnetostatic (dipolar) terms introduce frustration and long range
interactions in these systems. This makes it plausible that the Sherrington -
Kirkpatrick model may be able to capture some of the relevant physics of these
systems. We use scaling arguments, replica calculations and large scale
numerical simulations to characterize the hysteresis of the zero temperature SK
model. By constructing the distribution functions of the avalanche sizes,
magnetization jumps and local fields, we conclude that the system exhibits
self-organized criticality everywhere on the hysteresis loop.Comment: 4 pages, 4 eps figure
Weighted network modules
The inclusion of link weights into the analysis of network properties allows
a deeper insight into the (often overlapping) modular structure of real-world
webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with
weights) for weighted networks based on the concept of percolating k-cliques
with high enough intensity. The algorithm allows overlaps between the modules.
First, we give detailed analytical and numerical results about the critical
point of weighted k-clique percolation on (weighted) Erdos-Renyi graphs. Then,
for a scientist collaboration web and a stock correlation graph we compute
three-link weight correlations and with the CPMw the weighted modules. After
reshuffling link weights in both networks and computing the same quantities for
the randomised control graphs as well, we show that groups of 3 or more strong
links prefer to cluster together in both original graphs.Comment: 19 pages, 7 figure
Directed network modules
A search technique locating network modules, i.e., internally densely
connected groups of nodes in directed networks is introduced by extending the
Clique Percolation Method originally proposed for undirected networks. After
giving a suitable definition for directed modules we investigate their
percolation transition in the Erdos-Renyi graph both analytically and
numerically. We also analyse four real-world directed networks, including
Google's own webpages, an email network, a word association graph and the
transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The
obtained directed modules are validated by additional information available for
the nodes. We find that directed modules of real-world graphs inherently
overlap and the investigated networks can be classified into two major groups
in terms of the overlaps between the modules. Accordingly, in the
word-association network and among Google's webpages the overlaps are likely to
contain in-hubs, whereas the modules in the email and transcriptional
regulatory networks tend to overlap via out-hubs.Comment: 21 pages, 10 figures, version 2: added two paragaph
Closed Timelike Curves in Relativistic Computation
In this paper, we investigate the possibility of using closed timelike curves
(CTCs) in relativistic hypercomputation. We introduce a wormhole based
hypercomputation scenario which is free from the common worries, such as the
blueshift problem. We also discuss the physical reasonability of our scenario,
and why we cannot simply ignore the possibility of the existence of spacetimes
containing CTCs.Comment: 17 pages, 5 figure
The geometry of the Barbour-Bertotti theories I. The reduction process
The dynamics of interacting particles is investigated in the
non-relativistic context of the Barbour-Bertotti theories. The reduction
process on this constrained system yields a Lagrangian in the form of a
Riemannian line element. The involved metric, degenerate in the flat
configuration space, is the first fundamental form of the space of orbits of
translations and rotations (the Leibniz group). The Riemann tensor and the
scalar curvature are computed by a generalized Gauss formula in terms of the
vorticity tensors of generators of the rotations. The curvature scalar is
further given in terms of the principal moments of inertia of the system. Line
configurations are singular for . A comparison with similar methods in
molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit
Positive tension 3-branes in an bulk
In this work, we review and extend the so-called consistency conditions for
the existence of a braneworld scenario in arbitrary dimensions in the
Brans-Dicke (BD) gravitational theory. After that, we consider the particular
case of a five-dimensional scenario which seems to have phenomenological
interesting implications. We show that, in the BD framework, it is possible to
achieve necessary conditions pointing to the possibility of accommodating
branes with positive tensions in an AdS bulk by the presence of the additional
BD scalar field, avoiding in this way the necessity of including unstable
objects in the compactification scheme. Furthermore, in the context of time
variable brane tension, it is shown that the brane tension may change its sign,
following the bulk cosmological constant sign.Comment: 15 pages, new version to appear in JHE
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