3,109 research outputs found
Non semi-simple sl(2) quantum invariants, spin case
Invariants of 3-manifolds from a non semi-simple category of modules over a
version of quantum sl(2) were obtained by the last three authors in
[arXiv:1404.7289]. In their construction the quantum parameter is a root of
unity of order where is odd or congruent to modulo . In this
paper we consider the remaining cases where is congruent to zero modulo
and produce invariants of -manifolds with colored links, equipped with
generalized spin structure. For a given -manifold , the relevant
generalized spin structures are (non canonically) parametrized by
.Comment: 13 pages, 16 figure
Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame
The equations of motion of compact binary systems and their associated
Lagrangian formulation have been derived in previous works at the third
post-Newtonian (3PN) approximation of general relativity in harmonic
coordinates. In the present work we investigate the binary's relative dynamics
in the center-of-mass frame (center of mass located at the origin of the
coordinates). We obtain the 3PN-accurate expressions of the center-of-mass
positions and equations of the relative binary motion. We show that the
equations derive from a Lagrangian (neglecting the radiation reaction), from
which we deduce the conserved center-of-mass energy and angular momentum at the
3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent,
{\it via} a contact transformation of the particles' variables, to the
center-of-mass Hamiltonian in ADM coordinates that is known from the
post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the
dynamical stability of circular binary orbits at the 3PN order.Comment: 31 pages, to appear in Classical and Quantum Gravit
Spatial modeling of extreme snow depth
The spatial modeling of extreme snow is important for adequate risk
management in Alpine and high altitude countries. A natural approach to such
modeling is through the theory of max-stable processes, an infinite-dimensional
extension of multivariate extreme value theory. In this paper we describe the
application of such processes in modeling the spatial dependence of extreme
snow depth in Switzerland, based on data for the winters 1966--2008 at 101
stations. The models we propose rely on a climate transformation that allows us
to account for the presence of climate regions and for directional effects,
resulting from synoptic weather patterns. Estimation is performed through
pairwise likelihood inference and the models are compared using penalized
likelihood criteria. The max-stable models provide a much better fit to the
joint behavior of the extremes than do independence or full dependence models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS464 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
The inspiral of compact binaries, driven by gravitational-radiation reaction,
is investigated through 7/2 post-Newtonian (3.5PN) order beyond the quadrupole
radiation. We outline the derivation of the 3.5PN-accurate binary's
center-of-mass energy and emitted gravitational flux. The analysis consistently
includes the relativistic effects in the binary's equations of motion and
multipole moments, as well as the contributions of tails, and tails of tails,
in the wave zone. However the result is not fully determined because of some
physical incompleteness, present at the 3PN order, of the model of
point-particle and the associated Hadamard-type self-field regularization. The
orbital phase, whose prior knowledge is crucial for searching and analyzing the
inspiral signal, is computed from the standard energy balance argument.Comment: 12 pages, version which includes the correction of an Erratum to be
published in Phys. Rev. D (2005
Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
We compute the radiation reaction force on the orbital motion of compact
binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order
beyond the dominant effect. The method is based on a direct PN iteration of the
near-zone metric and equations of motion of an extended isolated system, using
appropriate ``asymptotically matched'' flat-space-time retarded potentials. The
formalism is subsequently applied to binary systems of point particles, with
the help of the Hadamard self-field regularisation. Our result is the 3.5PN
acceleration term in a general harmonic coordinate frame. Restricting the
expression to the centre-of-mass frame, we find perfect agreement with the
result derived in a class of coordinate systems by Iyer and Will using the
energy and angular momentum balance equations.Comment: 28 pages, references added, to appear in Classical and Quantum
Gravit
Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions
Two long-standing problems with the post-Newtonian approximation for isolated
slowly-moving systems in general relativity are: (i) the appearance at high
post-Newtonian orders of divergent Poisson integrals, casting a doubt on the
soundness of the post-Newtonian series; (ii) the domain of validity of the
approximation which is limited to the near-zone of the source, and prevents
one, a priori, from incorporating the condition of no-incoming radiation, to be
imposed at past null infinity. In this article, we resolve the problem (i) by
iterating the post-Newtonian hierarchy of equations by means of a new
(Poisson-type) integral operator that is free of divergencies, and the problem
(ii) by matching the post-Newtonian near-zone field to the exterior field of
the source, known from previous work as a multipolar-post-Minkowskian expansion
satisfying the relevant boundary conditions at infinity. As a result, we obtain
an algorithm for iterating the post-Newtonian series up to any order, and we
determine the terms, present in the post-Newtonian field, that are associated
with the gravitational-radiation reaction onto an isolated slowly-moving matter
system.Comment: 61 pages, to appear in Phys. Rev.
The Statistical Mechanics of Horizons and Black Hole Thermodynamics
Although we know that black holes are characterized by a temperature and an
entropy, we do not yet have a satisfactory microscopic ``statistical
mechanical'' explanation for black hole thermodynamics. I describe a new
approach that attributes the thermodynamic properties to ``would-be gauge''
degrees of freedom that become dynamical on the horizon. For the
(2+1)-dimensional black hole, this approach gives the correct entropy. (Talk
given at the Pacific Conference on Gravitation and Cosmology, Seoul, February
1996.)Comment: 11 pages, LaTe
Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates
We extend the description of gravitational waves emitted by binary black
holes during the final stages of inspiral and merger by introducing in the
third post-Newtonian (3PN) effective-one-body (EOB) templates seven new
``flexibility'' parameters that affect the two-body dynamics and gravitational
radiation emission. The plausible ranges of these flexibility parameters,
notably the parameter characterising the fourth post-Newtonian effects in the
dynamics, are estimated. Using these estimates, we show that the currently
available standard 3PN bank of EOB templates does ``span'' the space of signals
opened up by all the flexibility parameters, in that their maximized mutual
overlaps are larger than 96.5%. This confirms the effectualness of 3PN EOB
templates for the detection of binary black holes in gravitational-wave data
from interferometric detectors. The possibility to drastically reduce the
number of EOB templates using a few ``universal'' phasing functions is
suggested.Comment: 23 pages, 3 figures, 4 tables, with revtex4, Minor clarifications,
Final published versio
Automating Security Analysis: Symbolic Equivalence of Constraint Systems
We consider security properties of cryptographic protocols, that are either trace properties (such as confidentiality or authenticity) or equivalence properties (such as anonymity or strong secrecy). Infinite sets of possible traces are symbolically represented using deducibility constraints. We give a new algorithm that decides the trace equivalence for the traces that are represented using such constraints, in the case of signatures, symmetric and asymmetric encryptions. Our algorithm is implemented and performs well on typical benchmarks. This is the first implemented algorithm, deciding symbolic trace equivalence
Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order
Gravitational waves generated by inspiralling compact binaries are
investigated to the second--post-Newtonian (2PN) approximation of general
relativity. Using a recently developed 2PN-accurate wave generation formalism,
we compute the gravitational waveform and associated energy loss rate from a
binary system of point-masses moving on a quasi-circular orbit. The crucial new
input is our computation of the 2PN-accurate ``source'' quadrupole moment of
the binary. Tails in both the waveform and energy loss rate at infinity are
explicitly computed. Gravitational radiation reaction effects on the orbital
frequency and phase of the binary are deduced from the energy loss. In the
limiting case of a very small mass ratio between the two bodies we recover the
results obtained by black hole perturbation methods. We find that finite mass
ratio effects are very significant as they increase the 2PN contribution to the
phase by up to 52\%. The results of this paper should be of use when
deciphering the signals observed by the future LIGO/VIRGO network of
gravitational-wave detectors.Comment: 43 pages, LaTeX-ReVTeX, no figures
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