3,303 research outputs found
Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
The Fokker action of point-particle binaries at the fourth post-Newtonian
(4PN) approximation of general relativity has been determined previously.
However two ambiguity parameters associated with infra-red (IR) divergencies of
spatial integrals had to be introduced. These two parameters were fixed by
comparison with gravitational self-force (GSF) calculations of the conserved
energy and periastron advance for circular orbits in the test-mass limit. In
the present paper together with a companion paper, we determine both these
ambiguities from first principle, by means of dimensional regularization. Our
computation is thus entirely defined within the dimensional regularization
scheme, for treating at once the IR and ultra-violet (UV) divergencies. In
particular, we obtain crucial contributions coming from the Einstein-Hilbert
part of the action and from the non-local tail term in arbitrary dimensions,
which resolve the ambiguities.Comment: 25 pages, published versio
Nitrogen isotopic fractionation during abiotic synthesis of organic solid particles
The formation of organic compounds is generally assumed to result from
abiotic processes in the Solar System, with the exception of biogenic organics
on Earth. Nitrogen-bearing organics are of particular interest, notably for
prebiotic perspectives but also for overall comprehension of organic formation
in the young solar system and in planetary atmospheres. We have investigated
abiotic synthesis of organics upon plasma discharge, with special attention to
N isotope fractionation. Organic aerosols were synthesized from N2-CH4 and
N2-CO gaseous mixtures using low-pressure plasma discharge experiments, aimed
at simulating chemistry occurring in Titan s atmosphere and in the protosolar
nebula, respectively. Nitrogen is efficiently incorporated into the synthesized
solids, independently of the oxidation degree, of the N2 content of the
starting gas mixture, and of the nitrogen speciation in the aerosols. The
aerosols are depleted in 15N by 15-25 permil relative to the initial N2 gas,
whatever the experimental setup is. Such an isotopic fractionation is
attributed to mass-dependent kinetic effect(s). Nitrogen isotope fractionation
upon electric discharge cannot account for the large N isotope variations
observed among solar system objects and reservoirs. Extreme N isotope
signatures in the solar system are more likely the result of self-shielding
during N2 photodissociation, exotic effect during photodissociation of N2
and/or low temperature ion-molecule isotope exchange. Kinetic N isotope
fractionation may play a significant role in the Titan s atmosphere. We also
suggest that the low delta15N values of Archaean organic matter are partly the
result of abiotic synthesis of organics that occurred at that time
Conservative Dynamics of Binary Systems of Compact Objects at the Fourth Post-Newtonian Order
We review our recent derivation of a Fokker action describing the
conservative dynamics of a compact binary system at the fourth post-Newtonian
(4PN) approximation of general relativity. The two bodies are modeled by point
particles, which induces ultraviolet (UV) divergences that are cured by means
of dimensional regularization combined with a renormalization of the particle's
wordlines. Associated with the propagation of wave tails at infinity is the
appearance of a non-local-in-time conservative tail effect at the 4PN order in
the Lagrangian. In turn this implies the appearance of infrared (IR) divergent
integrals which are also regularized by means of dimensional regularization. We
compute the Noetherian conserved energy and periastron advance for circular
orbits at 4PN order, paying special attention to the treatment of the non-local
terms. One ambiguity parameter remaining in the current formalism is determined
by comparing those quantities, expressed as functions of the orbital frequency,
with self-force results valid in the small mass ratio limit.Comment: 7 pages; contribution to the proceedings of the 52nd Rencontres de
Moriond, "Gravitation
La singularité du Pacs
Étude synthétique sur le PacsLa loi du 17 mai 2013 s'inscrit dans la continuité des profondes évolutions que connut le droit des couples en quelques décennies. Désormais chaque individu peut choisir entre trois modes de conjugalité. Au sein de ce pluralisme affirmé, le pacs, introduit en 1999, occupe une place intermédiaire entre l'espace de non-droit que constitue le concubinage, et l'union encore fortement réglementée et ritualisée qu'est le mariage. Cependant, érigé sur le modèle du mariage, le pacs a été sans cesse rapproché de celui-ci par les récentes réformes. La question de sa singularité doit être posée afin que soit préservée l'existence d'un pluralisme équilibré des modes de conjugalité, au cœur duquel il se trouve
Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
The Fokker action governing the motion of compact binary systems without
spins is derived in harmonic coordinates at the fourth post-Newtonian
approximation (4PN) of general relativity. Dimensional regularization is used
for treating the local ultraviolet (UV) divergences associated with point
particles, followed by a renormalization of the poles into a redefinition of
the trajectories of the point masses. Effects at the 4PN order associated with
wave tails propagating at infinity are included consistently at the level of
the action. A finite part procedure based on analytic continuation deals with
the infrared (IR) divergencies at spatial infinity, which are shown to be fully
consistent with the presence of near-zone tails. Our end result at 4PN order is
Lorentz invariant and has the correct self-force limit for the energy of
circular orbits. However, we find that it differs from the recently published
result derived within the ADM Hamiltonian formulation of general relativity [T.
Damour, P. Jaranowski, and G. Sch\"afer, Phys. Rev. D 89, 064058 (2014)]. More
work is needed to understand this discrepancy.Comment: 47 pages; references added; Sec. VD enhanced; a few more minor
improvement
-constrained random matrices
International audienceLet be a set of -dimensional row vectors with entries in a -ary alphabet. A matrix with entries in the same -ary alphabet is -constrained if every set of columns of contains as a submatrix a copy of the vectors in , up to permutation. For a given set of -dimensional vectors, we compute the asymptotic probability for a random matrix to be -constrained, as the numbers of rows and columns both tend to infinity. If is the number of columns and the number of rows, then the threshold is at , where only depends on the dimension of vectors and not on the particular set . Applications to superimposed codes, shattering classes of functions, and Sidon families of sets are proposed. For , an explicit construction of a -constrained matrix is given
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