520 research outputs found
Functional integral derivation of the kinetic equation of two-dimensional point vortices
We present a brief derivation of the kinetic equation describing the secular
evolution of point vortices in two-dimensional hydrodynamics, by relying on a
functional integral formalism. We start from Liouville's equation which
describes the exact dynamics of a two-dimensional system of point vortices. At
the order , the evolution of the system is characterised by the first
two equations of the BBGKY hierarchy involving the system's 1-body distribution
function and its 1-body correlation function. Thanks to the introduction of
auxiliary fields, these two evolution constraints may be rewritten as a
functional integral. When functionally integrated over the 2-body correlation
function, this rewriting leads to a new constraint coupling the 1-body
distribution function and the two auxiliary fields. Once inverted, this
constraint provides, through a new route, the closed non-linear kinetic
equation satisfied by the 1-body distribution function. Such a method sheds new
lights on the origin of these kinetic equations complementing the traditional
derivation methods.Comment: 7 pages, 1 figur
Secular diffusion in discrete self-gravitating tepid discs I : analytic solution in the tightly wound limit
The secular evolution of an infinitely thin tepid isolated galactic disc made
of a finite number of particles is described using the inhomogeneous
Balescu-Lenard equation. Assuming that only tightly wound transient spirals are
present in the disc, a WKB approximation provides a simple and tractable
quadrature for the corresponding drift and diffusion coefficients. It provides
insight into the physical processes at work during the secular diffusion of a
self-gravitating discrete disc and makes quantitative predictions on the
initial variations of the distribution function in action space.
When applied to the secular evolution of an isolated stationary
self-gravitating Mestel disc, this formalism predicts initially the importance
of the corotation resonance in the inner regions of the disc leading to a
regime involving radial migration and heating. It predicts in particular the
formation of a "ridge like" feature in action space, in agreement with
simulations, but over-estimates the timescale involved in its appearance. Swing
amplification is likely to resolve this discrepancy.
In astrophysics, the inhomogeneous Balescu-Lenard equation and its WKB limit
may also describe the secular diffusion of giant molecular clouds in galactic
discs, the secular migration and segregation of planetesimals in
proto-planetary discs, or even the long-term evolution of population of stars
within the Galactic center.Comment: 22 pages, 12 figure
Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit
The secular thickening of a self-gravitating stellar galactic disc is
investigated using the dressed collisionless Fokker-Planck equation and the
inhomogeneous multicomponent Balescu-Lenard equation. The thick WKB limits for
the diffusion fluxes are found using the epicyclic approximation, while
assuming that only radially tightly wound transient spirals are sustained by
the disc. This yields simple quadratures for the drift and diffusion
coefficients, providing a clear understanding of the positions of maximum
vertical orbital diffusion within the disc, induced by fluctuations either
external or due to the finite number of particles. These thick limits also
offer a consistent derivation of a thick disc Toomre parameter, which is shown
to be exponentially boosted by the ratio of the vertical to radial scale
heights. Dressed potential fluctuations within the disc statistically induce a
vertical bending of a subset of resonant orbits, triggering the corresponding
increase in vertical velocity dispersion. When applied to a tepid stable
tapered disc perturbed by shot noise, these two frameworks reproduce
qualitatively the formation of ridges of resonant orbits towards larger
vertical actions, as found in direct numerical simulations, but overestimates
the time-scale involved in their appearance. Swing amplification is likely
needed to resolve this discrepancy, as demonstrated in the case of razor-thin
discs. Other sources of thickening are also investigated, such as fading
sequences of slowing bars, or the joint evolution of a population of giant
molecular clouds within the disc.Comment: 31 pages, 19 figure
Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems
General self-consistent expressions for the coefficients of diffusion and
dynamical friction in a stable, bound, multicomponent self-gravitating and
inhomogeneous system are derived. They account for the detailed dynamics of the
colliding particles and their self-consistent dressing by collective
gravitational interactions. The associated Fokker-Planck equation is shown to
be fully consistent with the corresponding inhomogeneous Balescu-Lenard
equation and, in the weak self-gravitating limit, to the inhomogeneous Landau
equation. Hence it provides an alternative derivation to both and demonstrates
their equivalence. The corresponding stochastic Langevin equations are
presented: they can be a practical alternative to numerically solving the
inhomogeneous Fokker-Planck and Balescu-Lenard equations. The present formalism
allows for a self-consistent description of the secular evolution of different
populations covering a spectrum of masses, with a proper accounting of the
induced secular mass segregation, which should be of interest to various
astrophysical contexts, from galactic centers to protostellar discs.Comment: 27 pages, 1 figur
Effective homology and periods of complex projective hypersurfaces
We provide an algorithm to compute an effective description of the homology
of complex projective hypersurfaces relying on Picard-Lefschetz theory. Next,
we use this description to compute high-precision numerical approximations of
the periods of the hypersurface. This is an improvement over existing
algorithms as this new method allows for the computation of periods of smooth
quartic surfaces in an hour on a laptop, which could not be attained with
previous methods. The general theory presented in this paper can be generalised
to varieties other than just hypersurfaces, such as elliptic fibrations as
showcased on an example coming from Feynman graphs. Our algorithm comes with a
SageMath implementation.Comment: 35 page
Thermal regime of the NW shelf of the Gulf of Mexico. 1) Thermal and pressure fields
National audienceThe thermal field of the Gulf of Mexico (GoM) is analyzed from a comprehensive temperature-depth database of about 8500 Bottom Hole Temperatures and Reservoir Temperatures. Our stochastic analysis reveals a widespread, systematic sharp thermal gradient increase between 2500 and 4000 m. The analysis of the pressure regime indicates a systematic correlation between the pressure and temperature fields
Nano mechanical and microstructural investigation of damage mechanisms in copper wire bonds
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VLTI/VINCI diameter constraints on the evolutionary status of delta Eri, xi Hya, eta Boo.
other location: http://www.obs-nice.fr/pichon/science.html ; Accepted for publication in Astron. Astrophys.International audienceUsing VLTI/VINCI angular diameter measurements, we constrain the evolutionary status of three asteroseismic targets: the stars Eri, Hya, Boo. Our predictions of the mean large frequency spacing of these stars are in agreement with published observational estimations. Looking without success for a companion of Eri we doubt on its classification as an RS CVn star
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