13,234 research outputs found
Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential
We prove the uniqueness of bounded solutions for the spatially homogeneous
Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in
time) existence of such solutions has been proved by Arsen'ev-Peskov (1977), we
deduce a local well-posedness result. The stability with respect to the initial
condition is also checked
On the surface tension of fluctuating quasi-spherical vesicles
We calculate the stress tensor for a quasi-spherical vesicle and we thermally
average it in order to obtain the actual, mechanical, surface tension of
the vesicle. Both closed and poked vesicles are considered. We recover our
results for by differentiating the free-energy with respect to the
proper projected area. We show that may become negative well before the
transition to oblate shapes and that it may reach quite large negative values
in the case of small vesicles. This implies that spherical vesicles may have an
inner pressure lower than the outer one.Comment: To appear in Eur. Phys. J. E, revised versio
On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity
We prove an inequality on the Wasserstein distance with quadratic cost
between two solutions of the spatially homogeneous Boltzmann equation without
angular cutoff, from which we deduce some uniqueness results. In particular, we
obtain a local (in time) well-posedness result in the case of (possibly very)
soft potentials. A global well-posedeness result is shown for all regularized
hard and soft potentials without angular cutoff. Our uniqueness result seems to
be the first one applying to a strong angular singularity, except in the
special case of Maxwell molecules.
Our proof relies on the ideas of Tanaka: we give a probabilistic
interpretation of the Boltzmann equation in terms of a stochastic process. Then
we show how to couple two such processes started with two different initial
conditions, in such a way that they almost surely remain close to each other
Generalization of the noise model for time-distance helioseismology
In time-distance helioseismology, information about the solar interior is
encoded in measurements of travel times between pairs of points on the solar
surface. Travel times are deduced from the cross-covariance of the random wave
field. Here we consider travel times and also products of travel times as
observables. They contain information about e.g. the statistical properties of
convection in the Sun. The basic assumption of the model is that noise is the
result of the stochastic excitation of solar waves, a random process which is
stationary and Gaussian. We generalize the existing noise model (Gizon and
Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using
a recurrence relation, we calculate the noise covariance matrices for the
moments of order 4, 6, and 8 of the observed wave field, for the moments of
order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and
4 of the travel times. All noise covariance matrices depend only on the
expectation value of the cross-covariance of the observed wave field. For
products of travel times, the noise covariance matrix consists of three terms
proportional to , , and , where is the duration of the
observations. For typical observation times of a few hours, the term
proportional to dominates and , where the are arbitrary travel times. This
result is confirmed for travel times by Monte Carlo simulations and
comparisons with SDO/HMI observations. General and accurate formulae have been
derived to model the noise covariance matrix of helioseismic travel times and
products of travel times. These results could easily be generalized to other
methods of local helioseismology, such as helioseismic holography and ring
diagram analysis
Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions
We prove the appearance of an explicit lower bound on the solution to the
full Boltzmann equation in the torus for a broad family of collision kernels
including in particular long-range interaction models, under the assumption of
some uniform bounds on some hydrodynamic quantities. This lower bound is
independent of time and space. When the collision kernel satisfies Grad's
cutoff assumption, the lower bound is a global Maxwellian and its asymptotic
behavior in velocity is optimal, whereas for non-cutoff collision kernels the
lower bound we obtain decreases exponentially but faster than the Maxwellian.
Our results cover solutions constructed in a spatially homogeneous setting, as
well as small-time or close-to-equilibrium solutions to the full Boltzmann
equation in the torus. The constants are explicit and depend on the a priori
bounds on the solution.Comment: 37 page
Discrimination of the light CP-odd scalars between in the NMSSM and in the SLHM
The presence of the light CP-odd scalar boson predicted in the
next-to-minimal supersymmetric model (NMSSM) and the simplest little Higgs
model (SLHM) dramatically changes the phenomenology of the Higgs sector. We
suggest a practical strategy to discriminate the underlying model of the CP-odd
scalar boson produced in the decay of the standard model-like Higgs boson. We
define the decay rate of "the non -tagged jet pair" with which we compute
the ratio of decay rates into lepton and jets. They show much different
behaviors between the NMSSM and the SLHM.Comment: 5 pages, 2 figures (5 figure files
Localization Effect in a 2D Superconducting Network without Disorder
The superconducting properties of a two-dimensional superconducting wire
network with a new geometry have been measured as a function of the external
magnetic field. The extreme localization effect recently predicted for this
periodic lattice is revealed as a suppression of the critical current when the
applied magnetic field corresponds to half a flux quantum per unit cell. For
this particular magnetic field, the observed vortex state configuration is
highly disordered.Comment: 6 pages, 2 eps figures, submitted to Physica C. Title change
Signal and noise in helioseismic holography
Helioseismic holography is an imaging technique used to study heterogeneities
and flows in the solar interior from observations of solar oscillations at the
surface. Holograms contain noise due to the stochastic nature of solar
oscillations. We provide a theoretical framework for modeling signal and noise
in Porter-Bojarski helioseismic holography. The wave equation may be recast
into a Helmholtz-like equation, so as to connect with the acoustics literature
and define the holography Green's function in a meaningful way. Sources of wave
excitation are assumed to be stationary, horizontally homogeneous, and
spatially uncorrelated. Using the first Born approximation we calculate
holograms in the presence of perturbations in sound-speed, density, flows, and
source covariance, as well as the noise level as a function of position. This
work is a direct extension of the methods used in time-distance helioseismology
to model signal and noise. To illustrate the theory, we compute the hologram
intensity numerically for a buried sound-speed perturbation at different depths
in the solar interior. The reference Green's function is obtained for a
spherically-symmetric solar model using a finite-element solver in the
frequency domain. Below the pupil area on the surface, we find that the spatial
resolution of the hologram intensity is very close to half the local
wavelength. For a sound-speed perturbation of size comparable to the local
spatial resolution, the signal-to-noise ratio is approximately constant with
depth. Averaging the hologram intensity over a number of frequencies above
3 mHz increases the signal-to-noise ratio by a factor nearly equal to the
square root of . This may not be the case at lower frequencies, where large
variations in the holographic signal are due to the individual contributions of
the long-lived modes of oscillation.Comment: Submitted to Astronomy and Astrophysic
Energy Conversion Using New Thermoelectric Generator
During recent years, microelectronics helped to develop complex and varied
technologies. It appears that many of these technologies can be applied
successfully to realize Seebeck micro generators: photolithography and
deposition methods allow to elaborate thin thermoelectric structures at the
micro-scale level. Our goal is to scavenge energy by developing a miniature
power source for operating electronic components. First Bi and Sb micro-devices
on silicon glass substrate have been manufactured with an area of 1cm2
including more than one hundred junctions. Each step of process fabrication has
been optimized: photolithography, deposition process, anneals conditions and
metallic connections. Different device structures have been realized with
different micro-line dimensions. Each devices performance will be reviewed and
discussed in function of their design structure.Comment: Submitted on behalf of TIMA Editions
(http://irevues.inist.fr/tima-editions
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