3,787 research outputs found
On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation
In the framework of toroidal Pseudodifferential operators on the flat torus
we begin by proving the closure under
composition for the class of Weyl operators with
simbols . Subsequently, we
consider when where and we exhibit the toroidal version of the
equation for the Wigner transform of the solution of the Schr\"odinger
equation. Moreover, we prove the convergence (in a weak sense) of the Wigner
transform of the solution of the Schr\"odinger equation to the solution of the
Liouville equation on written in the measure sense.
These results are applied to the study of some WKB type wave functions in the
Sobolev space with phase functions in the class
of Lipschitz continuous weak KAM solutions (of positive and negative type) of
the Hamilton-Jacobi equation for with , and to the study of the
backward and forward time propagation of the related Wigner measures supported
on the graph of
Damage as Gamma-limit of microfractures in anti-plane linearized elasticity
A homogenization result is given for a material having brittle inclusions arranged in a periodic structure.
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According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence.
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In particular, damage is obtained as limit of periodically distributed
microfractures
Precise determination of muon and electromagnetic shower contents from shower universality property
We consider two new aspects of Extensive Air Shower development universality
allowing to make accurate estimation of muon and electromagnetic (EM) shower
contents in two independent ways. In the first case, to get muon (or EM) signal
in water Cherenkov tanks or in scintillator detectors it is enough to know the
vertical depth of shower maximum and the total signal in the ground detector.
In the second case, the EM signal can be calculated from the primary particle
energy and the zenith angle. In both cases the parametrizations of muon and EM
signals are almost independent on primary particle nature, energy and zenith
angle. Implications of the considered properties for mass composition and
hadronic interaction studies are briefly discussed. The present study is
performed on 28000 of proton, oxygen and iron showers, generated with CORSIKA
6.735 for spectrum in the energy range log(E/eV)=18.5-20.0 and
uniformly distributed in cos^2(theta) in zenith angle interval theta=0-65
degrees for QGSJET II/Fluka interaction models.Comment: Submitted to Phys. Rev.
Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients
In this paper we give an affirmative answer to an open question mentioned in
[Le Bris and Lions, Comm. Partial Differential Equations 33 (2008),
1272--1317], that is, we prove the well-posedness of the Fokker-Planck type
equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie
Search for a Lorentz invariance violation contribution in atmospheric neutrino oscillations using MACRO data
Neutrino-induced upward-going muons in MACRO have been analysed in terms of
relativity principles violating effects, keeping standard mass-induced
atmospheric neutrino oscillations as the dominant source of nu_mu -> nu_tau
transitions. The data disfavor these exotic possibilities even at a
sub-dominant level, and stringent 90% C.L. limits are placed on the Lorentz
invariance violation parameter |Delta v| < 6 * 10^(-24) at sin2theta_v = 0 and
|Delta v| < 2.5--5 * 10^(-26) at sin2theta_v = +/-1. These limits can also be
re-interpreted as upper bounds on the parameters describing violation of the
Equivalence Principle.Comment: 8 pages, 2 figures, submitted to Physics Letters
Perimeter of sublevel sets in infinite dimensional spaces
We compare the perimeter measure with the Airault-Malliavin surface measure
and we prove that all open convex subsets of abstract Wiener spaces have finite
perimeter. By an explicit counter-example, we show that in general this is not
true for compact convex domains
Entropic and gradient flow formulations for nonlinear diffusion
Nonlinear diffusion is considered for
a class of nonlinearities . It is shown that for suitable choices of
, an associated Lyapunov functional can be interpreted as thermodynamics
entropy. This information is used to derive an associated metric, here called
thermodynamic metric. The analysis is confined to nonlinear diffusion
obtainable as hydrodynamic limit of a zero range process. The thermodynamic
setting is linked to a large deviation principle for the underlying zero range
process and the corresponding equation of fluctuating hydrodynamics. For the
latter connections, the thermodynamic metric plays a central role
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