6,123 research outputs found
Nonlocal First-Order Hamilton-Jacobi Equations Modelling Dislocations Dynamics
We study nonlocal first-order equations arising in the theory of
dislocations. We prove the existence and uniqueness of the solutions of these
equations in the case of positive and negative velocities, under suitable
regularity assumptions on the initial data and the velocity. These results are
based on new -type estimates on the viscosity solutions of first-order
Hamilton-Jacobi Equations appearing in the so-called ``level-sets approach''.
Our work is inspired by and simplifies a recent work of Alvarez, Cardaliaguet
and Monneau
Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications
In this paper, we prove a comparison result between semicontinuous viscosity
sub and supersolutions growing at most quadratically of second-order degenerate
parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we
characterize the value function of a finite horizon stochastic control problem
with unbounded controls as the unique viscosity solution of the corresponding
dynamic programming equation
Precision study of positronium and precision tests of the bound state QED
Despite its very short lifetime positronium provides us with a number of
accurate tests of the bound state QED. In this note a brief overview of QED
theory and precision experiments on the spectrum and annihilation decay of the
positronium atom is presented. Special attention is paid to the accuracy of
theoretical predictions.Comment: A talk presented at 9th International Workshop on Slow Positron Beam
Techniques for Solids and Surfaces (SLOPOS), Dresden, 200
Quantum-state input-output relations for absorbing cavities
The quantized electromagnetic field inside and outside an absorbing high-
cavity is studied, with special emphasis on the absorption losses in the
coupling mirror and their influence on the outgoing field. Generalized operator
input-output relations are derived, which are used to calculate the Wigner
function of the outgoing field. To illustrate the theory, the preparation of
the outgoing field in a Schr\"{o}dinger cat-like state is discussed.Comment: 12 pages, 5 eps figure
The reaction 2H(p,pp)n in three kinematical configurations at E_p = 16 MeV
We measured the cross sections of the H(p,pp)n breakup reaction at
E=16 MeV in three kinematical configurations: the np final-state
interaction (FSI), the co-planar star (CST), and an intermediate-star (IST)
geometry. The cross sections are compared with theoretical predictions based on
the CD Bonn potential alone and combined with the updated 2-exchange
Tucson-Melbourne three-nucleon force (TM99'), calculated without inclusion of
the Coulomb interaction. The resulting excellent agreement between data and
pure CD Bonn predictions in the FSI testifies to the smallness of three-nucleon
force (3NF) effects as well as the insignificance of the Coulomb force for this
particular configuration and energy. The CST also agrees well whereas the IST
results show small deviations between measurements and theory seen before in
the pd breakup space-star geometries which point to possible Coulomb effects.
An additional comparison with EFT predictions (without 3NF) up to order NLO
shows excellent agreement in the FSI case and a rather similar agreement as for
CD Bonn in the CST and IST situations.Comment: 20 pages, 11 figure
Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results
We consider one of the most important problems in directional statistics,
namely the problem of testing the null hypothesis that the spike direction
of a Fisher-von Mises-Langevin distribution on the -dimensional
unit hypersphere is equal to a given direction . After a reduction
through invariance arguments, we derive local asymptotic normality (LAN)
results in a general high-dimensional framework where the dimension goes
to infinity at an arbitrary rate with the sample size , and where the
concentration behaves in a completely free way with , which
offers a spectrum of problems ranging from arbitrarily easy to arbitrarily
challenging ones. We identify various asymptotic regimes, depending on the
convergence/divergence properties of , that yield different
contiguity rates and different limiting experiments. In each regime, we derive
Le Cam optimal tests under specified and we compute, from the Le Cam
third lemma, asymptotic powers of the classical Watson test under contiguous
alternatives. We further establish LAN results with respect to both spike
direction and concentration, which allows us to discuss optimality also under
unspecified . To investigate the non-null behavior of the Watson test
outside the parametric framework above, we derive its local asymptotic powers
through martingale CLTs in the broader, semiparametric, model of rotationally
symmetric distributions. A Monte Carlo study shows that the finite-sample
behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure
A Heating Mechanism via Magnetic Pumping in the Intracluster Medium
Turbulence driven by AGN activity, cluster mergers and galaxy motion
constitutes an attractive energy source for heating the intracluster medium
(ICM). How this energy dissipates into the ICM plasma remains unclear, given
its low collisionality and high magnetization (precluding viscous heating by
Coulomb processes). Kunz et al. 2011 proposed a viable heating mechanism based
on the anisotropy of the plasma pressure (gyroviscous heating) under ICM
conditions. The present paper builds upon that work and shows that particles
can be gyroviscously heated by large-scale turbulent fluctuations via magnetic
pumping. We study how the anisotropy evolves under a range of forcing
frequencies, what waves and instabilities are generated and demonstrate that
the particle distribution function acquires a high energy tail. For this, we
perform particle-in-cell simulations where we periodically vary the mean
magnetic field . When grows (dwindles), a
pressure anisotropy ()
builds up ( and are, respectively, the pressures
perpendicular and parallel to ). These pressure anisotropies
excite mirror () and oblique firehose
() instabilities, which trap and scatter the
particles, limiting the anisotropy and providing a channel to heat the plasma.
The efficiency of this mechanism depends on the frequency of the large-scale
turbulent fluctuations and the efficiency of the scattering the instabilities
provide in their nonlinear stage. We provide a simplified analytical heating
model that captures the phenomenology involved. Our results show that this
process can be relevant in dissipating and distributing turbulent energy at
kinetic scales in the ICM.Comment: 24 pages, 17 figures, submitted to Ap
Ground state study of simple atoms within a nano-scale box
Ground state energies for confined hydrogen (H) and helium (He) atoms, inside
a penetrable/impenetrable compartment have been calculated using Diffusion
Monte Carlo (DMC) method. Specifically, we have investigated spherical and
ellipsoidal encompassing compartments of a few nanometer size. The potential is
held fixed at a constant value on the surface of the compartment and beyond.
The dependence of ground state energy on the geometrical characteristics of the
compartment as well as the potential value on its surface has been thoroughly
explored. In addition, we have investigated the cases where the nucleus
location is off the geometrical centre of the compartment.Comment: 9 pages, 5 eps figures, Revte
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