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 $L^1$-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-$Q$ 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 $^2$H(p,pp)n breakup reaction at E$_p$=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$\pi$-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 N$^3$LO 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 $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, 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 $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ 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 $\kappa_n$. 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 $\textbf{B}(t)$. When $\textbf{B}(t)$ grows (dwindles), a pressure anisotropy $P_{\perp}>P_{\parallel}$ ($P_{\perp}< P_{\parallel}$) builds up ($P_{\perp}$ and $P_{\parallel}$ are, respectively, the pressures perpendicular and parallel to $\textbf{B}(t)$). These pressure anisotropies excite mirror ($P_{\perp}>P_{\parallel}$) and oblique firehose ($P_{\parallel}>P_{\perp}$) 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