A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Algorithm for calculating spectral intensity due to charged particles in arbitrary motion

An algorithm for calculating the spectral intensity of radiation due to the coherent addition of many particles with arbitrary trajectories is described. Direct numerical integration of the Lienard-Wiechert potentials, in the far-field, for extremely high photon energies and many particles is made computationally feasible by a mixed analytic and numerical method. Exact integrals of spectral intensity are made between discretely sampled trajectories, by assuming the space-time four-vector is a quadratic function of proper time. The integral Fourier transform of the trajectory with respect to time, the modulus squared of which comprises the spectral intensity, can then be formed by piecewise summation of exact integrals between discrete points. Because of this, the calculation is not restricted by discrete sampling bandwidth theory, and hence for smooth trajectories, time-steps many orders larger than the inverse of the frequency of interest can be taken.Comment: 19 pages, 6 figures, submitted to J. Comp. Phys. Changes in new version: axis labels of figure 3 correcte

Stochastically Fluctuating Black-Hole Geometry, Hawking Radiation and the Trans-Planckian Problem

We study the propagation of null rays and massless fields in a black hole fluctuating geometry. The metric fluctuations are induced by a small oscillating incoming flux of energy. The flux also induces black hole mass oscillations around its average value. We assume that the metric fluctuations are described by a statistical ensemble. The stochastic variables are the phases and the amplitudes of Fourier modes of the fluctuations. By averaging over these variables, we obtain an effective propagation for massless fields which is characterized by a critical length defined by the amplitude of the metric fluctuations: Smooth wave packets with respect to this length are not significantly affected when they are propagated forward in time. Concomitantly, we find that the asymptotic properties of Hawking radiation are not severely modified. However, backward propagated wave packets are dissipated by the metric fluctuations once their blue shifted frequency reaches the inverse critical length. All these properties bear many resemblences with those obtained in models for black hole radiation based on a modified dispersion relation. This strongly suggests that the physical origin of these models, which were introduced to confront the trans-Planckian problem, comes from the fluctuations of the black hole geometry.Comment: 32 page

SARS-CoV-2 Breakthrough Infections: Incidence and Risk Factors in a Large European Multicentric Cohort of Health Workers.

Background: The research aimed to investigate the incidence of SARS-CoV-2 breakthrough infections and their determinants in a large European cohort of more than 60,000 health workers. Methods: A multicentric retrospective cohort study, involving 12 European centers, was carried out within the ORCHESTRA project, collecting data up to 18 November 2021 on fully vaccinated health workers. The cumulative incidence of SARS-CoV-2 breakthrough infections was investigated with its association with occupational and social-demographic characteristics (age, sex, job title, previous SARS-CoV-2 infection, antibody titer levels, and time from the vaccination course completion). Results: Among 64,172 health workers from 12 European health centers, 797 breakthrough infections were observed (cumulative incidence of 1.2%). The primary analysis using individual data on 8 out of 12 centers showed that age and previous infection significantly modified breakthrough infection rates. In the meta-analysis of aggregated data from all centers, previous SARS-CoV-2 infection and the standardized antibody titer were inversely related to the risk of breakthrough infection (p = 0.008 and p = 0.007, respectively). Conclusion: The inverse correlation of antibody titer with the risk of breakthrough infection supports the evidence that vaccination plays a primary role in infection prevention, especially in health workers. Cellular immunity, previous clinical conditions, and vaccination timing should be further investigated

I. The investigation of stresses in a rectangular bar by means of polarized light

n/