The massless field perturbations of the accelerating Minkowski and Schwarzschild spacetimes are studied. The results are extended to the propagation of the Proca field in Rindler spacetime. We examine critically the possibility of existence of a general spin–acceleration coupling in complete analogy with the well-known spin–rotation coupling. We argue that such a direct coupling between spin and linear acceleration does not exist.

Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the zero angular momentum observers and of the Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing ``central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.

We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space $B^{s}_{p,q}$ for $p \geq 2$. For $1 \leq p < 2$, the Bayes Factor is still optimal for $(2s+2)/(2s+1) \leq p < 2$ and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.

We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, that is usually the case in the existing literature, we elicit the $\epsilon$-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The type II maximum likelihood approach to prior selection is used by maximizing the predictive distribution for the data in the wavelet domain over a suitable subclass of the $\epsilon$-contamination class of prior distributions. For the prior selected, the posterior mean yields a thresholding procedure which depends on one free prior parameter and it is level - and amplitude- dependent, allowing thus for better adaptation in function estimation. We consider an automatic choice of the free prior parameter, guided by considerations on an exact risk analysis and on the shape of the thresholding rule, enabling the resulting estimator to be fully automated in practice. We also compute pointwise Bayesian credible intervals for the resulting function estimate using a simulation-based approach. We use several simulated examples to illustrate the performance of the proposed empirical Bayes term-by-term wavelet scheme, and we make comparisons with other classical and empirical Bayes term-by-term wavelet schemes. As a practical illustration, we present an application to a real-life data set that was collected in an atomic force microscopy study.

In the Cultural Heritage area it is of fundamental importance to characterize and classify the conservation state of the materials constituting ancient monuments, in order to study and monitor their decay. Generally the decay diagnosis is provided by “naked eye” analysis done by expert scientists “walking around” the artifact and recording the conservation state of each individual element they observe. In this paper, a color image segmentation approach, based on histogram threshold and edge detection techniques is presented, to extract degradation regions, characterized by holes or cavities, from color images of stone-materials. The goal is to provide an aid to the decay diagnosis by segmenting degraded regions from color images, computing quantitative data, such as the area and perimeter of the extracted zones, and processing qualitative information, such as various levels of depth detected into the same zones. Since color is a powerful tool in the distinction between objects, a segmentation technique based on color, instead of intensity only, has been used to provide an clearer discrimination between regions. The study case concerns the impressive remains of the Roman Theatre in the city of Aosta (Italy). In particular we have processed and analyzed some color images of the Theatre puddingstones, acquired by a camera.

Using computer simulations, the finite sample performance of a number of classical and Bayesian wavelet shrinkage estimators for Poisson counts is examined. For the purpose of comparison, a variety of intensity functions, background intensity levels, sample sizes, primary resolution levels, wavelet filters and performance criteria are employed. A demonstration is given of the use of some of the estimators to analyse a data set arising in high-energy astrophysics. Following the philosophy of reproducible research, the Matlab programs and real-life data example used in this study are made freely available.

We consider the Cauchy problem for the 2 x 2 nonstrictly hyperbolic system [...] For possiblylarge, discontinuous and resonant data, the generalized solution to the Riemann problem is introduced, interaction estimates are carried out using an original change of variables and the convergence of Godunov approximations is shown. Uniqueness is addressed relying on a suitable extension of Kruz?kov's techniques

We present a computational approach for the WKB approximation of the wave function of an electron moving in a periodic one-dimensional crystal lattice. We derive a nonstrictly hyperbolic system for the phase and the intensity where the flux functions originate from the Bloch spectrum of the Schrodinger operator. Relying on the framework of the multibranch entropy solutions introduced by Brenier and Corrias, we compute efficiently multiphase solutions using well adapted and simple numerical schemes. In this first part we present computational results for vanishing exterior potentials which demonstrate the effectiveness of the proposed method.

We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow theWell-Balanced approach's canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type Dt <= O(Dx^2) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.

We review some ideas about the physics of small-scale turbulent statistics, focusing on the scaling behavior of anisotropic fluctuations. We present results from direct numerical simulations of three-dimensional homogeneous, anisotropically forced, turbulent systems: the Rayleigh–Bénard system, the random-Kolmogorov-flow, and a third flow with constant anisotropic energy spectrum at low wave numbers. A comparison of the anisotropic scaling properties displays good similarity among these very different flows. Our findings support the conclusion that scaling exponents of anisotropic fluctuations are universal, i.e., independent of the forcing mechanism sustaining turbulence.

We present a computational approach for the WKB approximation of the wavefunction of an electron moving in a periodic one-dimensional crystal lattice by means of a nonstrictly hyperbolic system whose flux function stems from the Bloch spectrum of the Schrodinger operator. This second part focuses on the handling of the source terms which originate from adding a slowly varying exterior potential. Physically, relevant examples are the occurrence of Bloch oscillations in case it is linear, a quadratic one modelling a confining field and the harmonic Coulomb term resulting from the inclusion of a ''donor impurity'' inside an otherwise perfectly homogeneous lattice.

We consider an hyperbolic singular perturbation of the incompressible Navier Stokes equations in two space dimensions. The approximating system under consideration, arises as a diffusive rescaled version of a standard relaxation approximation for the incompressible Euler equations. The aim of this work is to give a rigorous justification of its asymptotic limit toward the Navier Stokes equations using the modulated energy method.

We study the numerical approximation of viscosity solutions for Parabolic Integro-Differential Equations (PIDE). Similar models arise in option pricing, to generalize the Black-Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference scheme are not practically feasible. Here we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions. Numerical tests are presented to show the computational efficiency of the approximation.