Bound States of Energy Dependent Singular Potentials

We consider attractive power-law potentials depending on energy through their coupling constant. These potentials are proportional to 1/|x| ^m with m ≥ 1 in the D = 1 dimensional space, to 1/r ^m with m ≥ 2 in the D = 3 dimensional space. We study the ground state of such potentials. First, we show that all singular attractive potentials with an energy dependent coupling constant are bounded from below, contrarily to the usual case. In D = 1, a bound state of finite energy is found with a kind of universality for the eigenvalue and the eigenfunction, which become independent on m for m > 1. We prove the solution to be unique. A similar situation arises for D = 3 for m > 2, except that, in this case, the solution is not directly comparable to a bound state: the wave function, though square integrable, diverges at the origin.     

Wave propagation in a fractional viscoelastic Andrade medium: Diffusive approximation and numerical modeling

This study focuses on the numerical modeling of wave propagation in fractionally-dissipative media. These viscoelastic models are such that the attenuation is frequency-dependent and follows a power law with non-integer exponent within certain frequency regimes. As a prototypical example, the Andrade model is chosen for its simplicity and its satisfactory fits of experimental flow laws in rocks and metals. The corresponding constitutive equation features a fractional derivative in time, a non-local-in-time term that can be expressed as a convolution product whose direct implementation bears substantial memory cost. To circumvent this limitation, a diffusive representation approach is deployed, replacing the convolution product by an integral of a function satisfying a local time-domain ordinary differential equation. An associated quadrature formula yields a local-in-time system of partial differential equations, which is then proven to be well-posed. The properties of the resulting model are also compared to those of the Andrade model. The quadrature scheme associated with the diffusive approximation, and constructed either from a classical polynomial approach or from a constrained optimization method, is investigated. Finally, the benefits of using the latter approach are highlighted as it allows to minimize the discrepancy with the original model. Wave propagation simulations in homogeneous domains are performed within a split formulation framework that yields an optimal stability condition and which features a joint fourth-order time-marching scheme coupled with an exact integration step. A set of numerical experiments is presented to assess the overall approach. Therefore, in this study, the diffusive approximation is demonstrated to provide an efficient framework for the theoretical and numerical investigations of the wave propagation problem associated with the fractional viscoelastic medium considered.     

Polarization in proton-nucleus elastic scattering around 1 GeV

The main features of the polarization observed in proton-nucleus elastic scattering around 1 GeV are discussed. We shall first recall earlier results derived within a simple model. Calculations performed by using the Glauber multiple scattering model are presented and compared to recent experimental data.     

Method for identification of the nuclear collective modes

The analysing power measurements for inelastic scattering of polarized protons with excitation of the first 2⁺ level provide a sensitive method to distinguish two simple collective models-axially symmetric rotational and vibrational. The method is illustrated by the measurements of 24.5 MeV protons scattering on ^148,152Sm and some coupled channel calculations.     

The continuous energy dependence of pp differential elastic cross sections between 500 and 1200 MeV

Using an internal jet target in the Saturne synchrotron, we have measured the proton-proton differential elastic cross section at 90° c.m. as a continuous function of energy (from 500 to 1200 MeV) during the acceleration of the beam. The energy resolution is about 2 MeV. The results are compared to predictions of phase-shift analyses and discussed in connection with amplitude analyses at 90° c.m. No resonant structure was observed and no evidence for narrow dibaryons was found.     

Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions

The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of 1-D linear elastodynamics. The focus here is on the interactions between the waves and fractures: for this purpose, the mechanical behavior of the fractures is modeled using nonlinear jump conditions deduced from the Bandis–Barton model classically used in geomechanics. Well-posedness of the initial-boundary value problem thus obtained is proved. Numerical modeling is performed by coupling a time-domain finite-difference scheme with an interface method accounting for the jump conditions. The numerical experiments show the effects of contact nonlinearities. The harmonics generated may provide a nondestructive means of evaluating the mechanical properties of fractures.