Linear approximation in classical scattering by a moliégre potential

Abstract

In the context of a Monte Carlo simulation of channeling, it is shown how the scattering angle of an ion by a Molière potential can be calculated by linear interpolation. In the case of impulse approximation, this reduces the computing time to ?1/17 of that needed by the usual procedure.

The maximum error introduced by the linear approximation is calculated as a function of the interval width used for interpolation. Using Firsov's inversion formula, the corresponding approximation to the atomic potential is also evaluted. It is shown that such approximation is very good, if compared with the present knowledge of atomic potential.     

On the Floquet problem for second-order Marchaud differential systems

Solutions in a given set of the Floquet boundary value problem are investigated for second-order Marchaud systems. The methods used involve a fixed point index technique developed by ourselves earlier with a bound sets approach. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets. The main existence and localization theorem is illustrated by two examples for periodic and anti-periodic problems.     

Two-dimensional envelope localized waves in the anomalous dispersion regime

Narrowband localized wave packets that are nondispersing and nondiffracting in one transverse dimension are characterized in anomalously dispersive media by means of a Fourier approach. Depending on the group velocity, waves with a dispersion relationship characterized by real wavenumbers can be O or X waves, while we also find waves with evanescent wavenumbers.     

The systematics of nuclear single-particle states: (III). Widths and rearrangement energies

Widths and rearrangement energies are obtained from fragment distributions of single-particle states determined from one-nucleon pickup reactions on nuclei in the range 6 ≦ A ≦ 65. These show systematic features that are compared with the results of Brueckner-Hartree-Fock calculations.     

An exact approach for the Vertex Coloring Problem

Given an undirected graph $G=(V,E)$, the Vertex Coloring Problem (VCP) requires to assign a color to each vertex in such a way that colors on adjacent vertices are different and the number of colors used is minimized. In this paper, we present an exact algorithm for the solution of VCP based on the well-known Set Covering formulation of the problem. We propose a Branch-and-Price algorithm embedding an effective heuristic from the literature and some methods for the solution of the slave problem, as well as two alternative branching schemes. Computational experiments on instances from the literature show the effectiveness of the algorithm, which is able to solve, for the first time to proven optimality, five of the benchmark instances in the literature, and reduce the optimality gap of many others.     

Experimental evaluation of cutting dynamic models in soil bin facility

Computer Aided Engineering methods in earthmoving machines design and their automation require the development of soil-cutting models. These models both in two or three dimensions, static or dynamic, fitted for frictional or cohesive soils, must be mutually compatible and must function with soil transportation models and with machine locomotion characteristic models. In this work two different methods of soil cutting have been evaluated, both of them based on the classical wedge method, in order to verify their applicability to test conditions in the new soil bin facility of CEMOTER. From experimental results the possibility of using dynamic models of soil cutting in the frequency domain is discussed, to improve earthmoving machinery performance by automation and implementation of open and closed-loop control. After a preliminary analysis of a plane blade under different test conditions in sandy soil, soil cutting theoretical models of a simple implement are compared with respective scale models by tests performed in a soil bin facility at various operating speeds and depths, in order to investigate their applicability and the dynamic behaviour of the soil cutting force.     

Nonlocal Problems for Differential Inclusions in Hilbert Spaces

An existence theorem for differential inclusions in Hilbert spaces with nonlocal conditions is proved. Periodic, anti-periodic, mean value and multipoint conditions are included in this study. The investigation is based on a combination of the approximation solvability method with Hartman-type inequalities. A feedback control problem associated to a first order partial differential equation completes this discussion.     

Travelling Wavefronts in Reaction‐Diffusion Equations with Convection Effects and Non‐Regular Terms

This paper deals with the appearance of monotone bounded travelling wave solutions for a parabolic reaction‐diffusion equation which frequently meets both in chemical and biological systems. In particular, we prove the existence of monotone front type solutions for any wave speed c ≥ c* and give an estimate for the threshold value c*. Our model takes into account both of a density dependent diffusion term and of a non‐linear convection effect. Moreover, we do not require the main non‐linearity g to be a regular C¹ function; in particular we are able to treat both the case when g′(0) = 0, giving rise to a degenerate equilibrium point in the phase plane, and the singular case when g′(0) = +∞. Our results generalize previous ones due to Aronson and Weinberger [Adv. Math. 30 (1978), pp. 33–76 ], Gibbs and Murray (see Murray [Mathematical Biology, Springer‐Verlag, Berlin, 1993 ]) and McCabe , Leach and Needham [SIAM J. Appl. Math. 59 (1998), pp. 870–899 ]. Finally, we obtain our conclusions by means of a comparison‐type technique which was introduced and developed in this framework in a recent paper by the same authors.     

A note on selective line-graphs and partition colorings

We extend a one-to-one correspondence between the set of all colorings of any graph and the set of all stable sets of an auxiliary graph, from graphs to partitioned graphs. This correspondence has an application to Selective Coloring and to Selective Max-Coloring.