Electronic properties of b.c.c. transition metal solid solutions. a study of the Nr−Nb system

Summary Calculations of electron densities of states and of soft—X-ray absorption spectra in Zr−Nb alloys have been performed in the frame of the coherent potential approximation in its multiple-scattering version (KKR-CAP). It is shown that a lot of care is needed in applying the simple rigid-band model to these systems, in order to explain experimental data. Results are also diseussed in connection with existing experimental data and good agreement is found.

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Riassunto Sono stati eseguiti calcoli di densità di stati elettronici e di spettri di assorbimento di raggi X molli nella lega Zr−Nb a varie concentrazioni, nell'àmbito dell'approssimazione di potenziale coerente nella sua versione di scattering multiplo (KKR-CPA). Si mostra che è necessaria molta attenzione per poter interpretare dati sperimentali come semplice modello a bande rigide. I risultati sono inoltre, discussi in connessione con, i dati sperimentali esistenti con i quali si riscontra un buon accordo.

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Резюме в рамках приближения когерентного потенциала и его модификации для многократного рассеяния проводится вычисление плотностей электронных состояний и спектров поглощения мягких рентгеновских лучей в Zn−Nb сплавах. Показывается, что необходимо проявлять особое внимание при интерпретации экспериментальных данных с помощью простой модели недеформируемых зон. Полученные результаты обсуждаются в связи с имеющимися экспериментальными данными и овнаружено хорошее согласие.

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Work also sponsored by Assessorato Industria della Regione Siciliana.     

On the evolution law of weak discontinuities for hyperbolic quasi-linear systems

We show that the law of propagation of weak discontinuities obtained by A. Jeffrey is in agreement with the Bernoulli's law found by other authors.     

A new method to exploit the Entropy Principle and galilean invariance in the macroscopic approach of Extended Thermodynamics

Abstract In extended thermodynamic the entropy principle and the Galilean invariance dictate respectively constraints for the constitutive equations and the velocity dependence. The entropy principle in particular requires the existence of a privileged field, the main field u^′, such that the original system becomes symmetric hyperbolic and is generated by four potentials. It is not easy to solve the restrictions of both principles, if we use as field the non convective main field and the velocity v. This is due to the fact that are not independent. Rather its components satisfy three scalar constraints. The aim of this paper is to solve the full problem using as new strategy to consider as independent variables and requiring an appropriate differential constraint. This new procedure is very efficient and we are able to solve the problem of 13 moments in the full non linear case (far from equilibrium). It turns out that the knowledge of only the equilibrium state function is sufficient to close the system. Keywords: Extended Thermodynamics, Entropy Principle, Galilean invariance, Rarefied Gas, Hyperbolic systems Mathematics Subject Classification (2000): 74A20, 76P05, 35l60     

Pseudopotential method for higher partial wave scattering

We present a zero-range pseudopotential applicable for all partial wave interactions between neutral atoms. For p and d waves, we derive effective pseudopotentials, which are useful for problems involving anisotropic external potentials. Finally, we consider two nontrivial applications of the p-wave pseudopotential: we solve analytically the problem of two interacting spin-polarized fermions confined in a harmonic trap, and we analyze the scattering of p-wave interacting particles in a quasi-two-dimensional system.     

Replica Cluster Variational Method

We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi’s Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a variational expression of the replicated free energy of a system with quenched disorder, both averaged and on a single sample, and make the hierarchical ansatz using functionals of functions of fields to represent the messages. We obtain a set of integral equations for the message functionals. The main difference with the Bethe case is that the functionals appear in the equations in implicit form and are not positive definite, thus standard iterative population dynamic algorithms cannot be used to determine them. In the simplest cases the solution could be obtained iteratively using Fourier transforms.     

Localization of cold atoms in state-dependent optical lattices via a Rabi Pulse

We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.     

Maximum entropy principle for rarefied polyatomic gases

The aim of this paper is to show that the procedure of maximum entropy principle for the closure of the moments equations for rarefied monatomic gases can be extended also to polyatomic gases. The main difference with respect to the usual procedure is the existence of two hierarchies of macroscopic equations for moments of suitable distribution function, in which the internal energy of a molecule is taken into account. The field equations for 14 moments of the distribution function, which include dynamic pressure, are derived. The entropy and the entropy flux are shown to be a generalization of the ones for classical Grad’s distribution. The results are in perfect agreement with the recent macroscopic approach of extended thermodynamics for real gases.     

A hybrid model for opinion formation

This paper presents a hybrid model for opinion formation in a large group of agents exposed to the persuasive action of a small number of strong opinion leaders. The model is defined by coupling a finite difference equation for the dynamics of leaders opinion with a continuous integro-differential equation for the dynamics of the others. Such a definition stems from the idea that the leaders are few and tend to retain original opinions, so that their dynamics occur on a longer time scale with respect to the one of the other agents. A general well-posedness result is established for the initial value problem linked to the model. The asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic distinct social scenarios, where different emerging behaviors can be observed. Analytical results are illustrated and extended through numerical simulations.