P. Falsaperla

Maximum entropy principle for nonparabolic hydrodynamic transport in semiconductor devices

A closed hydrodynamic approach for a full nonparabolic band model is developed from the maximum entropy principle. Generalized kinetic fields are introduced within a total average-energy scheme. Numerical calculations for bulk and submicron Si structures are found to compare well with those obtained by ensemble Monte Carlo simulators thus validating the proposed approach.

Bidispersive-inclined convection

A model is presented for thermal convection in an inclined layer of porous material when the medium has a bidispersive structure. Thus, there are the usual macropores which are full of a fluid, but there are also a system of micropores full of the same fluid. The model we employ is a modification of the one proposed by Nield & Kuznetsov (2006 Int. J. Heat Mass Transf. 49, 3068–3074. (doi:10.1016/j.ijheatmasstransfer.2006.02.008)), although we consider a single temperature field only.

COMPETITION AND COOPERATION OF STABILIZING EFFECTS IN THE BÉNARD PROBLEM WITH ROBIN TYPE BOUNDARY CONDITIONS

Rotation and magnetic field have a stabilizing effect on the Bénard problem if they act separately. However, as is shown in the classical works of Chandrasekhar, when they are both present, these stabilizing effects are often conflictual. Instead, other stabilizing effects, such as rotation and concentration field, are cumulative. The previous results were obtained for stress-free boundary conditions, and fixed boundary temperatures and concentrations. In this work, we investigate, analytically and numerically, how different boundary conditions on the temperature, such as the Robin and Neumann b.c. used in, influence the competition and cooperation of the aforesaid stabilizing effects. The appearance of long-wavelength perturbations for low thermal conductivity of the boundaries is also investigated. The present work concerns a linear stability analysis of the problem and it is part of a larger project including a nonlinear analysis.

Parallel efficiency of the C.R.F. method on an IBM RS/6000 cluster platform

A new numerical method for kinetic equations in several dimensions has been recently presented by Motta and Wick (1991). The method has been then applied to simple models to test its applicability to realistic physical situations. In the present paper we discuss the parallel performance of the method on a distributed memory platform based on a cluster of IBM RS/6000 superscalar workstations.

Quantum Lyapunov Exponents

We show that it is possible to associate univocally with each given solution of the time-dependent Schrödinger equation a particular phase flow (“quantum flow”) of a non-autonomous dynamical system. This fact allows us to introduce a definition of chaos in quantum dynamics (quantum chaos), which is based on the classical theory of chaos in dynamical systems. In such a way we can introduce quantities which may be appelled quantum Lyapunov exponents. Our approach applies to a non-relativistic quantum-mechanical system of n charged particles; in the present work numerical calculations are performed only for the hydrogen atom. In the computation of the trajectories we first neglect the spin contribution to chaos, then we consider the spin effects in quantum chaos. We show how the quantum Lyapunov exponents can be evaluated and give several numerical results which describe some properties found in the present approach. Although the system is very simple and the classical counterpart is regular, the most non-stationary solutions of the corresponding Schrödinger equation are chaotic according to our definition.

Laminar hydromagnetic flows in an inclined heated layer

In this paper we investigate, analytically, stationary laminar flow solutions of an inclined layer filled with a hydromagnetic fluid heated from below and subject to the gravity field. In particular we describe in a systematic way the many basic solutions associated to the system. This extensive work is the basis to linear instability and nonlinear stability analysis of such motions.

Global Approximation of Solutions of Time-Dependent Variational Inequalities

We consider a class of parametric variational inequalities where both the operator and the convex set depend on time. This kind of variational inequalities are useful to model many time dependent equilibrium problems. We study the Lipschitz continuity of the solutions with respect to the time parameter and construct approximations for them which minimize the average worst case error. Some improved estimates of the Lipschitz constant for this class of problems are given. In order to illustrate our procedure, we study a classical network equilibrium problem.

LONG-WAVELENGTH INSTABILITIES IN BINARY FLUID LAYERS

It is known that a fluid layer heated from below, when the boundaries are poorly conducting, gives rise to long-wavelength instabilities (see e.g. Refs. 5,7). The same effect appears also in the case of convection in a porous medium. In this work we investigate, analytically and numerically, how this effect is influenced by a stabilizing solutal field, both in the case of a fluid layer and in porous media. The solutal field is assigned through fixed concentrations at the boundaries, or more general Robin boundary conditions. The present work concerns a linear stability analysis of the problem and it is part of a larger project including a nonlinear analysis.

A Hydrodynamic Model for Transport in Semiconductors without Free Parameters

We derive, using the Entropy Maximum Principle, an expression for the distribution function of carriers as a function of a set of macroscopic quantities (density, velocity, energy, deviatoric stress, energy flux). Given the distribution function, we obtain, for these macroscopic quantities, a hydrodynamic model in which all the constitutive functions (fluxes and collisional productions) are explicitely computed starting from their kinetic expressions. We have applied our model to the simulation of some onedimensional submicron devices in a temperature range of 77–300 K, obtaining results comparable with Monte Carlo. Computation times are of order of few seconds for a picosecond of simulation.

Hydrodynamic model for hot carriers in silicon based on the maximum entropy formalism

We describe the transport properties of hot electrons in silicon through a completely closed hydrodynamic (HD) model, without any free parameter. We apply our model to the simulation of some n + nn + devices at temperatures of 300K and 77K. Results are very accurate and the computation times are of few seconds for a picosecond of simulation.