Maximum-entropy principle for nonlinear hydrodynamic transport in semiconductors

We present, in a strong nonlinear context, a full-band hydrodynamic approach by using the first 13 moments of the distribution function in the framework of extended thermodynamics. Following this approach we show that: (1) the full-band effects of the band structure are described accurately up to high electric fields both in homogeneous and nonhomogeneous conditions; (2) the effectiveness of the dissipation processes can be properly investigated, in homogeneous conditions, only in a strong nonlinear context; and (3) the hyperbolicity region of the system is very large, also in the nonlinear conditions. In this way, by using a strong nonlinear closure, it is possible to describe accurately the transport phenomena in submicron devices, when very high electric fields and field gradients occur (E ≈ 220 kV/cm, E/(dE/dx) ≈ 100 Å).     

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.     

A mathematical model of anorexia and bulimia

In this paper, we propose a mathematical model to study the dynamics of anorexic and bulimic populations. The model proposed takes into account, among other things, the effects of peers' influence, media influence, and education. We prove the existence of three possible equilibria that without media influences are disease‐free, bulimic‐endemic, and endemic. Neglecting media and education effects, we investigate the stability of such equilibria, and we prove that under the influence of media, only one of such equilibria persists and becomes a global attractor. Which of the three equilibria becomes global attractor depends on the other parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

Improved Noniterative Algorithm for Solving the Traffic Equilibrium Problem

We provide an equivalent formulation of a previously proposed noniterative algorithm (see A. Maugeri, Appl. Math. Optim. 16, 169–185, 1987) for the traffic equilibrium problem. Moreover, under the strict monotonicity assumption, we provide an improved algorithm which enlarges the range of applicability of the previous algorithm and decreases considerably its computational effort. Our algorithm is based on a general algorithm for variational inequalities (see O. Mancino, G. Stampacchia, J. Optim. Theory Appl. 9, 3–23, 1972), which we further develop and adapt to the traffic equilibrium problem. Both our proofs and the algorithm exploit directly the equilibrium conditions which characterize our problem.     

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.     

Stability of hydromagnetic laminar flows in an inclined heated layer

Laminar flows of conducting fluids with an imposed magnetic field play an important role in many applications, for instance in geophysics, astrophysics, e.g. when dealing with solar winds, industry, biology, in metallurgy, in biofilms, etc. Also many engineering applications require heating at the boundaries. The inclination has been examined by some authors mainly in theoretical applications, geophysical studies, and materials processing. In Falsaperla et al. (Laminar hydromagnetic flows in an inclined heated layer, 2016) we have investigated analytical solutions of stationary laminar flows of an inclined layer filled with a hydromagnetic fluid heated from below and subject to the gravity field. In this article we study linear instability and nonlinear stability of some of the above solutions and investigate the critical stability/instability thresholds.     

Does Symmetry of the Operator of a Dynamical System Help Stability?

In this article, we address the question of relating the stability properties of an operator with the stability properties of its associate symmetric operator. The linear-algebra results of Bendixson and Hirsch indicate that the symmetric part of a matrix is always less stable than the matrix itself. We show that in a variety of cases, including infinite dimensional cases associated to systems of PDEs, the same result is valid. We also discuss the applicability to non-autonomous systems, and we show that, in general, this result is not valid. We also review some of the literature that in these years has appeared on the subject.