A multiband envelope function model for quantum transport in a tunneling diode

We present a simple model for electron transport in semiconductor devices that exhibit tunneling between the conduction and valence bands. The model is derived within the usual Bloch-Wannier formalism by a k-expansion, and is formulated in terms of a set of coupled equations for the electron envelope functions. Its connection with other models present in literature is discussed. As an application we consider the case of a Resonant Interband Tunneling Diode, demonstrating the ability of the model to reproduce the expected behaviour of the current as a function of the applied voltageComment: 8 pages, 4 figure

A New Strategy for Deep Wide-Field High Resolution Optical Imaging

We propose a new strategy for obtaining enhanced resolution (FWHM = 0.12 arcsec) deep optical images over a wide field of view. As is well known, this type of image quality can be obtained in principle simply by fast guiding on a small (D = 1.5m) telescope at a good site, but only for target objects which lie within a limited angular distance of a suitably bright guide star. For high altitude turbulence this 'isokinetic angle' is approximately 1 arcminute. With a 1 degree field say one would need to track and correct the motions of thousands of isokinetic patches, yet there are typically too few sufficiently bright guide stars to provide the necessary guiding information. Our proposed solution to these problems has two novel features. The first is to use orthogonal transfer charge-coupled device (OTCCD) technology to effectively implement a wide field 'rubber focal plane' detector composed of an array of cells which can be guided independently. The second is to combine measured motions of a set of guide stars made with an array of telescopes to provide the extra information needed to fully determine the deflection field. We discuss the performance, feasibility and design constraints on a system which would provide the collecting area equivalent to a single 9m telescope, a 1 degree square field and 0.12 arcsec FWHM image quality.Comment: 46 pages, 22 figures, submitted to PASP, a version with higher resolution images and other supplementary material can be found at http://www.ifa.hawaii.edu/~kaiser/wfhr

Energy-conserving methods for the nonlinear Schrödinger equation

In this paper, we further develop recent results in the numerical solution of Hamiltonian partial differential equations (PDEs) (Brugnano et al., 2015), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We shall use HBVMs for solving the nonlinear Schrödinger equation (NLSE), of interest in many applications. We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional, confers more robustness on the numerical solution of such a problem

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Glow discharge in low pressure plasma PVD: mathematical model and numerical simulations

In this paper we analyze the problem of glow discharge in low pressure plasma in industrial plant, for chambers of different shapes and various working parameters, like pressure and electric potential. The model described is based upon a static approximation of the AC configuration with two electrodes and a drift diffusion approximation for the current density of positive ions and electrons. A detailed discussion of the boundary conditions imposed is given, as well as the full description of the mathematical model. Numerical simulations were performed for a simple 1D model and two different 2D models, corresponding to two different settings of the industrial plant. The simpler case consists of a radially symmetric chamber, with one central electrode (cathode), based upon a DC generator. In this case, the steel chamber acts as the anode. The second model concerns a two dimensional horizontal cut of the most common plant configuration, with two electrodes connected to an AC generator. The case is treated in a "quasi-static" approximation. The three models show some common behaviours, particularly including the main expected features, such as dark spaces, glow regions and a wide "plasma region". Furthermore, the three shown models show some similarities with previously published results concerning 1D and simplified 2D models, as well as with some preliminary results of the full 3D case.Comment: 16 pages, 11 figures, in pres

Derivation of Isothermal Quantum Fluid Equations with Fermi-Dirac and Bose-Einstein Statistics

By using the quantum maximum entropy principle we formally derive, from a underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A semiclassical expansion of the quantum fluid equations, up to Ohstroke 2 -terms, leads to classical fluid equations with statistics-dependent quantum corrections, including a modified Bohm potential. The Maxwell-Boltzmann limit and the zero temperature limit are eventually discussed

Il premio Laboratorio Matematico “Riccardo Ricci” 2014-2016

Si pu\uf2 comprendere la matematica con forbici, colla, spago e mattoncini da costruzione? This volume, which features almost every work from the 2014 and 2016 editions of the Riccardo Ricci Mathematical Laboratory Award, explains how it is possible to understand Mathematics, even using the most advanced technologies such as lasers. The featured works were performed by groups of high school students, under the supervision of the teachers who have personally wrote the drafting. Those are creative and imaginative works, whose reading is recommended to teachers interested in a laboratory approach to Mathematics, as well as to all enthusiasts of the subject. The Award recalls Riccardo Ricci (1953-2013)’s didactic spirit: he was professor of Dynamic Systems at the University of Florence and a point of reference in the city’s mathematical community, also thanks to his roles as referent of the Scientific Degree Project and teacher in the courses of teacher training.Si pu\uf2 comprendere la matematica con forbici, colla, spago e mattoncini da costruzione? Questo volume, che presenta quasi tutte le opere in concorso nelle edizioni 2014 e 2016 del Premio Laboratorio Matematico Riccardo Ricci, racconta come ci\uf2 sia possibile, anche attraverso le tecnologie pi\uf9 avanzate come il laser. I lavori presentati sono prodotti da gruppi di studenti della scuola superiore di secondo grado, con la supervisione dei docenti che ne hanno curato personalmente la stesura. Sono opere ricche di creativit\ue0 e fantasia, la cui lettura \ue8 consigliata ai docenti interessati all’approccio laboratoriale alla matematica e a tutti gli appassionati e cultori della materia. Il Premio ricorda lo spirito didattico di Riccardo Ricci (1953-2013), docente di Sistemi dinamici presso l’Universit\ue0 di Firenze e punto di riferimento nella comunit\ue0 matematica fiorentina, grazie anche al suo ruolo di referente del Progetto Lauree Scientifiche e di docente nei corsi di formazione per gli insegnanti