41 research outputs found
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 RungeâKutta 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 âRiccardo Ricciâ 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)âs didactic spirit: he was professor of Dynamic Systems at the University of Florence and a point of reference in the cityâs 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 allâapproccio 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 lâUniversit\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