Paolo Falsaperla

Bio: Paolo Falsaperla is an academic researcher from University of Catania. The author has contributed to research in topics: Boundary value problem & Reynolds number. The author has an hindex of 12, co-authored 41 publications receiving 340 citations. Previous affiliations of Paolo Falsaperla include Istituto Nazionale di Fisica Nucleare.

Full nonlinear closure for a hydrodynamic model of transport in silicon

Abstract: The increasing miniaturization of modern electronic devices requires an accurate modelization of transport in semiconductors. This is of great importance for describing phenomena such those due to hot electrons, i.e., the conditions very far from thermodynamic equilibrium caused by strong electric fields and field gradients. The most general approach to the simulation of charge transport in semiconductors employes the semiclassical Boltzmann transport equation ~BTE! coupled with Poisson equation. A numerical solution of such system of equations with traditional techniques is extremely complex, and then approximate methods based on kinetic and fluid dynamic ~FD! models are often preferred. The most accurate kinetic description is given by Monte Carlo ~MC! methods, which can take into account explicitly both the band structure and the various scattering phenomena. 1,2 This method permits us to compute directly all the quantities relative to transport ~such as the distribution function, density of carriers, velocity, mean energy, and so on! but at a cost of long computation times and stochastic noise in data. The results obtained from MC simulations permit us also to calculate transport coefficients , which are used as an input to more simplified FD models. Other kinetic approaches are based on the choice of particular forms of the nonequilibrium distribution function of carriers. Common examples are the simple shifted Maxwellian 3 or an expansion of the distribution in spherical harmonics. 4 The cylindrical symmetry constraint in momentum space and the reduced number of terms of the expansion that can be practically used do not permit, however, to describe transport properties of carriers in conditions very far from equilibrium. 5

Bidispersive-inclined convection.

Abstract: 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.

Nonlinear stability results for plane Couette and Poiseuille flows.

Abstract: We prove that the plane Couette and Poiseuille flows are nonlinearly stable if the Reynolds number is less than Re_{Orr}(2π/(λsinθ))/sinθ when a perturbation is a tilted perturbation in the direction x^{'} which forms an angle θ∈(0,π/2] with the direction i of the basic motion and does not depend on x^{'}. Re_{Orr} is the critical Orr-Reynolds number for spanwise perturbations which is computed for wave number 2π/(λsinθ), with λ being any positive wavelength. By taking the minimum with respect to λ, we obtain the critical energy Reynolds number for a fixed inclination angle and any wavelength: for plane Couette flow, it is Re_{Orr}=44.3/sinθ, and for plane Poiseuille flow, it is Re_{Orr}=87.6/sinθ (in particular, for θ=π/2 we have the classical values Re_{Orr}=44.3 for plane Couette flow and Re_{Orr}=87.6 for plane Poiseuille flow). Here the nondimensional interval between the planes bounding the channel is [-1,1]. In particular, these results improve those obtained by Joseph, who found for streamwise perturbations a critical nonlinear value of 20.65 in the plane Couette case, and those obtained by Joseph and Carmi who found the value 49.55 for plane Poiseuille flow for streamwise perturbations. If we fix some wavelengths from the experimental data and the numerical simulations, the critical Reynolds numbers that we obtain are in a very good agreement both with the the experiments and the numerical simulation. These results partially solve the Couette-Sommerfeld paradox.

Quadratic Zeeman effect for hydrogen: A method for rigorous bound-state error estimates

Abstract: We present a variational method, based on direct minimization of energy, for the calculation of eigenvalues and eigenfunctions of a hydrogen atom in a strong uniform magnetic field in the framework of the nonrelativistic theory (quadratic Zeeman effect). Using semiparabolic coordinates and a harmonic-oscillator basis, we show that it is possible to give rigorous error estimates for both eigenvalues and eigenfunctions by applying some results of Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)]. The method can be applied in this simple form only to the lowest level of given angular momentum and parity, but it is also possible to apply it to any excited state by using the standard Rayleigh-Ritz diagonalization method. However, due to the particular basis, the method is expected to be more effective, the weaker the field and the smaller the excitation energy, while the results of Kato we have employed lead to good estimates only when the level spacing is not too small. We present a numerical application to the ${\mathit{m}}^{\mathit{p}}$=${0}^{+}$ ground state and the lowest ${\mathit{m}}^{\mathit{p}}$=${1}^{\mathrm{\ensuremath{-}}}$ excited state, giving results that are among the most accurate in the literature for magnetic fields up to about ${10}^{10}$ G.

An Introduction to Magneto-Fluid Mechanics. By V. C. A. Fekrabo and C. Plumpton. Pp. 181. 25s. 1961. (Oxford University Press)

Abstract: ing journals. At the head of each abstract is the name of the author and the title of the paper, although not its date or origin, and also a pair of numbers. The reader is able to find by trial that one of these numbers is the serial number of the same paper as entered in the bibliographical list, the other being a new serial number for the paper in the sequence of abstracts. At the end of the volume are three lists. The first, a short one, is of numbers entitled ‘List of the entries included in bibliography no. 1’; bibliography no. 1 is apparently what this bibliography used to be when it was issued informally by AGARD in February 1960. The second is an index to authors, which presumably serves to identify the number of a paper written by a known author who is one of several joint authors and not the first named, the latter alone being used in the bibliographical list. The last is a subject-index, in which there are seven main divisions, like ‘magnetohydrodynamics ’ and ‘magneto-gas-dynamics ),with afew sub-divisions for each. The value of the subject index will be limited by the fact that the subheading ‘ General’ swallows up about half the entries in four of the main divisions. It is obviously useful to prepare and disseminate an up-to-date and ordered list of papers on this important subject, and the initiative and work contributed by AGARD have been widely appreciated. But why print a second time, publish, and sell at a substantial price, a bibliography which pays little attention to the ordinary principles of fact-gathering and indexing? As well as being rather wasteful, the book does not maintain accepted standards in scientific publications. G. K. BATCHELOR

Gate-induced interlayer asymmetry in ABA-stacked trilayer graphene

Abstract: We calculate the electronic band structure of ABA-stacked trilayer graphene in the presence of external gates, using a self-consistent Hartree approximation to take account of screening. In the absence of a gate potential, there are separate pairs of linear and parabolic bands at low energy. A gate field perpendicular to the layers breaks mirror reflection symmetry with respect to the central layer and hybridizes the linear and parabolic low-energy bands, leaving a chiral Hamiltonian essentially different from that of monolayer or bilayer graphene. Using the self-consistent Born approximation, we find that the density of states and the minimal conductivity in the presence of disorder generally increase as the gate field increases, in sharp contrast with bilayer graphene.