An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field

We study the limiting behavior of a singularly perturbed Schr?dinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane (x, y) and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr?dinger equations in the plane (x, y), coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator.     

Correlation between thermal conductivity and bond length alternation in carbon nanotubes: A combined reverse nonequilibrium molecular dynamics—Crystal orbital analysis

The thermal conductivity (λ) of carbon nanotubes (CNTs) with chirality indices (5,0), (10,0), (5,5), and (10,10) has been studied by reverse nonequilibrium molecular dynamics (RNEMD) simulations as a function of different bond length alternation patterns (Δr_i). The Δr_i dependence of the bond force constant (k_rx) in the molecular dynamics force field has been modeled with the help of an electronic band structure approach. These calculations show that the Δr_i dependence of k_rx in tubes with not too small a diameter can be mapped by a simple linear bond length–bond order correlation. A bond length alternation with an overall reduction in the length of the nanotube causes an enhancement of λ, whereas an alternation scheme leading to an elongation of the tube is coupled to a decrease of the thermal conductivity. This effect is more pronounced in carbon nanotubes with larger diameters. The formation of a polyene‐like structure in the direction of the longitudinal axis has a negligible influence on λ. A comparative analysis of the RNEMD and crystal orbital results indicates that Δr_i‐dependent modifications of λ and the electrical conductivity are uncorrelated. This behavior is in‐line with a heat transfer that is not carried by electrons. Modifications of λ as a function of the bond alternation in the (10,10) nanotube are explained with the help of power spectra, which provide access to the density of vibrational states. We have suggested longitudinal low‐energy modes in the spectra that might be responsible for the Δr_i dependence of λ. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

The altitude profile of atmospheric ion concentration,and the determination of the recombination and attachment coefficients in the suburbs areas

In this paper is presented the study of altitude profile of atmospheric ions in the lower troposphere. The theoretical model, constructed to interpret the measurement results, was based on the influence of radon and the aerosols on the air ion concentration. Based on this model, we can determine the recombination and attachment coefficients, and find out the parameters which influence on the coefficients of the functional relations of the measurements results. The consistency of the theoretical model and the experimental results is very good.     

Genuine Equilibria of Three Body Coulomb Configurations

The problem analyzed is the classical non-regularized Hamiltonian formulation of a restricted three body problem under the influence of Coulomb-interactions. Completing the large literature on Helium-like systems we will consider the motions around a fixed positive point charge of (i) one negative and one positive point charge as well as the “classical” issue of (ii) two negative point charges. Thereby, all our considerations deal with arbitrary positive and negative charge values of the mass particles. Here, we give necessary and sufficient conditions for the existence of genuine equilibria in such systems—recall that there are none in the usual classical Helium-atom—and analyze their linearized stability. The thus obtained insights allow us to study the dynamics near such genuine equilibria.