Trapped modes in finite quantum waveguides

The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trapped eigenmode of finite L2 norm. We revisit this statement for resonators with long but finite branches that we call "finite waveguides". Although now there is no essential spectrum and all eigenfunctions have finite L2 norm, the trapping can be understood as an exponential decay of the eigenfunction inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from non-trapped to trapped states. These concepts are illustrated for several typical waveguides (L-shape, bent strip, crossing of two stripes, etc.). We conclude that the well-established theory of trapping in infinite waveguides may be incomplete and require further development for being applied to microscopic quantum devices

Finite element computation of absorbing boundary conditions for time-harmonic wave problems

International audienceThis paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations without much knowledge of the analytical behavior of the solutions and is thus very general. It is based on the computation of waves in periodic structures and needs the dynamic stiffness matrix of only one period in the medium which can be obtained by standard finite element software. Boundary conditions at various orders of accuracy can be obtained in a simple way. This is then applied to study some examples for which analytical or numerical results are available. Good agreements between the present results and analytical solutions allow to check the efficiency and the accuracy of the proposed method

Finite element procedures for nonlinear structures in moving coordinates. Part II: Infinite beam under moving harmonic loads

International audienceThis paper presents a numerical approach to the stationary solution of infinite Euler-Bernoulli beams posed on Winkler foundations under moving harmonic loads. The procedure proposed in Part 1 [1], which has been applied to consider the longitudinal vibration of rods under constant amplitude moving loads in moving coordinates, is enhanced herein for the case of moving loads with time-dependent amplitudes. Firstly, the separation of variables is used to distinguish the convection component from the amplitude component of the displacement function. Then, the stationary condition is applied to the convection component to obtain a dynamic formulation in the moving coordinates. Numerical examples are computed with a linear structure to validate the proposed method. Finally, nonlinear elastic foundation problems are presented

Interactive Processing of Landsat Image for Morphopedological Studies

With the increasing amount of data made available from Landsat there is a clear need for an integrated method of soil mapping in which these data can be exploited to provide valuable information for the various stages of conventional soil mapping: - preliminary study - detail mapping - verification of the results of photo-interpretation - updating of soil map by temporal study A joint research study was initiated between the Scientific Center of IBM France and IRAT, the Tropical Agriculture Research Institute to investigate these possible contributions

Quantum calculations of the carrier mobility in thin films: Methodology, Matthiessen's rule and comparison with semi-classical approaches

We discuss the calculation of the carrier mobility in silicon films within the quantum Non-Equilibrium Green's Functions (NEGF) framework. We introduce a new method for the extraction of the carrier mobility that is free from contact resistance contamination, and provides accurate mobilities at a reasonable cost, with minimal needs for ensemble averages. We then introduce a new paradigm for the definition of the partial mobility $\mu_{M}$ associated with a given elastic scattering mechanism "M", taking phonons (PH) as a reference ($\mu_{M}^{-1}=\mu_{PH+M}^{-1}-\mu_{PH}^{-1}$). We argue that this definition makes better sense in a quantum transport framework as it is free from long range interference effects that can appear in purely ballistic calculations. As a matter of fact, these mobilities satisfy Matthiessen's rule for three mechanisms [surface roughness (SR), remote Coulomb scattering (RCS) and phonons] much better than the usual, single mechanism calculations. We also discuss the problems raised by the long range spatial correlations in the RCS disorder. Finally, we compare semi-classical Kubo-Greenwood (KG) and quantum NEGF calculations. We show that KG and NEGF are in reasonable agreement for phonon and RCS, yet not for SR. We point to possible deficiencies in the treatment of SR scattering in KG, opening the way for further improvements.Comment: Submitted to Journal of Applied Physic