Breakdown of waves described by exact solutions of the Thomas-Fermi model

The dynamics of large localized repulsive clouds is examined by means of exact non-stationary solutions of the one-dimensional Thomas-Fermi model. The nonlinear flattening of the cloud peak, the wave breakdown at the cloud peripheries, and the condensate velocity distributions are thus described. Our solutions, which can contain an arbitrary amount of free parameters, show the nonlinear evolution of an arbitrary initial wave form. A unique procedure for analyzing these solutions is presented. The difference between our breakdown matter wave solutions and the well known Riemann shock waves is stressed. Received 22 March 2002 Published online 9 July 2002     

On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem

We present practical conditions under which the existence and uniqueness of a finite solution to a given equality quadratic program may be examined. Different sets of conditions allow this examination to take place when null-space, range-space or Lagrangian methods are used to find stationary points for the quadratic program.This research supported in part by the Natural Sciences and Engineering Research Council, Canada.     

Golubev series for solutions of elliptic equations

Let be an elliptic system with real analytic coefficients on an open set and let be a fundamental solution of Given a locally connected closed set we fix some massive measure on . Here, a non-negative measure is called massive, if the conditions and imply that We prove that, if is a solution of the equation in then for each relatively compact open subset of and every there exist a solution of the equation in and a sequence () in satisfying such that for This complements an earlier result of the second author on representation of solutions outside a compact subset of

     

An interactive weighted Tchebycheff procedure for multiple objective programming

The procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted Tchebycheff metric. Using ‘filtering’ techniques, maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration. The procedure has the advantage that it can converge to non-extreme final solutions. Especially suitable for multiple objective linear programming, the procedure is also applicable to integer and nonlinear multiple objective programs.     

Bound states in the continuum in a single-level Fano-Anderson model

Bound states in the continuum (BIC) are shown to exist in a single-level Fano-Anderson model with a colored interaction between the discrete state and a structured tight-binding continuum, which may describe mesoscopic electron or photon transport in a semi-infinite one-dimensional lattice. The existence of BIC is explained in the lattice realization as a boundary effect induced by lattice truncation.     

Distribution of eigenfrequencies for vibrating plates

Acoustic spectra of free plates with a chaotic billiard shape have been measured, and all resonance frequencies in the range 0-500 kHz have been identified. The spectral fluctuations are analyzed and compared to predictions of the Gaussian Orthogonal Ensemble (GOE) of random matrices. The best agreement is found with a superposition of two independent GOE spectra with equal density which indicates that two types of eigenmodes contribute to the same extent. To explain and predict these results a detailed theoretical analysis is carried out below the first cut-off frequency where only flexural and in-plane vibrations are possible. Using three-dimensional plate dispersion relations and two-dimensional models for flexural and in-plane vibrations we obtained two first terms of the asymptotic expansion of the counting function of these eigenmodes. The contribution of edge modes is also discussed. The results are in a very good agreement with the experimentally measured number of modes. The analysis shows that the two types of modes have almost equal level density in the measured frequency interval, and this explains the observed spectral statistics. For a plate with broken symmetry in the up-down direction (where flexural and in-plane modes are strongly coupled) experimentally observed spectral fluctuations correspond to a single GOE spectrum. Above the first cut-off frequency a greater complexity of the spectral fluctuations is expected since a larger number of types of modes will contribute to the spectrum. Received 5 January 1999 and Received in final form 5 September 1999     

Optimal control for a Timoshenko beamContrôle optimal d'une barre de Timoshenko

We consider a linear model of a rotating Timoshenko beam, which is clamped at one end to a disk the other being free. The motion of the beam is controlled by the angular acceleration of the disk. We study the minimization problem of mean square deviation of the Timoshenko beam from a given position. For the minimization problem of the first mode we prove that optimal control is the chattering control, i.e., it has an infinite number of switches in a finite time interval. We construct a suboptimal control with a finite number of switches. To cite this article: M.I. Zelikin, L.A. Manita, C. R. Mecanique 334 (2006).     

A two-step godunov-type scheme for the euler equations

A second-order Godunov-type scheme for the Euler equations in conservation form is derived. The method is based on the ENO formulation proposed by Harten et al. The fundamental difference lies in the use of a two-step scheme to compute the time evolution. The scheme is TVD in the linear scalar case, and gives oscillation-free solutions when dealing with nonlinear hyperbolic systems. The admissible time step is twice that of classical Godunovtype schemes. This feature makes it computationally cheaper than one-step schemes, while requiring the same computer storage.

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Sommario Viene data una nuova estensione al secondo ordine del metodo di Godunov per la soluzione delle equazioni di Eulero in forma conservativa. Il metodo é basato sulla formulazione ENO proposta da Harten et al. La differenza fondamentale consiste nel calcolo dell'evoluzione temporale, ottenuta mediante uno schema a due passi. Questo consente l'uso di un passo di integrazione nel tempo doppio rispetto agli altri schemi alla Godunov ad un solo passo. Il metodo proposto risulta quindi piú efficiente e puó inoltre essere implementato senza alcun aumento dell'occupazione di memoria. Viene dimostrato che lo schema é TVD nel caso lineare, e che fornisce soluzioni prive di oscillazioni spurie nel caso di sistemi non-lineari.

     

The Temperature‐Composition Phase Equilibria in the Hg0.8Cd0.2Te‐HgI2 Pseudobinary System

The temperature‐composition phase equilibria of the Hg_0.8Cd_0.2Te‐HgI₂ system were investigated between about 100 and 800 °C using Debye‐Scherrer powder X‐ray diffraction techniques, differential thermal analysis, differential scanning calorimetry, and thermochemical and structural calculations. This system is a pseudobinary temperature‐ composition plane in the HgTe‐CdTe‐HgI₂ pseudoternary phase diagram. Measurable solid solutions of HgI₂ in Hg_0.8Cd_0.2Te with the cubic zinc blende‐type structure exist between about 290 and 700 °C, with a maximum solubility of 4.9 ± 0.3 mole‐% HgI₂ at 363 ± 3 °C. Further addition of HgI₂ to HgI₂‐saturated Hg_0.8Cd_0.2Te yields the formation of CdI₂, which reduces the mole fraction (x) of CdTe in the Hg_1—xCd_xTe host lattice. After sufficient HgI₂ is added, the host lattice is depleted in CdTe and forms Hg₃Te₂I₂ in addition to CdI₂. Phase fields containing the ternary compound Hg₃TeI₄, which we first observed in the HgTe‐HgI₂ system, also exist in the present system. Quaternary analogs of the known ternary compounds Hg₃Te₂I₂ and Hg₃TeI₄, i.e., Hg_3—yCd_yTe₂I₂ and Hg_3—yCd_yTeI₄, were not observed under present experimental conditions.