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51.
This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum
transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a
product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure,
is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given
by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential.
In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit
circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function
for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder
and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also
prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies
spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known
to be true in the same three regimes. 相似文献
52.
Pioger P Couderc V Lefort L Barthelemy A Baronio F De Angelis C Min Y Quiring V Sohler W 《Optics letters》2002,27(24):2182-2184
We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted. 相似文献
53.
Christian Gruber Nicolas Macris Alain Messager Daniel Ueltschi 《Journal of statistical physics》1997,86(1-2):57-108
The Falicov-Kimball model is a lattice model of itinerant spinless fermions (electrons) interacting by an on-site potential with classical particles (ions). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles. 相似文献
54.
Alain Billionnet 《Applied Mathematical Modelling》2012,36(5):2213-2223
We consider a landscape divided into elementary cells, each of these cells containing some species to be protected. We search to select a set of cells to form a natural reserve in order to protect all the species present in the landscape. A species is considered protected if it is present in a certain number of cells of the reserve. There is an important spatial constraint concerning the set of selected cells: a species must be able to go from any cell to any cell without leaving the reserve. An integer linear programming model was proposed by Önal and Briers [2] for this reserve selection problem, but the size of the problems which can be handled by this model is limited: several hours of computation are required for solving instances with hundred of cells and hundred of species. Having proposed an improvement of this model which reduces appreciably the computation time, we propose another integer linear programming model, easy to carry out, which allows to obtain, in a few seconds of computation, optimal or near-optimal solutions for instances with hundred of cells and hundred of species. However, the computation time becomes prohibitive for instances with more than 200 cells and 100 species. But, this approach can be particularly useful to solve the problem, in an approximate way, by aggregation of cells as proposed by Önal and Briers [2]. 相似文献
55.
56.
We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance. 相似文献
57.
Abstract The paper is essentially devoted to a quantitative comparison of the exact (1D) model developed in Part I, with two approximate models indicated by Kittel (1Da1) and by Van der Ziel (1Da2). And this is made for identical values of their common parameters. This allows to show that models 1D and 1Da1 generally present no suitable intervals for fitting. The model of Van der Ziel is more suited, for, a good fitting with the 1D model can be obtained, for relatively reduced G values, and for temperatures bounded upward by the characteristic temperature T 0 defined previously. The role played by the sub-models, obtained after simplifying the 1Dai model equations, is studied also. 相似文献
58.
Alain Bachelot Eric Darrigrand Katherine Mer-Nkonga 《Comptes Rendus Mathematique》2003,336(6):505-510
The aim of this work is to propose an accurate and efficient numerical approximation for high frequency diffraction of electromagnetic waves. In the context of the boundary integral equations presented in F. Collino and B. Després, to be published in J. Comput. Appl. Math., the strategy we propose combines the microlocal discretization (T. Abboud et al., in: Third International Conference on Mathematical Aspects of Wave Propagation Phenomena, SIAM, 1995, pp. 178–187) and the multilevel fast multipole method (J.M. Song, W.C. Chew, Microw. Opt. Tech. Lett. 10 (1) (1995) 14–19). This leads to a numerical method with a reduced complexity, of order O(N4/3ln(N)+NiterN2/3), instead of the complexity O(NiterN2) for a classical numerical iterative solution of integral equations. Computations on an academic geometry show that the new method improves the efficiency, for a solution with a good level of accuracy. To cite this article: A. Bachelot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
59.
This study proposes a new method for automatic, iterative image registration in the context of dynamic contrast-enhanced ultrasound (DCE-US) imaging. By constructing a cost function of image registration using a combination of the tissue and contrast-microbubble responses, this new method, referred to as dual-mode registration, performs alignment based on both tissue and vascular structures. Data from five focal liver lesions (FLLs) were used for the evaluation. Automatic registration based on the dual-mode registration technique and tissue-mode registration obtained using the linear response image sequence alone were compared to manual alignment of the sequence by an expert. Comparison of the maximum distance between the transformations applied by the automatic registration techniques and those from expert manual registration reference showed that the dual-mode registration provided better precision than the tissue-mode registration for all cases. The reduction of maximum distance ranged from 0.25 to 9.3 mm. Dual-mode registration is also significantly better than tissue-mode registration for the five sequences with p -values lower than 0.03. The improved sequence alignment is also demonstrated visually by comparison of images from the sequences and the video playbacks of the motion-corrected sequences. This new registration technique better maintains a selected region of interest (ROI) within a fixed position of the image plane throughout the DCE-US sequence. This should reduce motion-related variability of the echo-power estimations and, thus, contribute to more robust perfusion quantification with DCE-US. 相似文献
60.
The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy. 相似文献