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Dynamics of wave packets for the nonlinear Schrödinger equation with a random potential

Physical Review E 2009年第3期80卷 037601-037601页

作者： Alexander Iomin Department of Physics Technion Haifa 32000 Israel

The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schrödinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator. An analytical expression for a wave function of the initial time dynamics is found by a perturbation approach. As follows from a perturbative solution the initially localized wave function remains localized. At asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function. It is shown that the probability distribution function may be governed by the fractional Fokker-Planck equation and corresponds to subdiffusion.

关键词： wave function described qualitatively probability function probability distribution functions WAVE functions Wave packets dynamics Fokker-Planck equation probability functions Schrodinger equation

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Reconstruction of periodic unit cells of multimodal random particulate composites using genetic algorithms

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COMPUTATIONAL MATERIALS SCIENCE 2008年第2期42卷 352-367页

作者： Kumar, Natarajan Chennimalai Matous, Karel Geubelle, Philippe H. Univ Illinois Dept Aerosp Engn Urbana IL 61801 USA

We develop a procedure for characterization and reconstruction of periodic unit cells of highly filled, multimodal, particulate composites. Rocpack, a particle packing software, is used to generate the solid propellant microstructures and one- and two-point probability functions are used to describe its statistical morphology. The reconstruction is carried out using a parallel Augmented Simulated Annealing algorithm with a novel mutation operator based on a mass-spring system to eliminate overlap and improve the code performance. Results from the reconstruction procedure, for four-phase random particulate composites of 40-70% packing fraction, are detailed to demonstrate the capabilities of the reconstruction model. The presented results suggest good convergence and repeatability of the optimization scheme, even for high volume fractions, and good scalability of the algorithm. (C) 2007 Elsevier B.V. All rights reserved.

关键词： microstructure reconstruction particle packing probability functions parallel genetic algorithm solid propellant

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Favorability functions based on kernel density estimation for logistic models:: A case study

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2008年第9期52卷 4533-4543页

作者： Colubi, Ana Gonzalez-Rodriguez, Gil Jose Dominguez-Cuesta, Maria Jimenez-Sanchez, Montserrat Univ Oviedo Dpto Estadist & IOyDM Oviedo 33007 Spain European Ctr Soft Comp Res Unit Intelligent Data Anal & Graph Models Mieres Spain Univ Oviedo Dpto Geol Oviedo Spain

Susceptibility or hazard models are often established by means of logistic regression techniques in order to describe the effect of a group of explanatory variables on the probability of a dichotomous or binary response. Since the available variables do not always meet the assumptions of logit-linearity of the logistic regression, a modified approach is proposed. Firstly a favorability function associated with each explanatory variable based on the conditional probability measures is introduced. Next, a simple transformation based on the empirical probability function for non-continuous variables is suggested, while nonparametric kernel estimation is considered for continuous ones. The favorability-based transformations lead to new explanatory variables for the logistic regression model. The performance of the method is evaluated using simulated data. In addition, a real case-study is presented, in which a GIS-based landslides susceptibility model is carried out. (C) 2008 Elsevier B.V. All rights reserved.

关键词： RISK-ASSESSMENT REGRESSION LANDSLIDES probability functions Logistic Models LOGIT ANALYSIS Logistic Regression Risk Assessment Kernel Density Estimation simulated data Risk Management Disease Susceptibility explanatory variable Conditional probability Case studies

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Combinatorial probability interpretation of certain modified orthogonal polynomials

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EUROPEAN JOURNAL OF COMBINATORICS 2008年第7期29卷 1704-1716页

作者： Charalambides, Charalambos A. Univ Athens Dept Math GR-15784 Athens Greece

A probabilistic interpretation of a modified Gegenbauer polynomial is supplied by its expression in terms of a combinatorial probability defined on a compound urn model. Also, a combinatorial interpretation of its coefficients is provided. In particular, probabilistic interpretations of a modified Chebyshev polynomial of the second kind and a modified Legendre polynomial together with combinatorial interpretations of their coefficients are deduced. Further, probabilistic interpretations of a modified Hermite and a modified Chebyshev polynomial of the first kind are supplied by their expressions in terms of combinatorial probability functions defined on two limiting forms of the compound urn model. Finally, combinatorial interpretations of their coefficients are obtained. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： CHEBYSHEV POLYNOMIALS Modified Orthogonal polynomials Urn model Coefficients probability functions interpretation

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Wind Resource Analysis and Characterization with Markov's-Transition Matrices

Wind Resource Analysis and Characterization with Markov's-Tr...

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IEEE/PES Transmission and Distribution Conference and Exposition - Latin America

作者： Castellanos, F. Univ W Indies Dept Elect & Comp Engn St Augustine Trinidad Tobago

ISBN: (纸本)9781424422173

Wind resource analysis and characterization is a key ingredient in the planning and operation of wind farms. The most popular method to perform it is based on the generation of histograms showing the frequency of occurrence of the wind speed and their approximation with probability density functions (PDF). This paper presents the mathematical bases and examples of application of two statistical methods using a matrix based representation. The main advantage of this representation is that allows the preservation of information related to the temporal patterns of the wind speed time series. The matrices are used on a specific wind speed time series and results are shown. Further studies are being carried out to use these matrixes to reconstruct and forecast the wind speed.

关键词： Wind energy wind resource wind speed statistical methods Markov process probability functions

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Variability studies for mobile digital TV reception at UHF

Variability studies for mobile digital TV reception at UHF

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SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference

作者： Siqueira, Glaucio L. Cavalcanti, Joao F. B. Jardim, Felipe S. Piazza, Ralph E. Silva, Rogerio M. L. Pontificia Univ Catolica Rio de Janeiro Ctr Telecommun Studies CETUC BR-22453900 Rio De Janeiro Brazil

ISBN: (纸本)9781424406609

This paper presents the results of a propagation measurements campaign carried out using a 641 MHz signal transmitted over a typical suburban area of Rio de Janeiro city. With a mobile receptor, the variability characteristics of the received signal were analyzed on different routes and speeds of the measurement environment. Large and small scale fading of the received signal envelope were measured and compared with some known probability density functions In the UHF band. Statistics of the level crossing rate (LCR) were also measured In order to address the effect of mobile speed.

关键词： microwave propagation in suburban enviroment path loss signal variability probability functions multipath experimental results

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Modeling heterogeneous materials via two-point correlation functions: Basic principles

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Physical Review E 2007年第3期76卷 031110-031110页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. Yeong and Torquato [Phys. Rev. E 57, 495 (1998)] introduced a stochastic optimization technique that enables one to generate realizations of heterogeneous materials from a prescribed set of correlation functions. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide examples of realizable two-point correlation functions and suggest a set of analytical basis functions. We also discuss an exact mathematical formulation of the (re)construction problem and prove that S2(r) cannot completely specify a two-phase heterogeneous material alone. Moreover, we devise an efficient and isotropy-preserving construction algorithm, namely, the lattice-point algorithm to generate realizations of materials from their two-point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions. We will mainly focus on basic principles in this paper. The algorithmic details and applications of the general scheme are given in the second part of this series of two papers.

关键词： RECONSTRUCTING RANDOM-MEDIA probability functions NONLINEAR COMPOSITES POROUS-MEDIA BOUNDS MICROSTRUCTURES OPTIMIZATION SCATTERING

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Modelling frequency distributions of 5 minute-averaged solar radiation indexes using Beta probability functions

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THEORETICAL AND APPLIED CLIMATOLOGY 2003年第3-4期75卷 213-224页

作者： Assunçao, HF Escobedo, JF Oliveira, AP Univ Estadual Paulista DRN Fac Ciencias Agron Sch Agron Sci BR-18603970 Botucatu SP Brazil Univ Sao Paulo Inst Astron Geophys & Atmospher Sci Dept Atmospher Sci Grp Micrometeorol Sao Paulo Brazil Univ Fed Goias Dept Geog Jatai Go Brazil

Five minute-averaged values of sky clearness, direct and diffuse indices, were used to model the frequency distributions of these variables in terms of optical air mass. From more than four years of solar radiation observations it was found that variations in the frequency distributions of the three indices of optical air mass for Botucatu, Brazil, are similar to those in other places, as published in the literature. The proposed models were obtained by linear combination of normalized Beta probability functions, using the observed distributions derived from three years of data. The versatility of these functions allows modelling of all three irradiance indexes to similar levels of accuracy. A comparison with the observed distributions obtained from one year of observations indicate that the models are able to reproduce the observed frequency distributions of all three indices at the 95% confidence level.

关键词： solar radiation probability functions Linear Combination Frequency distribution Indexes air masses Modeling

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Determined theories and limit laws

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INFORMATION AND COMPUTATION 2006年第7期204卷 1013-1022页

作者： Baldwin, JT Mazzucco, M Univ Illinois Dept Math Stat & Comp Sci Lab Adv Comp Chicago IL 60680 USA

We provide a new model theoretic technique for proving 0-1 and convergence laws. As an application, we obtain a new (slightly less computational) proof of convergence laws due to Spencer and Thoma for the probability ... 详细信息

关键词： SPENCER probability functions cyanogen Converge

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A physical model for silicon anisotropic chemical etching

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SEMICONDUCTOR SCIENCE AND TECHNOLOGY 2005年第6期20卷 524-531页

作者： Jiang, YF Huang, QA N China Univ Technol Ctr Microelect Coll Informat Engn Beijing 100041 Peoples R China Southeast Univ Minist Educ MEMS Key Lab Nanjing 210096 Peoples R China

A novel physical model for the process of silicon anisotropic wet chemical etching is proposed. Based on the actual process of chemical etching reaction, a series of microscopic parameters describing the process have been put forward and non-linear equations with a removal probability function have been listed. For the transfer probability function in the equations, not only have the removal probabilities corresponding to the different microscopic states been included, but also the influence of etching temperature and etchant concentration. Moreover, the influences of the first neighbourhood atom and second neighbourhood atoms on etch rate are all included in the transfer probability. Having compared the calculated results against the experimental data, the feasibility of the model has been demonstrated.

关键词： probability functions CHEMICAL ETCHING Atoms Wet etching

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