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Mechanism of enhanced broadening of the ionization level of Li outside transition metal surfaces

Physical Review B 2006年第11期74卷 115109-115109页

作者： Keith Niedfeldt Peter Nordlander Emily A. Carter Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA Department of Physics and Astronomy M.S. 61 Rice University P.O. Box 1892 6100 South Main Street Houston Texas 77251-1892 USA

We show that the d-band of a transition metal surface induces intra-atomic hybridization of an atom in its vicinity. It is demonstrated that such hybridization can have a profound influence on the resonance width and hence lifetime of the atomic ionization level. The degree of Li s−p hybridization is found to be directly correlated to the overlap of the d-band density of states with the Li 2s and 2p levels, and is shown to be not due solely to long-range electrostatic image potential effects.

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Packing hyperspheres in high-dimensional Euclidean spaces

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Physical Review E 2006年第4期74卷 041127-041127页

作者： Monica Skoge Aleksandar Donev Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be ϕMRJ≈0.46, 0.31, and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form ϕMRJ=c1∕2d+(c2d)∕2d, where c1=−2.72 and c2=2.56, which appears to be consistent with the high-dimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function g2(r) and structure factor S(k) for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed “decorrelation principle,” which, among other things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit d→∞. As in three dimensions (where ϕMRJ≈0.64), the packings show no signs of crystallization, are isostatic, and have a power-law divergence in g2(r) at contact with power-law exponent ≈0.4. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where g2(r) has its first minimum. Additionally, we obtain estimates for the freezing and melting packing fractions for the equilibrium hard-sphere fluid-solid transition, ϕF≈0.32 and ϕM≈0.39, respectively, for d=4, and ϕF≈0.20 and ϕM≈0.25, respectively, for d=5. Although our results indicate the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension.

关键词： RANDOM CLOSE PACKING 4TH VIRIAL-COEFFICIENTS HARD-PARTICLE PACKINGS ARBITRARY DIMENSIONALITY BOUNDARY-CONDITIONS MONTE-CARLO SPHERES EQUATION STATE SIMULATION

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Self-assembly of the simple cubic lattice with an isotropic potential

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Physical Review E 2006年第2期74卷 021404-021404页

作者： Mikael C. Rechtsman Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology Materials Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures [M. C. Rechtsman et al., Phys. Rev. Lett. 95, 228301 (2005); Phys. Rev. E 73, 011406 (2006)], we present an isotropic pair potential V(r) for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors, and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered-cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.

关键词： CRYSTALS CLUSTERS DENSE

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Collective coordinate control of density distributions

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Physical Review E 2006年第3期74卷 031104-031104页

作者： Obioma U. Uche Salvatore Torquato Frank H. Stillinger Department of Chemical Engineering Princeton University Princeton New Jersey 08544 USA 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 & Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Real collective density variables C(k) [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor S(k), where k denotes the wave vector. Our objective is to prescribe C(k) and then to find many-particle configurations that correspond to such a target C(k) using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control S(k) in the neighborhood of ∣k∣=0. The optimization method employed generates multiparticle configurations for which S(k)∝∣k∣α, ∣k∣⩽K, and α=1, 2, 4, 6, 8, and 10. The case α=1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid He4, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground states are configurationally degenerate and disordered.

关键词： STATISTICAL MECHANICS REALIZABILITY SYSTEM

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Parameter Stability of the Structural-Functional Model GREENLAB-Tomato as Affected by Plant Density and Biomass Data Acquisition

Parameter Stability of the Structural-Functional Model GREEN...

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International Symposium on Plant Growth Modeling and Applications (PMA)

作者： G. Louarn Q.X. Dong Y.M. Wang J.F. Barczi P. de Reffye Sino-French Laboratory of Informatics Automation and Applied Mathematics (LIAMA) Chinese Academy and Sciences Beijing China Department of Electronic Information College of Information and Electrical Engineering China Agricultural University Beijing China CIRAD UMR AMAP Montpellier France Digiplant Program INRIA Rocquencourt Le Chesnay France

In this study, we assessed the possibility of using the GREENLAB model to quantitatively simulate adaptive responses of tomato plants competing for light. The model was able to reproduce modifications induced by a reduction of plant spacing in dry matter production and in the allocation pattern. However, the analysis of parameter stability showed that some parameters were environment dependent and that an adjustment of model formalisms was required to explicitly represent the plant response. Model parameters also proved to be sensitive to the data acquisition procedure. We confirmed that target files composed of dry matter records lead to parameters that were better indicators of the carbohydrates metabolism at all densities.

关键词： Stability Bioinformatics Biomass Crops Predictive models Irrigation Production Data visualization Educational institutions Laboratories

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Diffusion-driven multiscale analysis on manifolds and graphs: Top-down and bottom-up constructions

Diffusion-driven multiscale analysis on manifolds and graphs...

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Wavelets XI

作者： Szlam, Arthur D. Maggioni, Mauro Coifman, Ronald R. Bremer Jr., James C. Department of Mathematics Program in Applied Mathematics Yale University 10 Hillhouse Ave New Haven CT 06520

Classically, analysis on manifolds and graphs has been based on the study of the eigenfunctions of the Laplacian and its generalizations. These objects from differential geometry and analysis on manifolds have proven useful in applications to partial differential equations, and their discrete counterparts have been applied to optimization problems, learning, clustering, routing and many other algorithms.1-7 The eigenfunctions of the Laplacian are in general global: their support often coincides with the whole manifold, and they are affected by global properties of the manifold (for example certain global topological invariants). Recently a framework for building natural multiresolution structures on manifolds and graphs was introduced, that greatly generalizes, among other things, the construction of wavelets and wavelet packets in Euclidean spaces.8,9 This allows the study of the manifold and of functions on it at different scales, which are naturally induced by the geometry of the manifold. This construction proceeds bottom-up, from the finest scale to the coarsest scale, using powers of a diffusion operator as dilations and a numerical rank constraint to critically sample the multiresolution subspaces. In this paper we introduce a novel multiscale construction, based on a top-down recursive partitioning induced by the eigenfunctions of the Laplacian. This yields associated local cosine packets on manifolds, generalizing local cosines in Euclidean spaces.10 We discuss some of the connections with the construction of diffusion wavelets. These constructions have direct applications to the approximation, denoising, compression and learning of functions on a manifold and are promising in view of applications to problems in manifold approximation, learning, dimensionality reduction.

关键词： Diffusion

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Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs

Biorthogonal diffusion wavelets for multiscale representatio...

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Wavelets XI

作者： Maggioni, Mauro Bremer Jr., James C. Coifman, Ronald R. Szlam, Arthur D. Department of Mathematics Program in Applied Mathematics Yale University 10 Hillhouse Ave New Haven CT 06520

Recent work by some of the authors presented a novel construction of a multiresolution analysis on manifolds and graphs, acted upon by a given symmetric Markov semigroup {Tt}t≥o, for which T t has low rank for large t.1 This includes important classes of diffusion-like operators, in any dimension, on manifolds, graphs, and in non-homogeneous media. The dyadic powers of an operator are used to induce a multiresolution analysis, analogous to classical Littlewood-Paley14 and wavelet theory, while associated wavelet packets can also be constructed.2 This extends multiscale function and operator analysis and signal processing to a large class of spaces, such as manifolds and graphs, with efficient algorithms. Powers and functions of T (notably its Green's function) are efficiently computed, represented and compressed. This construction is related and generalizes certain Fast Multipole Methods, 3 the wavelet representation of Calderón-Zygmund and pseudo-differential operators,4 and also relates to algebraic multigrid techniques.5 The original diffusion wavelet construction yields orthonormal bases for multiresolution spaces {Vj}. The orthogonality requirement has some advantages from the numerical perspective, but several drawbacks in terms of the space and frequency localization of the basis functions. Here we show how to relax this requirement in order to construct biorthogonal bases of diffusion scaling functions and wavelets. This yields more compact representations of the powers of the operator, better localized basis functions. This new construction also applies to non self-adjoint semigroups, arising in many applications.

关键词： Wavelet transforms

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Multiple time scale numerical methods for the inverted pendulum problem

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Lecture Notes in Computational Science and Engineering 2005年 44卷 241-261页

作者： Sharp, Richard Tsai, Yen-Hsi Engquist, Björn Program in Applied and Computational Mathematics Princeton University NJ 08544 United States Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin TX 78712 United States

ISBN: (纸本)9783540253358

In this article, we study a class of numerical ODE schemes that use a time filtering strategy and operate in two time scales. The algorithms follow the framework of the heterogeneous multiscale methods (HMM) [1]. We apply the methods to compute the averaged path of the inverted pendulum under a highly oscillatory vertical forcing on the pivot. The averaged equation for related problems has been studied analytically in [9]. We prove and show numerically that the proposed methods approximate the averaged equation and thus compute the average path of the inverted pendulum.

关键词： Inverted pendulum

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Value function approximation with diffusion wavelets and Laplacian eigenfunctions

Value function approximation with diffusion wavelets and Lap...

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2005 Annual Conference on Neural Information Processing Systems, NIPS 2005

作者： Mahadevan, Sridhar Maggioni, Mauro Department of Computer Science University of Massachusetts Amherst MA 01003 United States Program in Applied Mathematics Department of Mathematics Yale University New Haven CT 06511 United States

ISBN: (纸本)9780262232531

We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph;the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.

关键词： Diffusion

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Estimation of the spectral density of a homogeneous random stable discrete time field

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SORT 2005年第1期29卷 101-118页

作者： Demesh, N.N. Chekhmenok, S.L. Department of Information and Program-Mathematical Software of Automated Productions Faculty of Applied Mathematics and Computer Sciences Belarus State University F. Skoriny ave.4 Minsk 220000 Belarus

In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete-time random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homoge-neous symmetric α-stable discrete-time random field. These fields do not have second-order moments if 0 < α < 2. We construct an estimate of the spectrum, calculate the asymptotic mean and variance, and prove weak consistency of our estimate.

关键词： Homogeneous Stable Fields spectral density estimate

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