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Collective coordinate control of density distributions

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

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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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Core Collapse via Coarse Dynamic Renormalization

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Physical Review Letters 2005年第8期95卷 081102-081102页

作者： Andras Szell David Merritt Ioannis G. Kevrekidis Department of Chemical Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In the context of the recently developed “equation-free” approach to computer-assisted analysis of complex systems, we extract the self-similar solution describing core collapse of a stellar system from numerical experiments. The technique allows us to sidestep the core “bounce” that occurs in direct N-body simulations due to the small-N correlations that develop in the late stages of collapse, and hence to follow the evolution well into the self-similar regime.

关键词： Large scale systems

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Zone sculpting with partitioned electrokinetic injections

Zone sculpting with partitioned electrokinetic injections

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9th International Conference on Miniaturized Systems for Chemistry and Life Sciences, MicroTAS 2005

作者： Squires, Todd M. Narovlyansky, Max Whitesides, George M. Departments of Physics and Applied and Computational Mathematics Caltech United States Department of Chemistry and Chemical Biology Harvard University United States Department of Chemical Engineering UCSB United States

ISBN: (纸本)0974361119

The ultimate resolution of electrophoretic separations is limited by the quality of the initial plug. Here we describe and demonstrate a simple, general and versatile strategy for 'sculpting' high-resolution sample plugs for electrokinetic separations. We do so using solid partitions that have the effect of creating channels with highly anisotropic electrical permittivity, which permit electric fields parallel to the channel, but exclude electric fields oriented perpendicular to the channel. The technique is geometric in origin, and is thus works for arbitrary channel materials and solution characteristics. Using our technique, we demonstrate the repeatable injection and separation of (5:1) rectangular sample plugs. Copyright © 2005 by the Transducer Research Foundation, Inc.

关键词： Electrophoresis

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Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators

Diffusion maps, spectral clustering and eigenfunctions of Fo...

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2005 Annual Conference on Neural Information Processing Systems, NIPS 2005

作者： Nadler, Boaz Lafon, Stéphane Coifman, Ronald R. Kevrekidis, Ioannis G. Department of Mathematics Yale University New Haven CT 06520 United States Department of Chemical Engineering Program in Applied Mathematics Princeton University Princeton NJ 08544 United States Weizmann Institute of Science Rehovot Israel

ISBN: (纸本)9780262232531

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacencymatrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density p(x) = e-U(x) we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential 2U(x) with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.

关键词： Eigenvalues and eigenfunctions

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Multiscale simulations in simple metals: A density-functional-based methodology

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Physical Review B 2005年第9期71卷 094101-094101页

作者： Nicholas Choly Gang Lu Weinan E Efthimios Kaxiras Division of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We present a formalism for coupling a density-functional-theory-based quantum simulation to a classical simulation for the treatment of simple metallic systems. The formalism is applicable to multiscale simulations in which the part of the system requiring quantum-mechanical treatment is spatially confined to a small region. Such situations often arise in physical systems where chemical interactions in a small region can affect the macroscopic mechanical properties of a metal. We describe how this coupled treatment can be accomplished efficiently, and we present a coupled simulation for a bulk aluminum system.

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Diffusion Maps, spectral clustering and eigenfunctions of Fokker-Planck operators 05

Diffusion Maps, spectral clustering and eigenfunctions of Fo...

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Proceedings of the 19th International Conference on Neural Information Processing Systems

作者： Boaz Nadler Stéphane Lafon Ronald R. Coifman Ioannis G. Kevrekidis Department of Mathematics Yale University New Haven CT Department of Chemical Engineering and Program in Applied Mathematics Princeton University Princeton NJ

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density p(x) = e-U(x) we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential 2U(x) with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.

关键词： algorithms and architectures

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First-principles study of the interfacial adhesion between SiO2 and MoSi2

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Physical Review B 2005年第16期72卷 165410-165410页

作者： D. E. Jiang Emily A. Carter Department of Chemistry and Biochemistry Box 951569 University of California Los Angeles California 90095-1569 USA Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

Upon oxidation, a silica scale forms on MoSi2, a potential high-temperature coating material for metals. This silica scale protects MoSi2 against high-temperature corrosive gases or liquids. We use periodic density functional theory to examine the interface between SiO2 and MoSi2. The interfacial bonding is localized, as evidenced by an adhesion energy that changes only slightly with the thickness of the SiO2 layer. Moreover, the adhesion energy displays a relatively large (0.40J∕m2) variation with the relative lateral position of the SiO2 and MoSi2 lattices due to changes in Si−O bonding across the interface. The most stable interfacial structure yields an ideal work of adhesion of 5.75J∕m2 within the local density approximation (5.02J∕m2 within the generalized-gradient approximation) to electron exchange and correlation, indicating extremely strong adhesion. Local densities of states and electron density difference plots demonstrate that the interfacial Si−O bonds are covalent in character. Mo−O interactions are not found in the SiO2∕MoSi2 interface investigated here. Our work predicts that the SiO2 scale strongly adheres to MoSi2, and further supports the potential of MoSi2 as a high-temperature structural material and coating.

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Experiments on Random Packings of Ellipsoids

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Physical Review Letters 2005年第19期94卷 198001-198001页

作者： Weining Man Aleksandar Donev Frank H. Stillinger Matthew T. Sullivan William B. Russel David Heeger Souheil Inati Salvatore Torquato P. M. Chaikin Department of Physics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemistry and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical Engineering and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Psychology and Center for Neural Science New York University New York New York 10003 USA

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25∶1∶0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction ϕ(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain ϕ(r) from a magnetic resonance imaging scan. The measurements of the overall density ϕavr, ϕ(r) and the core density ϕ0=0.74±0.005 agree with simulations.

关键词： .ellipsoids Princeton New Jersey

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Stalactite Growth as a Free-Boundary Problem: A Geometric Law and Its Platonic Ideal

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Physical Review Letters 2005年第1期94卷 018501-018501页

作者： Martin B. Short James C. Baygents J. Warren Beck David A. Stone Rickard S. Toomey, III Raymond E. Goldstein Department of Physics University of Arizona Tucson Arizona 85721 USA Department of Chemical and Environmental Engineering University of Arizona Tucson Arizona 85721 USA Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA Accelerator Mass Spectrometry Facility University of Arizona Tucson Arizona 85721 USA Department of Soil Water and Environmental Science University of Arizona Tucson Arizona 85721 USA Kartchner Caverns State Park P.O. Box 1849 Benson Arizona 85602 USA

The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.

关键词： Limestone

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