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Novel Low-Temperature Behavior in Classical Many-Particle Systems

Physical Review Letters 2009年第5期103卷 050602-050602页

作者： Robert D. Batten Frank H. Stillinger Salvatore Torquato Department of Chemical Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Materials Institute Program in Applied and Computational Mathematics Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We show that classical many-particle systems interacting with certain soft pair interactions in two dimensions exhibit novel low-temperature behaviors. Ground states span from disordered to crystalline. At some densities, a large fraction of normal-mode frequencies vanish. Lattice ground-state configurations have more vanishing frequencies than disordered ground states at the same density and exhibit vanishing shear moduli. For the melting transition from a crystal, the thermal expansion coefficient is negative. These unusual results are attributed to the topography of the energy landscape.

关键词： Ground state

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Optimal packings of superballs

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Physical Review E 2009年第4期79卷 041309-041309页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Mechanical and Aerospace Engineering 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 Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|2p+|x2|2p+|x3|2p≤1) provide a versatile family of convex particles (p≥0.5) with both cubic-like and octahedral-like shapes as well as concave particles (0

关键词： Temperature

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Dense packings of polyhedra: Platonic and Archimedean solids

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Physical Review E 2009年第4期80卷 041104-041104页

作者： S. Torquato Y. Jiao Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science 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 School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the adaptive shrinking cell (ASC) scheme. This optimization problem is solved here (using a variety of multiparticle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3, except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823…, 0.836…, 0.904…, and 0.947…, respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other nontiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to Platonic solids, Archimedean solids, superballs, and ellipsoids. Provided that what we term the “asphericity” (ratio of the circumradius to inradius) is sufficiently small, the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric Platonic and Archimedean solids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This can be regarded to be

关键词： Optimization

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Interactions leading to disordered ground states and unusual low-temperature behavior

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Physical Review E 2009年第3期80卷 031105-031105页

作者： Robert D. Batten Frank H. Stillinger Salvatore Torquato Department of Chemical Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Materials Institute Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We have shown that any pair potential function v(r) possessing a Fourier transform V(k) that is positive and has compact support at some finite wave number K yields classical disordered ground states for a broad density range [R. D. Batten, F. H. Stillinger, and S. Torquato, J. Appl. Phys. 104, 033504 (2008)]. By tuning a constraint parameter χ (defined in the text), the ground states can traverse varying degrees of local order from fully disordered to crystalline ground states. Here, we show that in two dimensions, the “k-space overlap potential,” where V(k) is proportional to the intersection area between two disks of diameter K whose centers are separated by k, yields anomalous low-temperature behavior, which we attribute to the topography of the underlying energy landscape. At T=0, for the range of densities considered, we show that there is continuous energy degeneracy among Bravais-lattice configurations. The shear elastic constant of ground-state Bravais-lattice configurations vanishes. In the harmonic regime, a significant fraction of the normal modes for both amorphous and Bravais-lattice ground states have vanishing frequencies, indicating the lack of an internal restoring force. Using molecular-dynamics simulations, we observe negative thermal-expansion behavior at low temperatures, where upon heating at constant pressure, the system goes through a density maximum. For all temperatures, isothermal compression reduces the local structure of the system unlike typical single-component systems.

关键词： Ground state

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Method for obtaining upper bounds on photonic band gaps

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Physical Review B 2009年第15期80卷 155126-155126页

作者： Mikael C. Rechtsman Salvatore Torquato Courant Institute of Mathematical Sciences 251 Mercer Street New York New York 10012 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We present a method to calculate upper bounds on the photonic band gaps of two-component photonic crystals. The method involves calculating both upper and lower bounds on the frequency bands for a given structure, and then maximizing over all possible two-component structures. We apply this method to a number of examples, including a one-dimensional photonic crystal (or “Bragg grating”) and two-dimensional photonic crystals (in both the TM and TE polarizations) with both four and sixfold rotational symmetries. We compare the bounds to band gaps of numerically optimized structures and find that the bounds are extremely tight. We prove that the bounds are “sharp” in the limit of low dielectric contrast ratio between the two components. This method and the bounds derived here have important implications in the search for optimal photonic band-gap structures.

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Space distribution of the rescattering electron wavepacket in the laser-atom interactions

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Journal of Physics: Conference Series 2009年第1期185卷

作者： X M Tong K Sasaki K Hino N Toshima Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305–8573 Japan Center for Computational Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305–8577 Japan Doctoral Program in Frontier Science Graduate School of Pure and Applied Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305–8573 Japan

We investigated the space distribution of the rescattering electron wavepacket created in the laser-atom interaction by a full quantum simulation and a semiclassical calculation. Both the quantum simulation and the semiclassical calculation showed that the rescattering electron beam current intensity can reach the order of 109 A/cm2, much intense than the conventional electron beam. Different from the convention electron beam, the rescattering electron beam is of a non-uniform distribution both in energy and space. The simulated information is important for analyzing the molecular structure in the rescattering imaging experiments.

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A new time-dependent scattering theory and its application to the capture of antiprotons by atoms

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Journal of Physics: Conference Series 2009年第1期185卷

作者： X M Tong K Hino N Toshima Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305–8573 Japan Center for Computational Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305–8577 Japan Doctoral Program in Frontier Science Graduate School of Pure and Applied Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305–8573 Japan

We presented a theoretical method to study the capture of the antiprotrons by atoms solving a Chew-Goldberger-type integral equation directly. The scattering boundary conditions are automatically satisfied by adiabatically switching on the interaction between the antiprotons and targets. Hence the outgoing wave function is obtained without the tedious procedure of adjusting the total wave function in the asymptotic region. All the dynamical information can be derived from the scattering wave function obtained on pseudo-spectral grids numerically. Using this method, we obtained the state-specified capture cross sections when antiprotons collide with helium atoms. Differing from the capture processes of antiprotons by hydrogen atoms, the anomalous bumpy structures are revealed in the angular momentum dependent capture cross sections by helium atoms. Further analysis shows that the bumps arise from the partial channel closing due to the removal of the energy degeneracy in the antiprotonic helium atoms.

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Diffusion maps - A probabilistic interpretation for spectral embedding and clustering algorithms

Diffusion maps - A probabilistic interpretation for spectral...

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作者： Nadler, Boaz Lafon, Stephane Coifman, Ronald Kevrekidis, Ioannis G. Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100 Israel Google Inc. United States Department of Mathematics Yale University New Haven CT 06520-8283 United States Department of Chemical Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

ISBN: (纸本)9783540737490

Spectral embedding and spectral clustering are common methods for non-linear dimensionality reduction and clustering of complex high dimensional datasets. In this paper we provide a diffusion based probabilistic analysis of algorithms that use the normalized graph Laplacian. Given the pairwise adjacency matrix of all points in a dataset, we define a random walk on the graph of points and a diffusion distance between any two points. We show that the diffusion distance is equal to the Euclidean distance in the embedded space with all eigenvectors of the normalized graph Laplacian. This identity shows that characteristic relaxation times and processes of the random walk on the graph are the key concept that governs the properties of these spectral clustering and spectral embedding algorithms. Specifically, for spectral clustering to succeed, a necessary condition is that the mean exit times from each cluster need to be significantly larger than the largest (slowest) of all relaxation times inside all of the individual clusters. For complex, multiscale data, this condition may not hold and multiscale methods need to be developed to handle such situations.

关键词： Relaxation time

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The attractor of the stochastic generalized Ginzburg-Landau equation

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science China mathematics 2008年第5期51卷 955-964页

作者： GUO BoLing~1 WANG GuoLian~(2+) Li DongLong~3 1 Institute of applied Physics and computational mathematics,P.O.Box 8009,Beijing 100088,China 2 The graduate School of China Academy of Engineering Physics,P.O.Box 2101,Beijing 100088,China 3 Department of Information and Computer science,Guangxi University of Technology,Liuzhou 545006,China Institute of Applied Physics Computational Mathematics P. O. Box 8009 Beijing 100088 China The Graduate School of China Academy of Engineering Physics P. O. Box 2101 Beijing 100088 China Department of Information Computer Science Guangxi University of Technology Liuzhou 545006 China

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in ... 详细信息

关键词： generalized Ginzburg-Landau equation random dynamical systems random attractor 35K05

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A Primal Equation Free Projective Integration Scheme in Multi-Scale Plasma Dynamics

A Primal Equation Free Projective Integration Scheme in Mult...

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International Conference on Ultrahigh Intensity Lasers Development,science and Emerging Applications(第三届超强激光科学和应用国际会议)

作者： Li Baiwen S.Ishiguro M.M.Skoric R.Horiuchi Institute of Applied Physics and Computational Mathematics National Institute for Fusion Science Graduate University for Advanced Studies

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