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Microstructural degeneracy associated with a two-point correlation function and its information content

Physical Review E 2012年第5期85卷 051140-051140页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège Liège 4000 Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics 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 Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the

关键词： MICROSTRUCTURE CORRELATION (Statistics) INFORMATION theory ENTROPY (Information theory) GROUND state (Quantum mechanics) MONTE Carlo method POISSON processes

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Theoretical analysis of electronic and magnetic properties of NaV2O4: Crucial role of the orbital degrees of freedom

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Physical Review B 2012年第10期86卷 104409-104409页

作者： Z. V. Pchelkina I. V. Solovyev R. Arita Institute of Metal Physics Russian Academy of Sciences-Ural Division 620990 Ekaterinburg Russia Theoretical Physics and Applied Mathematics Department Ural Federal University Mira Str. 19 620002 Ekaterinburg Russia Computational Materials Science Unit National Institute for Materials Science 1-2-1 Sengen Tsukuba Ibaraki 305-0047 Japan Department of Applied Physics Graduate School of Engineering The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan PRESTO Japan Science and Technology Agency 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan

Using a realistic low-energy model with parameters derived from the first-principles electronic structure calculation, we address the origin of the quasi-one-dimensional behavior in orthorhombic NaV2O4, consisting of the double chains of edge-sharing VO6 octahedra. We argue that the geometrical aspect alone does not explain the experimentally observed anisotropy of electronic and magnetic properties of NaV2O4. Instead, we attribute the unique behavior of NaV2O4 to one particular type of the orbital ordering, which respects the orthorhombic Pnma symmetry. This orbital ordering acts to divide all t2g states into two types: The “localized” ones, which are antisymmetric with respect to the mirror reflection y→−y, and the symmetric “delocalized” ones. Thus, NaV2O4 can be classified as the double exchange system. The directional orientation of symmetric orbitals, which form the metallic band, appears to be sufficient to explain both quasi-one-dimensional character of interatomic magnetic interactions and the anisotropy of electrical resistivity.

关键词： ELECTRONIC structure MAGNETIC properties of crystals OXIDES DEGREES of freedom DENSITY functionals ANISOTROPY SYMMETRY (Physics)

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Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

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Physical Review Letters 2012年第11期109卷 114302-114302页

作者： Zi Chen Qiaohang Guo Carmel Majidi Wenzhe Chen David J. Srolovitz Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08544 USA Department of Biomedical Engineering Washington University St. Louis Missouri 63130 USA College of Materials Science and Engineering Fuzhou University Fuzhou Fujian 350108 China Department of Mathematics and Physics Fujian University of Technology Fuzhou Fujian 350108 China Department of Mechanical Engineering Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA Department of Materials Science and Engineering Fujian University of Technology Fuzhou Fujian 350108 China Institute for High Performance Computing 1 Fusionopolis Way Singapore 138632 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.

关键词： NONLINEAR theories DEFORMATIONS (Mechanics) PARAMETER estimation OPTICAL bistability STRUCTURAL shells PLATES (Engineering) CRYSTAL structure

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Simulation of Hydrogen Emission Spectrum in Debye Plasmas

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Chinese Physics Letters 2011年第5期28卷 84-87页

作者： DING Qi-Yong ZHANG Song-Bin WANG Jian-Guo The Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009Beijing 100088 Graduate School of China Academy of Engineering Physics P.O.Box 2101Beijing 100088 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of ChinaHefei 230026

We investigate the screening effects on the spectrum of spontaneous radiation and radiative recombination to the 1s,2s and 2p states of hydrogen with total atom density N=1.7×10^(19)cm^(-3)and electron temperatures 1eV,2eV and 5eV under the local thermodynamic equilibrium(LTE)*** needed atomic energy levels,the radiative transition probabilities and radiative recombination cross sections are calculated by solving the Schr(o)dinger equation numerically incorporating the Debye-Hückel model in *** plasma emission spectrum is simulated for the first time by using the screened atomic *** red shift and the cutoff of Rydberg spectra are observed and it is also found that the 2 eV electron temperature case has the strongest screening effects and the emission spectra to the 2s and 2p states are more likely affected by screening effects than that of the ls state.

关键词： Debye radiative spectrum

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Momentum distribution, vibrational dynamics, and the potential of mean force in ice

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Physical Review B 2011年第22期83卷 220302(R)-220302(R)页

作者： Lin Lin Joseph A. Morrone Roberto Car Michele Parrinello Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Department of Chemistry Princeton University Princeton NJ 08544 USA Department of Physics Princeton University Princeton NJ 08544 USA Computational Science Department of Chemistry and Applied Biosciences Eidgenössische Technische Hochschule Zürich USI Campus Via Giuseppe Buffi 12 CH-6900 Lugano Switzerland

By analyzing the momentum distribution obtained from path integral and phonon calculations we find that the protons in hexagonal ice experience an anisotropic quasiharmonic effective potential with three distinct principal frequencies that reflect molecular orientation. Due to the importance of anisotropy, anharmonic features of the environment cannot be extracted from existing experimental distributions that involve the spherical average. The full directional distribution is required, and we give a theoretical prediction for this quantity that could be verified in future experiments. Within the quasiharmonic context, anharmonicity in the ground-state dynamics of the proton is substantial and has quantal origin, a finding that impacts the interpretation of several spectroscopies.

关键词： PHYSICS research PHONONS ICE ANISOTROPY PROTON beams SPECTROSCOPIC imaging

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Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

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Physical Review B 2011年第15期84卷 155461-155461页

作者： Alexander A. Govyadinov George Y. Panasyuk John C. Schotland Vadim A. Markel Departments of Radiology and Bioengineering and the Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by F. Hache, D. Ricard, and C. Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat corrected form) by S. G. Rautian [Sov. Phys. JETP 85, 451 (1997)]. These references consider a metal nanoparticle as a degenerate Fermi gas of conduction electrons in an infinitely high spherical potential well. This model (referred to as the HRFR model below) yields mathematical expressions for the linear and the third-order nonlinear polarizabilities of a nanoparticle in terms of infinite nested series. These series have not been evaluated numerically so far and, in the case of nonlinear polarizability, they cannot be evaluated with the use of conventional computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian’s approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian’s approximations and find that they are surprisingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable to or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespective of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. Lett. 100, 47402 (2008)].

关键词： NANOPARTICLES ELECTRON gas QUANTUM theory QUANTUM wells APPROXIMATION theory

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Quantum theory of the electromagnetic response of metal nanofilms

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Physical Review B 2011年第15期84卷 155460-155460页

作者： George Y. Panasyuk John C. Schotland Vadim A. Markel Departments of Radiology Bioengineering and Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions imposed on the metal surface. We find that the sign and magnitude of the nonlinear polarizability depends dramatically on the type of boundary condition used.

关键词： QUANTUM theory FIELD theory (Physics) BOUNDARY value problems ELECTRIC fields NONLINEAR models (Statistics)

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Structure and dynamics of highly charged heavy ions studied with the electron beam ion trap in Tokyo

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Hyperfine Interactions 2011年第1期199卷 123-130页

作者： Nakamura, Nobuyuki Hu, Zhimin Watanabe, Hirofumi Li, Yueming Kato, Daiji Currell, Fred J. Tong, Xiao-Min Watanabe, Tsutomu Ohtani, Shunsuke Institute for Laser Science The University of Electro-Communications 1-5-1 Chofugaoka Chofu Tokyo 182-8585 Japan Chubu University 1200 Matsumoto-cho Kasugai-shi Aichi 487-8501 Japan Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 China National Institute for Fusion Science 322-6 Oroshi-cho Toki Gifu 509-5292 Japan Centre for Plasma Physics School of Mathematics and Physics Queen's University Belfast Belfast BT7 1NN United Kingdom Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki 305-8573 Japan

In this paper, we present the structure and the dynamics of highly charged heavy ions studied through dielectronic recombination (DR) observations performed with the Tokyo electron beam ion trap. By measuring the energy dependence of the ion abundance ratio in the trap at equilibrium, we have observed DR processes for open shell systems very clearly. Remarkable relativistic effects due to the generalized Breit interaction have been clearly shown in DR for highly charged heavy ions. We also present the first result for the coincidence measurement of two photons emitted from a single DR event. © 2011 Springer science+Business Media B.V.

关键词： Heavy ions

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Densest local sphere-packing diversity. II. Application to three dimensions

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Physical Review E 2011年第1期83卷 011304-011304页

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

The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N=1054. In the predecessor to this paper [A. B. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of N up to N=348. Here we analyze the properties and characteristics of the densest local packings in R3 and employ knowledge of the Rmin(N), using methods applicable in any d, to construct both a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In R3, we find wide variability in the densest local packings, including a multitude of packing symmetries such as perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest local packings of N spheres near a central sphere to minimal-energy configurations of N+1 points interacting with short-range repulsive and long-range attractive pair potentials, e.g., 12–6 Lennard-Jones, and find that they are in general completely different, a result that has possible implications for nucleation theory. We also compare the densest local packings to finite subsets of stacking variants of the densest infinite packings in R3 (the Barlow packings) and find that the densest local packings are almost always most similar as measured by a similarity metric, to the subsets of Barlow packings with the smallest number of coordination shells measured about a single central sphere, e.g., a subset of the fcc Barlow packing. Additionally, we observe that the densest local packings are dominated by the dense arrangement of spheres with centers at distance Rmin(N). In particular, we find two “maracas” packings at N=77 and N=93, each consisting of a few unjammed sphere

关键词： DENSITY functionals SPHERES MATHEMATICAL models EUCLIDEAN metric CORRELATION (Statistics) SYMMETRY

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Corrigendum: The Green's function for the radiative transport equation in the slab geometry

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Journal of Physics A: Mathematical and Theoretical 2012年第45期45卷

作者： Manabu Machida George Y Panasyuk John C Schotland Vadim A Markel Department of Mathematics University of Michigan Ann Arbor MI 48109 USA Aerospace Systems Directorate Air Force Research Laboratory Wright-Patterson Air Force Base OH 45433 USA Departments of Radiology and Bioengineering and the Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA 19104 USA

The full text of this article is available in the PDF provided.

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