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Uncertainity quantification for atomistic reaction models: An equation-free stochastic simulation algorithm example

Multiscale Modeling and Simulation 2007年第4期6卷 1217-1233页

作者： Zou, Yu Keverekidis, Ioannis G. Citigroup 388 Greenwhich Street New York NY 10013 United States Department of Chemical Engineering and Program in Applied and COmputational Mathematics Princeton University Princeton NJ 08544 United States

We describe a computational framework linking uncertainty quantification (UQ) methods for continuum problems depending on random parameters with equation-free (EF) methods for performing continuum deterministic numerics by acting directly on atomistic/stochastic simulators. Our illustrative example is a heterogeneous catalytic reaction mechanism with an uncertain atomistic kineticparameter;the "inner" dynamic simulator of choice is a Gillespie stochastic simulation algorithm(SSA). We demonstrate UQ computations at the coarse-grained level, in a nonintrusive way, throughthe design of brief, appropriately initialized computational experiments with the SSA code. The system is thus observed at three levels: (a) a fine scale for each stochastic simulation at each value of the uncertain parameter;(b) an intermediate coarse-grained state for the expected behavior of the SSA at each value of the uncertain parameter;and (c) the desired fully coarse-grained level: distributions of the coarse-grained behavior over the range of uncertain parameter values The latter are computed in the form of generalized polynomial chaos (gPC) coefficients in terms of the random parameter. Coarse projective integration and coarse fixed point computation are employed to accelerate the computational evolution of these desired observables, to converge on random stable/ unstable steady states, and to perform parametric studies with respect to other (nonrandom) system parameters. © 2008 Society for Industrial and applied mathematics.

关键词： Stochastic systems

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Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids

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Physical Review E 2007年第5期75卷 051304-051304页

作者： Aleksandar Donev Robert Connelly Frank H. Stillinger Salvatore Torquato Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Mathematics Cornell University Ithaca New York 14853 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science 303, 990 (2004)] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why an isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle (Z¯=2df), does not apply to nonspherical particles. We develop first- and second-order conditions for jamming and demonstrate that packings of nonspherical particles can be jammed even though they are underconstrained (hypoconstrained, Z¯<2df). We apply an algorithm using these conditions to computer-generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings, even close to the sphere point. We also consider packings that are nearly jammed and draw connections to packings of deformable (but stiff) particles. Finally, we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point.

关键词： GRANULAR-MATERIALS AMORPHOUS SOLIDS SPHERE PACKINGS DENSITY RIGIDITY ELASTICITY ALGORITHM DYNAMICS STRESS

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Evolution in LTPS AMLCD manufacturing via advances in laser crystallization techniques and systems

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Information Display 2007年第9期23卷 14-18页

作者： Im, James S. Limanov, A.B. Van Der Wilt, P.C. Chung, U.J. Chitu, A.M. Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University 500 W. 120th St. 1106A Mudd New York NY 10027-6623

Substantial R&D activities are presently under way toward the development of advanced pulsed-laser-based production tools and processes that can enable sophisticated yet effective crystallization of Si films for manufacturing advanced active-matrix liquid-crystal displays (AMLCDs) that utilize poly crystalline-Si films. Implementation of such techniques in volume production, which has actually already begun, is poised to potentially permit low-tempe rature polycrystalline-Si (LTPS) AMLCD technology to pursue a more aggressive product and manufacturing roadmap. © SID 2007.

关键词： Pulsed laser applications

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Symmetry classification and invariant geodesic equations characterization of two-dimensional

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12th Regional Conference on Mathematical physics

作者： Kashif, A.R. Mahomed, F.M. Qadir, A. College of Electrical and Mechanical Engineering National University of Sciences and Technology Peshawar Road Rawalpindi Pakistan Centre of Differential Equations Continuum Mechanics and Applications School of Computational and Applied Mathematics University of Witwatersrand Wits 2050 Johannesberg South Africa Centre of Advanced Mathematics and Physics National University of Sciences and Technology Peshawar Road Rawalpindi Pakistan Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Dhahran 30261 Saudi Arabia

ISBN: (纸本)9812705910

We present the point symmetry classification and invariant characterization of a system of two geodesic equations. Previously, Aminova and Aminovl attempted the point symmetry classification. However, they did not identify the Lie algebras nor did they provide an invariant characterization, in terms of coefficients, of the geodesic equations. In this paper we do both. Copyright © 2007 by World Scientific Publishing Co. Pvt. Ltd.

关键词： Geodesy

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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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Concentration Dependence of the Collective Dynamics of Swimming Bacteria

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Physical Review Letters 2007年第15期98卷 158102-158102页

作者： Andrey Sokolov Igor S. Aranson John O. Kessler Raymond E. Goldstein Argonne National Laboratory 9700 South Cass Avenue Argonne Illinois 60439 USA Illinois Institute of Technology 3101 South Dearborn Street Chicago Illinois 60616 USA Department of Physics Program in Applied Mathematics and BIO5 Institute University of Arizona Tucson Arizona 85721 USA Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road Cambridge CB3 0WA United Kingdom

At concentrations near the maximum allowed by steric repulsion, swimming bacteria form a dynamical state exhibiting extended spatiotemporal coherence. The viscous fluid into which locomotive energy of individual microorganisms is transferred also carries interactions that drive the coherence. The concentration dependence of correlations in the collective state is probed here with a novel technique that herds bacteria into condensed populations of adjustable concentration. For the particular thin-film geometry employed, the correlation lengths vary smoothly and monotonically through the transition from individual to collective behavior.

关键词： Bacteria

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Monte Carlo simulations of neutron time constants

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Qinghua Daxue Xuebao/Journal of Tsinghua University 2007年第SUPPL. 1期47卷 1057-1061页

作者： Li, Shu Tian, Dongfeng Deng, Li Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Graduate China Academy of Engineering Physics Beijing 100088 China

A Monte Carlo method was developed to calculate neutron time constants by first calculating the eigen-distribution of the neutron, then calculating the neutron time constant based on the distribution. For supercritical or critical systems, the results are consistent with the α calculational method in the MCNP code. For subcritical systems, the MCNP4C code fails to finish the calculation, while the DSMC code based on the new method runs successfully with reasonable results.

关键词： Neutrons

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Effects of a static electric field on nonsequential double ionization

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Physical Review A 2007年第3期76卷 033405-033405页

作者： Hongyun Li Bingbing Wang Jing Chen Hongbing Jiang Xiaofeng Li Jie Liu Qihuang Gong Zong-Chao Yan Panming Fu Laboratory of Optical Physics Institute of Physics Chinese Academy of Sciences Beijing 100080 China Department of Physics State Key Laboratory for Artificial Microstructures and Mesoscopic Physics Peking University Beijing 100871 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Physics University of New Brunswick P.O. Box 4400 Fredericton New Brunswick Canada E3B 5A3 Research Academy of Science and Technology Harbin Institute of Technology Harbin 150001 China

Using a three-dimensional semiclassical method, we perform a systematic analysis of the effects of an additional static electric field on nonsequential double ionization (NSDI) of a helium atom in an intense, linearly polarized laser field. It is found that the static electric field influences not only the ionization rate, but also the kinetic energy of the ionized electron returning to the parent ion, in such a way that, if the rate is increased, then the kinetic energy of the first returning electron is decreased, and vice versa. These two effects compete in NSDI. Since the effect of the static electric field on the ionization of the first electron plays a more crucial role in the competition, the symmetric double-peak structure of the He2+ momentum distribution parallel to the polarization of the laser field is destroyed. Furthermore, the contribution of the trajectories with multiple recollisions to the NSDI is also changed dramatically by the static electric field. As the static electric field increases, the trajectories with two recollisions, which start at the time when the laser and the static electric field are in the same direction, become increasingly important for the NSDI.

关键词： HIGH-HARMONIC-GENERATION RAY-ATOM SCATTERING HELIUM DEPENDENCE PLATEAU IONS

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Model for dynamical coherence in thin films of self-propelled microorganisms

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Physical Review E 2007年第4期75卷 040901(R)-040901(R)页

作者： Igor S. Aranson Andrey Sokolov John O. Kessler Raymond E. Goldstein Argonne National Laboratory 9700 South Cass Avenue Argonne Illinois 60439 USA Illinois Institute of Technology 3101 South Dearborn Street Chicago Illinois 60616 USA Department of Physics University of Arizona Tucson Arizona 85721 USA Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA BIO5 Institute University of Arizona Tucson Arizona 85721 USA Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road Cambridge CB3 0WA United Kingdom

Concentrated bacterial suspensions spontaneously develop transient spatiotemporal patterns of coherent locomotion whose correlation lengths greatly exceed the size of individual organisms. Continuum models have indicated that a state of uniform swimming order is linearly unstable at finite wavelengths, but have not addressed the nonlinear dynamics of the coherent state, with its biological implications for mixing, transport, and intercellular communication. We investigate a specific model incorporating hydrodynamic interactions in thin-film geometries and show by numerical studies that it displays large scale persistently recurring vortices, as actually observed.

关键词： ORDER DIFFUSION CELLS

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Semiclassical theory of molecular nonsequential double ionization

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Physical Review A 2007年第1期76卷 013418-013418页

作者： J. Chen J. Fan Y. Li S. P. Yang Institute of Applied Physics and Computational Mathematics P.O. Box 8009 (28) 100088 Beijing People’s Republic of China Department of Chemistry University of Kansas and Kansas Center for Advanced Scientific Computing Lawrence Kansas 66045 USA Optical Technology Division National Institute of Standards and Technology 100 Bureau Drive Gaithersburg Maryland 20899 USA Department of Physics Hebei Normal University Shijiazhuang 050016 People’s Republic of China

A semiclassical molecular nonsequential double ionization theory is developed based on the rescattering model. We show that, in the nonsequential double ionization of D2, the kinetic energy of the returning electron changes from below to above the ionization threshold of the parent ion as the laser varies from short to long wavelength, resulting in the dominance of collisional ionization at shorter laser wavelength and field ionization at longer laser wavelength. We also calculate the double ionization time distribution of D2 and the kinetic energy distribution of D+. The theoretical results are qualitatively consistent with experimental measurements. The nonsequential double to single ionization ratio of N22+∕N2+ is also calculated and compared with available experimental results.

关键词： STRONG LASER FIELDS MOMENTUM DISTRIBUTIONS HARMONIC-GENERATION DYNAMICS HELIUM SINGLE IONS

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