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Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes

Physical Review E 2010年第6期81卷 061105-061105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 Department of Physics 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 08544 USA

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball’s interior is defined by the inequality |x|2q+|y|2q+|z|2q≤1, which provides a versatile family of convex particles (q≥0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q=1) and the cube (q=∞). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1

关键词： Spheres

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Coarse-graining the dynamics of a driven interface in the presence of mobile impurities: Effective description via diffusion maps

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Physical Review E 2009年第3期80卷 031102-031102页

作者： Benjamin E. Sonday Mikko Haataja Ioannis G. Kevrekidis []Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an effective description of a driven interface in the presence of mobile impurities, based on an Ising variant model and a single empirical coarse variable, was partially successful [M. Haataja et al., Phys. Rev. Lett. 92, 160603 (2004)]; yet it underlined the necessity of selecting additional coarse variables in certain parameter regimes. In this paper we use a data mining approach to help identify the coarse variables required. We discuss the implementation of this diffusion map approach, the selection of a similarity measure between system snapshots required in the approach, and the correspondence between empirically selected and automatically detected coarse variables. We conclude by illustrating the use of the diffusion map variables in assisting the atomistic simulations and we discuss the translation of information between fine and coarse descriptions using lifting and restriction operators.

关键词： Data mining

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Dislocation climb strengthening in systems with immobile obstacles: Three-dimensional level-set simulation study

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Physical Review B 2010年第5期81卷 054104-054104页

作者： Zi Chen Kevin T. Chu David J. Srolovitz Jeffrey M. Rickman Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08540 USA Vitamin D Inc. Menlo Park California 94025 USA Institute of High Performance Computing Singapore Singapore Department of Materials Science and Engineering Lehigh University Bethlehem Pennsylvania 18015 USA Department of Physics Lehigh University Bethlehem Pennsylvania 18015 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08540 USA

We employ a parallel, three-dimensional level-set code to simulate the dynamics of isolated dislocation lines and loops in an obstacle-rich environment. This system serves as a convenient prototype of those in which extended, one-dimensional objects interact with obstacles and the out-of-plane motion of these objects is key to understanding their pinning-depinning behavior. In contrast to earlier models of dislocation motion, we incorporate long-ranged interactions among dislocation segments and obstacles to study the effect of climb on dislocation dynamics in the presence of misfitting penetrable obstacles/solutes, as embodied in an effective climb mobility. Our main observations are as follows. First, increasing climb mobility leads to more effective pinning by the obstacles, implying increased strengthening. Second, decreasing the range of interactions significantly reduces the effect of climb. The dependence of the critical stress on obstacle concentration and misfit strength is also explored and compared with existing models. In particular, our results are shown to be in reasonable agreement with the Friedel-Suzuki theory. Finally, the limitations inherent in the simplified model employed here, including the neglect of some lattice effects and the use of a coarse-grained climb mobility, are discussed.

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Study noise-induced transitions in the Kuramoto-Sivashinsky equation via the mini- mum action method

Study noise-induced transitions in the Kuramoto-Sivashinsky ...

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International Conference on Random Dynamical Systems(2009年随机动力系统国际会议)

作者： Xiaoliang Wan Xiang Zhou Weinan E Program in Applied and Computational Mathematics Princeton University USA

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Ergodic directional switching in mobile insect groups

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Physical Review E 2010年第1期82卷 011926-011926页

作者： Carlos Escudero Christian A. Yates Jerome Buhl Iain D. Couzin Radek Erban Ioannis G. Kevrekidis Philip K. Maini ICMAT (CSIC-UAM-UC3M-UCM) Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco 28049 Madrid Spain Centre for Mathematical Biology Mathematical Institute University of Oxford 24-29 St. Giles’ Oxford OX1 3LB United Kingdom School of Biological Sciences and Centre for Mathematical Biology Heydon-Laurence Building A08 The University of Sydney Sydney New South Wales Australia Department of Ecology and Evolutionary Biology Princeton University Princeton New Jersey 08544 USA Oxford Centre for Collaborative Applied Mathematics Mathematical Institute University of Oxford 24-29 St. Giles’ Oxford OX1 3LB United Kingdom Department of Chemical Engineering Program in Applied and Computational Mathematics and Mathematics Princeton University Princeton New Jersey 08544 USA Department of Biochemistry Oxford Centre for Integrative Systems Biology University of Oxford South Parks Road Oxford OX1 3QU United Kingdom

We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group’s direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation.

关键词： Fokker Planck equation

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Interatomic potentials for hydrogen in α–iron based on density functional theory

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Physical Review B 2009年第17期79卷 174101-174101页

作者： Ashwin Ramasubramaniam Mitsuhiro Itakura Emily A. Carter []Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We present two interatomic potentials for hydrogen in α–iron based on the embedded atom method potentials for iron developed by Mendelev et al. [Philos. Mag. 83, 3977 (2003)] and Ackland et al. [J. Phys.: Condens. Matter 16, S2629 (2004)]. Since these latter potentials are unique among existing iron potentials in their ability to produce the same core structure for screw dislocations as density functional theory (DFT) calculations, our interatomic potentials for hydrogen in iron also inherit this important feature. We use an extensive database of energies and atomic configurations from DFT calculations to fit the cross interaction of hydrogen with iron. Detailed tests on the dissolution and diffusion of hydrogen in bulk α–iron, as well as the binding of H to vacancies, free surfaces, and dislocations, indicate that our potentials are in excellent overall agreement with DFT calculations.

关键词： density functional theory diffusion dissolving hydrogen iron potential energy functions screw dislocations vacancies (crystal)

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STYLISTIC ANALYSIS OF PAINTINGS USING WAVELETS AND MACHINE LEARNING

STYLISTIC ANALYSIS OF PAINTINGS USING WAVELETS AND MACHINE L...

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European signal processing conference

作者： Sina Jafarpour Guengor Polatkan Eugene Brevdo Shannon Hughes Andrei Brasoveanu Ingrid Daubechies Departments of Electrical Engineering Computer Science and Mathematics and the Program in Applied and Computational Mathematics Princeton NJ 08544

ISBN: (纸本)9781617388767

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features".

关键词： Support vector machines Abstracts Image resolution Radio frequency

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Simultaneous tracking of movement and gene expression in multiple Drosophila melanogaster flies using GFP and DsRED fluorescent reporter transgenes

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BMC Research Notes 2009年第1期2卷 1-11页

作者： Grover, Dhruv Yang, Junsheng Ford, Daniel Tavaré, Simon Tower, John Molecular and Computational Biology Program Department of Biological Sciences University of Southern California Los Angeles CA 90089-2910 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 0WA United Kingdom

Background. Fluorescent proteins such as GFP (Green Fluorescent Protein) and DsRED (Discosoma *** Fluorescent Protein) are often used as reporter molecules for transgene expression in Drosophila and other species. We have recently reported methods that allow simultaneous tracking of animal movement and GFP expression in real time, however the assay was limited to single animals and a single transgene. Numerous studies would be facilitated by methods that allow for assay of multiple animals and multiple transgenes. Findings. Here we report an improved fly video tracking system that allows multiple transgenic flies to be tracked simultaneously using visible light, GFP fluorescence and DsRED fluorescence. The movement of multiple flies could be accurately tracked at real time rates, while simultaneously assaying the expression level of two different transgenes marked with GFP and DsRED. The individual flies could be accurately tracked and distinguished even during periods when transgene fluorescence was undetected. For example, characteristic patterns of hsp70 and hsp22 transgene induction could be simultaneously quantified and correlated with animal movement in aging flies, and as groups of flies died due to dessication/starvation. Conclusion. The improved methods allow for more efficient assay of the correlation between gene expression, behavior, aging and mortality: multiple animals can be assayed with simultaneous quantification of multiple transgenes using GFP and DsRED fluorescence. These methods should allow for increased flexibility in experimental designs. For example, in the future it should be possible to use gene expression levels to predict remaining life span more accurately, and to quantify gene expression changes caused by interactions between animals in real time. © 2009 Tower et al.

关键词： Green Fluorescent Protein Extended Kalman Filter Green Fluorescent Protein Expression Green Fluorescent Protein Fluorescence Daily Activity Pattern

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Constructions and existence of tight fusion frames

Constructions and existence of tight fusion frames

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Wavelets XIII

作者： Casazza, Peter G. Fickus, Matthew Mixon, Dustin G. Wang, Yang Zhou, Zhengfang Department of Mathematics and Statistics Air Force Institute of Technology Wright-Patterson Air Force Base OH 45433 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Mathematics Michigan State University East Lansing MI 48824 United States Department of Mathematics University of Missouri Columbia MO 65211 United States

ISBN: (纸本)9780819477361

Fusion frames are an emerging topic of frame theory, with applications to communications and distributed processing. However, until recently, little was known about the existence of tight fusion frames, much less how to construct them. We discuss a new method for constructing tight fusion frames which is akin to playing Tetris with the spectrum of the frame operator. When combined with some easily obtained necessary conditions, these Spectral Tetris constructions provide a near complete characterization of the existence of tight fusion frames. © 2009 SPIE.

关键词： Optical engineering

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Critical dynamics in multicomponent lipid membranes

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Physical Review E 2009年第2期80卷 020902(R)-020902(R)页

作者： Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes both in vivo and in vitro lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, the roles of membrane and exterior fluid hydrodynamics on domain formation kinetics have received less attention. A case in point is the impact of hydrodynamics on the dynamics of compositional heterogeneities in lipid membranes in the vicinity of a critical point. In this Rapid Communication it is argued that the asymptotic dynamic behavior of a lipid membrane system in the vicinity of a critical point is strongly influenced by hydrodynamic interactions. More specifically, a mode-coupling argument is developed which predicts a scaling behavior of lipid transport coefficients near the critical point for both symmetric and asymmetric bilayers immersed in a bulk fluid.

关键词： Hydrodynamics

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