检索结果-内蒙古大学图书馆

Tilings of space and superhomogeneous point processes

Physical Review E 2008年第3期77卷 031125-031125页

作者： A. Gabrielli M. Joyce S. Torquato SMC-INFM Dipartimento di Fisica Università La Sapienza P.le A. Moro 2 I-00185 Rome Italy ISC-CNR Via dei Taurini 19 I-00185 Rome Italy Laboratoire de Physique Nucléaire et de Hautes Energies UMR-7585 Université Pierre et Marie Curie Paris 6 75252 Paris Cedex 05 France Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are “superhomogeneous” (or “hyperuniform”)—i.e., for which the structure factor S(k) vanishes when the wave vector k tends to zero. The exponent γ characterizing the leading small-k behavior, S(k→0)∝kγ, depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent γ=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents in the range 4−d<γ<4 (and thus always superhomogeneous for d≤4) may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide an explicit analytical construction of point processes with γ>4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.

关键词： SIMULATIONS CAUSALITY SPECTRUM

来源：评论

学校读者我要写书评

暂无评论

Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: Treatment of the thermal bath

引用

Physical Review B 2007年第10期76卷 104107-104107页

作者： Xiantao Li Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism [R. Zwanzig, J. Chem. Phys. 32, 1173 (1960); in Systems Far from Equilibrium, edited by L. Garrido (Interscience, New York, 1980); H. Mori, Prog. Theor. Phys. 33, 423 (1965)] for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of α-iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Coarse-grained computations of demixing in dense gas-fluidized beds

引用

Physical Review E 2007年第5期75卷 051309-051309页

作者： Sung Joon Moon S. Sundaresan I. G. Kevrekidis []Department of Chemical Engineering & Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We use an “equation-free,” coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the coarse-grained dynamics of these phenomena in gently fluidized beds of solid mixtures of different densities, typically a slow process for which reasonable continuum models are currently unavailable.

关键词： DISCRETE PARTICLE SIMULATION EQUATION-FREE MIXTURES DYNAMICS SYSTEMS POWDERS MODEL

来源：评论

学校读者我要写书评

暂无评论

Affine Density in Wavelet Analysis /

引用

2007年

作者： Kutyniok Gitta.

来源：内蒙古大学图书馆图书评论

学校读者我要写书评

暂无评论

Ab initio evaluation of Coulomb and exchange parameters for DFT+U calculations

引用

Physical Review B 2007年第15期76卷 155123-155123页

作者： Nicholas J. Mosey Emily A. Carter []Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

Conventional density functional theory (DFT) fails for materials with strongly correlated electrons, such as late transition metal oxides. Large errors in the intra-atomic Coulomb and exchange interactions are the source of this failure. The DFT+U method has provided a means, through empirical parameters, to correct these errors. Here, we present a systematic ab initio approach in evaluating the intra-atomic Coulomb and exchange terms, U and J, respectively, in order to make the DFT+U method a fully first-principles technique. The method is based on a relationship between these terms and the Coulomb and exchange integrals evaluated in the basis of unrestricted Hartree-Fock molecular orbitals that represent localized states of the extended system. We used this ab initio scheme to evaluate U and J for chromia (Cr2O3). The resulting values are somewhat higher than those determined earlier either empirically or in constrained DFT calculations but have the advantage of originating from an ab initio theory containing exact exchange. Subsequent DFT+U calculations on chromia using the ab initio derived U and J yield properties consistent with experiment, unlike conventional DFT. Overall, the technique developed and tested in this work holds promise in enabling accurate and fully predictive DFT+U calculations of strongly correlated electron materials.

关键词： .electrons Empirical evaluation of Coulomb DFT calculations chromia

来源：评论

学校读者我要写书评

暂无评论

Locality and low-dimensions in the prediction of natural experience from fMRI 07

Locality and low-dimensions in the prediction of natural exp...

引用

Proceedings of the 21st International Conference on Neural Information Processing Systems

作者： François G. Meyer Greg J. Stephens Center for the Study of Brain Mind and Behavior Program in Applied and Computational Mathematics Princeton University Center for the Study of Brain Mind and Behavior Department of Physics Princeton University

ISBN: (纸本)9781605603520

Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding; how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-defined Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke's area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ~ 0.8) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience.

关键词：

来源：评论

学校读者我要写书评

暂无评论

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

引用

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

来源：评论

学校读者我要写书评

暂无评论

Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions

引用

Physical Review E 2007年第3期75卷 031403-031403页

作者： Mikael C. Rechtsman Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and PRISM Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton New Jersey 08544 USA

Using inverse statistical-mechanical optimization techniques, we have discovered isotropic pair interaction potentials with strongly repulsive cores that cause the tetrahedrally coordinated diamond and wurtzite lattices to stabilize, as evidenced by lattice sums, phonon spectra, positive-energy defects, and self-assembly in classical molecular dynamics simulations. These results challenge conventional thinking that such open lattices can only be created via directional covalent interactions observed in nature. Thus, our discovery adds to fundamental understanding of the nature of the solid state by showing that isotropic interactions enable the self-assembly of open crystal structures with a broader range of coordination number than previously thought. Our work is important technologically because of its direct relevance generally to the science of self-assembly and specifically to photonic crystal fabrication.

关键词： CRYSTALS NANOPARTICLES

来源：评论

学校读者我要写书评

暂无评论

Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids

引用

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

来源：评论

学校读者我要写书评

暂无评论

Modeling heterogeneous materials via two-point correlation functions: Basic principles

引用

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

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：