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Static structural signatures of nearly jammed disordered and ordered hard-sphere packings: Direct correlation function

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Physical Review E 2016年第3期94卷 032902-032902页

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

The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed “hyperuniformity”) has paved the way for the analysis of jamming as an “inverted critical point” in which the direct correlation function c(r), rather than the total correlation function h(r), diverges. We expand on the notion that c(r) provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the nth derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of c(r) with regards to singularities it inherits from h(r). These relations provide a concrete means of identifying features that must be expressed in c(r) if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter D as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling c(r)∝−1/r as r→0 that accompanies the formation of the delta function at c(D) that indicates the formation of contacts in all cases, and show that this scaling behavior is,

关键词： Jamming

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Hyperuniformity of quasicrystals

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Physical Review B 2017年第5期95卷 054119-054119页

作者： Erdal C. Oğuz Joshua E. S. Socolar Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

Hyperuniform systems, which include crystals, quasicrystals, and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity Z(k) to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of Z(k) as k tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, σ2(R), in the number of points contained in an interval of length 2R. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope 1/τ fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, Z(k)∼k4; for all others, Z(k)∼k2. This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.

关键词： Microstructure Structural properties

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High-order rogue waves in vector nonlinear Schrödinger equations

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Physical Review E 2014年第4期89卷 041201(R)-041201(R)页

作者： Liming Ling Boling Guo Li-Chen Zhao Department of Mathematics South China University of Technology Guangzhou 510640 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Physics Northeast University Xi'an 710069 China

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

关键词： ROGUE waves NONLINEAR Schrodinger equation DISTRIBUTION (Probability theory) ANALYTICAL solutions (Mathematical analysis) SHAPES DYNAMICS

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An immersed interface method for incompressible flows and geometries with sharp features

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Journal of computational physics 2025年 537卷

作者： Michael J. Facci Ebrahim M. Kolahdouz Boyce E. Griffith Department of Mathematics University of North Carolina Chapel Hill NC USA Flatiron Institute Simons Foundation New York NY USA Department of Biomedical Engineering University of North Carolina Chapel Hill NC USA Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel Hill NC USA Computational Medicine Program University of North Carolina School of Medicine Chapel Hill NC USA McAllister Heart Institute University of North Carolina School of Medicine Chapel Hill NC USA

The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamics applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly on engineered structures. The present study builds on our work to integrate finite element-type representations of interface geometries with the IIM. Initial realizations of this approach used a continuous Galerkin (CG) finite element discretization for the boundary, but as we show herein, these approaches generate large errors near sharp geometrical features. To overcome this difficulty, this study introduces an IIM approach using a discontinuous Galerkin (DG) representation of the jump conditions. Numerical examples explore the impacts of different interface representations on accuracy for both smooth and sharp boundaries, particularly flows interacting with fixed interface configurations. We demonstrate that using a DG approach provides accuracy that is comparable to the CG method for smooth cases. Further, we identify a time step size restriction for the CG representation that is directly related to the sharpness of the geometry. In contrast, time step size restrictions imposed by DG representations are demonstrated to be nearly insensitive to the presence of sharp features.

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A molecular dynamical study of granular fluids I: The unforced granular gas in two dimensions

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Journal of Scientific Computing 1993年第1期8卷 1-40页

作者： Goldhirsch, I. Tan, M.-L. Zanetti, G. Department of Fluid Mechanics and Heat Transfer Faculty of Engineering Tel-Aviv University Ramat Aviv 69978 Tel-Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton 08544 New Jersey United States

Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model for rapidly flowing granular materials, are markedly different from those known for atomic or moleclar gases, in which collisions are of elastic nature. The most prominent feature characterizing granular systems, even in the idealized situation in which no external forcing exists and the initial condition is statistically homogeneous, is their inherent instability to inhomogeneous fluctuations. Granular "gases" are thus generically nonuniform, a fact that suggests extreme caution in pursuing direct analogies with molecular gases. We find that once an inhomogeneous state sets in, the velocity distribution functions differ from the classical Maxwell-Boltzmann distribution. Other characteristics of the system are different from their counterparts in molecular systems as well. For a given value of the coefficient of restitution, e, a granular system forms clusters of typical separation L₀≈l/(1-e²)^1/2, where l is the mean free path in the corresponding homogeneous system. Most of the fluctuating kinetic energy then resides in the relatively dilute regions that surround the clusters. Systems whose linear dimensions are less then L⁰ do not give rise to clusters;still they are inhomogeneous, the scale of the corresponding inhomogeneity being the longest wavelength allowed by the system's size. The present article is devoted to a detailed numerical study of the above-mentioned clustering phenomenon in two dimensions and in the absence of external forcing. A theoretical framework explaining this phenomenon is outlined. Some general implications as well as practical ramifications are discussed. © 1993 Plenum Publishing Corporation.

关键词： Granular flow dynamics molecular dynamics numerical simulation

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Energy levels of the quantized discrete self-trapping equation

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Journal of Biological physics 1989年第1期17卷 1-17页

作者： Scott, A.C. Bernstein, L. Eilbeck, J.C. Laboratory of Applied Mathematical Physics The Technical University of Denmark Lyngby DK-2800 Denmark Program in Applied Mathematics The University of Arizona Tucson 85721 AZ United States Department of Mathematics Heriot-Watt University Edinburgh EH14 4AS Riccarton United Kingdom

Degenerate perturbation theory is used to calculate energy levels of stationary states of the quantized discrete self-trapping (QDST) equation in the weak dispersion limit. Two specific applications are described: (1) the CH stretch vibrations of benzene, and (2) a long molecular chain with nearest-neighbour interactions and periodic boundary conditions. © 1989 Kluwer Academic Publishers.

关键词： acetanilide benzene Local mode self-trapping soliton

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Epitaxial Growth Following Crystal Nucleation in Laser-Quenched Si Films on SiO2

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MRS Online Proceedings Library 2015年第1期1770卷 67-72页

作者： Wong, Vernon K. Chitu, A. M. Limanov, A. B. Im, James S. Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York USA

We have investigated the solidified microstructure of nucleation-generated grains obtained via complete melting of Si films on SiO2 at high nucleation temperatures. This was achieved using a high-temperature-capable hot stage in conjunction with excimer laser irradiation. As predicted by the direct-growth model that considers (1) the evolution in the temperature of the solidifying interface and (2) the subsequent modes of growth (consisting of amorphous, defective, and epitaxial) as key factors, we were able to observe the appearance of “normal” grains that possess a single-crystal core area. These grains, which are in contrast to previously reported flower-shaped grains that fully make up the microstructure of the solidified films obtained via irradiation at lower preheating temperatures (and amongst which these “normal” grains emerge), indicate that epitaxial growth of nucleated crystals must have taken place within the grains. We discuss the implications of our findings regarding (1) the validity of the direct-growth model, (2) the nature of the heterogeneous nucleation mechanism, and (3) the alternative explanations and assumptions that have been previously employed in order to explain the microstructure of Si films obtained via nucleation and growth within the complete melting regime.

关键词： Si thin film nucleation & growth

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LOCAL ONE-DIMENSIONAL ASE-I SCHEME FOR 2D DIFFUSION EQUATION

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Wuhan University Journal of Natural Sciences 1996年第Z1期1卷 515-521页

作者： LIU XIAO-YU and ZHANG BAO-LIN(department of applied Mathemattes, Tsinghua Unive rsiap Beijing, China Laboratory Of Commutational physics, IAPCM P.O. Box 8009, Beliing, China) Department of Applied Mathematics Tsinghua University Beijing China Laboratory of Computational Physics IAP CM Beijing China

A local alternating segment explicit - implicit method for the solution of 2D diffusion equations is presented in this paper .The method is unconditionally stable and has the obvious property of parallelism. Some nume... 详细信息

关键词： ASE LOCAL ONE-DIMENSIONAL ASE-I SCHEME FOR 2D DIFFUSION EQUATION

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The Weyl-Heisenberg ensemble: Statistical mechanics meets time-frequency analysis

The Weyl-Heisenberg ensemble: Statistical mechanics meets ti...

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International Conference on Sampling Theory and Applications

作者： Luis Daniel Abreu Joao Pereira Jose Luis Romero Salvatore Torquato Austrian Academy of Sciences Acoustics Research Institute Program in Applied and Computational Mathematics Princeton University Department of Chemistry Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781538615669

We present our recent work on the Weyl-Heisenberg ensemble and its statistical properties [4]. The WH ensemble is a class of determinantal point processes associated with the Schrodinger representation of the Heisenberg group. As a special example, WH ensembles include a multi-layer extension of the Ginibre ensemble modeling the distribution of electrons in higher Landau levels. We describe the hyperuniformity of WH ensembles, which characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. Our approach is based on methods from time-frequency analysis. We introduce the main results from [4] highlighting time-frequency techniques and connections to the theory of polyanalytic functions, and also present some small extensions.

关键词： Weyl-Heisenberg ensemble Hyperuniformity Higher Landau levels Disorder Fluctuations

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Differential gene expression in trabecular bone osteocytes is related to the local strain and strain gradient

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Scientific reports 2025年第1期15卷 18501页

作者： Meghana Machireddy Sarah Nano Lucas Debiase Jonathan Lewis Sara Cole Jun Li Glen L Niebur University of Notre Dame Bioengineering Graduate Program Notre Dame IN USA. Department of Aerospace and Mechanical Engineering Notre Dame IN USA. Notre Dame Integrated Imaging Facility Notre Dame IN USA. Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame IN USA. University of Notre Dame Bioengineering Graduate Program Notre Dame IN USA. gniebur@nd.edu. Department of Aerospace and Mechanical Engineering Notre Dame IN USA. gniebur@nd.edu.

Osteocytes regulate the response of osteoclasts and osteoblasts to mechanical loading through signaling molecules, the levels of which are controlled by post-translational modification or degradation and by differential gene transcription and translation. The magnitude and mode of bone tissue deformation that elicits a transcriptional response in individual osteocytes in situ has been difficult to quantify. We measured SOST, Wnt11, TNF, and FRZB gene expression in osteocytes within loaded and unloaded control porcine trabecular bone explants using RNAScope® and compared the local tissue level strain and strain gradient-which we used as an indicator of potential poroelastic fluid flow-in the tissue surrounding osteocytes with high vs. low gene expression. The measured expression of all four genes differed between loaded and unloaded explants, on average, with the mean SOST expression level decreasing by 45%. In the loaded explants, gene expression was altered from baseline in about 30% of the osteocytes, and they were surrounded by tissue with higher strain and strain gradient than the 20 to 25% of osteocytes that remained near baseline expression. Both deviatoric strain and hydrostatic strain gradient were sensitive and specific predictors of the mechanobiological response for individual genes as well as combinations. SOST expression was highly related to elevated strain gradient, providing evidence that osteocytes respond to fluid flow in the lacunar-canalicular system.

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