作者:
Steven AtkinsonFrank H. StillingerSalvatore TorquatoDepartment 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. Wh...
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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,
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 lackin...
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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.
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 sys...
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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.
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 boundar...
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.
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 f...
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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)...
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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 h...
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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.
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...
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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 numerical experiments show the method is not only simple but also more accurate.
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 Heisenbe...
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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.
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 differenti...
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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