检索结果-内蒙古大学图书馆

Can One Hear the Shape of a Crystal?

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question "Can one hear the shape of a drum?" concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n ≥ 2). Here, we ask, What is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multi-particle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral 4-, 3- and 2-particle bases in one, two and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identical g2(r) up to infinite r. Based on our analyses, we conjecture that nmin(d) = 4, 3, 2 for d = 1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n = 3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radia

关键词： Eigenvalues and eigenfunctions

Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2000年第2期16卷 207-218页

作者： Weinan E department of mathematics and program in applied and computational mathematics,Princeton University,USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton USA

A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.

关键词： Boundary layer Blow-up Zero-viscosity limit Prandtl’s equation

The Elastic Continuum Limit of the Tight Binding Model

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2007年第6期28卷 665-676页

作者： Weinan E Jianfeng LU Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

关键词： Continuum limit Elasticity theory Cauchy-Born rule Tight binding model

Effective Transport and Mechanical Properties of Two-Phase Materials Across the Order-Disorder Spectrum

学校读者我要写书评

暂无评论

SSRN

SSRN 2025年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Two-phase heterogeneous materials arise in a plethora of natural and synthetic situations, such as alloys, composites, geological media, complex fluids, and biological media, exhibit a wide-variety of microstructures, and thus display a broad-spectrum of effective physical properties. Elucidating how microstructural details (e.g., specific surface, phase volume fractions, geometries, and topologies) influence two-phase materials’ effective transport and mechanical properties enhances our fundamental understanding of microstructure-property relationships, and is of great practical use in the design of structural and functional materials. Here, we compute the three-point microstructural parameters ζ2 and η2 for phase 2 to evaluate bounds and accurate approximation formulas on the effective thermal/electrical conductivities σe as well as the bulk Ke and shear Ge moduli of a wide class of disordered 2D and 3D material microstructures;including various dispersions of hard and penetrable particles, certain amorphous dispersions, and networks. These parameters are determined using a Monte Carlo integration scheme that incorporates certain algorithmic enhancements that improve upon the accuracy and performance of previous methods. Our results reveal that ζ2 and η2 are sensitive to the phase-connectedness properties of microstructures. Using numerical simulations and rigorous approximations that incorporate ζ2 and η2, we show that certain disordered microstructures nearly realize the Hashin-Shtrikman lower and upper bounds on σe, Ke, and Ge across volume-fractions. We also describe how our algorithm can be used in inverse methodologies to realize ordered and disordered materials with desirable effective physical properties by targeting specific values of ζ2 and η2, and hence aid in materials by design. © 2025, The Authors. All rights reserved.

关键词： Inverse problems

Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Torquato, Salvatore Kim, Jaeuk Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Stealthy interactions are an emerging class of nontrivial, bounded long-ranged oscillatory pair potentials with classical ground states that can be disordered, hyperuniform, and infinitely degenerate. Their hybrid crystal-liquid nature endows them with novel physical properties with advantages over their crystalline counterparts. Here, we show the existence of nonequilibrium hard-sphere glasses within this unusual ground-state manifold as the stealthiness parameter χ tends to zero that are remarkably configurationally extremely close to hyperuniform 3D maximally random jammed (MRJ) sphere packings. The latter are prototypical glasses since they are maximally disordered, perfectly rigid, and perfectly nonergodic. Our optimization procedure, which leverages the maximum cardinality of the infinite ground-state set, not only guarantees that our packings are hyperuniform with the same structure-factor scaling exponent as the MRJ state, but they share other salient structural attributes, including a packing fraction of 0.638, a mean contact number per particle of 6, gap exponent of 0.44(1), and pair correlation functions g2(r) and structures factors S(k) that are virtually identical to one another for all r and k, respectively. Moreover, we demonstrate that stealthy hyperuniform packings can be created within the disordered regime (0 © 2025, CC0.

关键词： Liquid crystals

Three-dimensional construction of hyperuniform, nonhyperuniform, and antihyperuniform disordered heterogeneous materials and their transport properties via spectral density functions

学校读者我要写书评

暂无评论

Physical Review E 2025年第3期111卷 035310-035310页

作者： Wenlong Shi Yang Jiao Salvatore Torquato Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Department of Physics Arizona State University Tempe Arizona 85287 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ̃V(k), which can be obtained experimentally from scattering data, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability S(t) and effective dynamic dielectric constant εe for electromagnetic wave propagation. Moreover, χ̃V(k) determines rigorous upper bounds on the fluid permeability K. Given the importance of χ̃V(k), we present here an efficient Fourier-space based computational framework to construct three-dimensional (3D) statistically isotropic two-phase heterogeneous materials corresponding to targeted spectral density functions. In particular, we employ a variety of analytical functional forms for χ̃V(k) that satisfy all known necessary conditions to construct disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions. We show that by tuning the correlations in the system across length scales via the targeted functions, one can generate a rich spectrum of distinct structures within each of the above classes of materials. Importantly, we present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by autocovariance function χV(r) with a power-law tail, resulting in microstructures that contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability S(t) and estimate the fluid permeability K associated with all of the constructed materials directly from the corresponding spectral densities. Although it is well established that the long-time asymptotic scaling behavior of S(t) only depends on the functional form of χ̃V(k), with the stealthy hyperuniform a

关键词： Spectral density

Modeling Neural Activity with Conditionally Linear Dynamical Systems

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Geadah, Victor Nejatbakhsh, Amin Lipshutz, David Pillow, Jonathan W. Williams, Alex H. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Center for Computational Neuroscience Flatiron Institute New York CityNY United States Department of Neuroscience Baylor College of Medicine HoustonTX United States Princeton Neuroscience Institute PrincetonNJ United States Center for Neural Science New York University New York CityNY United States

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task. © 2025, CC BY.

关键词： Neurons

HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

GRAMMCell: Docking-based Cell Modeling Resource

学校读者我要写书评

暂无评论

Journal of Molecular Biology 2025年 169085页

作者： Singh, Amar Tytarenko, Andrii M. Ambati, Vineeth Kumar Copeland, Matthew M. Kundrotas, Petras J. Kasyanov, Pavlo O. Feinberg, Eugene A. Vakser, Ilya A. Computational Biology Program The University of Kansas Lawrence 66045 KS United States Institute for Applied System Analysis at the Igor Sikorsky Kyiv Polytechnic Institute Kyiv 03056 Ukraine Department of Applied Mathematics and Statistics Stony Brook University Stony Brook 11794 NY United States Department of Molecular Biosciences The University of Kansas Lawrence 66045 KS United States

The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecular interactions. computational approaches to cell modeling, such as molecular dynamics, provide details of macromolecular behavior in concentrated solutions. However, such simulations are either slow, when carried out at atomic resolution, or significantly coarse-grained. Protein docking has been widely used for predicting structures of protein complexes. Systematic docking approaches, such as those based on Fast Fourier Transform (FFT), map the entire intermolecular energy landscape by determining the position and depth of the energy minima. The GRAMMCell web server implements docking-based approach for simulating cell crowded environment by sampling the intermolecular energy landscape generated by GRAMM (Global RAnge Molecular Matching). GRAMM systematically maps the landscape by a spectrum of docking poses corresponding to stable (deep energy minima) and transient (shallow minima) protein interactions. The sampling of these energy landscapes of a large system of proteins is performed in GRAMMCell using highly optimized Markov Chain Monte Carlo protocol. The procedure allows simulation of extra-long trajectories of large, crowded protein systems with atomic resolution accuracy. GRAMMCell is available at https://***. © 2025 The Author(s)

关键词： cell-modelling energy landscape protein docking protein–protein interactions web-based resource