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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

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Transient rod-climbing in an Oldroyd-B fluid

arXiv

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arXiv 2025年

作者： Ruangkriengsin, Tachin Brandão, Rodolfo Wu, Katie Hwang, Jonghyun Boyko, Evgeniy Stone, Howard A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Mathematics University of Bristol Fry Building Woodland Road BristolBS8 1UG United Kingdom Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (Arch. Rat. Mech. Anal., vol. 49, 1973, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Oldroyd-B model. We begin by neglecting surface tension and inertia to focus on the interaction between gravity and viscoelasticity. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface profile on this short time scale and recover the steady-state profile on a longer time scale. Subsequently, we reintroduce small but finite inertial effects to investigate their interplay with viscoelasticity and propose a criterion for determining the conditions under which rod-climbing occurs. © 2025, CC BY.

关键词： Non Newtonian liquids

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Variational data assimilation for a nonlinear hydraulic model

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applied MATHEMATICAL MODELLING 1996年第9期20卷 675-682页

作者： Chertok, DL Lardner, RW Applied and Computational Mathematics Program Simon Fraser University Burnaby British Columbia Canada

A method is developed for the optimal estimation of the parameters in a fully nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate values of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a sufficient number of locations are available for assimilation.

关键词： parameter estimation data assimilation model identification

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THE BREAK-UP OF A HETEROCLINIC CONNECTION IN A VOLUME PRESERVING MAPPING

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PHYSICA D 1993年第1-4期62卷 51-65页

作者： ROMKEDAR, V KADANOFF, LP CHING, ESC AMICK, C Computational and Applied Mathematics Program The Department of Mathematics The University of Chicago Chicago IL 60637 USA

We consider a family of three-dimensional, volume preserving maps depending on a small parameter epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for small epsilon the heteroclinic connection breaks up and that the splitting between its components scales with epsilon like epsilon(gamma) exp(-beta/epsilon). We estimate beta using the singularities of the epsilon --> 0+ heteroclinic orbit in the complex plane. We then estimate gamma using linearization about orbits in the complex plane. While these estimates are not proven, they are well supported by our numerical calculations. The work described here is a special case of the theory derived by Amick et al. which applies to q-dimensional volume preserving mappings.

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FINITE-SIZE EFFECTS IN FORCED 2-DIMENSIONAL TURBULENCE

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JOURNAL OF FLUID MECHANICS 1994年 274卷 115-138页

作者： SMITH, LM YAKHOT, V [a1] Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is a white-in-time random noise acting in a narrow band of high wavenumbers. The inverse-cascade process and the presence of the boundary lead ultimately to a pile-up of energy in the lowest wavenumber (Bose condensation). In the asymptotic limit where the enstrophy cascade range is negligible, Bose condensation is solely responsible for the generation of coherent vortices and intermittency in the system. We present the evolution of the velocity and vorticity fields through the later stages of the condensate state, and explore the possible implications for atmospheric turbulence constrained by the periodic domain about the earth.

关键词： Turbulence

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SMOOTH SURFACE RECONSTRUCTION FROM SCATTERED DATA POINTS

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COMPUTERS & GRAPHICS 1991年第1期15卷 29-39页

作者： AGISHTEIN, ME MIGDAL, AA Program in Applied and Computational Mathematics Princeton University Fine Hall Princeton NJ 08544 USA

We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rational interpolation inside triangles. Preprocessing of data includes sorting and takes N log(N) time. Afterwards the computational cost is a linear function of the amount of data. This technique enables a user to construct a surface of any class of smoothness and degree of convergence. Our package reconstructs surfaces that can be uniquely projected either on a plane or on a sphere. The graphical section of this package includes three dimensional transformations, shading, hidden surface removal, interactive adding points into triangulation by mouse, etc. The graphics has been implemented on Iris-4D, SUN-4 and IBM-5080.

关键词： Computer Graphics

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GRAMMCell: Docking-based Cell Modeling Resource

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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

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Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 465-476页

作者： Weinan E Jian-feng LU Xu YANG Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University School of Mathematical Sciences Peking University

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

关键词： semiclassical limit Bloch-Wigner transform Bloch dynamics Berry phase asymptotic analysis

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ROTATION INVARIANCE FOR STEADY HELE-SHAW FLOWS

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PHYSICS OF FLUIDS A-FLUID DYNAMICS 1993年第8期5卷 1863-1865页

作者： TIAN, FR VASCONCELOS, GL Computational and Applied Mathematics Program The University of Chicago Chicago Illinois 60637

A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then the curve L obtained from a rotation of L about its center by an arbitrary angle is also a solution with the same velocity U. Similar results hold for the case with surface tension if and only if the Schwarz function of the curve L is regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.

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

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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

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