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Experiments on Random Packings of Ellipsoids

Physical Review Letters 2005年第19期94卷 198001-198001页

作者： Weining Man Aleksandar Donev Frank H. Stillinger Matthew T. Sullivan William B. Russel David Heeger Souheil Inati Salvatore Torquato P. M. Chaikin Department of Physics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemistry and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical Engineering and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Psychology and Center for Neural Science New York University New York New York 10003 USA

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25∶1∶0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction ϕ(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain ϕ(r) from a magnetic resonance imaging scan. The measurements of the overall density ϕavr, ϕ(r) and the core density ϕ0=0.74±0.005 agree with simulations.

关键词： .ellipsoids Princeton New Jersey

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Cross-system biological image quality enhancement based on the generative adversarial network as a foundation for establishing a multi-institute microscopy cooperative network

arXiv

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arXiv 2024年

作者： Panek, Dominik Rząca, Carina Szczypior, Maksymilian Sorysz, Joanna Misztal, Krzysztof Baster, Zbigniew Rajfur, Zenon Doctoral School of Exact and Natural Sciences Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland Department of Molecular and Interfacial Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate Program in Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate program in Biomedical Engineering Faculty of Electrical Engineering Automatics Computer Science and Biomedical Engineering AGH University of Science and Technology Al. A. Mickiewicza 30 Building B-1 Kraków30-059 Poland Division of Computational Mathematics Faculty of Mathematics and Computer Science Jagiellonian University 6 Lojasiewicza St. Kraków Poland

High-quality fluorescence imaging of biological systems is limited by processes like photobleaching and phototoxicity, and also in many cases, by limited access to the latest generations of microscopes. Moreover, low temporal resolution can lead to a motion blur effect in living systems. Our work presents a deep learning (DL) generative-adversarial approach to the problem of obtaining high-quality (HQ) images based on their low-quality (LQ) equivalents. We propose a generative-adversarial network (GAN) for contrast transfer between two different separate microscopy systems: a confocal microscope (producing HQ images) and a wide-field fluorescence microscope (producing LQ images). Our model proves that such transfer is possible, allowing us to receive HQ-generated images characterized by low mean squared error (MSE) values, high structural similarity index (SSIM), and high peak signal-to-noise ratio (PSNR) values. For our best model in the case of comparing HQ-generated images and HQ-ground truth images, the median values of the metrics are 6·10-4, 0.9413, and 31.87, for MSE, SSIM, and PSNR, respectively. In contrast, in the case of comparison between LQ and HQ ground truth median values of the metrics are equal to 0.0071, 0.8304, and 21.48 for MSE, SSIM, and PSNR respectively. Therefore, we observe a significant increase ranging from 14% to 49% for SSIM and PSNR respectively. These results, together with other single-system cross-modality studies, provide proof of concept for further implementation of a cross-system biological image quality enhancement. © 2024, CC BY-SA.

关键词： Fluorescence imaging

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Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes

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Physical Review E 2010年第6期81卷 061105-061105页

作者： Robert D. Batten Frank H. Stillinger Salvatore Torquato Department of Chemical Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science 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 School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball’s interior is defined by the inequality |x|2q+|y|2q+|z|2q≤1, which provides a versatile family of convex particles (q≥0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q=1) and the cube (q=∞). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1

关键词： Spheres

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Optimized Structures for Photonic Quasicrystals

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Physical Review Letters 2008年第7期101卷 073902-073902页

作者： Mikael C. Rechtsman Hyeong-Chai Jeong Paul M. Chaikin Salvatore Torquato Paul J. Steinhardt Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Physics Sejong University Gwangjin-gu Seoul 143-747 Korea Department of Physics and Center for Soft Condensed Matter Research New York University New York 10003 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 School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

A photonic quasicrystal consists of two or more dielectric materials arranged in a quasiperiodic pattern with noncrystallographic symmetry that has a photonic band gap. We use a novel method to find the pattern with the widest TM-polarized gap for two-component materials. Patterns are obtained by computing a finite sum of density waves, assigning regions where the sum exceeds a threshold to a material with one dielectric constant, ϵ1, and all other regions to another, ϵ0. Compared to optimized crystals, optimized quasicrystals have larger gaps at low constrasts ϵ1/ϵ0 and have gaps that are much more isotropic for all contrasts. For high contrasts, optimized hexagonal crystals have the largest gaps.

关键词： Quasicrystals

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Corrigendum to: A more accurate three-dimensional grain growth algorithm [Acta Mater. 59 (2011) 6837–6847]

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Acta Materialia 2014年 71卷 390-390页

作者： Emanuel A. Lazar Jeremy K. Mason Robert D. MacPherson David J. Srolovitz Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA School of Mathematics Institute for Advanced Study Princeton NJ 08540 USA IHPC 1 Fusionopolis Way 16-16 Connexis Singapore 138632 Singapore

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Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

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Physical Review Letters 2012年第11期109卷 114302-114302页

作者： Zi Chen Qiaohang Guo Carmel Majidi Wenzhe Chen David J. Srolovitz Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08544 USA Department of Biomedical Engineering Washington University St. Louis Missouri 63130 USA College of Materials Science and Engineering Fuzhou University Fuzhou Fujian 350108 China Department of Mathematics and Physics Fujian University of Technology Fuzhou Fujian 350108 China Department of Mechanical Engineering Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA Department of Materials Science and Engineering Fujian University of Technology Fuzhou Fujian 350108 China Institute for High Performance Computing 1 Fusionopolis Way Singapore 138632 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.

关键词： NONLINEAR theories DEFORMATIONS (Mechanics) PARAMETER estimation OPTICAL bistability STRUCTURAL shells PLATES (Engineering) CRYSTAL structure

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Moment-based metrics for molecules computable from cryogenic electron microscopy images

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Biological imaging 2024年 4卷 e3页

作者： Andy Zhang Oscar Mickelin Joe Kileel Eric J Verbeke Nicholas F Marshall Marc Aurèle Gilles Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ USA. Department of Mathematics and Oden Institute University of Texas at Austin Austin TX USA. Department of Mathematics Oregon State University Corvallis OR USA. Department of Mathematics Princeton University Princeton NJ USA.

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam's method, relies on the moments of the two-dimensional (2D) images. Inspired by Kam's method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3D alignment. Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3D reconstruction. Additionally, the latter metric does not assume a uniform distribution of viewing angles. We demonstrate the uses of the new metrics on synthetic and experimental datasets, highlighting their ability to measure structural similarity.

关键词： Kam’s method alignment-free metric method of moments protein structural similarity rotationally invariant distance structural search

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Erratum: ‘‘A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment’’ [Phys. Fluids 31, 256 (1988)]

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Physics of Fluids 1988年第8期31卷

作者： Gregory J. Hartke V. M. Canuto William P. Dannevik NASA Goddard Space Flight Center Institute for Space Studies 2880 Broadway New York New York 10025 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

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Hyperuniformity classes of quasiperiodic tilings via diffusion spreadability

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Physical Review E 2024年第6期109卷 064108-064108页

作者： Adam Hitin-Bialus Charles Emmett Maher Paul J. Steinhardt Salvatore Torquato Department of Physics <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA. Department of Chemistry <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA. Jefferson Physical Laboratory <a href="https://***/03vek6s52">Harvard University</a> Cambridge Massachusetts 02138 USA and Department of Physics <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA. Department of Chemistry <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA Department of Physics <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA Princeton Institute of Materials <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics <a href="https://***/00hx57361">Princeton University</a> Princeton New Jersey 08544 USA.

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α>0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wave number k≡|k| in the vicinity of the origin, e.g., S(k)∼|k|α in cases where S(k) varies continuously with k as k→0. In this paper, we show that the spreadability is an effective method for determining α for quasiperiodic systems where S(k) is discontinuous and consists of a dense set of Bragg peaks. It has been shown in [Phys. Rev. E 104, 054102 (2021)] that, for media with finite α, the long-time behavior of the excess spreadability S(∞)−S(t) can be fit to a power law of the form t−(d−α)/2, where d is the space dimension, to accurately extract α for the continuous case. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density χ̃V(k) of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract α for the one-dimensional (1D) limit-periodic period-doubling chain (α=1) and the 1D quasicrystalline Fibonacci chain (α=3) to within 0.02% of the analytically known exact results. Moreover, we obtain a value of α=5.97±0.06 for the two-dimensional Penrose tiling and present plausible theoretical arguments strongly suggesting that α is exactly equal to six. We also show that, due to the self-similarity of the structures examined here, one can truncate the small-k region of the scattering information used to compute the spreadability and obtain an accurate value of α, with a small deviation from the untruncated case that decreases as the system size increases. This strongly suggests that one can obtain a good estimate of

关键词： Quasicrystals

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Thermal Conductivity of Water at Extreme Conditions

arXiv

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arXiv 2023年

作者： Zhang, Cunzhi Puligheddu, Marcello Zhang, Linfeng Car, Roberto Galli, Giulia Pritzker School of Molecular Engineering University of Chicago ChicagoIL60637 United States Materials Science Division Center for Molecular Engineering Argonne National Laboratory LemontIL60439 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Chemistry University of Chicago ChicagoIL60637 United States

Measuring the thermal conductivity (κ) of water at extreme conditions is a challenging task and few experimental data are available. We predict κ for temperatures and pressures relevant to the conditions of the Earth mantle, between 1,000 and 2,000 K and up to 22 GPa. We employ close to equilibrium molecular dynamics simulations and a deep neural network potential fitted to density functional theory data. We then interpret our results by computing the equation of state of water on a fine grid of points and using a simple model for κ. We find that the thermal conductivity is weakly dependent on temperature and monotonically increases with pressure with an approximate square-root behavior. In addition we show how the increase of κ at high pressure, relative to ambient conditions, is related to the corresponding increase in the sound velocity. Although the relationships between the thermal conductivity, pressure and sound velocity established here are not rigorous, they are sufficiently accurate to allow for a robust estimate of the thermal conductivity of water in a broad range of temperatures and pressures, where experiments are still difficult to perform. Copyright © 2023, The Authors. All rights reserved.

关键词： Thermal conductivity

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