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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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Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

arXiv

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arXiv 2024年

作者： Morse, Peter K. Steinhardt, Paul J. 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 Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d = 2-8. © 2024, CC BY.

关键词： Ground state

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Relative magnetic field and slipping effect on Casson dusty fluid of two phase fluctuating flow over inclined parallel plate

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South African Journal of Chemical Engineering 2023年 44卷 135-146页

作者： khan, Dolat Kumam, Poom Kumam, Wiyada Suttiarporn, Panawan Rehman, Ali Fixed Point Research Laboratory Fixed Point Theory and Applications Research Group Center of Excellence in Theoretical and Computational Science (TaCS-CoE) Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd. Bang Mod Bangkok Thung Khru 10140 Thailand Center of Excellence in Theoretical and Computational Science (TaCS-CoE) Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd. Bang Mod Bangkok Thung Khru 10140 Thailand Applied Mathematics for Science and Engineering Research Unit (AMSERU) Program in Applied Statistics Department of Mathematics and Computer Science Faculty of Science and Technology Rajamangala University of Technology Thanyaburi (RMUTT) Pathum Thani 12110 Thailand Faculty of Science Energy and Environment King Mongkut's University of Technology North Bangkok Rayong Campus Rayong 21120 Thailand Special Interest Group for Modelling and Data Analytics Faculty of Ocean Engineering Technology and Informatics Universiti Malaysia Terengganu Terengganu Kuala Nerus 21030 Malaysia

Due to its significant applications in magnetic devices for cell separation, magnetic drugs for cancer tumor treatment, blood flow adjustment during surgery, magnetic endoscopy, and fluid pumping in industrial and engineering processes, magnetohydrodynamics (MHD) has a wide range of applications. Therefore, the aim of this study to investigate the Relative Magnetic Field and slipping effect on Casson dusty fluid of two-phase fluctuating flow over inclined parallel plate. More exactly, the relative magnetic phenomena are fixed relatively to the plate (MFFRP) or fixed relatively to the fluid (MFFRF). The mathematical modeling was established as the set of partial differential equations for dusty Casson fluid. Buckingham's pi theorem is used to find out the dimensionless variables, to make our system dimensionless. The solution in perturb form is to find out by incorporating Poincare–Lighthill perturbation technique (PLPT). To know in-depth different parameters the graphical results for both velocities are plotted with the help of software Mathcad- 15. It is clearly detected that the relative magnetic field performs a vital part in the fluid as well as particle motion. Moreover, the relative magnetic field play a vital role in the decreasing of skin friction of both plates. © 2023

关键词： Brinkman fluid Dust particles Fluctuating vertical plate Inclined relative magnetic field PLPT

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Method for obtaining upper bounds on photonic band gaps

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Physical Review B 2009年第15期80卷 155126-155126页

作者： Mikael C. Rechtsman Salvatore Torquato Courant Institute of Mathematical Sciences 251 Mercer Street New York New York 10012 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We present a method to calculate upper bounds on the photonic band gaps of two-component photonic crystals. The method involves calculating both upper and lower bounds on the frequency bands for a given structure, and then maximizing over all possible two-component structures. We apply this method to a number of examples, including a one-dimensional photonic crystal (or “Bragg grating”) and two-dimensional photonic crystals (in both the TM and TE polarizations) with both four and sixfold rotational symmetries. We compare the bounds to band gaps of numerically optimized structures and find that the bounds are extremely tight. We prove that the bounds are “sharp” in the limit of low dielectric contrast ratio between the two components. This method and the bounds derived here have important implications in the search for optimal photonic band-gap structures.

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Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network

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Physical Review Fluids 2019年第10期4卷 104605-104605页

作者： Chenyue Xie Ke Li Chao Ma Jianchun Wang Shenzhen Key Laboratory of Complex Aerospace Flows Center for Complex Flows and Soft Matter Research Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences Beijing 100190 People's Republic of China The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In this paper, the subgrid-scale (SGS) force and the divergence of SGS heat flux of compressible isotropic turbulence are modeled directly by an artificial neural network (ANN), which serves as a data-driven SGS modeling tool for large-eddy simulations (LESs). The unclosed SGS force and divergence of SGS heat flux are modeled based on the local stencil geometry with Galilean invariance. The input features include the first-order and second-order derivatives of filtered velocity and temperature, filtered density, and its first-order derivative. It is shown that the proposed ANN-F7 model shows an advantage over the gradient model in the a priori test. Specifically, the ANN-F7 model gives larger correlation coefficients and smaller relative errors than the gradient model. In an a posteriori analysis, the ANN-F7 model performs better than the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM) in the prediction of the statistical properties of flow fields at the Taylor microscale Reynolds number Reλ ranging from 180 to 250. The DSM and DMM models lead to the typical tilted spectral distribution of velocity, where low wave numbers are too energy rich, while those near the cutoff are damped too strongly. In contrast, it is shown that the velocity spectrum predicted by the ANN-F7 model almost overlaps with the filtered direct numerical simulation data. Besides, the ANN-F7 model reconstructs the probability density functions of SGS force and divergence of SGS heat flux much better than the DSM and DMM models. An artificial neural network with reasonable physical input features can deepen our understanding of turbulence modeling.

关键词： Compressible flows Turbulence Artificial neural networks

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End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems

arXiv

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arXiv 2018年

作者： Zhang, Linfeng Han, Jiequn Wang, Han Saidi, Wissam A. Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Institute of Applied Physics and Computational Mathematics China CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh United States Department of Chemistry and Department of Physics Princeton University United States Princeton Institute for the Science and Technology of Materials Princeton University United States Department of Mathematics Princeton University United States Beijing Institute of Big Data Research China

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES of a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity. Copyright © 2018, The Authors. All rights reserved.

关键词： Potential energy

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COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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Computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

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Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales

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Physical Review X 2023年第1期13卷 011038-011038页

作者： Oliver H. E. Philcox Salvatore Torquato Department of Astrophysical Sciences Princeton University Princeton New Jersey 08540 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Center for Theoretical Physics Department of Physics Columbia University New York New York 10027 USA Simons Foundation New York New York 10010 USA Department of Chemistry Department of Physics Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much l

关键词： Large scale structure of the Universe

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Deep Potential: A general representation of a many-body potential energy surface

arXiv

引用

arXiv 2017年

作者： Han, Jiequn Zhang, Linfeng Car, Roberto Weinan, E. 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 Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems. When tested on a wide variety of examples, Deep Potential is able to reproduce the original model, either empirical or quantum mechanics based, within chemical accuracy. The computational cost of this new model is not substantially larger than that of empirical force fields. In addition, the method has promising scalability properties. This brings us one step closer to being able to carry out molecular simulations with accuracy comparable to that of quantum mechanics models and computational cost comparable to that of empirical potentials. Copyright © 2017, The Authors. All rights reserved.

关键词： Deep neural networks

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Optimized Structures for Photonic Quasicrystals

引用

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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