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Jammed hard-particle packings: From Kepler to Bernal and beyond

Reviews of Modern Physics 2010年第3期82卷 2633-2633页

作者： S. Torquato F. H. Stillinger []Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute of Advanced Study Princeton New Jersey 08540 USA

Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and into selected aspects of biological systems. This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide and (in the large system limit) continuous range of intensive properties, including packing fraction ϕ, mean contact number Z, and several scalar order metrics. Application of these analytical tools to spheres in three dimensions (an analog to the venerable Ising model) covers a myriad of jammed states, including maximally dense packings (as Kepler conjectured), low-density strictly jammed tunneled crystals, and a substantial family of amorphous packings. With respect to the last of these, the current approach displaces the historically prominent but ambiguous idea of “random close packing” with the precise concept of “maximally random jamming.” Both laboratory procedures and numerical simulation protocols can and, frequently, have been used for creation of ensembles of jammed states. But while the resulting distributions of intensive properties may individually approach narrow distributions in the large system limit, the distinguishing varieties of possible operational details in these procedures and protocols lead to substantial variability among the resulting distributions, some examples of which are presented here. This review also covers recent advances in understanding jammed packings of polydisperse sphere mixtures, as well as convex nonspherical particles, e.g., ellipsoids, “

关键词： Spheres Euclidean space laboratory procedure jammed state Kepler

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Densest local sphere-packing diversity: General concepts and application to two dimensions

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Physical Review E 2010年第4期81卷 041305-041305页

作者： Adam B. Hopkins Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of configuration space. The knowledge of Rmin(N) in d-dimensional Euclidean space Rd allows for the construction both of a realizability condition for pair-correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings in Rd. In this paper, we focus on the two-dimensional circular disk problem. We find and present the putative densest packings and corresponding Rmin(N) for selected values of N up to N=348 and use this knowledge to construct such a realizability condition and an upper bound. We additionally analyze the properties and characteristics of the maximally dense packings, finding significant variability in their symmetries and contact networks, and that the vast majority differ substantially from the triangular lattice even for large N. Our work has implications for packaging problems, nucleation theory, and surface physics.

关键词： Spheres

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Displaced Path Integral Formulation for the Momentum Distribution of Quantum Particles

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Physical Review Letters 2010年第11期105卷 110602-110602页

作者： Lin Lin Joseph A. Morrone Roberto Car Michele Parrinello Program in Applied and Computational Mathematics 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 Computational Science Department of Chemistry and Applied Biosciences ETH Zurich USI Campus Via Giuseppe Buffi 12 CH-6900 Lugano Switzerland

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.

关键词： Statistical mechanics

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Multilayer thin film growth on crystalline and quasicrystalline surfaces: A phase-field crystal study

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Physical Review B 2012年第24期85卷 245428-245428页

作者： Srevatsan Muralidharan Raika Khodadad Ethan Sullivan Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA and School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

In this paper, we explore the effects of misfit strain fields on both heterogeneous nucleation behavior and anisotropic growth of islands at submonolayer coverages and compositional patterning at complete monolayer coverage via simulations of a phase-field crystal model. In particular, deposition on top of a herringbone structure and quasicrystalline (QC) substrate are considered, the former representing a system with spatially periodic misfit strain fields arising from the presence of surface dislocations, and the latter representing a system which inherently possesses a wide range of local, aperiodic misfit patterns. In the case of single-component systems, we demonstrate that misfit strain fields lead to heterogeneous nucleation behavior and anisotropic island growth. In the case of QC substrate, a wide range of morphologies, such as coexistence of locally hexagonally ordered atomic clusters within a larger scale arrangement with overall QC symmetry and so-called “starfish” aggregates, is observed in a pure system at submonolayer coverages when the adlayer-substrate interaction strength and lattice mismatch are tuned. In the case of bulk-immiscible binary systems at complete monolayer coverage, strain-stabilized compositional domains emerge at low line tension values for both substrates. Interestingly, the compositional domains on the QC substrate inherit their symmetries at sufficiently low line tension values, while at larger line tension values, the domain structure begins to resemble the classical spinodal microstructure. Such domain structures should be readily observable in colloidal systems in which attractive interparticle and particle-substrate interactions can be tuned.

关键词： THIN films CRYSTALS NUCLEATION DISLOCATIONS in crystals MICROSTRUCTURE

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NOMAD: Nonlinear Manifold Decoders for Operator Learning

arXiv

引用

arXiv 2022年

作者： Seidman, Jacob H. Kissas, Georgios Perdikaris, Paris Pappas, George J. Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost. © 2022, CC BY-NC-SA.

关键词： Benchmarking

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A Flow Artist for High-Dimensional Cellular Data

A Flow Artist for High-Dimensional Cellular Data

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IEEE Workshop on Machine Learning for Signal Processing

作者： Kincaid MacDonald Dhananjay Bhaskar Guy Thampakkul Nhi Nguyen Joia Zhang Michael Perlmutter Ian Adelstein Smita Krishnaswamy Department of Mathematics Yale University Department of Genetics Yale School of Medicine Department of Computer Science Yale University Department of Mathematics Pomona College Applied Mathematics Program Yale University Department of Statistics University of Washington Department of Mathematics Boise State University Computational Biology and Bioinformatics Program Yale University

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data.

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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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CAUCHY MARKOV RANDOM FIELD PRIORS FOR BAYESIAN INVERSION

arXiv

引用

arXiv 2021年

作者： Suuronen, Jarkko Chada, Neil K. Roininen, Lassi School of Engineering Science Lappeenranta-Lahti University of Technology PO Box 20 LappeenrantaFI-53851 Finland Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed In order to use such priors successfully, sophisticated optimization and Markov chain Monte Carlo (MCMC) methods are usually required In this paper, our focus is largely on reviewing recently developed Cauchy difference priors, while introducing interesting new variants, whilst providing a comparison We firstly propose a one-dimensional second order Cauchy difference prior, and construct new first and second order two-dimensional isotropic Cauchy difference priors Another new Cauchy prior is based on the stochastic partial differential equation approach, derived from Matérn type Gaussian presentation The comparison also includes Cauchy sheets Our numerical computations are based on both maximum a posteriori and conditional mean estimation We exploit state-of-the-art MCMC methodologies such as Metropolis-within-Gibbs, Repelling-Attracting Metropolis, and No-U-Turn sampler variant of Hamiltonian Monte Carlo We demonstrate the models and methods constructed for one-dimensional and two-dimensional deconvolution problems Thorough MCMC statistics are provided for all test cases, including potential scale reduction factors. Copyright © 2021, The Authors. All rights reserved.

关键词： Bayesian networks

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Fluid permeabilities of triply periodic minimal surfaces

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Physical Review E 2005年第5期72卷 056319-056319页

作者： Y. Jung S. Torquato Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. The multifunctionality of such two-phase systems has been further established by demonstrating that they are also extremal when a competition is set up between the effective bulk modulus and electrical (or thermal) conductivity of the bicontinuous composite. Here we compute the fluid permeabilities of these and other triply periodic bicontinuous structures at a porosity ϕ=1∕2 using the immersed-boundary finite-volume method. The other triply periodic porous media that we study include the Schoen gyroid (G) minimal surface, two different pore-channel models, and an array of spherical obstacles arranged on the sites of a simple cubic lattice. We find that the Schwartz P porous medium has the largest fluid permeability among all of the six triply periodic porous media considered in this paper. The fluid permeabilities are shown to be inversely proportional to the corresponding specific surfaces for these structures. This leads to the conjecture that the maximal fluid permeability for a triply periodic porous medium with a simply connected pore space at a porosity ϕ=1∕2 is achieved by the structure that globally minimizes the specific surface.

关键词： EXACT COMPUTATION FLOW SIMULATIONS COMPOSITES TRANSPORT SYSTEMS PHASES STEP

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Deep learning inter-atomic potential for thermal and phonon behaviour of silicon carbide with quantum accuracy

arXiv

引用

arXiv 2021年

作者： Fu, Baoqin Sun, Yandong Zhang, Linfeng Wang, Han Xu, Ben Key Laboratory of Radiation Physics and Technology of the Ministry of Education Institute of Nuclear Science and Technology Sichuan University Chengdu610064 China Graduate School China Academy of Engineering Physics Beijing100193 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Silicon carbide (SiC) is an essential material for next generation semiconductors and components for nuclear plants. It’s applications are strongly dependent on its thermal conductivity, which is highly sensitive to microstructures. Molecular dynamics (MD) simulation is the most used methods to address thermal transportation mechanisms in devices or microstructures of nano-meters. However, the implementation of MD is limited in SiC because of lacking accurate inter-atomic potentials. In this work, using the Deep Potential (DP) methodology, we developed two inter-atomic potentials (DP-*Corresponding author. IAPs) for SiC based on two adaptively generated datasets within the density functional approximations at the local density and the generalized gradient levels. These two DP-IAPs manifest their speed with quantum accuracy in lattice dynamics simulations as well as scattering rate analysis of phonon transportation. Combining with molecular dynamics simulations, the thermal transport and mechanical properties were systematically investigated. The presented methodology and the inter-atomic potentials pave the way for a systematic approach to model heat transport in SiC related devices using multiscale modelling. Copyright © 2021, The Authors. All rights reserved.

关键词： Silicon carbide

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