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Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming

Physical Review E 2010年第6期82卷 061302-061302页

作者： S. Torquato Y. Jiao Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d-dimensional Euclidean space Rd, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in Rd for d=2, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408…], where π/18=0.7408… corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d=2, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust an

关键词： Packing

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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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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

arXiv

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

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Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

Inferring System and Optimal Control Parameters of Closed-Lo...

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IEEE Conference on Decision and Control

作者： Victor Geadah Juncal Arbelaiz Harrison Ritz Nathaniel D. Daw Jonathan D. Cohen Jonathan W. Pillow Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mechanical and Aerospace Engineering Princeton University Princeton NJ USA Princeton Neuroscience Institute Princeton University Princeton NJ USA

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic statespace model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finitehorizon setting. We further illustrate the performance of our methodology through numerical examples.

关键词： Regulators Optimal control Stochastic processes Probabilistic logic System identification Numerical models Closed loop systems

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INTERACTION OF THE PRIMITIVE EQUATIONS WITH SEA ICE DYNAMICS

arXiv

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arXiv 2022年

作者： Binz, Tim Brandt, Felix Hieber, Matthias Princeton University Program in Applied & Computational Mathematics Fine Hall Washington Road PrincetonNJ08544 United States Technische Universität Darmstadt Schloßgartenstraße 7 Darmstadt64289 Germany

This article establishes local strong well-posedness and global strong well-posedness close to constant equilibria of a model coupling the primitive equations of ocean and atmospheric dynamics with Hibler's viscous-plastic sea ice model. In order to treat the coupling conditions, an approach involving the hydrostatic Dirichlet and Dirichlet-to-Neumann operator is developed. Mapping properties of the latter operators are investigated for the first time and are of central importance for showing that the operator associated with the linearized coupled system admits a bounded H∞-calculus on suitable Lqspaces. Quasilinear methods allow then to obtain the strong well-posedeness results described *** Codes 35Q35, 35Q86, 35K59, 86A05, 86A10 © 2022, CC BY.

关键词： Hydraulics

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Comparison between a priori and a posteriori slope limiters for high-order finite volume schemes

arXiv

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arXiv 2024年

作者： Palafoutas, Jonathan Velasco Romero, David A. Teyssier, Romain Program in Applied & Computational Mathematics Princeton University Washington Road PrincetonNJ08544 United States Department of Astrophysical Sciences Princeton University 171 Broadmead Street PrincetonNJ08540 United States

High-order finite volume and finite element methods offer impressive accuracy and cost efficiency when solving hyperbolic conservation laws with smooth solutions. However, if the solution contains discontinuities, these high-order methods can introduce unphysical oscillations and severe overshoots/undershoots. Slope limiters are an effective remedy, combating these oscillations by preserving monotonicity. Some limiters can even maintain a strict maximum principle in the numerical solution. They can be classified into one of two categories: a priori and a posteriori limiters. The former revises the high-order solution based only on data at the current time tn, while the latter involves computing a candidate solution at tn+1 and iteratively recomputing it until some conditions are satisfied. These two limiting paradigms are available for both finite volume and finite element methods. In this work, we develop a methodology to compare a priori and a posteriori limiters for finite volume solvers at arbitrarily high order. We select the maximum principle preserving scheme presented in [1, 2] as our a priori limited scheme. For a posteriori limiting, we adopt the methodology presented in [3] and search for so-called troubled cells in the candidate solution. We revise them with a robust MUSCL fallback scheme. The linear advection equation is solved in both one and two dimensions and we compare variations of these limited schemes based on their ability to maintain a maximum principle, solution quality over long time integration and computational cost. This analysis reveals a fundamental tradeoff between these three aspects. The high-order a posteriori limited solutions boast great quality at long time-scales, taking full advantage of the sharp gradients of the high-order finite volume method. However, they introduce consistent maximum principle violations. On the other hand, the high-order a priori limited solutions can preserve a strict maximum principle. Interestingly, thi

关键词： Polynomials

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INTERACTION OF LIQUID CRYSTALS WITH A RIGID BODY

arXiv

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arXiv 2023年

作者： Binz, Tim Brandt, Felix Hieber, Matthias Roy, Arnab Princeton University Program in Applied & Computational Mathematics Fine Hall Washington Road PrincetonNJ08544 United States Technische Universität Darmstadt Schloßgartenstraße 7 Darmstadt64289 Germany

This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global strong solution for initial data close to constant equilibria. The proof of the global strong solution relies on a new splitting method for the director in a mean value zero and average *** Codes 35Q35, 76A15, 74F10, 76D03, 35K59 © 2023, CC BY.

关键词： Nematic liquid crystals

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AMUSE: Empowering Users for Cost-Aware Offloading with Throughput-Delay Tradeoffs

AMUSE: Empowering Users for Cost-Aware Offloading with Throu...

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IEEE INFOCOM Conference

作者： Youngbin Im Carlee Joe-Wong Sangtae Ha Soumya Sen Ted "Taekyoung" Kwon Mung Chiang School of Computer Science and Engineering Seoul National University Seoul Korea Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Electrical Engineering Princeton University Princeton NJ USA

ISBN: (纸本)9781467359443

Mobile users face a tradeoff between cost, through-put, and delay in making their offloading decisions. To navigate this tradeoff, we propose AMUSE (Adaptive bandwidth Management through USer-Empowerment), a practical, cost-aware WiFi offloading system that takes into account a user's throughput-delay tradeoffs and cellular budget constraint. Based on predicted future usage and WiFi availability, AMUSE decides which applications to offload to what times of the day. To practically enforce the assigned rate of each TCP application, we introduce a receiver-side TCP bandwidth control algorithm that adjusts the rate by controlling the TCP advertisement window from the user side. We implement AMUSE on Windows 7 tablets and evaluate its effectiveness with 3G and WiFi usage data obtained from a trial with 25 mobile users. Our results show that AMUSE improves user utility.

关键词： tradeoffs UNLOADING Wi-Fi third generation rate control

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A Neural Network-Based Approach to Normality Testing for Dependent Data

arXiv

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arXiv 2023年

作者： Kim, Minwoo Genton, Marc G. Huser, Raphaël Castruccio, Stefano Department of Statistics Pusan National University Korea Republic of Statistics program King Abdullah University of Science and Technology Saudi Arabia Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States

There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is considerably more challenging, as the marginal behavior is impacted by the degree of dependence. We propose a new approach to assess normality for dependent data by non-linearly incorporating existing statistics from normality tests as well as sample moments such as skewness and kurtosis through a neural network. We calibrate (deep) neural networks by simulated normal and non-normal data with a wide range of dependence structures and we determine the probability of rejecting the null hypothesis. We compare several approaches for normality tests and demonstrate the superiority of our method in terms of statistical power through an extensive simulation study. A real world application to global temperature data further demonstrates how the degree of spatio-temporal aggregation affects the marginal normality in the data. © 2023, CC BY.

关键词： Higher order statistics

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Neural network representation of electronic structure from ab initio molecular dynamics

arXiv

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arXiv 2020年

作者： Gu, Qiangqiang Zhang, Linfeng Feng, Ji International Center for Quantum Materials School of Physics Peking University Beijing100871 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Collaborative Innovation Center of Quantum Matter Beijing100871 China

Despite their rich information content, electronic structure data amassed at high volumes in ab initio molecular dynamics simulations are generally under-utilized. We introduce a transferable high-fidelity neural network representation of such data in the form of tight-binding Hamiltonians for crystalline materials. This predictive representation of ab initio electronic structure, combined with machine-learning boosted molecular dynamics, enables efficient and accurate electronic evolution and sampling. When applied to a one-dimension charge-density wave material, carbyne, we are able to compute the spectral function and optical conductivity in the canonical ensemble. The spectral functions evaluated during soliton-antisoliton pair annihilation process reveal significant renormalization of low-energy edge modes due to retarded electron-lattice coupling beyond the Born-Oppenheimer limit. The availability of an efficient and reusable surrogate model for the electronic structure dynamical system will enable calculating many interesting physical properties, paving way to previously inaccessible or challenging avenues in materials modeling. © 2020, CC-BY.

关键词： Electronic structure

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