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Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

Physical Review E 2021年第1期104卷 014127-014127页

作者： Michael A. Klatt Robert M. Ziff Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany Center for the Study of Complex Systems and Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ2〉, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size 〈δ2〉, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to 〈δ2〉. However, unlike 〈δ2〉, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm 〈δ2〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targete

关键词： Geophysical networks Materials Patterns in complex systems

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OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

arXiv

引用

arXiv 2020年

作者： Yu, Haijun Tian, Xinyuan Weinan, E. Li, Qianxiao NCMIS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics National University of Singapore Singapore119077 Singapore Institute of High Performance Computing A*STAR Singapore138632 Singapore

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion and external forces. For high dimensional problems with a low dimensional slow manifold, an autoencoder with metric preserving regularization is introduced to find the low dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Bénard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced order models for forced dissipative *** Codes 76E30, 34D20, 68T05/07, 82C35 Copyright © 2020, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Kinetic Frustration Effects on Dense Two-Dimensional Packings of Convex Particles and Their Structural Characteristics

arXiv

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arXiv 2021年

作者： Maher, Charles Emmett Stillinger, Frank H. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The study of hard-particle packings is of fundamental importance in physics, chemistry, cell biology, and discrete geometry. Much of the previous work on hard-particle packings concerns their densest possible arrangements. By contrast, we examine kinetic effects inevitably present in both numerical and experimental packing protocols. Specifically, we determine how changing the compression/shear rate of a two-dimensional packing of noncircular particles causes it to deviate from its densest possible configuration, which is always periodic. The adaptive shrinking cell (ASC) optimization scheme maximizes the packing fraction of a hard-particle packing by first applying random translations and rotations to the particles and then isotropically compressing and shearing the simulation box repeatedly until a possibly jammed state is reached. We use a stochastic implementation of the ASC optimization scheme to mimic different effective time scales by varying the number of particle moves between compressions/shears. We generate dense, effectively jammed, monodisperse, two-dimensional packings of obtuse scalene triangle, rhombus, curved triangle, lens, and "ice cream cone" (a semicircle grafted onto an isosceles triangle) shaped particles, with a wide range of packing fractions and degrees of order. To quantify these kinetic effects, we introduce the kinetic frustration index K, which measures the deviation of a packing from its maximum possible packing fraction. To investigate how kinetics affect short- and long-range ordering in these packings, we compute their spectral densities χV (k) and characterize their contact networks. We find that kinetic effects are most significant when the particles have greater asphericity, less curvature, and less rotational symmetry. This work may be relevant to the design of laboratory packing protocols. Copyright © 2021, The Authors. All rights reserved.

关键词： Kinetic theory

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Stability result for a viscoelastic wave equation in the presence of finite and infinite memories

arXiv

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arXiv 2021年

作者： Al-Mahdi, Adel M. Al-Gharabli, Mohammad M. Kafini, Mohammad Al-Omari, Shadi The Preparatory Year Program King Fahd University of Petroleum and Minerals Dhahran31261 Saudi Arabia Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran31261 Saudi Arabia The Interdisciplinary Research Center in Construction and Building Materials King Fahd University of Petroleum and Minerals Dhahran31261 Saudi Arabia

In this paper, we are concerned with the following viscoelastic wave equation (Equation presented), in a bounded domain Ω. Under suitable conditions on a1 and a2 and for a wide class of relaxation functions g1 and g2. We establish a general decay result. The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data ∇u0. This study generalizes and improves previous literature outcomes. © 2021, CC BY-SA.

关键词： Wave equations

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Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

arXiv

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arXiv 2021年

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by |x1|2p + |x2|2p + |x3|2p ≤ 1, where p ∈ (0, ∞) is a deformation parameter indicating to what extent the shape deviates from a sphere. As p increases from the sphere point (p = 1), the superball tends to a cuboidal shape and approaches a cube in the p → ∞ limit. As p → 0.5, it approaches an octahedron, becomes a concave body with octahedral symmetry for p ¯) vary nonanalytically as p diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with 0.85 ≤ p ≤ 1.50. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors S(Q) and spectral densities χV (Q), as the wave number Q tends to zero, and find that these packings are effectively hyperuniform for all values of p examined. We show that the mean width w¯ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution F (δ) and find that the pore sizes tend to decrease as |1 − p| increases. From F (δ), we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of p. Additionally, we compute the diffusion "spreadability" S(t) [Torquato, Phys. Rev. E, 104, 054102, (2021)] of these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-Q power law scaling of the spectral density χV (Q) ∼ Qα with an exponent α that ranges from 0.64 at th

关键词： Spheres

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Poisson stochastic master equation unravellings and the measurement problem: a quantum stochastic calculus perspective

arXiv

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arXiv 2019年

作者： Keys, Dustin Wehr, Jan Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Mathematics and Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L2 (+). Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-Rimini-Weber model. A purely quantum object, the norm process, is found which plays the role of an observer (in the sense of Everett [H. Everett III, Reviews of modern physics, 29.3, 454, (1957)]), encoding all events occurring in the system space. An algorithm introduced by Dalibard et al [J. Dalibard, Y. Castin, and K. Mølmer, Physical review letters, 68.5, 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unravellings and the trajectories of expected values of system observables are calculated. © 2019, CC BY.

关键词： Poisson distribution

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Navigating the challenges in creating complex data systems: a development philosophy

arXiv

引用

arXiv 2022年

作者： Dittmer, Sören Roberts, Michael Gilbey, Julian Biguri, Ander Preller, Jacobus Rudd, James H.F. Aston, John A.D. Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Thorpe, Matthew Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Stanczuk, Jan Tang, Jing Babar, Judith Sánchez, Lorena Escudero Teare, Philip Patel, Mishal Wassin, Marcel Holzer, Markus Walton, Nicholas Lió, Pietro Shadbahr, Tolou Sala, Evis Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Department of Radiology University of Cambridge Cambridge United Kingdom Faculty of Mathematics University of Vienna Austria Department of Mathematics University of Manchester Manchester United Kingdom Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom

In this perspective, we argue that despite the democratization of powerful tools for data science and machine learning over the last decade, developing the code for a trustworthy and effective data science system (DSS) is getting harder. Perverse incentives and a lack of widespread software engineering (SE) skills are among many root causes we identify that naturally give rise to the current systemic crisis in reproducibility of DSSs. We analyze why SE and building large complex systems is, in general, hard. Based on these insights, we identify how SE addresses those difficulties and how we can apply and generalize SE methods to construct DSSs that are fit for purpose. We advocate two key development philosophies, namely that one should incrementally grow – not biphasically plan and build – DSSs, and one should always employ two types of feedback loops during development: one which tests the code’s correctness and another that evaluates the code’s efficacy. Copyright © 2022, The Authors. All rights reserved.

关键词： Software engineering

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Threshold and decay properties of transient isolated turbulent band in plane Couette flow

引用

applied mathematics and Mechanics(English Edition) 2019年第10期40卷 1449-1456页

作者： Jianzhou LU Jianjun TAO Weitao ZHOU Xiangming XIONG CAPT-HEDPS SKLTCS Collaborative Innovation Center of IFSA Department of Mechanics and Engineering Science College of Engineering Peking University Beijing 100871 China The Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 U. S.A.

By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

关键词： plane Couette flow (PCF) subcritical transition turbulent band

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Local two-sample testing over graphs and point-clouds by random-walk distributions

arXiv

引用

arXiv 2020年

作者： Landa, Boris Qu, Rihao Chang, Joseph Kluger, Yuval Program in Applied Mathematics Yale University Department of Pathology Yale University School of Medicine Department of Statistics and Data Science Yale University Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Immunology Yale School of Medicine

Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how the two distributions differ. Given samples from two densities f1and f0, we consider the task of localizing occurrences of the inequality f1> f0. To avoid the challenges associated with high-dimensional space, we propose a general hypothesis testing framework where hypotheses are formulated adaptively to the data by conditioning on the combined sample from the two densities. We then investigate a special case of this framework where the notion of locality is captured by a random walk on a weighted graph constructed over this combined sample. We derive a tractable testing procedure for this case employing a type of scan statistic, and provide non-asymptotic lower bounds on the power and accuracy of our test to detect whether f1> f0in a local sense. Furthermore, we characterize the test's consistency according to a certain problem-hardness parameter, and show that our test achieves the minimax detection rate for this parameter. We conduct numerical experiments to validate our method, and demonstrate our approach on two real-world applications: detecting and localizing arsenic well contamination across the United States, and analyzing two-sample single-cell RNA sequencing data from melanoma *** Codes 62G10 Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

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Early Detection of Preeclampsia using a Rule-Based System Information System 1

Early Detection of Preeclampsia using a Rule-Based System In...

引用

1st International Conference on Computer, Science, Engineering and Technology, ICComSET 2018

作者： Aini, F.N. Widyawati, M.N. Suryono, S. Purwokerto Midwifery Program Poltekkes Kemenkes Semarang Indonesia Postgraduate Applied Science Midwifery Program Poltekkes Kemenkes Semarang Indonesia Department of Physics Faculty of Science and Mathematics University Diponegoro Semarang Indonesia

Preeclampsia is the highest cause of maternal death. One program to reduce Maternal Mortality Rate (MMR) is by early detection. The incomplete history of maternal history that has occurred has led to the determination of an incorrect diagnosis and has resulted in errors in decision making. The results of the survey in the detection of preeclampsia include midwives not conducting a history of past medical history, physical examination during the first antenatal care visit is incomplete. During this time the detection and diagnosis model is still done manually, so it was not effective and efficient. The inspection data obtained using the information system becomes more complete and faster. Data obtained with information systems can be seen anywhere and anytime. This study produced innovations for the detection of preeclampsia in pregnant women using a rule-based system information system. This study uses the Quasy experimental posttest-only design. The subjects of this study were 66 pregnant women. Data collection was carried out using questionnaires and checklists. The results showed that early detection of preeclampsia using a rule-based system information system could improve the completeness of data on pregnant women up to 35.66%, and speed up the detection time of preeclampsia up to 35.60%. This system also has an effectivenessvalue 84.8%. © 2019 IOP Publishing Ltd. All rights reserved.

关键词： Decision making

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