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Microstructural degeneracy associated with a two-point correlation function and its information content

Physical Review E 2012年第5期85卷 051140-051140页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège Liège 4000 Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics 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

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the

关键词： MICROSTRUCTURE CORRELATION (Statistics) INFORMATION theory ENTROPY (Information theory) GROUND state (Quantum mechanics) MONTE Carlo method POISSON processes

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Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling

Symplectic time-domain finite element method (STD-FEM) exten...

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2023 International Conference for Acoustic and vibration Engineers, NVHH 2023

作者： Huszty, Csaba Firtha, Gergely Izsák, Ferenc ENTEL Engineering Research & Consulting Ltd. Szépvölgyi út 32. BudapestH-1025 Hungary Department of Networked Systems and Services Faculty of Electric Engineering Budapest University of Technology and Economics Muegyetem rkp. 3. BudapestH-1111 Hungary Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Pázmány P. stny. 1.C BudapestH-1117 Hungary

The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity. © Published under licence by IOP Publishing Ltd.

关键词： Acoustic fields

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Spectral Top-Down Recovery of Latent Tree Models

arXiv

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arXiv 2021年

作者： Aizenbud, Yariv Jaffe, Ariel Wang, Meng Hu, Amber Amsel, Noah Nadler, Boaz Chang, Joseph T. Kluger, Yuval Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Computer Science Weizmann Institute of Science Rehovot76100 Israel Department of Statistics Yale University New HavenCT06520 United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University New HavenCT06511 United States Department of Pathology Yale University New HavenCT06511 United States

Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, recover the structure separately of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop Spectral Top-Down Recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy. Copyright © 2021, The Authors. All rights reserved.

关键词： Recovery

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Intensity dependence of intramolecular interference from a full quantum analysis of high-order harmonic generation

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Physical Review A 2009年第3期79卷 033405-033405页

作者： Y. J. Chen J. Liu Bambi Hu Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Physics Centre for Nonlinear Studies and The Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong) Hong Kong Baptist University Kowloon Tong Hong Kong China Department of Physics Hebei Normal University Shijiazhuang 050016 China Center for Applied Physics and Technology Peking University Beijing 100084 China Department of Physics University of Houston Houston Texas 77204-5005 USA

We develop a numerical scheme to investigate the high-order harmonic generation (HHG) in intense laser-matter interactions. We represent the time-dependent wave function in the basis of the eigenstates of the field-free Hamiltonian and trace its temporal evolution. Our full quantum simulations reveal that continuum electrons with a broad energy distribution contribute equally to one harmonic and the excited state also plays an important role in the molecular HHG. These results imply a laser-intensity-dependent picture of intramolecular interference in the HHG.

关键词： Excited states

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High-throughput investigations of configurational-transformation-dominated serrations in CuZr/Cu nanolaminates

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Journal of Materials Science & Technology 2020年第18期52卷 192-199页

作者： William Yi Wang Bin Gana Deye Lin Jun Wang Yiguang Wang Bin Tang Hongchao Kou Shunli Shang Yi Wang Xingyu Gao Haifeng Song Xidong Hui Laszlo J.Kecskes Zhenhai Xia Karin A.Dahmen Peter K.Liaw Jinshan Lia Zi-Kui Liu State Key Laboratory of Solidification Processing Northwestern Polytechnical UniversityXi'an.710072China Beijing Key Laboratory of Advanced High Temperature Materials Central Iron and Steel Research InstituteBeijing100081China IMDEA Materials Institute Calle Eric Kandel 2GetafeMadrid28906Spain CAEP Software Center for High Performance Numerical Simulation Institute of Applied Physics and Computational MathematicsBeijing100088China Department of Materials Science and Engineering The Pennsylvania State UniversityUniversity ParkPA16802USA State Key Laboratory for Advanced Metals and Materials University of Science and Technology BeijingBeijing100083China Hopkins Extreme Materials Institute Johns Hopkins UniversityBaltimoreMD21218USA Department of Physics University of Illinois at Urbana ChampaignUrbanaIL61801USA Department of Materials Science and Engineering The University of TennesseeKnoxvilleTN37996USA

Metallic amorphous/crystalline(A/C)nanolaminates exhibit excellent ductility while retaining their high ***,the underlying physical mechanisms and the resultant structural changes during plastic deformation still remain *** the present work,the structure-property relationship of CuZr/Cu A/C nanolaminates is established through integrated high-throughput micro-compression tests and molecular dynamics simulations together with high-resolution transmission electron *** serrated flow of nanolaminates results from the formation of hexagonal-close-packed(HCP)-type stacking faults and twins inside the face-centered-cubic(FCC)Cu nano-grains,the body-centered-cubic(BCC)-type ordering at their grain boundaries,and the crystallization of the amorphous CuZr *** serration behavior of CuZr/Cu A/C nanolaminates is determined by several factors,including the formation of dense dislocation networks from the multiplication of initial dislocations that formed after yielding,weak-spots-related configurational-transitions and shear-transition-zone activities,and deformation-induced *** present work provides an insight into the heterogeneous deformation mechanism of A/C nanolaminates at the atomic scale,and mechanistic base for the microstructural design of self-toughening metallic-glass(MG)-based composites and A/C nanolaminates.

关键词： Nanolaminates Serration Configurational transformation Molecular dynamics Metallic glass

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Learning equations from biological data with limited time samples

arXiv

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arXiv 2020年

作者： Nardini, John T. Lagergren, John H. Hawkins-Daarud, Andrea Curtin, Lee Morris, Bethan Rutter, Erica M. Swanson, Kristin R. Flores, Kevin B. Department of Mathematics North Carolina State University RaleighNC United States Statistical and Applied Mathematical Sciences Insitute DurhamNC United States Mathematical NeuroOncology Laboratory Precision Neurotherapeutics Innovation Program Mayo Clinic PhoenixAZ United States Centre for Mathematical Medicine and Biology University of Nottingham Nottingham United Kingdom Department of Applied Mathematics University of California Merced MercedCA United States

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets, however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data is sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions. Copyright © 2020, The Authors. All rights reserved.

关键词： Learning systems

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Heterogeneous cellular network performance analysis under open and closed access

Heterogeneous cellular network performance analysis under op...

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IEEE Globecom Workshops

作者： Prasanna Madhusudhanan Juan G. Restrepo Youjian Liu Timothy X Brown Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO USA Department of Applied Mathematics University of Colorado Boulder CO USA Department of Electrical Computer and Energy Engineering Interdisciplinary Telecommunications Program University of Colorado Boulder CO USA

We study the downlink signal-to-interference ratio (SIR) in a multi-tier heterogeneous cellular network under the open and closed access schemes. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain density, constant transmission power and random shadow fading factors with arbitrary distribution. The mobile-station (MS) communicates with the BS that has the maximum instantaneous received power among those to which it is allowed access. The chosen BS provides coverage to the MS if the SIR is above a certain threshold determined by the BS's tier. The coverage probability and average rate expressions are derived for the open access scheme for any arbitrary SIR threshold assigned for each tier, and for the closed access scheme when the SIR thresholds are greater than one.

关键词： Fading Macrocell networks Random variables Measurement computational modeling Femtocell networks Downlink

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Chiral Quasi-Bound States in the Continuum

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Physical Review Letters 2021年第7期126卷 073001-073001页

作者： Adam Overvig Nanfang Yu Andrea Alù Photonics Initiative Advanced Science Research Center at the Graduate Center of the City University of New York New York New York 10031 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Physics Program Graduate Center City University of New York New York New York 10016 USA

Quasi-bound states in the continuum (QBICs) are Fano resonant states with long optical lifetimes controlled by symmetry-breaking perturbations. While conventional Fano responses are limited to linear polarizations and do not support tailored phase control, here we introduce QBICs born of chiral perturbations that encode arbitrary elliptical polarization states and enable geometric phase engineering. We thereby design metasurfaces with ultrasharp spectral features that shape the impinging wave front with near-unity efficiency. Our findings extend Fano resonances beyond their conventional limits, opening opportunities for nanophotonics, classical and quantum optics, and acoustics.

关键词： Metamaterials Photonic crystals

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Analysis of nucleon and triton emissions from nucleon-Li7 collisions below 20 MeV

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Physical Review C 2019年第3期99卷 034602-034602页

作者： Hairui Guo Yukinobu Watanabe Takuma Matsumoto Kohei Nagaoka Kazuyuki Ogata Masanobu Yahiro Institute of Applied Physics and Computational Mathematics Beijing 100094 China Department of Advanced Energy Engineering Science Kyushu University Kasuga Fukuoka 816-8580 Japan Department of Physics Kyushu University Fukuoka 812-8581 Japan Research Center for Nuclear Physics Osaka University Ibaraki Osaka 567-0047 Japan

The understanding of nucleon (N) and triton emissions from nucleon-Li7 collision is important for the development of some fusion-related facilities. Both nucleon and triton emissions from nucleon-induced reactions on Li7 leading to three final particles at incident energies below 20 MeV are analyzed by using a three-body continuum discretized coupled-channels method (CDCC), final-state interaction (FSI) model, and sequential decay (SD) model. The CDCC is applied to predict nucleon and triton emissions via breakup continuum channels, Li7(N,N′)Li*7→t+α. Triton emission from the p(n) + Li7→t+Li5(He5) channel and nucleon emission from sequential decay of the ground-state Li5(He5) are described by the FSI model and the SD model, respectively. The double differential cross sections (DDXs) of nucleon and triton emissions are calculated and compared with experimental data. In most cases, the calculated DDXs are in good agreement with the measured ones except at relatively low nucleon emission energies. It is clarified that triton production takes place mainly via the breakup continuum channels.

关键词： Breakup reactions Direct reactions Nuclear reactions Nucleon induced nuclear reactions 6 ≤ A ≤ 19 Optical, coupled-channel & distorted wave models

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Atomistic Modelling of All Dislocations and Twins in HCP and BCC Ti

SSRN

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SSRN 2022年

作者： Wen, Tongqi Liu, Anwen Wang, Rui Zhang, Linfeng Han, Jian Wang, Han Srolovitz, David J. Wu, Zhaoxuan Department of Mechanical Engineering The University of Hong Kong Hong Kong Department of Materials Science and Engineering City University of Hong Kong Hong Kong DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China Hong Kong Institute for Advanced Study City University of Hong Kong Hong Kong

Ti exhibits complex plastic deformation controlled by active dislocation and twinning systems. Understandings on dislocation cores and twin interfaces are currently not complete or quantitative, despite extensive experimental and simulation studies. Here, we determine all the core and twin interface properties in both HCP and BCC Ti using a Deep Potential (DP) and DFT. We determine the core structures, critical resolved shear stresses and mobilities of hai, hc + ai, hci dislocations in HCP and h111i/2 dislocations in BCC Ti. The hai slip consists of slow core migration on pyramidal-I planes and fast migration on prism-planes, and is kinetically limited by cross-slips among them. This behaviour is consistent with 'locking-unlocking' phenomena in TEM and is likely an intrinsic property. Large-scale DFT calculations provide a peek at thescrew hc + ai core and glide behaviour, which is further quantified using DP-Ti. The screw hc + ai is unstable on pyramidal-II planes. The mixed hc + ai is nearly sessile on pyramidal-I planes, consistent with observations of long dislocations in this orientation. The edge and mixed hc + ai are unstable against a pyramidal-to-basal (PB) transition and become sessile at high temperatures, corroborate the difficulties in hci-axis compression of Ti. Finally, in BCC Ti, the h111i/2 screw has a degenerate core with average glide on {112} planes;the h111i/2 edge and mixed dislocations have non-dissociated cores on {110} planes. This work paints a self-consistent, complete picture on all dislocations in Ti, rationalises previous experimental observations and points to future HRTEM examinations of unusual dislocations such as the mixedand PB transformed hc + ai cores. © 2022, The Authors. All rights reserved.

关键词： Molecular dynamics

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