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Novel linear algebraic theory and one-hundred-million-atom quantum material simulations on the K computer 1

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Novel linear algebraic theory and one-hundred-million-atom q...

1st International Workshop on computational science and Engineering, IWCSE 2013

作者： Hoshi, Takeo Sogabe, Tomohiro Miyata, Takafumi Lee, Dongjin Zhang, Shao-Liang Imachi, Hiroto Kawai, Yoshifumi Akiyama, Yohei Yamazaki, Keita Yokoyama, Seiya Department of Applied Mathematics and Physics Tottori University Koyama Minami Tottori680-8550 Japan 5 Sanbancho Chiyoda-ku Tokyo102-0075 Japan Graduate School of Information Science and Technology Aichi Prefectural University 1522-3 Ibaragabasama Kumabari Nagakute-cho Aichi-gun Aichi480-1198 Japan Department of Computational Science and Engineering Nagoya University Furo-cho Chikusa-ku Nagoya464-8603 Japan Center for Research and Development of Higher Education University of Tokyo Bunkyo-ku Tokyo113-8656 Japan

The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are Krylov-subspace (iterative) solvers for generalized shifted linear equations, in the form of (zS-H)x = b, in stead of conventional generalized eigen-value equation. The method was implemented in our order-N calculation code ELSES (http://***/) with modelled systems based on ab initio calculations. The code realized one-hundred-million-atom, or 100-nm-scale, quantum material simulations on the K computer in a high parallel efficiency with up to all the built-in processor cores. The present paper also explains several methodological aspects, such as use of XML files and 'novice' mode for general users. A sparse matrix data library in our real problems (http://***/matrix/) was prepared. Internal eigen-value problem is discussed as a general need from the quantum material simulation. The present study is a interdisciplinary one and is sometimes called 'Application-Algorithm-Architecture co-design'. The co-design will play a crucial role in exa-scale scientific computations. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

关键词： Iterative methods

Irregular oscillatory-patterns in the early-time region of coherent phonon generation in silicon

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arXiv 2017年

作者： Watanabe, Yohei Hino, Ken-Ichi Hase, Muneaki Maeshima, Nobuya Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki305-8573 Japan Division of Materials Science Faculty of Pure and Applied Sciences University of Tsukuba Tsukuba305-8573 Japan Center for Computational Sciences University of Tsukuba Tsukuba305-8577 Japan Division of Applied Physics Faculty of Pure and Applied Sciences University of Tsukuba Tsukuba305-8573 Japan

Coherent phonon (CP) generation in an undoped Si crystal is theoretically investigated to shed light on unexplored quantum-mechanical effects in the early-time region immediately after the irradiation of ultrashort laser pulse. One examines time signals attributed to an induced charge density of an ionic core, placing the focus on the effects of the Rabi frequency ωocvon the signals;this frequency corresponds to the peak electric-field of the pulse. It is found that at specific ωocv's where the energy of plasmon caused by photoexcited carriers coincides with the longitudinal-optical phonon energy, the energetically resonant interaction between these two modes leads to striking anticrossings, revealing irregular oscillations with anomalously enhanced amplitudes in the observed time signals. Also, the oscillatory pattern is subject to the Rabi flopping of the excited carrier density that is controlled by ωocv. These findings show that the early-time region is enriched with quantum-mechanical effects inherent in the CP generation, though experimental signals are more or less masked by the so-called coherent artifact due to nonlinear optical effects. Copyright © 2017, The Authors. All rights reserved.

关键词： Ultrashort pulses

Gel’fand’s inverse problem for the graph Laplacian

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arXiv 2021年

作者： Blåsten, Emilia Isozaki, Hiroshi Lassas, Matti Lu, Jinpeng Computational Engineering School of Engineering Science LUT University Lahti campus Lahti15210 Finland Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We study the discrete Gel’fand’s inverse boundary spectral problem of determining a finite weighted graph. Suppose that the set of vertices of the graph is a union of two disjoint sets: X = B ∪ G, where B is called the set of the boundary vertices and G is called the set of the interior vertices. We consider the case where the vertices in the set G and the edges connecting them are unknown. Assume that we are given the set B and the pairs (λj, φj|B), where λj are the eigenvalues of the graph Laplacian and φj|B are the values of the corresponding eigenfunctions at the vertices in B. We show that the graph structure, namely the unknown vertices in G and the edges connecting them, along with the weights, can be uniquely determined from the given data, if every boundary vertex is connected to only one interior vertex and the graph satisfies the following property: any subset S ⊆ G of cardinality |S| ≥ 2 contains two extreme points. A point x ∈ S is called an extreme point of S if there exists a point z ∈ B such that x is the unique nearest point in S from z with respect to the graph distance. This property is valid for several standard types of lattices and their *** Codes 05C50, 05C22, 52C25 Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

INVERSE PROBLEMS FOR DISCRETE HEAT EQUATIONS AND RANDOM WALKS FOR A CLASS OF GRAPHS

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arXiv 2021年

MSC Codes 05C50, 05C81, 05C22We study the inverse problem of determining a finite weighted graph (X, E) from the source-to-solution map on a vertex subset B ⊂ X for heat equations on graphs, where the time variable can be either discrete or continuous. We prove that this problem is equivalent to the discrete version of the inverse interior spectral problem, provided that there does not exist a nonzero eigenfunction of the weighted graph Laplacian vanishing identically on B. In particular, we consider inverse problems for discrete-time random walks on finite graphs. We show that under a novel geometric condition (called the Two-Points Condition), the graph structure and the transition matrix of the random walk can be uniquely recovered from the distributions of the first passing times on B, or from the observation on B of one realization of the random walk. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

Effects of size polydispersity on the extinction spectra of colloidal nanoparticle aggregates

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Physical Review B 2012年第4期85卷 045421-045421页

作者： Alexander E. Ershov Ivan L. Isaev Polina N. Semina Vadim A. Markel Sergei V. Karpov L. V. Kirenskiy Institute of Physics Russian Academy of Sciences Kransoyarsk 660036 Russian Federation Siberian Federal University Krasnoyarsk 660041 Russian Federation Department of Radiology Department of Bioengineering and the Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We investigate the effect of particle polydispersity on the optical extinction spectra of colloidal aggregates of spherical metallic (silver) nanoparticles, taking into account the realistic interparticle gaps caused by layers of stabilizing polymer adsorbed on the metal surface (adlayers). The spectra of computer-generated aggregates are computed using two different methods. The coupled-multipole method is used in the quasistatic approximation and the coupled-dipole method beyond the quasistatics. The latter approach is applicable if the interparticle gaps are sufficiently wide relative to the particle radii. Simulations are performed for two different particle size distribution functions (bimodal and Gaussian), varying the number of particles per aggregate, and different distribution functions of the interparticle gap width. The strong influence of the latter factor on the spectra is demonstrated and investigated in detail.

关键词： DISPERSION METAL nanoparticles COLLOIDS SPECTRUM analysis SIMULATION methods & models CLUSTERING of particles METALLIC surfaces

Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods

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arXiv 2023年

作者： Moral, Pierre Del Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux FR Bordeaux33405 France School of Mathematics and Statistics Wenlan School of Business China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Zhongnan University of Economics and Law CN China

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE);see [12]. These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of O(ϵ2), for ϵ > 0 given, the associated work is O(ϵ−2). Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Diffusion

Subfemtosecond glory hologrammetry for vectorial optical waveform reconstruction

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arXiv 2019年

作者： Tao, J.F. Cai, J. Xia, Q.Z. Liu, J. Beijing Computational Science Research Center Beijing100193 China School of Physics and Electronic Engineering Jiangsu Normal University Xuzhou221116 China National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Graduate School of China Academy of Engineering Physics Beijing100193 China CAPT HEDPS IFSA Collaborative Innovation Center of MoE Peking University Beijing100871 China

In this Letter, we propose a new method to characterize the temporal structure of arbitrary optical laser pulses with low pulse energies. This approach is based on strong field photoelectron holography with the glory rescattering effect as the underlying mechanism in the near-forward direction. Utilizing the subfemtosecond glory rescattering process as a fast temporal gate to sample the unknown light pulse, the time-dependent vectorial electric field can be retrieved from the streaking photoelectron momentum spectra. Our method avoids the challenging task of generation or manipulation of attosecond pulses and signifies important progress in arbitrary optical waveform characterization. Copyright © 2019, The Authors. All rights reserved.

关键词： Photons

Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks

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Physical Review Letters 2021年第3期127卷 037401-037401页

作者： Michael A. Klatt Paul J. Steinhardt Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik University of Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany Department of Chemistry Princeton Institute for the Science and Technology of Materialsand Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α)≡dΔ(α)/dα, the first derivative of the optimal gap-to-midgap ratio Δ(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a 1D quarter-wave stack, SQWS(α). Even more surprisingly, the values of S(α) for our disordered networks converge to SQWS(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic heterostructures.

关键词： Photonic crystals Diamond structure Networks & random structures Random & disordered media Band structure methods

Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

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Physical Review X 2021年第2期11卷 021028-021028页

作者： Salvatore Torquato Jaeuk Kim Michael A. Klatt Department of Physics Princeton University Princeton New Jersey 08544 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 Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany

The local number variance σ2(R) associated with a spherical sampling window of radius R enables a classification of many-particle systems in d-dimensional Euclidean space Rd according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To more completely characterize density fluctuations, we carry out an extensive study of higher-order moments or cumulants, including the skewness γ1(R), excess kurtosis γ2(R), and the corresponding probability distribution function P[N(R)] of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. To carry out this comprehensive program, we derive new theoretical results that apply to general point processes, and we conduct high-precision numerical studies. Specifically, we derive explicit closed-form integral expressions for γ1(R) and γ2(R) that encode structural information up to three-body and four-body correlation functions, respectively. We also derive rigorous bounds on γ1(R), γ2(R), and P[N(R)] for general point processes and corresponding exact results for general packings of identical spheres. High-quality simulation data for γ1(R), γ2(R), and P[N(R)] are generated for each model. We also ascertain the proximity of P[N(R)] to the normal distribution via a novel Gaussian “distance” metric l2(R). Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes in two or higher dimensions such that γ1(R)∼l2(R)∼R−(d+1)/2 and γ2(R)∼R−(d+1) for large R. The convergence to a CLT is slower for standard nonhyperuniform models and slowest for the “antihyperuniform” model studied here. We prove that one-dimensional hyperuniform systems of class I or any d-dimensional lattice cannot obey a CLT. Remarkably, we discover a type of universality in that, for all of ou

关键词： Exotic phases of matter Fluctuations & noise Nonequilibrium statistical mechanics Surface & interfacial phenomena