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Extending Perfect Spatial Hashing to Index Tuple-based Graphs Representing Super Carbon Nanotubes

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Procedia Computer Science 2017年 108卷 435-444页

作者： Michael Burger Giang Nam Nguyen Christian Bischof Graduate School of Computational Engineering Dolivostr. 15 Darmstadt Germany Institute for Scientific Computing Mornewegstr. 30 Darmstadt Germany

In this paper, we demonstrate how to extend perfect spatial hashing (PSH) in order to hash multidimensional scientific data. As a use case we employ the problem domain of indexing nodes in a graph that represents Super Carbon Nanotubes (SCNTs). The goal of PSH is to hash multidimensional data without collisions. Since PSH results from the research on computer graphics, its principles and methods have only been tested on 2- and 3-dimensional problems. In our case, we need to hash up to 28 dimensions. In contrast to the original applications of PSH, we do not focus on GPUs as target hardware but on an efficient CPU implementation. Thus, this paper highlights the extensions to the original algorithm to make it suitable for higher dimensions. Comparing the compression and performance results of the new PSH based graphs and a structure-tailored custom data structure in our parallelized SCNT simulation software, we find that PSH in some cases achieves better compression by a factor of 1.7 while only increasing the total runtime by several percent. In particular, after our extension, PSH can also be employed to index sparse multidimensional scientific data from other domains where PSH can avoid additional index-structures like KD- or R-trees.

关键词： perfect spatial hashing data indexing super carbon nanotubes simulation

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF A PARABOLIC OPTIMAL CONTROL PROBLEM WITH UNCERTAIN INPUTS

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arXiv 2018年

作者： Benner, Peter Onwunta, Akwum Stoll, Martin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstrasse 1 Magdeburg39106 Germany Department of Computer Science University of Maryland College ParkMD20742 United States Technische Universität Chemnitz Faculty of Mathematics Professorship Scientific Computing Chemnitz09107 Germany

In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions’ Lemma for deterministic problems, we furthermore characterize the optimal control of the stochastic problem. Copyright © 2018, The Authors. All rights reserved.

关键词： Optimal control systems

NANOGrav 15-year gravitational-wave background methods

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Physical Review D 2024年第10期109卷 103012-103012页

作者： Aaron D. Johnson Patrick M. Meyers Paul T. Baker Neil J. Cornish Jeffrey S. Hazboun Tyson B. Littenberg Joseph D. Romano Stephen R. Taylor Michele Vallisneri Sarah J. Vigeland Ken D. Olum Xavier Siemens Justin A. Ellis Rutger van Haasteren Sophie Hourihane Gabriella Agazie Akash Anumarlapudi Anne M. Archibald Zaven Arzoumanian Laura Blecha Adam Brazier Paul R. Brook Sarah Burke-Spolaor Bence Bécsy J. Andrew Casey-Clyde Maria Charisi Shami Chatterjee Katerina Chatziioannou Tyler Cohen James M. Cordes Fronefield Crawford H. Thankful Cromartie Kathryn Crowter Megan E. DeCesar Paul B. Demorest Timothy Dolch Brendan Drachler Elizabeth C. Ferrara William Fiore Emmanuel Fonseca Gabriel E. Freedman Nate Garver-Daniels Peter A. Gentile Joseph Glaser Deborah C. Good Kayhan Gültekin Ross J. Jennings Megan L. Jones Andrew R. Kaiser David L. Kaplan Luke Zoltan Kelley Matthew Kerr Joey S. Key Nima Laal Michael T. Lam William G. Lamb T. Joseph W. Lazio Natalia Lewandowska Tingting Liu Duncan R. Lorimer Jing Luo Ryan S. Lynch Chung-Pei Ma Dustin R. Madison Alexander McEwen James W. McKee Maura A. McLaughlin Natasha McMann Bradley W. Meyers Chiara M. F. Mingarelli Andrea Mitridate Cherry Ng David J. Nice Stella Koch Ocker Timothy T. Pennucci Benetge B. P. Perera Nihan S. Pol Henri A. Radovan Scott M. Ransom Paul S. Ray Shashwat C. Sardesai Carl Schmiedekamp Ann Schmiedekamp Kai Schmitz Brent J. Shapiro-Albert Joseph Simon Magdalena S. Siwek Ingrid H. Stairs Daniel R. Stinebring Kevin Stovall Abhimanyu Susobhanan Joseph K. Swiggum Jacob E. Turner Caner Unal Haley M. Wahl Caitlin A. Witt Olivia Young Center for Gravitation Cosmology and Astrophysics Department of Physics University of Wisconsin-Milwaukee P.O. Box 413 Milwaukee Wisconsin 53201 USA Division of Physics Mathematics and Astronomy California Institute of Technology Pasadena California 91125 USA Department of Physics and Astronomy Widener University One University Place Chester Pennsylvania 19013 USA Department of Physics Montana State University Bozeman Montana 59717 USA Department of Physics Oregon State University Corvallis Oregon 97331 USA NASA Marshall Space Flight Center Huntsville Alabama 35812 USA Department of Physics Texas Tech University Box 41051 Lubbock Texas 79409 USA Department of Physics and Astronomy Vanderbilt University 2301 Vanderbilt Place Nashville Tennessee 37235 USA Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Drive Pasadena California 91109 USA Institute of Cosmology Department of Physics and Astronomy Tufts University Medford Massachusetts 02155 USA Department of Astronomy University of Maryland College Park Maryland 20742 Center for Research and Exploration in Space Science and Technology NASA/GSFC Greenbelt Maryland 20771 NASA Goddard Space Flight Center Greenbelt Maryland 20771 USA Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) Callinstrasse 38 D-30167 Hannover Germany Newcastle University NE1 7RU Newcastle United Kingdom X-Ray Astrophysics Laboratory NASA Goddard Space Flight Center Code 662 Greenbelt Maryland 20771 USA Physics Department University of Florida Gainesville Florida 32611 USA Cornell Center for Astrophysics and Planetary Science and Department of Astronomy Cornell University Ithaca New York 14853 USA Cornell Center for Advanced Computing Cornell University Ithaca New York 14853 USA Institute for Gravitational Wave Astronomy and School of Physics and Astronomy University of Birmingham Edgbaston Birmingham B15 2TT United Kingdom Department of Physics and Astronomy West

Pulsar timing arrays (PTAs) use an array of millisecond pulsars to search for gravitational waves in the nanohertz regime in pulse time of arrival data. This paper presents rigorous tests of PTA methods, examining their consistency across the relevant parameter space. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms enterprise and ptmcmcsampler are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster in gravitational wave searches, reducing the required resources facilitating the computation of Bayes factors via thermodynamic integration and sampling a large number of realizations for computing Bayesian false-alarm probabilities. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis methods. For the Bayesian analysis, we test prior recovery, simulation recovery, and Bayes factors. For the frequentist analysis, we test that the optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both gravitational wave background detection and parameter estimation perspectives. The tests presented here validate current analyses of PTA data.

关键词： Gravitational waves Gravitational wave detection

Author Correction: Enhanced energy coupling for indirect-drive fast-ignition fusion targets

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Nature Physics 2020年第7期16卷 815-815页

作者： F. Zhang H. B. Cai W. M. Zhou Z. S. Dai L. Q. Shan H. Xu J. B. Chen F. J. Ge Q. Tang W. S. Zhang L. Wei D. X. Liu J. F. Gu H. B. Du B. Bi S. Z. Wu J. Li F. Lu H. Zhang B. Zhang M. Q. He M. H. Yu Z. H. Yang W. W. Wang H. S. Zhang B. Cui L. Yang J. F. Wu W. Qi L. H. Cao Z. Li H. J. Liu Y. M. Yang G. L. Ren C. Tian Z. Q. Yuan W. D. Zheng L. F. Cao C. T. Zhou S. Y. Zou Y. Q. Gu K. Du Y. K. Ding B. H. Zhang S. P. Zhu W. Y. Zhang X. T. He Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center CAEP Mianyang China Institute of Applied Physics and Computational Mathematics Beijing China HEDPS Center for Applied Physics and Technology Peking University Beijing China College of Computing Science National University of Defense Technology Changsha China Center for Advanced Material Diagnostic Technology Shenzhen Technology University Shenzhen China Graduate School China Academy of Engineering Physics Beijing China

A stochastic pitchfork bifurcation in most probable phase portraits

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arXiv 2018年

作者： Wang, Hui Chen, Xiaoli Duan, Jinqiao Center for Mathematical Sciences School of Mathematics and Statistics Hubei Key Laboratory for Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan430074 China

We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i) When the non-Gaussianity parameter in Lévy noise varies, there is either one, two or none backward pitchfork type bifurcations;(ii) When a parameter in the vector field varies, there are two or three forward pitchfork bifurcations;(iii) The non-Gaussian Lévy noise clearly leads to fundamentally more complex bifurcation scenarios, since in the special case of Gaussian noise, there is only one pitchfork bifurcation which is reminiscent of the deterministic situation. Copyright © 2018, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections

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arXiv 2018年

作者： Vučičević, J. Kokalj, J. Žitko, R. Wentzell, N. Tanasković, D. Mravlje, J. Scientific Computing Laboratory Center for the Study of Complex Systems Institute of Physics Belgrade University of Belgrade Pregrevica 118 Belgrade11080 Serbia University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova 2 Ljubljana Slovenia Jozef Stefan Institute Jamova 39 LjubljanaSI-1000 Slovenia University of Ljubljana Faculty of Mathematics and Physics Jadranska 19 Ljubljana Slovenia Center for Computational Quantum Physics Simons Foundation Flatiron Institute New YorkNY10010 United States

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results and the question of the exact solution for the conductivity in the Hubbard model remained open. In this letter we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity, and identify the best available result to be compared to experiment. We find that at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4 × 4 and the corresponding Lanczos diagonalization result is therefore close to the exact result in the thermodynamic limit. Copyright © 2018, The Authors. All rights reserved.

关键词： Crystal lattices

Convergence Analysis of an Unconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard Equation

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arXiv 2017年

作者： Wang, Lin Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 Ncmis and Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190

Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the Cahn-Hilliard equation with provable unconditional stability. In this scheme the nonlinear bulk force are treated explicitly with two second-order linear stabilization terms. The semi-discretized equation is a linear elliptic system with constant coefficients, thus robust and efficient solution procedures are guaranteed. Rigorous error analysis show that, when the time step-size is small enough, the scheme is second order accurate in time with a prefactor controlled by some lower degree polynomial of 1/". Here " is the interface thickness parameter. Numerical results are presented to verify the accuracy and efficiency of the *** Codes 65M12, 65M15, 65P40 Copyright © 2017, The Authors. All rights reserved.

关键词： Phase interfaces

High order fast algorithm for the Caputo fractional derivative

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arXiv 2017年

作者： Wang, Kun Huang, Jizu College of Mathematics and Statistics Chongqing University Chongqing401331 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of u′(t) with the kernel (tn- t)-α. In the fast algorithm, the interval [0, tn-1] is split into nonuniform subintervals. The number of the subintervals is in the order of log n at the n-th time step. The fractional kernel function is approximated by a polynomial function of K-th degree with a uniform absolute error on each subinterval. We save K+1 integrals on each subinterval, which can be written as a convolution of u′(t) with a polynomial base function. As compared with the direct method, the proposed fast algorithm reduces the storage requirement and computational cost from O(n) to O((K + 1) log n) at the n-th time step. We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order direct method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples. Copyright © 2017, The Authors. All rights reserved.

关键词： Polynomial approximation

Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

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arXiv 2017年

作者： Xu, Xianmin Di, Yana Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 Ncmis and Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter in the boundary condition are considered. In asymptotic analysis, we focus on the case that the mobility number is the same order of the Cahn number and derive the sharp-interface limits for several setups of the boundary relaxation parameter. It is shown that the sharp interface limit of the phase field model is the standard two-phase incompressible Navier-Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters. Copyright © 2017, The Authors. All rights reserved.

关键词： Asymptotic analysis