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A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

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arXiv 2017年

作者： Cheng, Jun-Bo Huang, Weizhang Jiang, Song Tian, Baolin Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China Department of Mathematics University of Kansas LawrenceKS66045 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.65N08, 76M12 Copyright © 2017, The Authors. All rights reserved.

关键词： Elastoplasticity

Inventory of fungi from termite nests at Gunung Leuser National Park, northern Sumatra

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IOP Conference Series: Earth and Environmental Science 2021年第1期667卷

作者： S Hanum L Fitri O Lisa S Samingan A Alfizar D Sutekad N Novita S Muarrif S Syaukani Master Program in Biological Science Faculty of Mathematic and Natural Sciences Universitas Syiah Kuala Darussalam 23111 Banda Aceh Indonesia Biology Department Faculty of Mathematic and Natural Sciences Universitas Syiah Kuala Darussalam 23111 Banda Aceh Indonesia Faculty of Teacher Training and Education Universitas Syiah Kuala Darussalam 23111 Banda Aceh Indonesia Plant Protection Department Faculty of Agriculture Universitas Syiah Kuala Darussalam 23111 Banda Aceh Indonesia Graduate School of Mathematics and Applied Science Universitas Syiah Kuala Darussalam 23111 Banda Aceh Indonesia

Fungi and termite coexisted each other and have diverse symbiotic relationship in tropical forest. This research aims to determine the fungus found on termite nests in Suaq Balimbing Research Station so it can be used that as initial information in developing environmentally friendly termite control. The method used for collecting samples of fungus is a Standarized Sampling Protocol and for identification used slide culture method. The results showed that 5 of 12 termites nest are invaded by fungi. Based on macroscopic and microscopic observation, fungus species that obtained from termite nests are 2 species, namely: Penicillium sp.1, Trichoderma sp. 1

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Structural variability from noisy tomographic projections

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arXiv 2017年

作者： Andén, Joakim Singer, Amit Center for Computational Biology Flatiron Institute New YorkNY United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ United States

In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low-rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For n images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O(nN4 + √κN6 log N), where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in 6D. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed non-consistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.92C55, 68U10, 44A12, 65R32, 62G05, 62H30, 62J10, 62J07 Copyright © 2017, The Authors. All rights reserved.

关键词： Conjugate gradient method

Setting the physical scale of dimensional reduction in causal dynamical triangulations

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arXiv 2018年

作者： Cooperman, Joshua H. Dorghabekov, Manuchehr Department of Physics and Astronomy Bucknell University LewisburgPA United States Physics Program Bard College Annandale-on-Hudson NY United States Applied Mathematics and Informatics Program American University of Central Asia Bishkek Kyrgyzstan

Within the causal dynamical triangulations approach to the quantization of gravity, striking evidence has emerged for the dynamical reduction of spacetime dimension on sufficiently small scales. Specifically, the spectral dimension decreases from the topological value of 4 towards a value near 2 as the scale being probed decreases. The physical scales over which this dimensional reduction occurs have not previously been ascertained. We present and implement a method to determine these scales in units of either the Planck length or the quantum spacetime geometry’s effective de Sitter length. We find that dynamical reduction of the spectral dimension occurs over physical scales of the order of 10 Planck lengths, which, for the numerical simulation considered below, corresponds to the order of 10−1 de Sitter lengths. Copyright © 2018, The Authors. All rights reserved.

关键词： Triangulation

Observation of indirect ionization of W7+ in EBIT plasma

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Journal of Physics: Conference Series 2020年第13期1412卷

作者： Q Lu J He H Tian M Li Y Yang K Yao C Chen J Xiao J G Li B Tu Y Zou Institute of Modern Physics Department of Nuclear Science and Technology Fudan University Shanghai 200433 China Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) Fudan University Shanghai 200433 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Max-Planck-Institute für Kernphysik Saupfercheckweg 1 69117 Heidelberg Germany

In this work, visible and EUV spectra of W7+ have been measured using the high-temperature super-conducting electron-beam ion trap at the Shanghai EBIT laboratory under extremely low-energy conditions. The relevant atomic structure has been calculated by using the flexible atomic code package and the GRASP2K code. A hypothesis for the charge-state evolution of W7+ is proposed based on our results. The occurrence of W7+ ions results from indirect ionization caused by stepwise excitation between some metastable states of lower-charge-state W ions, at the nominal electron beam energy of 59 eV.

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3D ab initio modeling in cryo-em by autocorrelation analysis

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arXiv 2017年

作者： Levin, Eitan Bendory, Tamir Boumal, Nicolas Kileel, Joe Singer, Amit Princeton University Program in Applied and Computational Mathematics PrincetonNJ United States

Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is the task of estimating the 3D structure of a molecule from a set of noisy 2D projections, taken from unknown viewing directions. Many algorithms for SPR start from an initial reference molecule, and alternate between refining the estimated viewing angles given the molecule, and refining the molecule given the viewing angles. This scheme is called iterative refinement. Reliance on an initial, user-chosen reference introduces model bias, and poor initialization can lead to slow convergence. Furthermore, since no ground truth is available for an unsolved molecule, it is difficult to validate the obtained results. This creates the need for high quality ab initio models that can be quickly obtained from experimental data with minimal priors, and which can also be used for validation. We propose a procedure to obtain such an ab initio model directly from raw data using Kam's autocorrelation method. Kam's method has been known since 1980, but it leads to an underdetermined system, with missing orthogonal matrices. Until now, this system has been solved only for special cases, such as highly symmetric molecules or molecules for which a homologous structure was already available. In this paper, we show that knowledge of just two clean projections is sufficient to guarantee a unique solution to the system. This system is solved by an optimization-based heuristic. For the first time, we are then able to obtain a low-resolution ab initio model of an asymmetric molecule directly from raw data, without 2D class averaging and without tilting. Numerical results are presented on both synthetic and experimental data. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecules

Optomechanically induced nonreciprocity in a three-mode optomechanical system

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Physical Review A 2018年第6期98卷 063845-063845页

作者： Xun-Wei Xu L. N. Song Qiang Zheng Z. H. Wang Yong Li Department of Applied Physics East China Jiaotong University Nanchang 330013 China Beijing Computational Science Research Center Beijing 100193 China School of Mathematics Guizhou Normal University Guiyang 550001 China Center for Quantum Sciences and School of Physics Northeast Normal University Changchun 130024 China

We propose to create optical nonreciprocity in a three-mode optomechanical system comprising one mechanical and two optical modes, where the mechanical mode is coupled with only one of the optical modes. The optical nonreciprocal response of the system is based on the nonlinearity induced by the optomechanical interaction. However, nonlinearity is a necessary but not a sufficient condition for observing nonreciprocity. Another necessary condition for nonreciprocal response of the system to a classical driving field is demonstrated analytically. The effects of the parameters on the nonreciprocal response of the system are discussed numerically. The three-mode optomechanical system provides a platform to realize nonreciprocity for strong optical signal fields.

关键词： Optical bistability Optomechanics

An unstructured spectral element method for hydrodynamic instability and bifurcation analysis

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AIP Conference Proceedings 2019年第1期2186卷

作者： Dong-Jun Ma Da-Wei Chen De-Jun Sun Pei Wang 1Institute of Applied Physics and Computational Mathematics Beijing 100094 China 2Department of Modern Mechanics University of Science and Technology of China Hefei 230027 Anhui China

A high order unstructured spectral element method with a domain decomposition Stokes solver is presented for the hydrodynamic instability and bifurcation analysis. A Jacobian-Free Inexact-Newton-Krylov algorithm with a Stokes time-stepping preconditioning technique is introduced for the steady-state solution of incompressible flow. A matrix-free arc-length approach with Householder transformation is used for the numerical continuation near a turning point. An Arnoldi method is utilized to calculate the leading eigenvalues and their corresponding eigenvectors for the big system of linearized incompressible Navier-Stokes equations, which are responsible for initiating the hydrodynamic instability. The new method can do the steady and unsteady simulations in the similar way without time-splitting divergence error, it do not form the Jacobian matrix, which can reduce the memory allocation, decrease the computation cost, and speed up the convergence rate. The symmetric-breaking Hopf and Pitchfork bifurcations are considered in the flow passed a circular cylinder between two parallel plates. An antisymmetric sinusoidal velocity driven cavity problem is considered and the stable and unstable patterns are analyzed by checking the leading eigenvalues of their steady states. Besides the stable patterns of steady symmetric and steady asymmetric solutions£a new pair of unsteady asymmetric solutions are found depending on the different initial conditions.

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CEMRACS 2017: numerical probabilistic approach to MFG

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arXiv 2018年

作者： Angiuli, Andrea Graves, Christy V. Li, Houzhi Chassagneux, Jean-François Delarue, François Carmona, René Department of Statistics and Applied Probability University of California Santa Barbara Program in Applied and Computational Mathematics Princeton University Laboratoire de Probabilités Modélisation et Statistiques Université Paris Diderot Laboratoire Jean-Alexandre Dieudonné Université de Nice Sophia-Antipolis Operations Research and Financial Engineering Bendheim Center for Finance Princeton University

This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [27], and by Huang, Caines, and Malhamé, see [24]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme;importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges. Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods