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Reinforced dynamics for enhanced sampling in large atomic and molecular systems

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arXiv 2017年

作者： Zhang, Linfeng Wang, Han Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

A new approach for efficiently exploring the configuration space and computing the free energy of large atomic and molecular systems is proposed, motivated by an analogy with reinforcement learning. There are two major components in this new approach. Like metadynamics, it allows for an efficient exploration of the configuration space by adding an adaptively computed biasing potential to the original dynamics. Like deep reinforcement learning, this biasing potential is trained on the fly using deep neural networks, with data collected judiciously from the exploration and an uncertainty indicator from the neural network model playing the role of the reward function. Parameterization using neural networks makes it feasible to handle cases with a large set of collective variables. This has the potential advantage that selecting precisely the right set of collective variables has now become less critical for capturing the structural transformations of the system. The method is illustrated by studying the full-atom, explicit solvent models of alanine dipeptide and tripeptide, as well as the system of a polyalanine-10 molecule with 20 collective variables. Copyright © 2017, The Authors. All rights reserved.

关键词： Wave functions

Local and global strong solutions for SQG in bounded domains

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arXiv 2017年

作者： Constantin, Peter Nguyen, Huy Quang DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States

We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of R2. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for small data for critical and supercritical cases. Global existence of strong solutions with arbitrary data is obtained in the subcritical *** Codes 35Q35, 35Q86 Copyright © 2017, The Authors. All rights reserved.

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Hyperuniformity of quasicrystals

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Physical Review B 2017年第5期95卷 054119-054119页

作者： Erdal C. Oğuz Joshua E. S. Socolar Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

Hyperuniform systems, which include crystals, quasicrystals, and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity Z(k) to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of Z(k) as k tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, σ2(R), in the number of points contained in an interval of length 2R. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope 1/τ fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, Z(k)∼k4; for all others, Z(k)∼k2. This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.

关键词： Microstructure Structural properties

Gait transitions in a phase oscillator model of an insect central pattern generator

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arXiv 2017年

作者： Aminzare, Zahra Srivastava, Vaibhav Holmes, Philip Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Princeton University NJ United States Department of Electrical and Computer Engineering Michigan State University LansingMI United States Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Princeton Neuroscience Institute Princeton University NJ United States

Legged locomotion involves various gaits. It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in swing, while slow walking insects (stick insects) use a tetrapod gait with two legs lifted off the ground simultaneously. Fruit flies use both gaits and exhibit a transition from tetrapod to tripod at intermediate speeds. Here we study the effect of stepping frequency on gait transition in an ion-channel bursting neuron model in which each cell represents a hemi-segmental thoracic circuit of the central pattern generator. Employing phase reduction, we collapse the network of bursting neurons represented by 24 ordinary differential equations to 6 coupled nonlinear phase oscillators, each corresponding to a sub-network of neurons controlling one leg. Assuming that the left and right legs maintain constant phase differences (contralateral symmetry), we reduce from 6 equations to 3, allowing analysis of a dynamical system with 2 phase differences defined on a torus. We show that bifurcations occur from multiple stable tetrapod gaits to a unique stable tripod gait as speed increases. Finally, we consider gait transitions in two sets of data fitted to freely walking fruit flies.34C16, 34C60, 37G10, 92B20, 92C2034C16, 34C60, 37G10, 92B20, 92C20 Copyright © 2017, The Authors. All rights reserved.

关键词： Bifurcation (mathematics)

Domain morphology and mechanics of the H/T′ transition metal dichalcogenide monolayers

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Physical Review Materials 2018年第11期2卷 114002-114002页

作者： Joel Berry Songsong Zhou Jian Han David J. Srolovitz Mikko P. Haataja Department of Materials Science and Engineering University of Pennsylvania Philadelphia Pennsylvania 19104 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia Pennsylvania 19104 USA Department of Materials Science and Engineering City University of Hong Kong Hong Kong SAR People's Republic of China Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The properties of two-dimensional (2D) transition metal dichalcogenide (TMD) monolayers can be dynamically controlled via strain-induced displacive structural transformations between semiconducting (H) and metallic or semimetallic (T′) crystal structures. The shapes, symmetries, and kinetics of crystalline domains generated during these transformations and the mechanical response of transforming monolayers are of fundamental and applied interest in, e.g., phase change memory devices and the study of topologically protected edge states in quantum spin Hall insulating T′ crystals. We quantitatively characterize T′ domain morphologies during H→T′ transformations in both flat and bendable TMD monolayers using a combination of first principles and continuum calculations. Wulff constructions for MoTe2 and MoS2 show that T′ domains within much larger T′ domains are either rhombi of fixed proportions (if nonmisfitting) or rectangles whose aspect ratio AR increases with domain size L0 (if misfitting). Isolated T′ domains within much larger H domains undergo a morphological crossover from compact to elongated shapes at L0≈100–200 nm if the sheet is constrained to be flat or L0≳2μm if the sheet is free to bend. This crossover is driven by a competition between anisotropic interfacial energy and elastic misfit energy, and its position can be tuned via the monolayer-substrate interaction strength. It is shown that the aspect ratio AR obeys a scaling law AR∼L02/3. Stress-strain response characterized as a function of strain orientation reveals extreme anisotropy in the effective elastic modulus through H/T′ coexistence. Ferroelastic multidomain T′−WTe2 monolayers are found to exhibit two to three regimes of reversible mechanical response, and localized buckling in freely suspended T′ monolayers is shown to qualitatively alter T′ domain symmetries.

关键词： Bending Domain walls Mechanical deformation Microstructure Structural phase transition 2-dimensional systems Transition metal dichalcogenides Density functional theory Phase-field modeling

Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics

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arXiv 2017年

作者： Zhang, Linfeng Han, Jiequn Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecular dynamics

Author Correction: Hysteresis control of epithelial-mesenchymal transition dynamics conveys a distinct program with enhanced metastatic ability

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Nature communications 2019年第1期10卷 527页

作者： Toni Celià-Terrassa Caleb Bastian Daniel D Liu Brian Ell Nicole M Aiello Yong Wei Jose Zamalloa Andres M Blanco Xiang Hang Dmitriy Kunisky Wenyang Li Elizabeth D Williams Herschel Rabitz Yibin Kang Department of Molecular Biology Princeton University Princeton NJ 08544 USA. Cancer Program IMIM (Hospital del Mar Medical Research Institute) 08003 Barcelona Spain. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. cbastian@princeton.edu. Lewis-Sigler Institute of Integrative Genomics Princeton University Princeton NJ 08544 USA. Department of Mathematics Princeton University Princeton NJ 08544 USA. School of Biomedical Sciences Translational Research Institute Queensland University of Technology (QUT) Brisbane QLD 4102 Australia. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. Department of Chemistry Princeton University Princeton NJ 08544 USA. Department of Molecular Biology Princeton University Princeton NJ 08544 USA. ykang@princeton.edu.

The original version of this Article contained an error in the spelling of the author Daniel D. Liu, which was incorrectly given as Daniel Liu. This has now been corrected in both the PDF and HTML versions of the Arti...

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DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

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arXiv 2017年

作者： Wang, Han Zhang, Linfeng Han, Jiequn Weinan, E. Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model. Copyright © 2017, The Authors. All rights reserved.

关键词： Potential energy

A spectral-infinite-element solution of Poisson’s equation: An application to self gravity

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arXiv 2017年

作者： Gharti, Hom Nath Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ08544 United States Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

We solve Poisson’s equation by combining a spectral-element method with a mapped infinite-element method. We focus on problems in geostatics and geodynamics, where Earth’s gravitational field is determined by Poisson’s equation inside the Earth and Laplace’s equation in the rest of space. Spectral elements are used to capture the internal field, and infinite elements are used to represent the external field. To solve the weak form of Poisson/Laplace equation, we use Gauss-Legendre-Lobatto quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and Gauss-Legendre-Lobatto quadrature in the other directions. We illustrate the efficiency and accuracy of the method by comparing the gravitational fields of a homogeneous sphere and the Preliminary Reference Earth Model (PREM) with (semi-)analytical solutions. Copyright © 2017, The Authors. All rights reserved.

关键词： Earth (planet)