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作者： Sun, Bing Guo, Bao-Zhu Institute of Systems Science Academy of Mathematics and System Sciences Beijing 100080 China Graduate School Chinese Academy of Sciences Beijing 100039 China School of Computational and Applied Mathematics University of the Witwatersrand Private 3 Wits 2050 Johannesburg South Africa

ISBN: (纸本)008045108X

in this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain the Hamilton-Jacobi-Bellman equation and prove that the value function is its viscosity solution. By the derived classical verification theorem, the optimal birth feedback control is found explicitly. A finite difference scheme is designed to solving numerically the optimal birth feedback control. Under the same constraint, by comparing with different controls, the validity of the optimality of the obtained control is verified numerically. Copyright © 2005 IFAC.

关键词： Dynamic programming

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STYLISTIC ANALYSIS OF PAINTINGS USING WAVELETS AND MACHINE LEARNING

STYLISTIC ANALYSIS OF PAINTINGS USING WAVELETS AND MACHINE L...

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European signal processing conference

作者： Sina Jafarpour Guengor Polatkan Eugene Brevdo Shannon Hughes Andrei Brasoveanu Ingrid Daubechies Departments of Electrical Engineering Computer Science and Mathematics and the Program in Applied and Computational Mathematics Princeton NJ 08544

ISBN: (纸本)9781617388767

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features".

关键词： Support vector machines Abstracts Image resolution Radio frequency

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Inertial Hegselmann-Krause systems

Inertial Hegselmann-Krause systems

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American Control Conference (ACC)

作者： Bernard Chazelle Chu Wang Department of Computer Science Princeton University Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781467386838

We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of HK systems with closed-minded agents, which settles a conjecture of long standing. This paper also introduces anchored HK systems and show their equivalence to the symmetric heterogeneous model.

关键词： Convergence Communication networks Kinetic theory Protocols Nickel Mobile communication Turning

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Machine-learning-based non-Newtonian fluid model with molecular fidelity

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Physical Review E 2020年第4期102卷 043309-043309页

作者： Huan Lei Lei Wu Weinan E Department of Computational Mathematics Science & Engineering and Department of Statistics & Probability Michigan State University East Lansing Michigan 48824 USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN2 where models based on empirical closures show limitations.

关键词： Learning Neuronal networks Complex fluids Non-Newtonian fluids Rheology Viscoelasticity Multiscale modeling

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Enhanced energy coupling for indirect-drive fast-ignition fusion targets (vol 17, pg 435, 2020)

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NATURE PHYSICS 2020年第7期16卷 815-815页

作者： Zhang, F. Cai, H. B. Zhou, W. M. Dai, Z. S. Shan, L. Q. Xu, H. Chen, J. B. Ge, F. J. Tang, Q. Zhang, W. S. Wei, L. Liu, D. X. Gu, J. F. Du, H. B. Bi, B. Wu, S. Z. Li, J. Lu, F. Zhang, H. Zhang, B. He, M. Q. Yu, M. H. Yang, Z. H. Wang, W. W. Zhang, H. S. Cui, B. Yang, L. Wu, J. F. Qi, W. Cao, L. H. Li, Z. Liu, H. J. Yang, Y. M. Ren, G. L. Tian, C. Yuan, Z. Q. Zheng, W. D. Cao, L. F. Zhou, C. T. Zou, S. Y. Gu, Y. Q. Du, K. Ding, Y. K. Zhang, B. H. Zhu, S. P. Zhang, W. Y. He, X. T. 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

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

关键词： Electrons

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Ellipticity of the harmonic emission from graphene irradiated by a linearly polarized laser

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Physical Review A 2021年第3期104卷 033119-033119页

作者： Fulong Dong Qinzhi Xia Jie Liu Graduate School China Academy of Engineering Physics Beijing 100193 China National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We investigate the high-order harmonic generation in graphene irradiated by a linearly polarized intense laser, addressing the ellipticity or polarization properties of the harmonics. We exploit time-dependent density functional theory to calculate the harmonic spectra for a laser wavelength of 4770 nm and an intensity of 1.7 TW/cm2, and our numerical results can qualitatively reproduce recent experimental data. Our simulations also reveal that the harmonic ellipticity depends on both the harmonic order and the orientation angle between the graphene symmetric axis and the laser polarization direction. It can reach 0.68 for the ninth-order harmonic at the orientation angle of 20∘. To understand the mechanism of the high ellipticity, we develop a two-band model based on the tight-binding approximation. We may explain the ellipticity of high-order harmonic generation by investigating the transition dipole moments in the two-band model. Our theory further predicts a sensitive dependence of the harmonic ellipticity on the laser intensity for various laser wavelengths.

关键词： High-order harmonic generation Graphene Polarization Dipole approximation Tight-binding model Time-dependent DFT

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Deep potentials for materials science

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Materials Futures 2022年第2期1卷 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople’s Republic of China AI for Science Institute BeijingPeople’s Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople’s Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople’s Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America International Digital Economy Academy(IDEA) ShenzhenPeople’s Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network

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Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

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Physical Review B 2011年第15期84卷 155461-155461页

作者： Alexander A. Govyadinov George Y. Panasyuk John C. Schotland Vadim A. Markel Departments of Radiology and Bioengineering and the Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by F. Hache, D. Ricard, and C. Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat corrected form) by S. G. Rautian [Sov. Phys. JETP 85, 451 (1997)]. These references consider a metal nanoparticle as a degenerate Fermi gas of conduction electrons in an infinitely high spherical potential well. This model (referred to as the HRFR model below) yields mathematical expressions for the linear and the third-order nonlinear polarizabilities of a nanoparticle in terms of infinite nested series. These series have not been evaluated numerically so far and, in the case of nonlinear polarizability, they cannot be evaluated with the use of conventional computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian’s approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian’s approximations and find that they are surprisingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable to or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespective of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. Lett. 100, 47402 (2008)].

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Surface plasmon polaritons in curved chains of metal nanoparticles

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Physical Review B 2014年第7期90卷 075405-075405页

作者： Ilia L. Rasskazov Sergei V. Karpov Vadim A. Markel Departments of Radiology and Bioengineering and the Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We investigate numerically the propagation of steady-state monochromatic surface plasmon polaritons (SPPs) in curved chains of metal nanoparticles of various spheroidal shapes. We discuss the SPP propagation (decay of the amplitude), the polarization conversion due to coupling of orthogonally polarized SPPs, and the electromagnetic field localization in the near-field vicinity of a chain.

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Quantum theory of the electromagnetic response of metal nanofilms

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Physical Review B 2011年第15期84卷 155460-155460页

作者： George Y. Panasyuk John C. Schotland Vadim A. Markel Departments of Radiology Bioengineering and Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions imposed on the metal surface. We find that the sign and magnitude of the nonlinear polarizability depends dramatically on the type of boundary condition used.

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