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DYNAMICS OF VORTEX SURFACES IN 3 DIMENSIONS - THEORY AND SIMULATIONS

PHYSICA D-NONLINEAR PHENOMENA 1989年第1期40卷 91-118页

作者： AGISHTEIN, ME MIGDAL, AA Department of Physics University of California at San Diego La Jolla CA 92093 USA1 1 Current address: Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road Princeton NY 08544-100 USA.

The dynamics of vortex surfaces in an ideal fluid is considered. The Hamiltonian and the action are constructed and topological conservation laws are discussed. The axially symmetric case is reduced to an effective 2d problem and studied numerically. There is qualitative correspondence with the results of Moore and Krasny for the purely 2d problem. The general case is approximated by means of a triangulated surface and a corresponding computer model is constructed, taking into account the topological conservation laws. The axially symmetric motion of the triangulated surface agrees with the 2d model, but there are some angular instabilities, which may lead to new vortex structures. The large-scale asymmetric 3d simulations with fairly developed instabilities are reported. The results agree with the general scenario of hierarchy of vortex structures.

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Integer programming and Combinatorial Optimization 1

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丛书名： Lecture Notes in Computer Science

1000年

作者： William J. Cook Andreas S. Schulz

ISBN: (数字)9783540478676

ISBN: (纸本)9783540436768

This volume contains the papers selected for presentation at IPCO 2002, the NinthInternationalConferenceonIntegerprogrammingandCombinatorial- timization, Cambridge, MA (USA), May 27–29, 2002. The IPCO series of c- ferences highlights recent developments in theory, computation, and application of integer programming and combinatorial optimization. IPCO was established in 1988 when the ?rst IPCO program committee was formed. IPCO is held every year in which no International Symposium on Ma- ematical programming (ISMP) takes places. The ISMP is triennial, so IPCO conferences are held twice in every three-year period. The eight previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995, Vancouver (Canada) 1996, Houston (USA) 1998, Graz (Austria) 1999, and Utrecht (The Netherlands) 2001. In response to the call for papers for IPCO 2002, the program committee received 110 submissions, a record number for IPCO. The program committee met on January 7 and 8, 2002, in Aussois (France), and selected 33 papers for inclusion in the scienti?c program of IPCO 2002. The selection was based on originality and quality, and re?ects many of the current directions in integer programming and combinatorial optimization research.

关键词： Theory of Computation Probability Theory and Stochastic Processes Software Engineering/programming and Operating Systems Discrete mathematics in Computer Science Numeric Computing Algorithm Analysis and Problem Complexity

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Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations 63

Inferring System and Optimal Control Parameters of Closed-Lo...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Geadah, Victor Arbelaiz, Juncal Ritz, Harrison Daw, Nathaniel D. Cohen, Jonathan D. Pillow, Jonathan W. Princeton University Department of Mechanical and Aerospace Engineering PrincetonNJ United States Princeton University Program in Applied and Computational Mathematics PrincetonNJ United States Princeton Neuroscience Institute Princeton University PrincetonNJ United States

ISBN: (纸本)9798350316339

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic statespace model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finitehorizon setting. We further illustrate the performance of our methodology through numerical examples. © 2024 IEEE.

关键词： Stochastic systems

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Optimal frames and Newton's method

Optimal frames and Newton's method

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作者： Fickus, Matthew Mixon, Dustin G. Department of Mathematics Air Force Institute of Technology Wright-Patterson AFB OH 45433 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ United States

Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally in the context of a certain type of radar system. We derive analytic expressions for the first and second partial derivatives of the objective function in question, permitting this optimization problem to be efficiently solved using Newton's method. We also consider how sensitive the location of this minimizer is to noise in the data vector. We further provide conditions under which one should expect the minimizer of this objective function to be unique. We conclude by discussing a related variational-calculus- based approach for solving this frame optimization problem over an interval of time. © 2012 Copyright.

关键词： Newton-Raphson method

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An Iterative Thresholding Method for the Minimum Compliance Problem

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Communications in computational Physics 2023年第4期33卷 1189-1216页

作者： Luyu Cen Wei Hu Dong Wang Xiaoping Wang Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA School of Science and Engineering The Chinese University of Hong KongShenzhenGuangdong 518172China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big DataGuangdong 518172China

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

关键词： Minimum compliance convolution thresholding linear elasticity

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From point patterns to networks: to what extent does the Delaunay triangulation reproduce key spatial and density information?

arXiv

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arXiv 2025年

作者： Newby, Eli Shi, Wenlong Jiao, Yang Torquato, Salvatore Albert, Réka Department of Physics Pennsylvania State University University ParkPA16802 United States Department of Cardiovascular and Metabolic Sciences Lerner Research Institute Cleveland Clinic ClevelandOH44195 United States Arizona State University TempeAZ85287 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Biology Pennsylvania State University University ParkPA16802 United States

To be used as an analysis tool, it is important that a spatial network’s construction algorithm reproduces the structural properties of the original physical embedding. One method for converting a two-dimensional (2D) point pattern into a spatial network is the Delaunay triangulation. Here, we apply the Delaunay triangulation to seven different types of 2D point patterns, including hyperuniform systems. The latter are characterized by completely suppressed normalized infinite-wavelength density fluctuations. We demonstrate that the quartile coefficients of dispersion of multiple centrality measures are capable of rank-ordering hyperuniform and nonhyperuniform systems independently, but they cannot distinguish a system that is nearly hyperuniform from hyperuniform systems. Thus, in each system, we investigate the local densities of the point pattern ρP (ri;) and of the network ρG(ni;). We reveal that there is a strong correlation between ρP (ri;) and ρG(ni;) in nonhyperuniform systems, but there is no such correlation in hyperuniform systems. When calculating the pair-correlation function and local density covariance function on the point pattern and network, the point pattern and network functions are similar only in nonhyperuniform systems. In hyperuniform systems, the triangulation has a positive covariance of local network densities in pairs of nodes that are close together;such covariance is not present in the point patterns. Thus, we demonstrate that the Delaunay triangulation accurately captures the density fluctuations of the underlying point pattern only when the point pattern possesses a positive correlation between ρP (ri;) for points that are close together. Such positive correlation is seen in most real-world systems, so the Delaunay triangulation is generally an effective tool for building a spatial network from a 2D point pattern, but there are situations (i.e., disordered hyperuniform systems) where we caution that the Delaunay triangulation would not

关键词： Triangulation

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Coarse-grained spectral projection: A deep learning assisted approach to quantum unitary dynamics

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Physical Review B 2021年第2期103卷 024304-024304页

作者： Pinchen Xie Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University New Jersey 08544 USA

We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spectral components of many-body quantum states systematically with a sophisticated neural network quantum ansatz. CGSP fully exploits the linear unitary nature of the quantum dynamics and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on one-dimensional XXZ models with periodic boundary conditions are carried out to demonstrate the practicality of CGSP.

关键词： Quantum quench Quantum statistical mechanics Nonequilibrium lattice models Machine learning Monte Carlo methods

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From Dyson models to many-body quantum chaos

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Physical Review B 2025年第3期111卷 035147-035147页

作者： Alexei Andreanov Matteo Carrega Jeff Murugan Jan Olle Dario Rosa Ruth Shir Center for Theoretical Physics of Complex Systems Institute for Basic Science (IBS) Daejeon 34126 Korea Basic Science Program Korea University of Science and Technology (UST) Daejeon 34113 Korea CNR-SPIN Via Dodecaneso 33 16146 Genova Italy The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town 7701 South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland 7602 South Africa Max Planck Institute for the Science of Light 91058 Erlangen Germany ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP—University of Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Department of Physics and Materials Science University of Luxembourg L-1511 Luxembourg Luxembourg

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

关键词： Quantum chaos

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Computing Optimal Interfacial Structure of Modulated Phases

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Communications in computational Physics 2017年第1期21卷 1-15页

作者： Jie Xu Chu Wang An-Chang Shi Pingwen Zhang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew Jersey 08544USA Department of Physics and Astronomy McMaster UniversityHamiltonOntario L8S4M1Canada

We propose a general framework of computing interfacial structures between two modulated *** we propose to use a computational box consisting of two half spaces,each occupied by a modulated phase with given position and *** boundary conditions and basis functions are chosen to be commensurate with the bulk *** observe that the ordered nature of modulated structures stabilizes the interface,which enables us to obtain optimal interfacial structures by searching local minima of the free energy *** framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and *** types of novel complex interfacial structures emerge from the calculations.

关键词： Interface modulated phase metastable state compatibility Landau-Brazovskiimodel

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Atomic and electronic structures of single-layer FeSe on SrTiO3(001): The role of oxygen deficiency

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Physical Review B 2013年第22期87卷 220503(R)-220503(R)页

作者： Junhyeok Bang Zhi Li Y. Y. Sun Amit Samanta Y. Y. Zhang Wenhao Zhang Lili Wang X. Chen Xucun Ma Q.-K. Xue S. B. Zhang Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA Institute of Physics The Chinese Academy of Sciences Beijing 100190 China Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Physics Tsinghua University Beijing 100084 China

Using first-principles calculation, we propose an interface structure for single triple-layer FeSe on the SrTiO3(001) surface, a high-Tc superconductor found recently. The key component of this structure is the oxygen deficiency on the top layer of the SrTiO3 substrate, as a result of Se etching used in preparing the high-Tc samples. The O vacancies strongly bind the FeSe triple layer to the substrate giving rise to a (2×1) reconstruction, as observed by scanning tunneling microscopy. The enhanced binding correlates to the significant increase of Tc observed in experiment. The O vacancies also serve as the source of electron doping, which modifies the Fermi surface of the first FeSe layer by filling the hole pocket near the center of the surface Brillouin zone, as suggested from angle-resolved photoemission spectroscopy measurement.

关键词： ELECTRONIC structure SCANNING probe microscopy PARTICLES (Nuclear physics) WAVE mechanics ELECTRIC properties of crystals

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