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arXiv 2019年

作者： Levin, Eitan Bendory, Tamir Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel

The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can be interpreted as variants of Douglas-Rachford splitting. In this work, we establish a connection between Douglas-Rachford and gradient algorithms. Specifically, we show that in some cases a generalization of Douglas-Rachford, called relaxed-reflect-reflect (RRR), can be viewed as subgradient descent on a certain objective function. The solutions coincide with the critical points of that objective, which—in contrast to standard gradient techniques—are not its minimizers. Using the objective function, we analyze the RRR algorithm, describe its set of solutions, show a local convexity around any solution, and derive stability guarantees. Nevertheless, in its present state, the analysis does not elucidate the remarkable empirical performance of RRR and its global properties. Copyright © 2019, The Authors. All rights reserved.

关键词： Machine learning

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Free vibration analysis of functionally graded porous curved nanobeams on elastic foundation in hygro-thermo-magnetic environment

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Frontiers of Structural and Civil engineering 2023年第4期17卷 584-605页

作者： Quoc-Hoa PHAM Parviz MALEKZADEH Van Ke TRAN Trung NGUYEN-THOI Faculty of Engineering and Technology Nguyen Tat Thanh UniversityHo Chi Minh City 700000Vietnam Department of Mechanical Engineering Persian Gulf UniversityBushehr ***Iran Faculty of Mechanical Engineering Le Quy Don Technical UniversityHanoi 100000Vietnam Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh City 700000Vietnam Faculty of Mechanical-Electrical and Computer Engineering School of TechnologyVan Lang UniversityHo Chi Minh City 700000Vietnam Bualuang ASEAN Chair Professor Thammasat School of EngineeringThammasat UniversityPathumtani 12120Thailand

Herein,a two-node beam element enriched based on the Lagrange and Hermite interpolation function is proposed to solve the governing equation of a functionally graded porous(FGP)curved nanobeam on an elastic foundation in a hygro–thermo–magnetic *** material properties of curved nanobeams change continuously along the thickness via a power-law distribution,and the porosity distributions are described by an uneven porosity *** effects of magnetic fields,temperature,and moisture on the curved nanobeam are assumed to result in axial loads and not affect the mechanical properties of the *** equilibrium equations of the curved nanobeam are derived using Hamilton’s principle based on various beam theories,including the classical theory,first-order shear deformation theory,and higher-order shear deformation theory,and the nonlocal elasticity *** accuracy of the proposed method is verified by comparing the results obtained with those of previous reliable ***,the effects of different parameters on the free vibration behavior of the FGP curved nanobeams are investigated comprehensively.

关键词： functionally graded porous material curved nanobeam hygro-thermo-magnetic enriched finite element method

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Estimation in the group action channel

arXiv

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arXiv 2018年

作者： Abbe, Emmanuel Pereira, João M. Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

MSC Codes 94A15, 62B10We analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryoelectron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when N=σ2dis bounded from above, where N is the number of observations, σ is the noise standard deviation, and d is the so-called moment order cutoff. In contrast, the maximum likelihood estimator is shown to be consistent if N=σ2ddiverges. Copyright © 2018, The Authors. All rights reserved.

关键词： Mean square error

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Multireference alignment is easier with an aperiodic translation distribution

arXiv

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arXiv 2017年

作者： Abbe, Emmanuel Bendory, Tamir Leeb, William Pereira, João M. Sharon, Nir Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (the signal energy divided by the noise variance) in order to drive the mean-square error (MSE) to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as ω(1/SNR3). In this work, using a generalization of the Chapman-Robbins bound for orbits and expansions of the X2divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as ω(1/SNR2). This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation-maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model. Copyright © 2017, The Authors. All rights reserved.

关键词： Maximum principle

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Minimum-Time Trajectory Planning for Helicopter UAVs using computational Dynamic Optimization

Minimum-Time Trajectory Planning for Helicopter UAVs using C...

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IEEE International Conference on Systems, Man, and Cybernetics

作者： Nathan Xu Wei Kang Guowei Cai Ben M. Chen Summer Intern Program Department of Applied Mathematics Naval Postgraduate School Department of Applied Mathematics Naval Postgraduate School Department of Electrical and Computer Engineering National University of Singapore

ISBN: (纸本)9781467317139

In this paper, we apply pseudospectral optimal control, a computational algorithm of dynamic optimization, to the problem of helicopter UAV for minimum-time trajectory planning in the presence of obstacles. The problem is formulated as a nonlinear optimal control subject to the dynamics and limitations of helicopter UAVs, in which the obstacles are formulated as inequality constraints by using p-norms. The dynamical system is defined by a set of fifteen states nonlinear differential equations developed for HeLion, a helicopter UAV constructed in National University of Singapore (NUS). The problem does not have an analytic solution. We numerically solve the problem using a pseudospectral method. Various terrain scenarios were tested, from a single obstacle to multiple obstacles. We found bifurcation points of minimum-time trajectories near obstacles. The bifurcation points and their relationship with the distance to the obstacle are analyzed.

关键词： Minimum-time control Helicopter UAV computational optimal control Obstacle avoidance Unmanned Aerial Vehicle Helicopters trajectory planning barriers BIFURCATION nonlinear differential equations inequality constraint drone honey bees

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Spectral Dynamics of Spatially Incoherent Modulation Instability

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Physical Review Letters 2012年第26期108卷 263902-263902页

作者： Can Sun Laura Waller Dmitry V. Dylov Jason W. Fleischer Department of Electrical Engineering Princeton University Princeton New Jersey 08544 USA General Electric Global Research Center Niskayuna New York 12309 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

To date, all experiments in nonlinear statistical optics have relied on beams whose transverse spatial statistics were Gaussian. Here, we present a new technique to generalize these studies by using a spatial light modulator to create spatially incoherent beams with arbitrary spectral distributions. As a specific example of the new dynamics possible, we consider the spatial modulation instability of a partially coherent beam. We show that, for statistical beams of uniform intensity and equal correlation length, the underlying spectral shape determines the threshold and visibility of intensity modulations as well as the spectral profile of the growing sidebands. We demonstrate the behavior using statistical light, but the results will hold for any wave-kinetic system, such as plasma, ultracold gases, and turbulent acoustic waves.

关键词： NONLINEAR optics MODULATION theory SPECTRUM analysis BEAM optics GAUSSIAN processes LIGHT modulators SOUND waves COLD gases

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Direct minimization of the optimized effective problem based on efficient finite differences

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Physical Review B 2011年第16期84卷 165122-165122页

作者： Chen Huang Emily A. Carter Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and the Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

To avoid the difficult-to-solve optimized effective potential (OEP) integral equation, we introduce an efficient direct minimization scheme for performing OEP calculations within Kohn–Sham density functional theory (KS-DFT). We reformulated the functional derivative of the total energy with respect to the KS effective potential in terms of efficient finite differences. Our method only uses the orbitals involved in the construction of the KS exchange-correlation functionals. We demonstrate our scheme by performing exact-exchange OEP for sodium clusters, in which only occupied KS orbitals are needed to obtain the OEP. Our efficient direct minimization scheme should aid future development of orbital-dependent density functionals and render OEP to be a practical choice for various applications.

关键词： INTEGRAL equations DENSITY functionals TOTAL energy systems (On-site electric power production) FINITE differences PHYSICS

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Angular momentum dependent orbital-free density functional theory: Formulation and implementation

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Physical Review B 2014年第15期89卷 155112-155112页

作者： Youqi Ke Florian Libisch Junchao Xia Emily A. Carter []Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

Orbital-free density functional theory (OFDFT) directly solves for the ground-state electron density. It scales linearly with respect to system size, providing a promising tool for large-scale material simulations. Removal of the orbitals requires use of approximate noninteracting kinetic energy density functionals. If replacing ionic cores with pseudopotentials, removal of the orbitals also requires these pseudopotentials to be local. These are two severe challenges to the capabilities of conventional OFDFT. While main group elements are often well described within conventional OFDFT, transition metals remain intractable due to their localized d electrons. To advance the accuracy and general applicability of OFDFT, we have recently reported a general angular momentum dependent formulation as a next-generation OFDFT. In this formalism, we incorporate the angular momenta of electrons by devising a hybrid scheme based on a muffin tin geometry: inside spheres centered at the ionic cores, the electron density is expanded in a set of atom-centered basis functions combined with an onsite density matrix. The explicit treatment of the angular momenta of electrons provides an important basis for accurately describing the important ionic core region, which is not possible in conventional OFDFT. In addition to the conventional OFDFT total energy functional, we introduce a nonlocal energy term containing a set of angular momentum dependent energies to correct the errors due to the approximate kinetic energy density functional and local pseudopotentials. Our approach greatly increases the accuracy of OFDFT while largely preserving its numerical simplicity. Here, we provide details of the theoretical formulation and practical implementation, including the hybrid scheme, the derivation of the nonlocal energy term, the choice of basis functions, the direct minimization of the total energy, the procedure to determine the angular momentum dependent energies, the force formula with Pu

关键词： ANGULAR momentum (Nuclear physics) DENSITY functional theory GROUND state (Quantum mechanics) ELECTRON density SIMULATION methods & models DENSITY functionals

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Modeling of multilayer ion etching processes

Journal of Vacuum Science & Technology B: Microelectronics a...

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Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 1993年第4期11卷 1310-1313页

作者： S. J. Sherwin E. Barouch G. E. Karniadakis S. A. Orszag Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540

Numerical simulation is used to model ion etching in trilayer lithography. The simulations are capable of capturing the evolution of the boundary between two materials as well as the physically observed phonemena reactive ion etching lag and undercutting. Numerical results are compared with experimental data and a good agreement is found except close to the material interface where the slope of the surface is large. This error is attributed to a purely energy dependent yield used in the simulations.

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Roadmap on Nonlocality in Photonic Materials and Metamaterials

arXiv

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arXiv 2025年

作者： Monticone, Francesco Mortensen, N. Asger Fernández-Domínguez, Antonio I. Luo, Yu Tserkezis, Christos Khurgin, Jacob B. Shahbazyan, Tigran V. Chaves, André J. Peres, Nuno M.R. Wegner, Gino Busch, Kurt Hu, Huatian della Sala, Fabio Zhang, Pu Ciracì, Cristian Aizpurua, Javier Babaze, Antton Borisov, Andrei G. Chen, Xue-Wen Christensen, Thomas Yan, Wei Yang, Yi Hohenester, Ulrich Huber, Lorenz Wubs, Martijn de Liberato, Simone Gonçalves, P.A.D. de Abajo, F. Javier García Hess, Ortwin Tarasenko, Illya Cox, Joel D. Jelver, Line Dias, Eduardo J.C. Sánchez, Miguel Sánchez Margetis, Dionisios Gómez-Santos, Guillermo Stauber, Tobias Tretyakov, Sergei Simovski, Constantin Pakniyat, Samaneh Gómez-Díaz, J. Sebastián Bondarev, Igor V. Biehs, Svend-Age Boltasseva, Alexandra Shalaev, Vladimir M. Krasavin, Alexey V. Zayats, Anatoly V. Alù, Andrea Song, Jung-Hwan Brongersma, Mark L. Levy, Uriel Long, Olivia Y. Guo, Cheng Fan, Shanhui Bozhevolnyi, Sergey I. Overvig, Adam Prudêncio, Filipa R. Silveirinha, Mário G. Gangaraj, S. Ali Hassani Argyropoulos, Christos Huidobro, Paloma A. Galiffi, Emanuele Yang, Fan Pendry, John B. Miller, David A.B. School of Electrical and Computer Engineering Cornell University IthacaNY14853 United States POLIMA Center for Polariton-driven Light–Matter Interactions University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark D-IAS—Danish Institute for Advanced Study University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark Departamento de Física Teórica de la Materia Condensada Universidad Autónoma de Madrid MadridE-28049 Spain Universidad Autónoma de Madrid MadridE-28049 Spain School of Electrical and Electronic Engineering Nanyang Technological University Singapore639798 Singapore Key Laboratory of Radar Imaging and Microwave Photonics Ministry of Education College of Electronic and Information Engineering Nanjing University of Aeronautics and Astronautics Nanjing211106 China Department of Electrical and Computer Engineering Johns Hopkins University BaltimoreMD21218 United States Department of Physics Jackson State University JacksonMS39217 United States Department of Physics Aeronautics Institute of Technology SP So Jos dos Campos12228-900 Brazil Departamento de Física Universidade do Minho BragaP-4710-057 Portugal Av Mestre José Veiga Braga4715-330 Portugal Max-Born-Institut Berlin12489 Germany Humboldt-Universität zu Berlin Institut für Physik AG Theoretische Optik and Photonik Berlin12489 Germany Center for Biomolecular Nanotechnologies Istituto Italiano di Tecnologia Via Barsanti 14 Arnesano73010 Italy Via Monteroni Campus Unisalento Lecce73100 Italy School of physics Huazhong University of Science and Technology Luoyu Road 1037 Wuhan430074 China Donostia International Physics Center DIPC Donostia-San Sebastián20018 Spain Ikerbasque Basque Foundation for Science Bilbao48009 Spain Department of Electricity and Electronics University of the Basque Country Leioa48940 Spain Department of Applied Physics University of the Basque Country Donostia20018 Spain Université Paris-Saclay CNRS Institut des Scienc

Photonic technologies continue to drive the quest for new optical materials with unprecedented responses. A major frontier in this field is the exploration of nonlocal (spatially dispersive) materials, going beyond the local, wavevector-independent assumption traditionally made in optical material modeling. On one end, the growing interest in plasmonic, polaritonic and quantum materials has revealed naturally occurring nonlocalities, emphasizing the need for more accurate models to predict and design their optical responses. This has major implications also for topological, nonreciprocal, and time-varying systems based on these material platforms. Beyond natural materials, artificially structured materials—metamaterials and metasurfaces–can provide even stronger and engineered nonlocal effects, emerging from long-range interactions or multipolar effects. This is a rapidly expanding area in the field of photonic metamaterials, with open frontiers yet to be explored. In the case of metasurfaces, in particular, nonlocality engineering has become a powerful tool for designing strongly wavevector-dependent responses, enabling enhanced wavefront control, spatial compression, multifunctional devices, and wave-based computing. Furthermore, nonlocality and related concepts play a critical role in defining the ultimate limits of what is possible in optics, photonics, and wave physics. This Roadmap aims to survey the most exciting developments in nonlocal photonic materials, highlight new opportunities and open challenges, and chart new pathways that will drive this emerging field forward–toward new scientific discoveries and technological advancements. Copyright © 2025, The Authors. All rights reserved.

关键词： Nanocrystals

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