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Microstructural degeneracy associated with a two-point correlation function and its information content

Physical Review E 2012年第5期85卷 051140-051140页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège Liège 4000 Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the

关键词： MICROSTRUCTURE CORRELATION (Statistics) INFORMATION theory ENTROPY (Information theory) GROUND state (Quantum mechanics) MONTE Carlo method POISSON processes

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Possible signals in differentiating the quantum radiation reaction from the classical one

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Physical Review A 2020年第3期101卷 032108-032108页

作者： X. B. Li B. Qiao Y. L. Liao J. Wang L. F. Gan C. T. Zhou S. P. Zhu X. T. He School of Physics Center for Applied Physics and Technology HEDPS and SKLNPT Peking University Beijing 100871 China Collaborative Innovation Center of IFSA Shanghai Jiao Tong University Shanghai 200240 China Center for Advanced Material Diagnostic Technology Shenzhen Technology University Shenzhen 518118 China School of Physics and Materials Science Anhui University Hefei 230039 China Institute of Applied Physics and Computational Mathematics Beijing 100094 China Graduate School of China Academy of Engineering Physics P.O. Box 2101 Beijing 100088 China

A configuration to identify the stochastic effect of the quantum radiation reaction is proposed, where electrons are put in a standing wave of two colliding ultraintense lasers. By comparing the simulation results of the semiclassical and quantum models, we find that if the semiclassical model is used, a particular trapping of electrons between two electric-field nodes is induced, which, however, does not exist once the correct quantum model is applied. This results in different features of the electron density, energy, and angular distributions, which can be measured in experiments.

关键词： Gamma-ray generation in plasmas High intensity laser-plasma interactions Quantum electrodynamics Radiation & particle generation in plasmas Monte Carlo methods Particle-in-cell methods

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Exploring 3D Reconstruction with Drone Images: Advances and Challenges in Urban Environments

Exploring 3D Reconstruction with Drone Images: Advances and ...

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Annual Conference of Industrial Electronics Society

作者： Thiago João Miranda Baldivieso Taise Grazielle Da Silva Batista Fabio Suim Chagas Luiz Carlos Pacheco Rodrigues Velho Paulo Fernando Ferreira Rosa Defense Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil State Institute of the Environment Inea/RJ Rio de Janeiro Brazil Department of Science and Industry Systems University of South-Eastern Norway Kongsberg Norway Department of Computer Graphics Institute for Pure and Applied Mathematics Rio de Janeiro Brazil Electrical Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil

ISBN: (数字)9781665464543

ISBN: (纸本)9781665464550

This working-in-progress paper aims to present a three-dimensional reconstruction using aerial images in different environments. The experiments were conducted with aircraft in both external and internal settings, starting with image acquisition, followed by the application of specific photogrammetry software—both commercial and open-source—and concluding with a qualitative evaluation of the results.

关键词： Industrial electronics Three-dimensional displays Urban areas Aircraft Image reconstruction Photogrammetry Drones

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Deep Potential: A general representation of a many-body potential energy surface

arXiv

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arXiv 2017年

作者： Han, Jiequn Zhang, Linfeng Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of 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 present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems. When tested on a wide variety of examples, Deep Potential is able to reproduce the original model, either empirical or quantum mechanics based, within chemical accuracy. The computational cost of this new model is not substantially larger than that of empirical force fields. In addition, the method has promising scalability properties. This brings us one step closer to being able to carry out molecular simulations with accuracy comparable to that of quantum mechanics models and computational cost comparable to that of empirical potentials. Copyright © 2017, The Authors. All rights reserved.

关键词： Deep neural networks

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Wire Before You Walk

Wire Before You Walk

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Asilomar Conference on Signals, Systems & Computers

作者： Tesfa Asmara Dhananjay Bhaskar Ian Adelstein Smita Krishnaswamy Michael Perlmutter Department of Computer Science Pomona College Claremont CA USA Mathematics and Statistics Pomona College Claremont CA USA Department of Genetics Yale School of Medicine New Haven CT USA Department of Mathematics Yale University New Haven CT USA Department of Computer Science Yale University New Haven CT USA Program for Applied Mathematics Yale University New Haven CT USA Computational Biology and Bioinformatics Program Yale University New Haven CT USA Wu Tsai Institute Yale University New Haven CT USA Department of Mathematics Boise State University Boise ID USA

Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.

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The underestimation of high pressure in DFT+U simulation for the wide range cold-pressure of lanthanide metals

arXiv

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arXiv 2021年

作者： Wang, Yue-Chao Liu, Bei-Lei Liu, Yu Liu, Hai-Feng Bi, Yan Gao, Xing-Yu Sheng, Jie Song, Hong-Zhou Tian, Ming-Feng Song, Hai-Feng Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematical Sciences Beijing Normal University Beijing100875 China Center for High Pressure Science and Technology Advanced Research Beijing100094 China National Key Laboratory for Shock Wave and Detonation Physics Institute of Fluid Physics CAEP Mianyang621900 China Graduate School of China Academy of Engineering Physics Beijing100088 China

Density functional theory plus U (DFT+U) is one of the most efficient first-principles methods to simulate the cold pressure properties of strongly-correlated materials. However, the applicability of DFT+U at ultra-high pressure is not sufficiently studied, especially in the widely-used augmented schemes [such as projector augmented wave (PAW) and linearized augmented plane wave (LAPW)]. This work has systematically investigated the performance of DFT+U in PAW and LAPW at the pressure up to several hundred GPa for the lanthanide metals, which is a typical strongly-correlated series. We found DFT+U simulation in PAW exhibits an unphysical underestimation of pressure in high-pressure region, which was not observed in conventional DFT simulation. By delicate analysis and comparison with local-orbital-independent hybrid functional results, we have demonstrated that this unphysical behavior is related to a normalization problem on the local density matrix caused by the overlap of local orbitals in PAW under high pressure. Additionally, we observed a slight underestimating of pressure in correlation correction methods in heavy lanthanides (Tm, Yb and Lu) in high-pressure region comparing with the DFT results without the influence of local orbital overlap, and it might be related to the enhancement of binding between atoms in correlation correction methods at high pressure. Our work reveals the underestimation of high pressure in DFT+U simulation, analyses two sources of this unusual behavior and proposes their mechanism. Most importantly, our investigation highlights the breakdown of DFT+U for high pressure simulation in VASP package based on PAW framework. Copyright © 2021, The Authors. All rights reserved.

关键词： Density functional theory

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Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

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Physical Review B 2022年第6期105卷 064204-064204页

作者： F. Sgrignuoli S. Torquato L. Dal Negro Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary's Street Boston Massachusetts 02215 USA 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 Division of Material Science and Engineering Boston University 15 Saint Mary's Street Brookline Massachusetts 02446 USA Department of Physics Boston University 590 Commonwealth Avenue Boston Massachusetts 02215 USA

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed subradiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

关键词： Anderson localization Light-matter interaction Mesoscopics Photonics Scattering theory Weak localization Metamaterials

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Semiclassical Trajectory Perspective of Glory Rescattering in Strong-field Photoelectron Holography

arXiv

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arXiv 2021年

作者： Liao, L.G. Xia, Qinzhi Z. Cai, J. Liu, J. School of Physics Peking University Beijing100871 China CAPT HEDPS IFSA Collaborative Innovation Center of MoE Peking University Beijing100871 China National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Physics and Electronic Engineering Jiangsu Normal University Xuzhou221116 China Graduate School of China Academy of Engineering Physics Beijing100193 China

We investigate theoretically the photoelectron momentum distribution (PMD) of the ionized atoms irradiated by a linearly polarized intense laser, focusing on the holography interference patterns in PMD that carry important information of the initial wavefunction of a tunneled electron and its experienced atomic potential in rescattering. With the help of Dyson series and semiclassical propagator, we calculate the scattering amplitudes in the cylindrical coordinate representation. In contrast to conventional recognitions that the photoelectron holography is the interference of two branches of electron trajectories, however, we find strikingly that infinite semiclassical trajectories can be deflected by the combined Coulomb potential and laser field into the same final momentum: The initial momenta are found to be distributed on a ring-shape curve in the transverse momentum plane and the initial positions of these trajectories are perpendicular to their initial momentum vectors. For the zero final transverse momentum, the above ring-source trajectories degenerate into the point-source axial caustic trajectories (or Glory trajectories) and the quantum interference of these trajectories will dramatically alter the scattering amplitudes that is termed as Glory rescattering effect. With following Berry's spirit of uniform approximation for Glory scattering in optics, we can finally derive a uniform formulation of the rescattering amplitude in the Bessel functions for the strong-field photoelectron holography (SFPH) patterns. Our results are in good agreement with solutions of the time-dependent Schrödinger equation and can account for recent photoelectron holography experiments. Important applications of our theory are also discussed. Copyright © 2021, The Authors. All rights reserved.

关键词： Trajectories

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The Role of Heterogeneity in Autonomous Perimeter Defense Problems

arXiv

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arXiv 2022年

作者： Adler, Aviv Mickelin, Oscar Ramachandran, K. Sukhatme, Gaurav S. Karaman, Sertac Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Computer Science University of Southern California Los AngelesCA90089 United States Department of Aeronautics and Astronautics Massachusetts Institute of Technology CambridgeMA02139 United States

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamic programming

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Interface-driven unusual anomalous Hall effect in MnxGa/Pt bilayers

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Physical Review B 2019年第18期100卷 184410-184410页

作者： K. K. Meng L. J. Zhu Z. H. Jin E. K. Liu X. P. Zhao I. A. Malik Z. G. Fu Y. Wu J. Miao X. G. Xu J. X. Zhang J. H. Zhao Y. Jiang Beijing Advanced Innovation Center for Materials Genome Engineering School of Materials Science and Engineering University of Science and Technology Beijing Beijing China Cornell University Ithaca New York 14853 USA Department of Applied Physics Graduate School of Engineering Tohoku University 6-6-05 Aoba-yama 980-8579 Sendai Japan Institute of Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Superlattices and Microstructures Institute of Semiconductors Chinese Academy of Sciences Beijing China Department of Physics Beijing Normal University Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

The effects of spin-orbit coupling and symmetry breaking at the interface between a ferromagnet and heavy metal are particularly important for spin-based information storage and computation. Recent discoveries suggest they can create novel chiral spin structures (e.g., skyrmions), which have often been identified through the appearance of the bump/dip features of Hall signals, the so-called topological Hall effect (THE). In this work, however, we present an unusual anomalous Hall effect (UAHE) in MnxGa/Pt bilayers and demonstrate that the features extremely similar to THE can be generated without involving any chiral spin structures. Low-temperature magnetic force microscopy has been used to explore the magnetic field-dependent behavior of spin structures, and the UAHE as a function of magnetic field does not peak near the maximal density of magnetic bubbles. Our results unambiguously evidence that the UAHE in MnxGa/Pt bilayers shows no correlation with chiral spin structures but is driven by the modified interfacial properties, indicating a wealth of underlying and interesting physics.

关键词： Anomalous Hall effect Spin-orbit coupling Topological Hall effect

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