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Local-order metric for condensed-phase environments

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Physical Review B 2018年第6期97卷 064105-064105页

作者： Fausto Martelli Hsin-Yu Ko Erdal C. Oğuz Roberto Car Department of Chemistry Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik II Heinrich-Heine-Universität D-40225 Düsseldorf Germany Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that perfectly match the reference. The site-averaged LOM and its standard deviation define two scalar order parameters, S and δS, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that S, δS, and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling.

关键词： Glass transition Nucleation Order parameters Phase transitions

Classical many-particle systems with unique disordered ground states

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Physical Review E 2017年第4期96卷 042146-042146页

作者： G. Zhang F. H. Stillinger S. Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 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 08544 USA

Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By contrast, the few previously known disordered classical ground states of many-particle systems are all high-entropy (highly degenerate) states. Here we show computationally that our recently proposed “perfect-glass” many-particle model [Sci. Rep. 6, 36963 (2016)] possesses disordered classical ground states with a zero entropy: a highly counterintuitive situation . For all of the system sizes, parameters, and space dimensions that we have numerically investigated, the disordered ground states are unique such that they can always be superposed onto each other or their mirror image. At low energies, the density of states obtained from simulations matches those calculated from the harmonic approximation near a single ground state, further confirming ground-state uniqueness. Our discovery provides singular examples in which entropy and disorder are at odds with one another. The zero-entropy ground states provide a unique perspective on the celebrated Kauzmann-entropy crisis in which the extrapolated entropy of a supercooled liquid drops below that of the crystal. We expect that our disordered unique patterns to be of value in fields beyond glass physics, including applications in cryptography as pseudorandom functions with tunable computational complexity.

关键词： Nonequilibrium statistical mechanics Pattern formation

Long term study of the blazar S5 0716+714: investigating a turbulent jet at all wavelengths 38

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Long term study of the blazar S5 0716+714: investigating a t...

38th International Cosmic Ray Conference, ICRC 2023

作者： Podobnik, F. Manganaro, M. Jormanainen, J. Lindfors, E. Bonnoli, G. Paoletti, R. Jorstad, S. Kiehlmann, S. Agudo, I. Elsasser, D. Lorey, C. Raiteri, C. Villata, M. Redhead, A.C. Marscher, A. Abe, H. Abe, S. Abhir, J. Acciari, V.A. Aniello, T. Ansoldi, S. Antonelli, L.A. Arbet Engels, A. Arcaro, C. Artero, M. Asano, K. Baack, D. Babić, A. Baquero, A. Barres de Almeida, U. Barrio, J.A. Batković, I. Baxter, J. Becerra González, J. Bednarek, W. Bernardini, E. Bernardos, M. Bernete, J. Berti, A. Besenrieder, J. Bigongiari, C. Biland, A. Blanch, O. Bošnjak, Ž. Burelli, I. Busetto, G. Campoy-Ordaz, A. Carosi, A. Carosi, R. Carretero-Castrillo, M. Castro-Tirado, A.J. Ceribella, G. Chai, Y. Chilingarian, A. Cifuentes, A. Cikota, S. Colombo, E. Contreras, J.L. Cortina, J. Covino, S. D’Amico, G. D’Elia, V. Da Vela, P. Dazzi, F. De Angelis, A. De Lotto, B. Del Popolo, A. Delfino, M. Delgado, J. Delgado Mendez, C. Depaoli, D. Di Pierro, F. Di Venere, L. Dominis Prester, D. Donini, A. Dorner, D. Doro, M. Elsaesser, D. Emery, G. Escudero, J. Fariña, L. Fattorini, A. Foffano, L. Font, L. Fröse, S. Fukami, S. Fukazawa, Y. García López, R.J. Garczarczyk, M. Gasparyan, S. Gaug, M. Giesbrecht Paiva, J.G. Giglietto, N. Giordano, F. Gliwny, P. Godinović, N. Grau, R. Green, D. Green, J.G. Hadasch, D. Hahn, A. Hassan, T. Heckmann, L. Herrera, J. Hrupec, D. Hütten, M. Imazawa, R. Inada, T. Iotov, R. Ishio, K. Jiménez Martínez, I. Kerszberg, D. Kluge, G.W. Kobayashi, Y. Kouch, P.M. Kubo, H. Kushida, J. Láinez Lezáun, M. Lamastra, A. Lelas, D. Leone, F. Linhoff, L. Lombardi, S. Longo, F. López-Coto, R. López-Moya, M. López-Oramas, A. Loporchio, S. Lorini, A. Lyard, E. Machado de Oliveira Fraga, B. Majumdar, P. Makariev, M. Maneva, G. Mang, N. Manganaro, M. Mangano, S. Mannheim, K. Mariotti, M. Martínez, M. Martínez-Chicharro, M. Mas-Aguilar, A. Mazin, D. Menchiari, S. Mender, S. Mićanović, S. Miceli, D. Miener, T. Miranda, J.M. Università di Siena INFN Pisa Via Roma 56 SienaI-53100 Italy Faculty of Physics University of Rijeka Radmile Matječić 2 Rijeka51000 Croatia Finnish MAGIC Group Finnish Centre for Astronomy with ESO University of Turku TurkuFI-20014 Finland RomeI-00136 Italy Institute of Astrophysics Foundation for Research and Technology-Hellas HeraklionGR-71110 Greece Instituto de Astrofisica de Andalucia-CSIC Glorieta de la Astronomía Granada18008 Spain Department of Physics Otto-Hahn-Str. 4a Dortmund44227 Germany Hans-Haffner-Sternwarte Naturwissenschaftliches Labor für Schüler am FKG Friedrich-Koenig-Gymnasium WürzburgD-97082 Germany INAF Osservatorio Astrofisico di Torino via Osservatorio 20 Pino TorineseI-10025 Italy Caltech The Division of Physics Mathematics and Astronomy 1200 E California Blvd PasadenaCA91125 United States Institute for Astrophysical Research Boston University 725 Commonwealth Avenue BostonMA02215 United States The University of Tokyo Kashiwa Chiba 277-8582 Japan ETH Zürich ZürichCH-8093 Switzerland Instituto de Astrofísica de Canarias Dpto. de Astrofísica Universidad de La Laguna Tenerife La LagunaE-38200 Spain Università di Udine INFN Trieste UdineI-33100 Italy Max-Planck-Institut für Physik MünchenD-80805 Germany Università di Padova INFN PadovaI-35131 Italy Bellaterra BarcelonaE-08193 Spain Technische Universität Dortmund DortmundD-44221 Germany Zagreb10000 Croatia IPARCOS Institute EMFTEL Department Universidad Complutense de Madrid MadridE-28040 Spain URCA RJ Rio de Janeiro22290-180 Brazil University of Lodz Faculty of Physics and Applied Informatics Department of Astrophysics Lodz90-236 Poland Centro de Investigaciones Energéticas Medioambientales y Tecnológicas MadridE-28040 Spain Departament de Física CERES-IEEC Universitat Autònoma de Barcelona BellaterraE-08193 Spain Università di Pisa INFN Pisa PisaI-56126 Italy Universitat de Barcelona ICCUB IEEC-UB BarcelonaE-08028 S

The blazar S5 0716+714 is an intermediate BL Lacertae object remarkable for its variability in many energy bands. It was discovered by MAGIC in the very-high-energy (VHE) gamma-ray range in 2008. Later in 2015 an impressive electric vector polarization angle (EVPA) swing was detected in connection with a multiwavelength flaring event including the VHE gamma-ray band. This generated interest in further studies of the jet of this source and its electromagnetic emission at all wavelengths. Since then, MAGIC has monitored the source in coordination with other observatories and here we present the long-term study using data from 2015 to 2022 in a MWL context. The data set also includes the extraordinary flaring activity of 2017, so far the historical maximum detected for this source in the optical and VHE gamma-ray band. © Copyright owned by the author(s) under the terms of the Creative Commons.

关键词： Gamma rays

Benchmark problems for phase retrieval

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arXiv 2017年

作者： Elser, Veit Lan, Ti-Yen Bendory, Tamir Department of Physics Cornell University IthacaNY14853-2501 United States Program in Applied and Computational Mathematics Princeton University Princeton08544-1000 United States

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be recovered is periodic and comprised of atomic distributions arranged homogeneously in the unit cell of the crystal. The crystallographic problem is both the leading application and one of the hardest forms of phase retrieval. We have constructed a graded set of benchmark problems for evaluating algorithms that perform this type of phase retrieval. The data, publicly available online1, is provided in an easily interpretable format. We also propose a simple and unambiguous success/failure criterion based on the actual needs in crystallography. Baseline runtimes were obtained with an iterative algorithm that is similar but more transparent than those used in crystallography. Empirically,the runtimes grow exponentially with respect to a new hardness parameter: the sparsity of the signal autocorrelation. We also review the algorithms used by the leading software packages. This set of benchmark problems, we hope, will encourage the development of new algorithms for the phase retrieval problem in general, and crystallography in particular. Copyright © 2017, The Authors. All rights reserved.

关键词： Benchmarking

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

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arXiv 2017年

作者： Weinan, E. Hutzenthaler, Martin Jentzen, Arnulf Kruse, Thomas Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544-1000 United States BICMR and School of Mathematical Sciences Peking University Beijing100870 China Faculty of Mathematics University of Duisburg-Essen Essen45117 Germany Seminar für Angewandte Mathematik ETH Zurich Zürich8092 Switzerland

Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineering. In particular, parabolic PDEs and BSDEs are fundamental tools in the state-of-the-art pricing and hedging of financial derivatives. The PDEs and BSDEs appearing in such applications are often high-dimensional and nonlinear. Since explicit solutions of such PDEs and BSDEs are typically not available, it is a very active topic of research to solve such PDEs and BSDEs approximately. In the recent article [E, W., Hutzenthaler, M., Jentzen, A., & Kruse, T. Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations. arXiv:1607.03295 (2017)] we proposed a family of approximation methods based on Picard approximations and multilevel Monte Carlo methods and showed under suitable regularity assumptions on the exact solution for semilinear heat equations that the computational complexity is bounded by O(d ϵ-(4+δ)) for any δ 2 (0,∞), where d is the dimensionality of the problem and ϵ ∈ (0,∞) is the prescribed accuracy. In this paper, we test the applicability of this algorithm on a variety of 100-dimensional nonlinear PDEs that arise in physics and finance by means of numerical simulations presenting approximation accuracy against runtime. The simulation results for these 100-dimensional example PDEs are very satisfactory in terms of accuracy and speed. In addition, we also provide a review of other approximation methods for nonlinear PDEs and BSDEs from the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Monte Carlo methods

A fourth-order accurate finite volume method for ideal mhd via upwind constrained transport

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arXiv 2017年

作者： Felker, Kyle Gerard Stone, James Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States

We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme. Copyright © 2017, The Authors. All rights reserved.

关键词： Numerical methods

Symmetrized importance samplers for stochastic differential equations

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arXiv 2017年

作者： Leach, Andrew Lin, Kevin K. Morzfeld, Matthias Program in Applied Mathematics University of Arizona 617 N. Santa Rita Ave. TucsonAZ85721 United States Department of Mathematics University of Arizona 617 N. Santa Rita Ave. TucsonAZ85721 United States

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of our importance sampling schemes when the noise is not too large. We demonstrate that this is indeed the case for a number of linear and nonlinear examples. Potential applications, e.g., data assimilation, are discussed. Copyright © 2017, The Authors. All rights reserved.

关键词： Importance sampling

Inversion problems for fourier transforms of particle distributions

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arXiv 2018年

作者： Kim, Jaeuk Zhang, Ge Stillinger, Frank H. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Physics and Astronomy University of Pennsylvania PhiladelphiaPA19104-6396 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Collective coordinates in a many-particle system are complex Fourier components of the particle density n(x) ≡ PNj=1 δ(x − rj), and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates via inverse transformations. In principle, a sufficiently large set of collective coordinates are equivalent to particle coordinates, but the nonlinear relation between collective and particle coordinates makes the inversion procedure highly nontrivial. Given a "target" configuration in one-dimensional Euclidean space, we investigate the minimal set of its collective coordinates that can be uniquely inverted into particle coordinates. For this purpose, we treat a finite number M of the real and/or the imaginary parts of collective coordinates of the target configuration as constraints, and then reconstruct "solution" configurations whose collective coordinates satisfy these constraints. Both theoretical and numerical investigations reveal that the number of numerically distinct solutions depends sensitively on the chosen collective-coordinate constraints and target configurations. From detailed analysis, we conclude that collective coordinates at the dN2 e smallest wavevectors is the minimal set of constraints for unique inversion, where d·e represents the ceiling function. This result provides useful groundwork to the inverse transform of collective coordinates in higher-dimensional systems. Copyright © 2018, The Authors. All rights reserved.

关键词： Inverse transforms

A multi-frequency study of sub-parsec jets with the Event Horizon Telescope

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arXiv 2025年

作者： Röder, Jan Wielgus, Maciek Lobanov, Andrei P. Krichbaum, Thomas P. Nair, Dhanya G. Lee, Sang-Sung Ros, Eduardo Fish, Vincent L. Blackburn, Lindy Chan, Chi-Kwan Issaoun, Sara Janssen, Michael Johnson, Michael D. Doeleman, Sheperd S. Bower, Geoffrey C. Crew, Geoffrey B. Tilanus, Remo P.J. Savolainen, Tuomas Impellizzeri, C.M. Violette Alberdi, Antxon Baczko, Anne-Kathrin Gómez, José L. Lu, Ru-Sen Paraschos, Georgios F. Traianou, Efthalia Goddi, Ciriaco Kim, Daewon Lisakov, Mikhail Kovalev, Yuri Y. Voitsik, Petr A. Sokolovsky, Kirill V. Akiyama, Kazunori Albentosa-Ruíz, Ezequiel Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Ball, David Baloković, Mislav Bandyopadhyay, Bidisha Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blundell, Raymond Bouman, Katherine L. Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chang, Dominic O. Chatterjee, Koushik Chatterjee, Shami Chen, Ming-Tang Chen, Yongjun Cheng, Xiaopeng Cho, Ilje Christian, Pierre Conroy, Nicholas S. Conway, John E. Cordes, James M. Crawford, Thomas M. Cruz-Osorio, Alejandro Cui, Yuzhu Curd, Brandon Dahale, Rohan Davelaar, Jordy De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Dhruv, Vedant Dihingia, Indu K. Dougall, Sean Taylor Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fomalont, Edward H. Ford, Alyson Foschi, Marianna Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Gold, Roman Gómez-Ruiz, Arturo I. Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Haggard, Daryl Haworth, Kari Hecht, Michael H. Hesper, Ronald Heumann, Dirk Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Inoue, Makoto James, David J. Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Astronomy Department Universidad de Concepción Casilla 160-C Concepción Chile Korea Astronomy and Space Science Institute Daedeok-daero 776 Yuseong-gu Daejeon34055 Korea Republic of Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Ave. TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita TucsonAZ85721 United States NASA Hubble Fellowship Program United States Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Institute of Astronomy and Astrophysics Academia Sinica 645 N. A’ohoku Place HiloHI96720 United States Department of Physics and Astronomy University of Hawaii at Manoa 2505 Correa Road HonoluluHI96822 United States Leiden Observatory Leiden University Postbus 2300 Leiden9513 RA Netherlands Postbus 93138 Den Haag2509 AC Netherlands Aalto University Department of Electronics and Nanoengineering PL 15500 AaltoFI-00076 Finland Aalto University Metsähovi Radio Observatory Metsähovintie 114 KylmäläFI-02540 Finland National Radio Astronomy Observatory 520 Edgemont Road CharlottesvilleVA22903 United States Department of Space Earth and Environment Chalmers University of Technology Onsala Space Observatory OnsalaSE-43992 Sweden Shanghai Astronomical Observatory Chinese Academy of Sciences 80 Nandan Road Shanghai200030 China Key Laboratory of Radio Astronomy Chinese Academy of Scien

Context. The 2017 observing campaign of the Event Horizon Telescope (EHT) delivered the first very long baseline interferometry (VLBI) images at the observing frequency of 230 GHz, leading to a number of unique studies on black holes and relativistic jets from active galactic nuclei (AGN). In total, eighteen sources were observed, including the main science targets, Sgr A* and M 87 and various calibrators. Sixteen sources were AGN. Aims. We investigated the morphology of the sixteen AGN in the EHT 2017 data set, focusing on the properties of the VLBI cores: size, flux density, and brightness temperature. We studied their dependence on the observing frequency in order to compare it with the Blandford-Königl (BK) jet model. In particular, we aimed to study the signatures of jet acceleration and magnetic energy conversion. Methods. We modeled the source structure of seven AGN in the EHT 2017 data set using linearly polarized circular Gaussian components (1749+096, 1055+018, BL Lac, J0132–1654, J0006–0623, CTA 102, 3C 454.3) and collected results for the other nine AGN from dedicated EHT publications, complemented by lower frequency data in the 2-86 GHz range. Combining these data into a multi-frequency EHT+ data set, we studied the dependences of the VLBI core component flux density, size, and brightness temperature on the frequency measured in the AGN host frame (and hence on the distance from the central black hole), characterizing them with power law fits. We compared the observations with the BK jet model and estimated the magnetic field strength dependence on the distance from the central black hole. Results. Our observations spanning event horizon- to parsec scales indicate a deviation from the standard BK model, particularly in the decrease of the brightness temperature with the observing frequency. Only some of the discrepancies may be alleviated by tweaking the model parameters or the jet collimation profile. Either bulk acceleration of the jet material, energ

关键词： Luminance