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Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions

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Physical Review E 2018年第1期97卷 012118-012118页

作者： Michael A. Klatt Salvatore Torquato 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

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.

关键词： Classical statistical mechanics

Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications

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Physical Review E 2018年第1期98卷 013307-013307页

作者： Zheng Ma Salvatore Torquato 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

The quantitative characterization of the microstructure of random heterogeneous media in d-dimensional Euclidean space Rd via a variety of n-point correlation functions is of great importance, since the respective infinite set determines the effective physical properties of the media. In particular, surface-surface Fss and surface-void Fsv correlation functions (obtainable from radiation scattering experiments) contain crucial interfacial information that enables one to estimate transport properties of the media (e.g., the mean survival time and fluid permeability) and complements the information content of the conventional two-point correlation function. However, the current technical difficulty involved in sampling surface correlation functions has been a stumbling block in their widespread use. We first present a concise derivation of the small-r behaviors of these functions, which are linked to the mean curvature of the system. Then we demonstrate that one can reduce the computational complexity of the problem, without sacrificing accuracy, by extracting the necessary interfacial information from a cut of the d-dimensional statistically homogeneous and isotropic system with an infinitely long line. Accordingly, we devise algorithms based on this idea and test them for two-phase media in continuous and discrete spaces. Specifically for the exact benchmark model of overlapping spheres, we find excellent agreement between numerical and exact results. We compute surface correlation functions and corresponding local surface-area variances for a variety of other model microstructures, including hard spheres in equilibrium, decorated “stealthy” patterns, as well as snapshots of evolving pattern formation processes (e.g., spinodal decomposition). It is demonstrated that the precise determination of surface correlation functions provides a powerful means to characterize a wide class of complex multiphase microstructures.

关键词： Structural properties

An Extremely Deep Rubin Survey to Explore the Extended Kuiper Belt and Identify Objects Observable by New Horizons

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arXiv 2025年

作者： Kavelaars, J.J. Buie, Marc W. Fraser, Wesley C. Peltier, Lowell Benecchi, Susan D. Porter, Simon B. Verbiscer, Anne J. Gerdes, David W. Napier, Kevin J. Murtagh, Joseph Ito, Takashi Singer, Kelsi N. Stern, S. Alan Terai, Tsuyoshi Yoshida, Fumi Bannister, Michele T. Bernardinelli, Pedro H. Bernstein, Gary M. Chandler, Colin Orion Gladman, Brett Jones, Lynne Petit, Jean-Marc Schwamb, Megan E. Brandt, Pontus C. Parker, Joel W. National Research Council of Canada Herzberg Astronomy and Astrophysics Research Centre 5071 W. Saanich Rd. VictoriaBCV9E 2E7 Canada Department of Physics and Astronomy University of Victoria Elliott Building 3800 Finnerty Road VictoriaBCV8P 5C2 Canada Department of Physics & Astronomy University of British Columbia 6224 Agricultural Road VancouverBCV6T 1Z1 Canada Southwest Research Institute 1301 Walnut St. Suite 400 BoulderCO80302 United States Planetary Science Institute 1700 East Fort Lowell Suite 106 TucsonAZ85719 United States Department of Astronomy University of Virginia P.O. Box 400325 CharlottesvilleVA22904-4325 United States Department of Physics University of Michigan Ann ArborMI48109 United States Department of Astronomy University of Michigan Ann ArborMI48109 United States Michigan Institute for Data Science University of Michigan Ann ArborMI48109 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Astrophysics Research Centre School of Mathematics and Physics Queen’s University Belfast BelfastBT7 1NN United Kingdom Center for Computational Astrophysics National Astronomical Observatory of Japan Osawa 2-21-1 Mitaka Tokyo181-8588 Japan Subaru Telescope National Astronomical Observatory of Japan 650 North A‘ohoku Place HiloHI96720 United States University of Occupational and Environmental Health 1-1 Iseigaoka Yahata Kitakyushu807-8555 Japan Planetary Exploration Research Center Chiba Institute of Technology 2-17-1 Tsudanuma Narashino Chiba275-0016 Japan School of Physical and Chemical Sciences — Te Kura Matū University of Canterbury Private Bag 4800 Christchurch8140 New Zealand DiRAC Institute The Department of Astronomy University of Washington Seattle United States Department of Physics and Astronomy University of Pennsylvania PhiladelphiaPA19104 United States Department of Astronomy and Planetary Science Northern Arizona University PO Box 6010

A proposed Vera C. Rubin Observatory Deep Drilling micro-survey of the Kuiper Belt will investigate key properties of the distant solar system. Utilizing 30 hours of Rubin time across six 5-hour visits over one year starting in summer 2026, the survey aims to discover and determine orbits for up to 730 Kuiper Belt Objects (KBOs) to an r-magnitude of 27.5. These discoveries will enable precise characterization of the KBO size distribution, which is critical for understanding planetesimal formation. By aligning the survey field with NASA’s New Horizons spacecraft trajectory, the micro-survey will facilitate discoveries for the mission operating in the Kuiper Belt. Modeling based on the Outer Solar System Origin Survey (OSSOS) predicts at least 12 distant KBOs observable with the New Horizons LOng Range Reconnaissance Imager (LORRI) and approximately three objects within 1 au of the spacecraft, allowing higher-resolution observations than Earth-based facilities. LORRI’s high solar phase angle monitoring will reveal these objects’ surface properties and shapes, potentially identifying contact binaries and orbit-class surface correlations. The survey could identify a KBO suitable for a future spacecraft flyby. The survey’s size, depth, and cadence design will deliver transformative measurements of the Kuiper Belt’s size distribution and rotational properties across distance, size, and orbital class. Additionally, the high stellar density in the survey field also offers synergies with transiting exoplanet studies. © 2025, CC BY.

关键词： NASA

Universal approximation of symmetric and anti-symmetric functions

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arXiv 2019年

作者： Han, Jiequn Li, Yingzhou Lin, Lin Lu, Jianfeng Zhang, Jiefu Zhang, Linfeng Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Duke University DurhamNC27708 United States Department of Mathematics University of California BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics Department of Physics Department of Chemistry Duke University DurhamNC27708 United States Department of Mathematics University of California BerkeleyCA94720 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ǫ. While the approximation still suffers from curse of dimensionality, to the best of our knowledge, these are first results in the literature with explicit error bounds. Moreover, we also discuss neural network architecture that can be suitable for approximating symmetric and anti-symmetric functions. Copyright © 2019, The Authors. All rights reserved.

关键词： Network architecture

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

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arXiv 2022年

作者： Aubry, Jean-Francois Bates, Oscar Boehm, Christian Pauly, Kim Butts Christensen, Douglas Cueto, Carlos Gélat, Pierre Guasch, Lluis Jaros, Jiri Jing, Yun Jones, Rebecca Li, Ningrui Marty, Patrick Montanaro, Hazael Neufeld, Esra Pichardo, Samuel Pinton, Gianmarco Pulkkinen, Aki Stanziola, Antonio Thielscher, Axel Treeby, Bradley Van't Wout, Elwin Physics for Medicine Paris INSERM U1273 ESPCI Paris PSL University CNRS UMR 8063 France Department of Bioengineering Imperial College London Exhibition Road LondonSW7 2AZ United Kingdom Institute of Geophysics ETH Zürich Sonneggstrasse 5 Zürich8092 Switzerland Department of Radiology Stanford University StanfordCA United States Department of Biomedical Engineering Department of Electrical and Computer Engineering University of Utah United States Department of Surgical Biotechnology Division of Surgery and Interventional Science University College London LondonNW3 2PF United Kingdom Earth Science and Engineering Department Imperial College London London United Kingdom Centre of Excellence IT4Innovations Faculty of Information Technology Brno University of Technology Bozetechova 2 Brno612 00 Czech Republic Graduate Program in Acoustics The Pennsylvania State University University Park PA16802 United States Joint Department of Biomedical Engineering University of North Carolina at Chapel Hill North Carolina State University NC United States Department of Electrical Engineering Stanford University StanfordCA United States Zurich Switzerland Laboratory for Acoustics / Noise control Empa Swiss Federal Laboratories for Materials Science and Technology Dubendorf Switzerland Zurich Switzerland Radiology and Clinical Neurosciences Departments Cumming School of Medicine University of Calgary Canada Department of Applied Physics University of Eastern Finland Kuopio70211 Finland Department of Medical Physics and Biomedical Engineering University College London Gower Street LondonWC1E 6BT United Kingdom Technical University of Denmark Denmark Danish Research Center for Magnetic Resonance Copenhagen University Hospital Hvidovre Denmark Institute for Mathematical and Computational Engineering School of Engineering and Faculty of Mathematics Pontificia Universidad Catolica de Chile Santiago Chile

computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular-spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons. Copyright © 2022, The Authors. All rights reserved.

关键词： Bone

Inferring a network from dynamical signals at its nodes

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arXiv 2020年

作者： Weistuch, Corey Agozzino, Luca Mujica-Parodi, Lilianne R. Dill, Ken Laufer Center for Physical and Quantitative Biology Stony Brook University Department of Applied Mathematics and Statistics Stony Brook University Department of Physics and Astronomy Stony Brook University Department of Biomedical Engineering Stony Brook University Program in Neuroscience Stony Brook University Athinoula A. Martinos Center for Biomedical Imaging Massachusetts General Hospital Harvard Medical School Department of Chemistry Stony Brook University

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network. Copyright © 2020, The Authors. All rights reserved.

关键词： Toys

Seismic vulnerability based on microtremor data and HVSR method in Krueng Raya, Aceh Besar

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AIP Conference Proceedings 2023年第1期2613卷

作者： Yusran Asnawi Umar Muksin Yuni Putri Tarniati Andrean V. H. Simanjuntak Syamsul Rizal Muhammad Syukri 1Universitas Islam Negeri Ar-Raniry Banda Aceh Indonesia 2Doctoral Program of Mathematics and Applied Sciences Universitas Syiah Kuala Indonesia 3Tsunami and Disaster Mitigation Research Center (TDMRC) Universitas Syiah Kuala Indonesia 4Department of Physics Universitas Syiah Kuala Banda Aceh Indonesia 5Meteorological Climatological and Geophysical Agency BMKG Banda Aceh Indonesia

Geology Krueng Raya, Aceh Besar is formed from thick sediment and hard rock consisting of young alluvium and volcanic rock. The study area is characterized by the Seulimeum fault which is recently very active in generating earthquakes. This study aims to analyze microtremor data to determine the value of the seismic vulnerability index in the Krueng Raya area, Aceh Besar. Data acquisition was carried out at 20 measurement points located across the Mesjid Raya District. The data were analyzed using the Horizontal to Vertical Spectral Ratio (HVSR) method. Based on the dominant frequency value and the amplification value, the seismic vulnerability index value in the Krueng Raya area ranges from 0.20 to 12.92 which is categorized as low to moderate. Areas that have low seismic vulnerability index values are in the villages of Lamreh. Areas with a moderate seismic vulnerability index value are Meunasah Kulam Village, and Paya Kameng Village.

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Constraining the coupled channel dynamics using femtoscopic correlations at the LHC

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The European Physical Journal C 2023年第4期83卷 1-21页

作者： Acharya, S. Adamová, D. Adler, A. Aglieri Rinella, G. Agnello, M. Agrawal, N. Ahammed, Z. Ahmad, S. Ahn, S. U. Ahuja, I. Akindinov, A. Al-Turany, M. Suaide, A. A. P. Aleksandrov, D. Alessandro, B. Alfanda, H. M. Alfaro Molina, R. Ali, B. Ali, Y. Alici, A. Alizadehvandchali, N. Alkin, A. Alme, J. Alocco, G. Alt, T. Altsybeev, I. Garcia, J. R. A. Anaam, M. N. Andrei, C. Andronic, A. Anguelov, V. Antinori, F. Antonioli, P. Apadula, N. Aphecetche, L. Appelshäuser, H. Arata, C. Arcelli, S. Arnaldi, R. Arsene, I. C. Arslandok, M. Diaz, R. A. Augustinus, A. Averbeck, R. Aziz, S. Azmi, M. D. Badalà, A. Saramela, T. B. Baek, Y. W. Bai, X. Bailhache, R. Bailung, Y. Bala, R. Balbino, A. Baldisseri, A. Balis, B. Banerjee, D. Banoo, Z. Barbera, R. Barioglio, L. Barlou, M. Barnaföldi, G. G. Barnby, L. S. Barreto, L. Bartels, C. Barth, K. Bartsch, E. Baruffaldi, F. Butt, J. B. Bastid, N. Basu, S. Batigne, G. Battistini, D. Batyunya, B. Bauri, D. Bazo Alba, J. L. Bearden, I. G. Beattie, C. Becht, P. Behera, D. Belikov, I. Bell Hechavarria, A. D. C. Bellini, F. Bellwied, R. Belokurova, S. Belyaev, V. Bencedi, G. Beole, S. Bercuci, A. Berdnikov, Y. Berdnikova, A. Bergmann, L. Ferrer, M. B. Besoiu, M. G. Betev, L. Bhaduri, P. P. Bhasin, A. Bhat, M. A. Bhattacharjee, B. Bianchi, L. Bianchi, N. Bielčík, J. Bielčíková, J. Biernat, J. Bigot, A. P. Bilandzic, A. Biro, G. Biswas, S. Bize, N. Blair, J. T. Blau, D. Blidaru, M. B. Bluhme, N. Blume, C. Boca, G. Bock, F. Bodova, T. Bogdanov, A. Boi, S. Bok, J. Boldizsár, L. Bolozdynya, A. Bombara, M. Bond, P. M. Bonomi, G. Borel, H. Borissov, A. Bossi, H. Botta, E. Bratrud, L. Braun-Munzinger, P. Bregant, M. Broz, M. Bruno, G. E. Buckland, M. D. Budnikov, D. Buesching, H. Bufalino, S. Bugnon, O. Buhler, P. Buthelezi, Z. Bylinkin, A. Bysiak, S. A. Cai, M. Caines, H. Caliva, A. Calvo Villar, E. Camerini, P. Carabas, M. Carnesecchi, F. Caron, R. Castillo Castellanos, J. Catalano, F. Ceballos Sanchez, C. Chakaberia, I. Chakraborty, P. Anuj, C. Chandra, S. Chapeland, S. Chartier, M. Chattopadhyay, Université Clermont Auvergne CNRS/IN2P3 LPC Clermont-Ferrand France Variable Energy Cyclotron Centre Homi Bhabha National Institute Kolkata India Nuclear Physics Institute of the Czech Academy of Sciences Husinec-Řež Czech Republic Fachbereich Informatik und Mathematik Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik Frankfurt Germany European Organization for Nuclear Research (CERN) Geneva Switzerland Dipartimento DISAT del Politecnico and Sezione INFN Turin Italy Sezione di Bologna INFN Bologna Italy Department of Physics Aligarh Muslim University Aligarh India Korea Institute of Science and Technology Information Daejeon Republic of Korea Faculty of Science P.J. Šafárik University Kosice Slovak Republic Affiliated with an Institute Covered by a Cooperation Agreement with CERN Geneva Switzerland Research Division and ExtreMe Matter Institute EMMI GSI Helmholtzzentrum für Schwerionenforschung GmbH Darmstadt Germany Universidade de São Paulo (USP) São Paulo Brazil Sezione di Torino INFN Turin Italy Central China Normal University Wuhan China Instituto de Física Universidad Nacional Autónoma de México Mexico City Mexico COMSATS University Islamabad Islamabad Pakistan Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN Bologna Italy University of Houston Houston USA Department of Physics and Technology University of Bergen Bergen Norway Sezione di Cagliari INFN Cagliari Italy Institut für Kernphysik Johann Wolfgang Goethe-Universität Frankfurt Frankfurt Germany High Energy Physics Group Universidad Autónoma de Puebla Puebla Mexico Horia Hulubei National Institute of Physics and Nuclear Engineering Bucharest Romania Westfälische Wilhelms-Universität Münster Institut für Kernphysik Münster Germany Physikalisches Institut Ruprecht-Karls-Universität Heidelberg Heidelberg Germany Sezione di Padova INFN Padua Italy Lawrence Berkeley National Laboratory Berkeley USA SUBATECH IMT Atlantique Nantes Université CNR

The interaction of $$\textrm{K}^{-}$$ with protons is characterised by the presence of several coupled channels, systems like $${\overline{\textrm{K}}}^0$$ n and $$\uppi \Sigma $$ with a similar mass and the same quantum numbers as the $$\textrm{K}^{-}$$ p state. The strengths of these couplings to the $$\textrm{K}^{-}$$ p system are of crucial importance for the understanding of the nature of the $$\Lambda (1405)$$ resonance and of the attractive $$\textrm{K}^{-}$$ p strong interaction. In this article, we present measurements of the $$\textrm{K}^{-}$$ p correlation functions in relative momentum space obtained in pp collisions at $$\sqrt{s}~=~13$$ Te, in p–Pb collisions at $$\sqrt{s_{\textrm{NN}}}~=~5.02$$ Te, and (semi)peripheral Pb–Pb collisions at $$\sqrt{s_{\textrm{NN}}}~=~5.02$$ Te. The emitting source size, composed of a core radius anchored to the $$\textrm{K}^{+}$$ p correlation and of a resonance halo specific to each particle pair, varies between 1 and 2 fm in these collision systems. The strength and the effects of the $${\overline{\textrm{K}}}^0$$ n and $$\uppi \Sigma $$ inelastic channels on the measured $$\textrm{K}^{-}$$ p correlation function are investigated in the different colliding systems by comparing the data with state-of-the-art models of chiral potentials. A novel approach to determine the conversion weights $$\omega $$ , necessary to quantify the amount of produced inelastic channels in the correlation function, is presented. In this method, particle yields are estimated from thermal model predictions, and their kinematic distribution from blast-wave fits to measured data. The comparison of chiral potentials to the measured $$\textrm{K}^{-}$$ p interaction indicates that, while the $$\uppi \Sigma $$ – $$\textrm{K}^{-}$$ p dynamics is well reproduced by the model, the coupling to the $${\overline{\textrm{K}}}^0$$ n channel in the model is currently underestimated.

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Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

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arXiv 2019年

作者： Arjika, S. Calixto, M. Guerrero, J. Department of Mathematics and Computers Sciences University of Agadez Niger Department of Applied Mathematics Institute Carlos I of Theoretical and Computational Physics University of Granada Fuentenueva s/n Granada18071 Spain Department of Mathematics University of Jaen Campus Las Lagunillas s/n Jaen23071 Spain

We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schrödinger cat states, defined as orthonormalized eigenstates of k-th powers of nonlinear f-oscillator annihilation operators, with f of hypergeometric type. These "k-hypercats" can be written as an equally weighted superposition of hypergeometric coherent states |zli, l = 0, 1, . . ., k − 1, with zl = ze2πil/k a k-th root of zk, and they interpolate between number and coherent states. This fact motivates a continuous circle representation for high k. We also extend our study to truncated hypergeometric functions (finite dimensional Hilbert spaces) and a discrete exact circle representation is provided. We also show how to generate k-hypercats by amplitude dispersion in a Kerr medium and analyze their generalized Husimi Q-function in the super- and sub-Poissonian cases at different fractions of the revival *** Codes 81R50, 81V80, 81S05 Copyright © 2019, The Authors. All rights reserved.

关键词： Mathematical operators