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Classical many-particle systems with unique disordered ground states

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

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Inversion problems for fourier transforms of particle distributions

arXiv

引用

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

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Multireference alignment is easier with an aperiodic translation distribution

arXiv

引用

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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A spectral-infinite-element solution of Poisson’s equation: An application to self gravity

arXiv

引用

arXiv 2017年

作者： Gharti, Hom Nath Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ08544 United States Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

We solve Poisson’s equation by combining a spectral-element method with a mapped infinite-element method. We focus on problems in geostatics and geodynamics, where Earth’s gravitational field is determined by Poisson’s equation inside the Earth and Laplace’s equation in the rest of space. Spectral elements are used to capture the internal field, and infinite elements are used to represent the external field. To solve the weak form of Poisson/Laplace equation, we use Gauss-Legendre-Lobatto quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and Gauss-Legendre-Lobatto quadrature in the other directions. We illustrate the efficiency and accuracy of the method by comparing the gravitational fields of a homogeneous sphere and the Preliminary Reference Earth Model (PREM) with (semi-)analytical solutions. Copyright © 2017, The Authors. All rights reserved.

关键词： Earth (planet)

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Author Correction: Genetic drivers and cellular selection of female mosaic X chromosome loss

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Nature 2024年第8043期636卷 E7页

作者： Aoxing Liu Giulio Genovese Yajie Zhao Matti Pirinen Seyedeh M Zekavat Katherine A Kentistou Zhiyu Yang Kai Yu Caitlyn Vlasschaert Xiaoxi Liu Derek W Brown Georgi Hudjashov Bryan R Gorman Joe Dennis Weiyin Zhou Yukihide Momozawa Saiju Pyarajan Valdislav Tuzov Fanny-Dhelia Pajuste Mervi Aavikko Timo P Sipilä Awaisa Ghazal Wen-Yi Huang Neal D Freedman Lei Song Eugene J Gardner Vijay G Sankaran Aarno Palotie Hanna M Ollila Taru Tukiainen Stephen J Chanock Reedik Mägi Pradeep Natarajan Mark J Daly Alexander Bick Steven A McCarroll Chikashi Terao Po-Ru Loh Andrea Ganna John R B Perry Mitchell J Machiela Institute for Molecular Medicine Finland (FIMM) HiLIFE University of Helsinki Helsinki Finland. liuaoxin@***. Analytic and Translational Genetics Unit Massachusetts General Hospital Boston MA USA. liuaoxin@***. Center for Genomic Medicine Massachusetts General Hospital Boston MA USA. liuaoxin@***. Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA. liuaoxin@***. Stanley Center for Psychiatric Research Broad Institute of MIT and Harvard Cambridge MA USA. liuaoxin@***. Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA. giulio@***. Stanley Center for Psychiatric Research Broad Institute of MIT and Harvard Cambridge MA USA. giulio@***. Department of Genetics Harvard Medical School Boston MA USA. giulio@***. MRC Epidemiology Unit Institute of Metabolic Science University of Cambridge Cambridge UK. Institute for Molecular Medicine Finland (FIMM) HiLIFE University of Helsinki Helsinki Finland. Department of Public Health University of Helsinki Helsinki Finland. Department of Mathematics and Statistics University of Helsinki Helsinki Finland. Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA. Cardiovascular Research Center Massachusetts General Hospital Boston MA USA. Department of Ophthalmology Massachusetts Eye and Ear Harvard Medical School Boston MA USA. Division of Cancer Epidemiology and Genetics National Cancer Institute Rockville MD USA. Department of Medicine Queen's University Kingston Ontario Canada. Laboratory for Statistical and Translational Genetics RIKEN Center for Integrative Medical Sciences Yokohama Japan. Cancer Prevention Fellowship Program Division of Cancer Prevention National Cancer Institute Rockville MD USA. Estonian Genome Centre Institute of Genomics University of Tartu Tartu Estonia. Center for Data and Computational Sciences (C-DACS) VA Cooperative Studies Program VA Boston Health

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DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

arXiv

引用

arXiv 2017年

作者： Wang, Han Zhang, Linfeng Han, Jiequn Weinan, E. Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational 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

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model. Copyright © 2017, The Authors. All rights reserved.

关键词： Potential energy

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Comparison of Polarized Radiative Transfer Codes used by the EHT Collaboration

arXiv

引用

arXiv 2023年

作者： Prather, Ben S. Dexter, Jason Moscibrodzka, Monika Pu, Hung-Yi Bronzwaer, Thomas Davelaar, Jordy Younsi, Ziri Gammie, Charles F. Gold, Roman Wong, And George N. Akiyama, Kazunori Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Baczko, Anne-Kathrin Ball, David Baloković, Mislav Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blackburn, Lindy Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chan, Chi-Kwan 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. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dhruv, Vedant Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Alyson Ford, H. Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gómez-Ruiz, Arturo I. Gómez, José L. 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 Violette Impellizzeri, C.M. Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kino, Motoki Koay, Jun Yi Kocherlakota, Prashant K CCS-2 Los Alamos National Laboratory P.O. Box 1663 Los AlamosNM87545 United States JILA Department of Astrophysical and Planetary Sciences University of Colorado BoulderCO80309 United States Department of Astrophysics IMAPP Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Department of Physics National Taiwan Normal University No. 88 Sec.4 Tingzhou Rd. Taipei116 Taiwan Center of Astronomy and Gravitation National Taiwan Normal University No. 88 Sec. 4 Tingzhou Road Taipei116 Taiwan Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Department of Astronomy Columbia Astrophysics Laboratory Columbia University 550 W 120th Street New YorkNY10027 United States Center for Computational Astrophysics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Mullard Space Science Laboratory University College London Holmbury St. Mary Dorking SurreyRH5 6NT United Kingdom Institut für Theoretische Physik Goethe-Universität Frankfurt Max-von-Laue-Straße 1 Frankfurt am MainD-60438 Germany Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Department of Astronomy University of Illinois at Urbana-Champaign 1002 West Green Street UrbanaIL61801 United States NCSA University of Illinois 1205 W Clark St UrbanaIL61801 United States CP3-Origins University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Princeton Gravity Initiative Princeton University PrincetonNJ08544 United States Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Harvard University 20 Gar

Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes, which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT codes used within the EHT collaboration is evaluated for accuracy and consistency in producing a selection of test images, demonstrating that the various methods and implementations of radiative transfer calculations are highly consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04, 0.04, and 0.12 in Stokes I, Q, U, and V respectively. We additionally find the values of several image metrics relevant to published EHT results to be in agreement to much better precision than measurement uncertainties. © 2023, CC BY.

关键词： Mean square error

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First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

arXiv

引用

arXiv 2023年

作者： Akiyama, Kazunori Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Baczko, Anne-Kathrin Ball, David Baloković, Mislav Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blackburn, Lindy Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope 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 Chan, Chi-Kwan 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. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu Davelaar, Jordy De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Dhruv, Vedant Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Ford, H. Alyson Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gómez-Ruiz, Arturo I. Gómez, José L. 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 Impellizzeri, C.M. Violette Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kino, Motoki Koay, Jun Yi Kocherlakota, Prashant Kofuji, Yutaro Koch, Patrick M. Koyama, Shoko Kramer, Carsten Kramer, Michael Krichbaum, Thomas P. Ku Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia Center for Astrophysics | Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Department of Physics & Astronomy The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Departament d'Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 Paterna ValènciaE-46980 Spain Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Yale Center for Astronomy & Astrophysics Yale University 52 Hillhouse Avenue New HavenCT06511 United States Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Fermi National Accelerator Laboratory MS209 P.O. Box 500 BataviaIL60510 United States Department of Astronomy and Astrophysics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States East Asian Observatory 660 N. A'ohoku Place HiloHI96720 United States 660 N. A'ohoku Place HiloHI96720 United States California Institute of Technology 1200 East California Boulevard PasadenaCA91125 United States Institute of Astronomy and Astrophysics Academia Sinica 645 N. A'ohoku Place HiloHI

We present the first Event Horizon Telescope (EHT) observations of Sagittarius A* (Sgr A∗), the Galactic center source associated with a supermassive black hole. These observations were conducted in 2017 using a global interferometric array of eight telescopes operating at a wavelength of λ = 1.3 mm. The EHT data resolve a compact emission region with intrahour variability. A variety of imaging and modeling analyses all support an image that is dominated by a bright, thick ring with a diameter of 51.8 ± 2.3 µas (68% credible interval). The ring has modest azimuthal brightness asymmetry and a comparatively dim interior. Using a large suite of numerical simulations, we demonstrate that the EHT images of Sgr A∗ are consistent with the expected appearance of a Kerr black hole with mass ∼4 × 106 M☉, which is inferred to exist at this location based on previous infrared observations of individual stellar orbits as well as maser proper motion studies. Our model comparisons disfavor scenarios where the black hole is viewed at high inclination (i > 50◦), as well as non-spinning black holes and those with retrograde accretion disks. Our results provide direct evidence for the presence of a supermassive black hole at the center of the Milky Way galaxy, and for the first time we connect the predictions from dynamical measurements of stellar orbits on scales of 103 − 105 gravitational radii to event horizon-scale images and variability. Furthermore, a comparison with the EHT results for the supermassive black hole M87∗ shows consistency with the predictions of general relativity spanning over three orders of magnitude in central mass. © 2023, CC BY.

关键词： Telescopes

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Structural Effects and Aggregation in a Social-Network Model of Natural Resource Consumption

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IFAC-PapersOnLine 2017年第1期50卷 7675-7680页

作者： Manzoor T. Rovenskaya E. Muhammad A. Department of Electrical Engineering Lahore University of Management Sciences (LUMS) Lahore Pakistan Center for Water Informatics & Technology (WIT) Lahore University of Management Sciences (LUMS) Pakistan Advanced Systems Analysis Program International Institute for Applied Systems Analysis (IIASA) Laxenburg Austria Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russian Federation

In this paper we consider a networked system of natural-resource consumption, where the agents are governed by a recently reported model of consumer psychology Dynamics of the consumption for each agent are influenced by the state of the resource and consumption of her neighbors. The process is parameterized by the psychological characteristics of each agent. This study extends the original model to incorporate the underlying network topology and explores the effects of aggregation via densely-connected communities present in the network. The exercise yields new interpretations of the predictions made by the original model in context of the influence network. We present aggregation mechanisms first for certain canonical structures of the consuming population and later on for a class of non-canonically structured populations. In the end we present an approximate aggregation scheme for populations where only some inaccurate information of the consumer characteristics is available. © 2017

关键词： Control in economics identification of environmental systems Modeling Multi-agent systems Natural resources management Social Networks

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Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings

arXiv

引用

arXiv 2018年

作者： Oguz, Erdal C. Socolar, Joshua E.S. Steinhardt, Paul J. Torquato, Salvatore School of Mechanical Engineering Sackler Center for Computational Molecular and Materials Science Tel Aviv University Tel Aviv Israel Physics Department Duke University DurhamNC27708 United States Department of Physics Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Center for Cosmology and Particle Physics Department of Physics New York University New YorkNY10003 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution tilings. We present a simple argument that predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and confirm with numerical computations that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra, and limit-periodic tilings. Tilings with quasiperiodic or singular continuous spectra can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law. Copyright © 2018, The Authors. All rights reserved.

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