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Experimental Mathematics Volume 15, 2006 - Issue 3
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Original Article

New Conjectural Lower Bounds on the Optimal Density of Sphere Packings

S. Torquato Department of Chemistry, Program in Applied and Computational Mathematics, Princeton Institute for the Science and Technology of Materials and Princeton Center for Theoretical Physics, Princeton University, Princeton, NJ 08544
&
F. H. Stillinger Department of Chemistry, Princeton University, Princeton, NJ 08544
Pages 307-331 | Published online: 30 Jan 2011

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Amin S. Azar & Spyros Diplas. (2022) Fundamental aspects of processing multi-metallic components using additive manufacturing technologies. European Journal of Materials 2:1, pages 234-364.
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Articles from other publishers (114)

Sam Wilken, Ashley Z. Guo, Dov Levine & Paul M. Chaikin. (2023) Dynamical Approach to the Jamming Problem. Physical Review Letters 131:23.
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Charles Emmett Maher, Yang Jiao & Salvatore Torquato. (2023) Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions. Physical Review E 108:6.
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Rahul Dandekar & P L Krapivsky. (2023) Dynamic space packing. Journal of Statistical Mechanics: Theory and Experiment 2023:10, pages 103403.
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Michal Jex, Mathieu Lewin & Peter S. Madsen. (2023) Classical Density Functional Theory: Representability and Universal Bounds. Journal of Statistical Physics 190:4.
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Oliver H. E. Philcox & Salvatore Torquato. (2023) Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales. Physical Review X 13:1.
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Haina Wang & Salvatore Torquato. (2023) Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics. Soft Matter 19:3, pages 550-564.
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Sheng ChenSheng Chen. 2023. Microparticle Dynamics in Electrostatic and Flow Fields. Microparticle Dynamics in Electrostatic and Flow Fields 101 118 .
Haina Wang, Frank H. Stillinger & Salvatore Torquato. (2022) Realizability of iso- g 2 processes via effective pair interactions . The Journal of Chemical Physics 157:22.
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Nikolaos Angelinos, Debarghya Chakraborty & Anatoly Dymarsky. (2022) Optimal Narain CFTs from codes. Journal of High Energy Physics 2022:11.
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Salvatore Torquato & Haina Wang. (2022) Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium. Physical Review E 106:4.
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Salvatore Torquato & Yang Jiao. (2022) Exclusion volumes of convex bodies in high space dimensions: applications to virial coefficients and continuum percolation. Journal of Statistical Mechanics: Theory and Experiment 2022:9, pages 093404.
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Salvatore Torquato, Murray Skolnick & Jaeuk Kim. (2022) Local order metrics for two-phase media across length scales*. Journal of Physics A: Mathematical and Theoretical 55:27, pages 274003.
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Alexander I. P. Taylor & Rosemary A. Staniforth. (2022) General Principles Underpinning Amyloid Structure. Frontiers in Neuroscience 16.
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Henry Cohn & Nicholas Triantafillou. (2021) Dual linear programming bounds for sphere packing via modular forms. Mathematics of Computation 91:333, pages 491-508.
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Ferina Saati, Karl-Alexander Hoppe, Steffen Marburg & Kirill V. Horoshenkov. (2022) The accuracy of some models to predict the acoustical properties of granular media. Applied Acoustics 185, pages 108358.
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Patrick Charbonneau, Peter K. Morse, Will Perkins & Francesco Zamponi. (2021) Three simple scenarios for high-dimensional sphere packings. Physical Review E 104:6.
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Salvatore Torquato, Jaeuk Kim & Michael A. Klatt. (2021) Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions. Physical Review X 11:2.
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Salvatore Torquato. (2021) Structural characterization of many-particle systems on approach to hyperuniform states. Physical Review E 103:5.
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Takato Matsui, Makoto Katori & Tomoyuki Shirai. (2021) Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes. Journal of Physics A: Mathematical and Theoretical 54:16, pages 165201.
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Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartman, David de Laat & Amirhossein Tajdini. (2020) High-dimensional sphere packing and the modular bootstrap. Journal of High Energy Physics 2020:12.
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Timothy M Middlemas & Salvatore Torquato. (2020) Nearest-neighbor functions for disordered stealthy hyperuniform many-particle systems. Journal of Statistical Mechanics: Theory and Experiment 2020:10, pages 103302.
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Haina Wang, Frank H. Stillinger & Salvatore Torquato. (2020) Sensitivity of pair statistics on pair potentials in many-body systems. The Journal of Chemical Physics 153:12.
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Salvatore Torquato. (2020) Predicting transport characteristics of hyperuniform porous media via rigorous microstructure-property relations. Advances in Water Resources 140, pages 103565.
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Mariano López de Haro, Andrés Santos & Santos B. Yuste. (2020) Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures. Entropy 22:4, pages 469.
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Ge Zhang & Salvatore Torquato. (2020) Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions. Physical Review E 101:3.
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Giorgio Cinacchi & Salvatore Torquato. (2019) Hard convex lens-shaped particles: Characterization of dense disordered packings. Physical Review E 100:6.
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Thomas Hartman, Dalimil Mazáč & Leonardo Rastelli. (2019) Sphere packing and quantum gravity. Journal of High Energy Physics 2019:12.
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T. M. Middlemas, F. H. Stillinger & S. Torquato. (2019) Hyperuniformity order metric of Barlow packings. Physical Review E 99:2.
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MATTHEW JENSSEN, FELIX JOOS & WILL PERKINS. (2019) ON THE HARD SPHERE MODEL AND SPHERE PACKINGS IN HIGH DIMENSIONS. Forum of Mathematics, Sigma 7.
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Andrés Santos. (2018) Finite-size estimates of Kirkwood-Buff and similar integrals. Physical Review E 98:6.
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Henry Cohn & Matthew de Courcy-Ireland. (2018) The Gaussian core model in high dimensions. Duke Mathematical Journal 167:13.
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S. Torquato. (2018) Perspective: Basic understanding of condensed phases of matter via packing models. The Journal of Chemical Physics 149:2.
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Thibaud Maimbourg, Mauro Sellitto, Guilhem Semerjian & Francesco Zamponi. (2018) Generating dense packings of hard spheres by soft interaction design. SciPost Physics 4:6.
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Salvatore Torquato. (2018) Hyperuniform states of matter. Physics Reports 745, pages 1-95.
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Laurent Bétermin & Mircea Petrache. (2017) Dimension reduction techniques for the minimization of theta functions on lattices. Journal of Mathematical Physics 58:7.
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Zheng Ma & Salvatore Torquato. (2017) Random scalar fields and hyperuniformity. Journal of Applied Physics 121:24.
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Jaeuk Kim & Salvatore Torquato. (2017) Effect of window shape on the detection of hyperuniformity via the local number variance. Journal of Statistical Mechanics: Theory and Experiment 2017:1, pages 013402.
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A Andreanov, A Scardicchio & S Torquato. (2016) Extreme lattices: symmetries and decorrelation. Journal of Statistical Mechanics: Theory and Experiment 2016:11, pages 113301.
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Salvatore Torquato. (2016) Disordered hyperuniform heterogeneous materials. Journal of Physics: Condensed Matter 28:41, pages 414012.
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Wen-Sheng Xu, Jack F. Douglas & Karl F. Freed. 2016. Advances in Chemical Physics. Advances in Chemical Physics 443 497 .
Salvatore Torquato. (2016) Hyperuniformity and its generalizations. Physical Review E 94:2.
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Emanuele Caglioti, Maria Infusino & Tobias Kuna. (2016) Translation invariant realizability problem on the $d$-dimensional lattice: an explicit construction. Electronic Communications in Probability 21:none.
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Sheng Chen, Shuiqing Li, Wenwei Liu & Hernán A. Makse. (2016) Effect of long-range repulsive Coulomb interactions on packing structure of adhesive particles. Soft Matter 12:6, pages 1836-1846.
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Andrés SantosAndrés Santos. 2016. A Concise Course on the Theory of Classical Liquids. A Concise Course on the Theory of Classical Liquids 33 96 .
René D. Rohrmann & Andrés Santos. (2015) Equation of state for five-dimensional hyperspheres from the chemical-potential route. Physical Review E 92:2.
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Claudio Grimaldi. (2015) Continuum percolation of polydisperse hyperspheres in infinite dimensions. Physical Review E 92:1.
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Johann S. Brauchart & Peter J. Grabner. (2015) Distributing many points on spheres: Minimal energy and designs. Journal of Complexity 31:3, pages 293-326.
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S. Torquato, G. Zhang & F. H. Stillinger. (2015) Ensemble Theory for Stealthy Hyperuniform Disordered Ground States. Physical Review X 5:2.
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Wenwei Liu, Shuiqing Li, Adrian Baule & Hernán A. Makse. (2015) Adhesive loose packings of small dry particles. Soft Matter 11:32, pages 6492-6498.
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Hajime Yoshino & Francesco Zamponi. (2014) Shear modulus of glasses: Results from the full replica-symmetry-breaking solution. Physical Review E 90:2.
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Yoav Kallus, Étienne Marcotte & Salvatore Torquato. (2013) Jammed lattice sphere packings. Physical Review E 88:6.
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G. Zhang & S. Torquato. (2013) Precise algorithm to generate random sequential addition of hard hyperspheres at saturation. Physical Review E 88:5.
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Ryan Jadrich & Kenneth S. Schweizer. (2013) Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics. The Journal of Chemical Physics 139:5.
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Adam B. Hopkins, Frank H. Stillinger & Salvatore Torquato. (2013) Disordered strictly jammed binary sphere packings attain an anomalously large range of densities. Physical Review E 88:2.
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Étienne Marcotte & Salvatore Torquato. (2013) Efficient linear programming algorithm to generate the densest lattice sphere packings. Physical Review E 87:6.
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S. Torquato & Y. Jiao. (2013) Effect of dimensionality on the percolation thresholds of various -dimensional lattices . Physical Review E 87:3.
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S. Torquato & Y. Jiao. (2013) Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles. Physical Review E 87:2.
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Károly BezdekKároly Bezdek. 2013. Lectures on Sphere Arrangements – the Discrete Geometric Side. Lectures on Sphere Arrangements – the Discrete Geometric Side 1 16 .
A. Andreanov & A. Scardicchio. (2012) Random perfect lattices and the sphere packing problem. Physical Review E 86:4.
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S. Torquato & Y. Jiao. (2012) Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses. The Journal of Chemical Physics 137:7.
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Adam R. Williamson, Tsung-Yi Chen & Richard D. Wesel. (2012) A rate-compatible sphere-packing analysis of feedback coding with limited retransmissions. A rate-compatible sphere-packing analysis of feedback coding with limited retransmissions.
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Stephanie Vance. (2011) Improved sphere packing lower bounds from Hurwitz lattices. Advances in Mathematics 227:5, pages 2144-2156.
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András Sütő. (2011) Ground State at High Density. Communications in Mathematical Physics 305:3, pages 657-710.
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Chase E. Zachary, Yang Jiao & Salvatore Torquato. (2011) Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape. Physical Review E 83:5.
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Chase E. Zachary, Yang Jiao & Salvatore Torquato. (2011) Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres. Physical Review E 83:5.
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Paula A. Whitlock, Marvin Bishop & John L. Tiglias. (2007) Structure factor for hard hyperspheres in higher dimensions. The Journal of Chemical Physics 126:22.
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