{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T07:35:50Z","timestamp":1789803350143,"version":"4.0.1"},"reference-count":86,"publisher":"AIP Publishing","issue":"2","funder":[{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF- 22-2-0103"],"award-info":[{"award-number":["W911NF- 22-2-0103"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,7,14]]},"abstract":"<jats:p>Disordered stealthy hyperuniform (SHU) packings are an emerging class of exotic amorphous two-phase materials endowed with novel optical, transport, chemical, and mechanical properties. Such packings of identical spheres have been created from SHU ground-state point patterns via a modified collective-coordinate optimization scheme that includes a soft-core repulsion, in addition to the standard \u201cstealthy\u201d pair potential. To explore the maximal ranges of the packing fraction \u03d5, we investigate the distributions of minimum pair distances as well as nearest-neighbor distances of ensembles of SHU point patterns without and with soft-core repulsions in the first three space dimensions as a function of the stealthiness parameter \u03c7 and number of particles N within a hypercubic simulation box under periodic boundary conditions. Within the disordered regime (\u03c7 &amp;lt; 0.5), we find that the maximal values of \u03d5, denoted by \u03d5max(\u03c7, d), decrease to zero on average as N increases if there are no soft-core repulsions. By contrast, the inclusion of soft-core repulsions results in very large \u03d5max(\u03c7, d) independent of N, reaching up to \u03d5max(\u03c7, d) = 1.0, 0.86, 0.63 in the zero-\u03c7 limit and decreasing to \u03d5max(\u03c7, d) = 1.0, 0.67, 0.47 at \u03c7 = 0.45 for d = 1, 2, 3, respectively. We obtain explicit formulas for \u03d5max(\u03c7, d) as functions of \u03c7 and N for a given value of d in both cases with and without soft-core repulsions. In two and three dimensions, our soft-core SHU ground-state packings for small \u03c7 become configurationally very close to the corresponding jammed hard-particle packings created by fast compression algorithms, as measured by their pair statistics. As \u03c7 increases beyond 0.20, the particles in this family of disordered packings form fewer contacts and linear polymer-like chains as \u03c7 tends to 1\/2. The resulting structure factors Sk and pair correlation functions g2r reveal that soft-core repulsions significantly alter the short- and intermediate-range correlations in the SHU ground states. We show that the degree of large-scale order of the soft-core SHU ground states increases as \u03c7 increases from 0 to 0.45 for d = 2, 3. We also compute the spectral density \u03c7\u0303Vk, which can be used to estimate various physical properties, including electromagnetic properties, fluid permeability, and mean survival time of SHU two-phase dispersions. Our results offer a new route for the discovery of novel disordered hyperuniform two-phase materials with unprecedentedly high density.<\/jats:p>","DOI":"10.1063\/5.0276041","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T06:19:16Z","timestamp":1751955556000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Ultradense sphere packings derived from disordered stealthy hyperuniform ground states"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5562-2937","authenticated-orcid":false,"given":"Jaeuk","family":"Kim","sequence":"first","affiliation":[{"name":"Princeton Materials Institute, Department of Physics, Department of Chemistry, Princeton University 1 , Princeton, New Jersey 08544,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4614-335X","authenticated-orcid":false,"given":"Salvatore","family":"Torquato","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Department of Physics, Princeton Materials Institute, Program in Applied and Computational Mathematics, Princeton University 2 , Princeton, New Jersey 08544,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"key":"2025070806191193200_c1","doi-asserted-by":"publisher","first-page":"041113","DOI":"10.1103\/physreve.68.041113","article-title":"Local density fluctuations, hyperuniformity, and order metrics","volume":"68","year":"2003","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2018.03.001","article-title":"Hyperuniform states of matter","volume":"745","year":"2018","journal-title":"Phys. Rep."},{"key":"2025070806191193200_c3","doi-asserted-by":"publisher","first-page":"110602","DOI":"10.1103\/physrevlett.114.110602","article-title":"Hyperuniformity of critical absorbing states","volume":"114","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c4","doi-asserted-by":"publisher","first-page":"2411","DOI":"10.1080\/00268976.2016.1159742","article-title":"Consequences of minimising pair correlations in fluids for dynamics, thermodynamics and structure","volume":"114","year":"2016","journal-title":"Mol. Phys."},{"key":"2025070806191193200_c5","doi-asserted-by":"publisher","first-page":"258002","DOI":"10.1103\/physrevlett.121.258002","article-title":"Hidden hyperuniformity in soft polymeric materials","volume":"121","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c6","doi-asserted-by":"publisher","first-page":"2836","DOI":"10.1038\/s41467-018-05195-4","article-title":"Hyperuniformity with no fine tuning in sheared sedimenting suspensions","volume":"9","year":"2018","journal-title":"Nat. Commun."},{"key":"2025070806191193200_c7","doi-asserted-by":"publisher","first-page":"055212","DOI":"10.1103\/physreve.106.055212","article-title":"Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids","volume":"106","year":"2022","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c8","doi-asserted-by":"publisher","first-page":"804","DOI":"10.1038\/s41467-022-28375-9","article-title":"Hyperuniformity and phase enrichment in vortex and rotor assemblies","volume":"13","year":"2022","journal-title":"Nat. Commun."},{"key":"2025070806191193200_c9","doi-asserted-by":"publisher","first-page":"206602","DOI":"10.1103\/physrevlett.133.206602","article-title":"Topological bound on the structure factor","volume":"133","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c10","doi-asserted-by":"publisher","first-page":"3635","DOI":"10.1177\/00219983221116432","article-title":"Extraordinary disordered hyperuniform multifunctional composites","volume":"56","year":"2022","journal-title":"J.\u00a0Compos. Mater."},{"key":"2025070806191193200_c11","doi-asserted-by":"publisher","first-page":"046122","DOI":"10.1103\/physreve.70.046122","article-title":"Constraints on collective density variables: Two dimensions","volume":"70","year":"2004","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c12","doi-asserted-by":"publisher","first-page":"022119","DOI":"10.1103\/physreve.92.022119","article-title":"Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations","volume":"92","year":"2015","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c13","doi-asserted-by":"publisher","first-page":"021020","DOI":"10.1103\/physrevx.5.021020","article-title":"Ensemble theory for stealthy hyperuniform disordered ground states","volume":"5","year":"2015","journal-title":"Phys. Rev. X"},{"key":"2025070806191193200_c14","doi-asserted-by":"publisher","first-page":"033504","DOI":"10.1063\/1.2961314","article-title":"Classical disordered ground states: Super-ideal gases and stealth and equi-luminous materials","volume":"104","year":"2008","journal-title":"J.\u00a0Appl. Phys."},{"key":"2025070806191193200_c15","doi-asserted-by":"publisher","first-page":"20658","DOI":"10.1073\/pnas.0907744106","article-title":"Designer disordered materials with large, complete photonic band gaps","volume":"106","year":"2009","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2025070806191193200_c16","doi-asserted-by":"publisher","first-page":"2200232","DOI":"10.1002\/adom.202200232","article-title":"Fabrication of hyperuniform dielectric networks via heat-induced shrinkage reveals a bandgap at telecom wavelengths","volume":"2022","journal-title":"Adv. Opt. Mater."},{"key":"2025070806191193200_c17","doi-asserted-by":"publisher","first-page":"015001","DOI":"10.1088\/2399-7532\/aaca91","article-title":"Multifunctional hyperuniform cellular networks: Optimality, anisotropy and disorder","volume":"1","year":"2018","journal-title":"Multifunct. Mater."},{"key":"2025070806191193200_c18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/jstqe.2019.2938069","article-title":"Ultra-broadband hyperuniform disordered silicon photonic polarizers","volume":"26","year":"2020","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"2025070806191193200_c19","doi-asserted-by":"publisher","first-page":"e2213633119","DOI":"10.1073\/pnas.2213633119","article-title":"Wave propagation and band tails of two-dimensional disordered systems in the thermodynamic limit","volume":"119","year":"2022","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2025070806191193200_c20","doi-asserted-by":"publisher","first-page":"2102565","DOI":"10.1002\/adom.202102565","article-title":"Near-field investigation of luminescent hyperuniform disordered materials","volume":"10","year":"2022","journal-title":"Adv. Opt. Mater."},{"key":"2025070806191193200_c21","doi-asserted-by":"publisher","first-page":"244109","DOI":"10.1063\/1.4972862","article-title":"Transport, geometrical, and topological properties of stealthy disordered hyperuniform two-phase systems","volume":"145","year":"2016","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025070806191193200_c22","doi-asserted-by":"publisher","first-page":"8764","DOI":"10.1073\/pnas.1914086117","article-title":"Multifunctional composites for elastic and electromagnetic wave propagation","volume":"117","year":"2020","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2025070806191193200_c23","doi-asserted-by":"publisher","first-page":"054076","DOI":"10.1103\/physrevapplied.11.054076","article-title":"Stealth acoustic materials","volume":"11","year":"2019","journal-title":"Phys. Rev. Appl."},{"key":"2025070806191193200_c24","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1364\/optica.489797","article-title":"Effective electromagnetic wave properties of disordered stealthy hyperuniform layered media beyond the quasistatic regime","volume":"10","year":"2023","journal-title":"Optica"},{"key":"2025070806191193200_c25","doi-asserted-by":"publisher","first-page":"18509","DOI":"10.1364\/oe.484232","article-title":"Bandgap fluctuations and robustness in two-dimensional hyperuniform dielectric materials","volume":"31","year":"2023","journal-title":"Opt. Express"},{"key":"2025070806191193200_c26","doi-asserted-by":"publisher","first-page":"065001","DOI":"10.1103\/PhysRevE.108.065001","article-title":"Experimental evidence of isotropic transparency and complete band gap formation for ultrasound propagation in stealthy hyperuniform media","volume":"108","year":"2023","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c27","doi-asserted-by":"publisher","first-page":"8666","DOI":"10.1364\/oe.27.008666","article-title":"Enhanced absorption of waves in stealth hyperuniform disordered media","volume":"27","year":"2019","journal-title":"Opt. Express"},{"key":"2025070806191193200_c28","doi-asserted-by":"publisher","first-page":"9570","DOI":"10.1073\/pnas.1705130114","article-title":"Band gap formation and anderson localization in disordered photonic materials with structural correlations","volume":"114","year":"2017","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2025070806191193200_c29","doi-asserted-by":"publisher","first-page":"064204","DOI":"10.1103\/physrevb.105.064204","article-title":"Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems","volume":"105","year":"2022","journal-title":"Phys. Rev. B"},{"key":"2025070806191193200_c30","doi-asserted-by":"publisher","first-page":"1206","DOI":"10.1021\/acsphotonics.1c01668","article-title":"Over 65% sunlight absorption in a 1\u00a0\u03bcm Si slab with hyperuniform texture","volume":"9","year":"2022","journal-title":"ACS Photonics"},{"key":"2025070806191193200_c31","doi-asserted-by":"publisher","first-page":"2300256","DOI":"10.1002\/adpr.202300256","article-title":"Stealthy hyperuniform surface structures for efficiency enhancement of organic solar cells","volume":"5","year":"2023","journal-title":"Adv. Photonics Res."},{"key":"2025070806191193200_c32","doi-asserted-by":"publisher","first-page":"094120","DOI":"10.1103\/physrevb.95.094120","article-title":"Hyperuniform disordered phononic structures","volume":"95","year":"2017","journal-title":"Phys. Rev. B"},{"key":"2025070806191193200_c33","doi-asserted-by":"publisher","first-page":"353","DOI":"10.3390\/cryst7120353","article-title":"Freeform phononic waveguides","volume":"7","year":"2017","journal-title":"Crystals"},{"key":"2025070806191193200_c34","doi-asserted-by":"publisher","first-page":"101101","DOI":"10.1063\/5.0059928","article-title":"Wave transport in 1d stealthy hyperuniform phononic materials made of non-resonant and resonant scatterers","volume":"9","year":"2021","journal-title":"APL Mater."},{"key":"2025070806191193200_c35","doi-asserted-by":"publisher","first-page":"053001","DOI":"10.1103\/physreve.102.053001","article-title":"Impact of particle size and multiple scattering on the propagation of waves in stealthy-hyperuniform media","volume":"102","year":"2020","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c36","doi-asserted-by":"publisher","first-page":"064206","DOI":"10.1103\/physrevb.106.064206","article-title":"Experimental characterization of rigid-scatterer hyperuniform distributions for audible acoustics","volume":"106","year":"2022","journal-title":"Phys. Rev. B"},{"key":"2025070806191193200_c37","doi-asserted-by":"publisher","first-page":"285703","DOI":"10.1088\/1361-648x\/ad3b5c","article-title":"Vibrational properties of disordered stealthy hyperuniform 1d atomic chains","volume":"36","year":"2024","journal-title":"J.\u00a0Phys.: Condens. Matter"},{"key":"2025070806191193200_c38","doi-asserted-by":"publisher","first-page":"061302","DOI":"10.1063\/1.4983990","article-title":"Reciprocal space engineering with hyperuniform gold disordered surfaces","volume":"2","year":"2017","journal-title":"APL Photonics"},{"key":"2025070806191193200_c39","doi-asserted-by":"publisher","first-page":"110801","DOI":"10.1063\/1.5124302","article-title":"Engineered hyperuniformity for directional light extraction","volume":"4","year":"2019","journal-title":"APL Photonics"},{"key":"2025070806191193200_c40","doi-asserted-by":"publisher","first-page":"19325","DOI":"10.1038\/srep19325","article-title":"Hyperuniform disordered terahertz quantum cascade laser","volume":"6","year":"2016","journal-title":"Sci. Rep."},{"key":"2025070806191193200_c41","doi-asserted-by":"publisher","first-page":"053507","DOI":"10.1063\/1.5055295","article-title":"Experimental demonstration of luneburg lens based on hyperuniform disordered media","volume":"114","year":"2019","journal-title":"Appl. Phys. Lett."},{"key":"2025070806191193200_c42","doi-asserted-by":"publisher","first-page":"014062","DOI":"10.1103\/physrevapplied.15.014062","article-title":"Extraordinary directive emission and scanning from an array of radiation sources with hyperuniform disorder","volume":"15","year":"2021","journal-title":"Phys. Rev. Appl."},{"key":"2025070806191193200_c43","doi-asserted-by":"publisher","first-page":"054035","DOI":"10.1103\/physrevapplied.19.054035","article-title":"Hyperuniform disordered parametric loudspeaker array","volume":"19","year":"2023","journal-title":"Phys. Rev. Appl."},{"key":"2025070806191193200_c44","doi-asserted-by":"publisher","first-page":"101601","DOI":"10.1063\/5.0041911","article-title":"Hyperuniform disordered distribution metasurface for scattering reduction","volume":"118","year":"2021","journal-title":"Appl. Phys. Lett."},{"key":"2025070806191193200_c45","doi-asserted-by":"publisher","first-page":"1878","DOI":"10.1080\/17455030.2021.1948630","article-title":"Stealth and equiluminous materials for scattering cancellation and wave diffusion","volume":"34","year":"2021","journal-title":"Waves Random Complex Media"},{"key":"2025070806191193200_c46","first-page":"1","article-title":"Hyperuniform disordered sparse array for 3d ultrasound imaging","year":"2023"},{"key":"2025070806191193200_c47","doi-asserted-by":"publisher","first-page":"6197","DOI":"10.1039\/c7sm01028a","article-title":"Can exotic disordered \u2018stealthy\u2019 particle configurations tolerate arbitrarily large holes?","volume":"13","year":"2017","journal-title":"Soft Matter"},{"key":"2025070806191193200_c48","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00220-018-3226-5","article-title":"Generalized stealthy hyperuniform processes: Maximal rigidity and the bounded holes conjecture","volume":"363","year":"2018","journal-title":"Commun. Math. Phys."},{"key":"2025070806191193200_c49","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1007\/s10955-012-0619-2","article-title":"Exotic ground states of directional pair potentials via collective-density variables","volume":"150","year":"2013","journal-title":"J.\u00a0Stat. Phys."},{"key":"2025070806191193200_c50","doi-asserted-by":"publisher","first-page":"022122","DOI":"10.1103\/physreve.94.022122","article-title":"Hyperuniformity and its generalizations","volume":"94","year":"2016","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c53","doi-asserted-by":"publisher","first-page":"36963","DOI":"10.1038\/srep36963","article-title":"The perfect glass paradigm: Disordered hyperuniform glasses down to absolute zero","volume":"6","year":"2016","journal-title":"Sci. Rep."},{"key":"2025070806191193200_c54","doi-asserted-by":"publisher","first-page":"033190","DOI":"10.1103\/physrevresearch.5.033190","article-title":"Generating large disordered stealthy hyperuniform systems with ultrahigh accuracy to determine their physical properties","volume":"5","year":"2023","journal-title":"Phys. Rev. Res."},{"key":"2025070806191193200_c55","doi-asserted-by":"publisher","first-page":"034122","DOI":"10.1103\/physreve.110.034122","article-title":"Fast generation of spectrally shaped disorder","volume":"110","year":"2024","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c57","doi-asserted-by":"publisher","first-page":"103302","DOI":"10.1088\/1742-5468\/abb8cb","article-title":"Nearest-neighbor functions for disordered stealthy hyperuniform many-particle systems","volume":"2020","journal-title":"J.\u00a0Stat. Mech."},{"key":"2025070806191193200_c58","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1364\/ome.507918","article-title":"Theoretical prediction of the effective dynamic dielectric constant of disordered hyperuniform anisotropic composites beyond the long-wavelength regime [Invited]","volume":"14","year":"2024","journal-title":"Opt. Mater. Express"},{"key":"2025070806191193200_c59","doi-asserted-by":"publisher","first-page":"2064","DOI":"10.1103\/physrevlett.84.2064","article-title":"Is random close packing of spheres well defined?","volume":"84","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c60","doi-asserted-by":"publisher","first-page":"090604","DOI":"10.1103\/physrevlett.95.090604","article-title":"Unexpected density fluctuations in jammed disordered sphere packings","volume":"95","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c61","doi-asserted-by":"publisher","first-page":"064602","DOI":"10.1103\/physreve.108.064602","article-title":"Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions","volume":"108","year":"2023","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c62","doi-asserted-by":"crossref","unstructured":"S.\n            Torquato\n           and J.Kim, \u201cExistence of nonequilibrium glasses in the degenerate stealthy hyperuniform ground-state manifold,\u201d Soft Matter21(24), 4898\u20134907 (2025).10.1039\/D5SM00379B","DOI":"10.1039\/D5SM00379B"},{"key":"2025070806191193200_c63","doi-asserted-by":"publisher","first-page":"103565","DOI":"10.1016\/j.advwatres.2020.103565","article-title":"Predicting transport characteristics of hyperuniform porous media via rigorous microstructure-property relations","volume":"140","year":"2020","journal-title":"Adv. Water Resour."},{"key":"2025070806191193200_c64","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1080\/10586458.2006.10128964","article-title":"New conjectural lower bounds on the optimal density of sphere packings","volume":"15","year":"2006","journal-title":"Exp. Math."},{"key":"2025070806191193200_c65","doi-asserted-by":"crossref","DOI":"10.1007\/1-4020-4415-1","volume-title":"Extremes in Nature: An Approach Using Copulas","author":"Salvadori","year":"2007"},{"key":"2025070806191193200_c66","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1111\/insr.12058","article-title":"Extreme value theory and statistics of univariate extremes: A review","volume":"83","year":"2015","journal-title":"Int. Stat. Rev."},{"key":"2025070806191193200_c67","doi-asserted-by":"publisher","first-page":"P12015","DOI":"10.1088\/1742-5468\/2009\/12\/p12015","article-title":"Hyperuniformity in point patterns and two-phase random heterogeneous media","volume":"2009","journal-title":"J.\u00a0Stat. Mech.: Theory Exp."},{"key":"2025070806191193200_c68","doi-asserted-by":"publisher","first-page":"052126","DOI":"10.1103\/physreve.103.052126","article-title":"Structural characterization of many-particle systems on approach to hyperuniform states","volume":"103","year":"2021","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c69","doi-asserted-by":"publisher","first-page":"011306","DOI":"10.1103\/physreve.68.011306","article-title":"Jamming at zero temperature and zero applied stress: The epitome of disorder","volume":"68","year":"2003","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c70","doi-asserted-by":"publisher","first-page":"184205","DOI":"10.1103\/physrevb.83.184205","article-title":"Approximate analytical description of the nonaffine response of amorphous solids","volume":"83","year":"2011","journal-title":"Phys. Rev. B"},{"key":"2025070806191193200_c71","doi-asserted-by":"publisher","first-page":"205501","DOI":"10.1103\/physrevlett.109.205501","article-title":"Universal microstructure and mechanical stability of jammed packings","volume":"109","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c72","doi-asserted-by":"publisher","first-page":"e2021794118","DOI":"10.1073\/pnas.2021794118","article-title":"A jamming plane of sphere packings","volume":"118","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2025070806191193200_c73","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198570837.003.0020","article-title":"Satisfiability","volume-title":"Information, Physics, and Computation","author":"M\u00e9zard","year":"2009"},{"key":"2025070806191193200_c74","doi-asserted-by":"publisher","first-page":"019","DOI":"10.21468\/scipostphys.2.3.019","article-title":"Universality of the sat-unsat (jamming) threshold in non-convex continuous constraint satisfaction problems","volume":"2","year":"2017","journal-title":"SciPost Phys."},{"key":"2025070806191193200_c76","doi-asserted-by":"publisher","first-page":"773","DOI":"10.2307\/2006193","article-title":"Updating quasi-Newton matrices with limited storage","volume":"35","year":"1980","journal-title":"Math. Comput."},{"key":"2025070806191193200_c77","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/bf01589116","article-title":"On the limited memory BFGS method for large scale optimization","volume":"45","year":"1989","journal-title":"Math. Program."},{"key":"2025070806191193200_c79","doi-asserted-by":"publisher","first-page":"124509","DOI":"10.1063\/1.2775928","article-title":"Configurational entropy of binary hard-disk glasses: Nonexistence of an ideal glass transition","volume":"127","year":"2007","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025070806191193200_c80","doi-asserted-by":"publisher","first-page":"020901","DOI":"10.1063\/1.5036657","article-title":"Perspective: Basic understanding of condensed phases of matter via packing models","volume":"149","year":"2018","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025070806191193200_c81","doi-asserted-by":"publisher","first-page":"1634","DOI":"10.1103\/physrevlett.81.1634","article-title":"Isostatic phase transition and instability in stiff granular materials","volume":"81","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"2025070806191193200_c82","doi-asserted-by":"publisher","first-page":"011105","DOI":"10.1103\/physreve.71.011105","article-title":"Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings","volume":"71","year":"2005","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c84","unstructured":"C.\n            Vanoni\n          , J.Kim, P. J.Steinhardt, and S.Torquato, \u201cDynamical properties of particulate composites derived from ultradense stealthy hyperuniform sphere packings,\u201d Phys. Rev. E (in press) (2025)."},{"key":"2025070806191193200_c85","doi-asserted-by":"publisher","first-page":"7689","DOI":"10.3390\/ma7127689","article-title":"Effective interactions between multilayered ionic microgels","volume":"7","year":"2014","journal-title":"Materials"},{"key":"2025070806191193200_c86","doi-asserted-by":"publisher","first-page":"126601","DOI":"10.1088\/1361-6633\/aad1a7","article-title":"Assembly of colloidal particles in solution","volume":"81","year":"2018","journal-title":"Rep. Prog. Phys."},{"key":"2025070806191193200_c87","doi-asserted-by":"publisher","first-page":"033502","DOI":"10.1088\/1468-6996\/16\/3\/033502","article-title":"A review on powder-based additive manufacturing for tissue engineering: Selective laser sintering and inkjet 3d printing","volume":"16","year":"2015","journal-title":"Sci. Technol. Adv. Mater."},{"key":"2025070806191193200_c88","doi-asserted-by":"publisher","first-page":"5756563","DOI":"10.1155\/2021\/5756563","article-title":"3d printing manufacturing techniques, materials, and applications: An overview","volume":"2021","journal-title":"Adv. Mater. Sci. Eng."},{"key":"2025070806191193200_c89","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.actamat.2019.01.026","article-title":"New tessellation-based procedure to design perfectly hyperuniform disordered dispersions for materials discovery","volume":"168","year":"2019","journal-title":"Acta Mater."},{"key":"2025070806191193200_c90","doi-asserted-by":"publisher","first-page":"061302","DOI":"10.1103\/physreve.82.061302","article-title":"Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming","volume":"82","year":"2010","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c91","doi-asserted-by":"publisher","first-page":"012902","DOI":"10.1103\/physreve.94.012902","article-title":"Critical slowing down and hyperuniformity on approach to jamming","volume":"94","year":"2016","journal-title":"Phys. Rev. E"},{"key":"2025070806191193200_c92","doi-asserted-by":"publisher","first-page":"414012","DOI":"10.1088\/0953-8984\/28\/41\/414012","article-title":"Disordered hyperuniform heterogeneous materials","volume":"28","year":"2016","journal-title":"J.\u00a0Phys.: Condens. Matter"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0276041\/20582521\/024902_1_5.0276041.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0276041\/20582521\/024902_1_5.0276041.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T06:19:19Z","timestamp":1751955559000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/163\/2\/024902\/3351854\/Ultradense-sphere-packings-derived-from-disordered"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,8]]},"references-count":86,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,7,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0276041","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,7,14]]},"published":{"date-parts":[[2025,7,8]]},"article-number":"024902"}}