{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T18:08:18Z","timestamp":1789754898256,"version":"4.0.1"},"reference-count":48,"publisher":"National Academy of Sciences","issue":"38","license":[{"start":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T00:00:00Z","timestamp":1789689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000183","name":"DOW | USA | AFC | CCDC | 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":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,9,22]]},"abstract":"<jats:p>\n                    Complete phononic band gaps\u2013frequency intervals that exclude elastic waves of every polarization\u2013have so far been realized only in periodic phononic crystals, whose band structures are direction-dependent and defect-sensitive. Disordered stealthy hyperuniform composites have produced complete and isotropic photonic band gaps, but analogous elastic designs have so far fallen short. Here we show that pushing such composites to the ultradense inclusion packing fractions recently shown to be achievable\u2013using stiff, high-mass-density disk inclusions embedded in a compliant, low-mass-density matrix\u2013breaks this barrier. As inclusion packing fraction\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi>\u03d5<\/mml:mi>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    increases, the in-plane and out-of-plane polarization band gaps widen until they overlap, yielding the first complete and isotropic phononic band gap, which persists for systems as large as\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:mo>=<\/mml:mo>\n                          <mml:mn>4<\/mml:mn>\n                          <mml:mo>,<\/mml:mo>\n                          <mml:mn>000<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    disks. Full-wave finite-element calculations and Rayleigh quotient analysis show that conventional, lower-packing-fraction stealthy hyperuniform composites never achieve this overlap because nearly contacting inclusion pairs and large matrix pore regions keep the two polarization gaps apart. Our analysis further reveals a general microstructural requirement for complete phononic\u2013but not photonic\u2013band gaps: a high-volume-fraction, disconnected stiff phase embedded in a connected compliant matrix. These results establish a route to disordered media with large, direction-independent phononic band gaps for shielding, filtering, and guiding elastic waves across length scales, with potential applications ranging from thermal-phonon management in microdevices to sound, vibration, and seismic-wave insulation.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2622259123","type":"journal-article","created":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T17:35:06Z","timestamp":1789752906000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Large complete and isotropic phononic band gaps in ultradense stealthy hyperuniform composites"],"prefix":"10.1073","volume":"123","author":[{"given":"Murray","family":"Skolnick","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Princeton Materials Institute, Princeton University","place":["Princeton"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3488-1603","authenticated-orcid":false,"given":"Paul J.","family":"Steinhardt","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Princeton University","place":["Princeton"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4614-335X","authenticated-orcid":false,"given":"Salvatore","family":"Torquato","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Princeton Materials Institute, Princeton University","place":["Princeton"]},{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Princeton University","place":["Princeton"]},{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Chemistry, Princeton University","place":["Princeton"]},{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Program in Applied and Computational Mathematics, Princeton University","place":["Princeton"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,9,18]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0038-1098(93)90888-T"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1121\/1.408301"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.110940"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.3012"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1515\/9783110641189"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0042337"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1666713"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature12608"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms4435"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1700027"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.055505"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.77.014301"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1080\/17455030903394568"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.046122"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2961314"},{"key":"e_1_3_4_16_2","first-page":"021020","article-title":"Ensemble theory for stealthy hyperuniform disordered ground states","volume":"5","author":"Torquato S.","year":"2015","unstructured":"S. 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