{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T13:01:38Z","timestamp":1785416498947,"version":"3.56.0"},"reference-count":12,"publisher":"American Physical Society (APS)","issue":"5","license":[{"start":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T00:00:00Z","timestamp":1763337600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,10,31]]},"abstract":"<jats:p>\n                    We present a class of self-similar solutions describing ultrahigh compression of a uniform-density target by spherically converging, stacked shock waves. Extending the classical Guderley model, we derive a scaling law for the final density of the form\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <a:mrow>\n                        <a:msub>\n                          <a:mi>\u03c1<\/a:mi>\n                          <a:mi>r<\/a:mi>\n                        <\/a:msub>\n                        <a:mo>\/<\/a:mo>\n                        <a:msub>\n                          <a:mi>\u03c1<\/a:mi>\n                          <a:mn>0<\/a:mn>\n                        <\/a:msub>\n                        <a:mo>\u221d<\/a:mo>\n                        <a:msup>\n                          <a:mover accent=\"true\">\n                            <a:mi>P<\/a:mi>\n                            <a:mo>\u0302<\/a:mo>\n                          <\/a:mover>\n                          <a:mrow>\n                            <a:mi>\u03b2<\/a:mi>\n                            <a:mo>(<\/a:mo>\n                            <a:mi>N<\/a:mi>\n                            <a:mo>\u2212<\/a:mo>\n                            <a:mn>1<\/a:mn>\n                            <a:mo>)<\/a:mo>\n                          <\/a:mrow>\n                        <\/a:msup>\n                      <\/a:mrow>\n                    <\/a:math>\n                    , where\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <c:mi>N<\/c:mi>\n                    <\/c:math>\n                    is the number of shocks,\n                    <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <d:mover accent=\"true\">\n                        <d:mi>P<\/d:mi>\n                        <d:mo>\u0302<\/d:mo>\n                      <\/d:mover>\n                    <\/d:math>\n                    the stage pressure ratio, and\n                    <f:math xmlns:f=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <f:mi>\u03b2<\/f:mi>\n                    <\/f:math>\n                    a numerical exponent determined by the adiabatic index\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <g:mi>\u03b3<\/g:mi>\n                    <\/g:math>\n                    . One-dimensional hydrodynamic simulations confirm the validity of this scaling across a broad parameter range. Notably, the relation remains accurate even in the strongly nonlinear regime up to\n                    <h:math xmlns:h=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <h:mrow>\n                        <h:mover accent=\"true\">\n                          <h:mi>P<\/h:mi>\n                          <h:mo>\u0302<\/h:mo>\n                        <\/h:mover>\n                        <h:mo>\u223c<\/h:mo>\n                        <h:mn>70<\/h:mn>\n                      <\/h:mrow>\n                    <\/h:math>\n                    , well beyond the perturbative limit, highlighting the robustness and practical relevance of the model. Owing to its volumetric geometry, this compression scheme inherently avoids the Rayleigh-Taylor instability, which typically compromises shell-based implosions, and thereby establishes a theoretical benchmark for instability-free compression in inertial confinement fusion.\n                  <\/jats:p>","DOI":"10.1103\/bbvn-x95v","type":"journal-article","created":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T18:09:24Z","timestamp":1763402964000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Self-similar multishock implosions for ultrahigh compression of matter"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2220-7638","authenticated-orcid":true,"given":"M.","family":"Murakami","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/035t8zc32","id-type":"ROR","asserted-by":"publisher"}],"name":"The University of Osaka"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,11,17]]},"reference":[{"key":"bbvn-x95vCc1R1","first-page":"302","type":"journal-article","volume":"19","author":"G. Guderley","year":"1942","journal-title":"Luftfahrtforschung"},{"key":"bbvn-x95vCc2R1","volume-title":"Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena","author":"B. Ya. Zel' dovich","year":"2002","type":"book"},{"key":"bbvn-x95vCc3R1","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198562641.001.0001","type":"book","volume-title":"The Physics of Inertial Fusion: Beam-Plasma Interaction, Hydrodynamics, Hot Dense Matter","author":"S. Atzeni","year":"2004"},{"key":"bbvn-x95vCc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.075001","type":"journal-article"},{"key":"bbvn-x95vCc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.065102","type":"journal-article"},{"key":"bbvn-x95vCc6R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1772377","type":"journal-article"},{"key":"bbvn-x95vCc7R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.2890123","type":"journal-article"},{"key":"bbvn-x95vCc8R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4876609","type":"journal-article"},{"key":"bbvn-x95vCc9R1","doi-asserted-by":"publisher","DOI":"10.1088\/0029-5515\/16\/1\/001","type":"journal-article"},{"key":"bbvn-x95vCc10R1","doi-asserted-by":"publisher","DOI":"10.1088\/0029-5515\/56\/5\/056010","type":"journal-article"},{"key":"bbvn-x95vCc11R1","doi-asserted-by":"publisher","DOI":"10.3390\/app12031444","type":"journal-article"},{"key":"bbvn-x95vCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.3336","type":"journal-article"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/bbvn-x95v","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/bbvn-x95v\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T18:09:25Z","timestamp":1763402965000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/bbvn-x95v"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,17]]},"references-count":12,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,11]]}},"URL":"https:\/\/doi.org\/10.1103\/bbvn-x95v","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,17]]},"assertion":[{"value":"2025-07-24","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"055206"}}