{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/20119"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/20119","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Group analysis of shock wave phenomena in solids","abstract":"The group theoretic, or Lie's method of continuous point transformations is applied to the study of shock wave propagation through solid media. Theoretically, this method allows for the systematic investigation of all solutions of the set of governing partial differential flow equations that leave the original set of equations invariant.","abstract_html":"The group theoretic, or Lie's method of continuous point transformations is applied to the study of shock wave propagation through solid media. Theoretically, this method allows for the systematic investigation of all solutions of the set of governing partial differential flow equations that leave the original set of equations invariant.","abstract_has_math":false,"creators":["Hrbek, George Michael"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear, Plasma, and Radiological Engineering","degree_department":null,"school":null,"contributors":["Axford, Roy A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:29:25Z","date_published":"2011-05-07T12:29:25Z","updated_at":"2026-07-22T22:25:15Z","subjects":["Engineering, Nuclear","Physics, Condensed Matter","Physics, Fluid and Plasma"],"languages":["eng"],"rights":["Copyright 1992 Hrbek, George Michael"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9305557","(UMI)AAI9305557"],"render_values":[{"text":"AAI9305557","href":null,"code":true},{"text":"(UMI)AAI9305557","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/20119","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Axford, Roy A."]},{"key":"dc:creator","label":"Author","values":["Hrbek, George Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:29:25Z","10000-01-01","1992"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear, Plasma, and Radiological Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Nuclear","Physics, Condensed Matter","Physics, Fluid and Plasma"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1992 Hrbek, George Michael"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9305557","(UMI)AAI9305557","http://hdl.handle.net/2142/20119"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The group theoretic, or Lie's method of continuous point transformations is applied to the study of shock wave propagation through solid media. Theoretically, this method allows for the systematic investigation of all solutions of the set of governing partial differential flow equations that leave the original set of equations invariant.","This method is applied to determine the invariance properties of three different problems.","First the cold compression case is analyzed for a general one-dimensional geometry (j = 0,1,2), then for each of the individual cases of rectangular (j = 0), cylindrical (j = 1), and spherical geometries (j = 2). This analysis explores mathematical forms of the specific internal energy which are functions of the density only.","An important example of cold compression with a Mie potential is the Lennard-Jones 6-12 Potential. This next problem is explored for the general geometry condition. Each of the separate geometries is then examined individually.","Finally, an analysis of the adiabatic shock wave problem involving an arbitrary adiabatic bulk modulus K$\\sb{\\rm s}$ is performed. This system is explored for the general geometry condition, and then for each of the specific geometries separately.","Once the invariance properties are determined, the group generator is used to transform the governing equations from first order, linear, hyperbolic partial differential equations to non-linear, first order, ordinary differential equations.","Classical self-similar motion for a spherical explosion is recovered as a subcase of the general motion. Numerical modeling of these reduced equations is used to validate the analysis.","Knowledge of the invariance properties of the self-similar problem permits the study of a possible equation of state for aluminum, copper, and lead.","Made available in DSpace on 2011-05-07T12:29:25Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9305557.pdf: 5474748 bytes, checksum: fc228a7014230489c64e4239035f0f73 (MD5) Previous issue date: 1992","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:41:42Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:18:04-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Group analysis of shock wave phenomena in solids"]}]}],"canonical_facts":{"dc:contributor":["Axford, Roy A."],"dc:creator":["Hrbek, George Michael"],"dc:date":["2011-05-07T12:29:25Z","10000-01-01","1992"],"dc:description":["The group theoretic, or Lie's method of continuous point transformations is applied to the study of shock wave propagation through solid media. Theoretically, this method allows for the systematic investigation of all solutions of the set of governing partial differential flow equations that leave the original set of equations invariant.","This method is applied to determine the invariance properties of three different problems.","First the cold compression case is analyzed for a general one-dimensional geometry (j = 0,1,2), then for each of the individual cases of rectangular (j = 0), cylindrical (j = 1), and spherical geometries (j = 2). This analysis explores mathematical forms of the specific internal energy which are functions of the density only.","An important example of cold compression with a Mie potential is the Lennard-Jones 6-12 Potential. This next problem is explored for the general geometry condition. Each of the separate geometries is then examined individually.","Finally, an analysis of the adiabatic shock wave problem involving an arbitrary adiabatic bulk modulus K$\\sb{\\rm s}$ is performed. This system is explored for the general geometry condition, and then for each of the specific geometries separately.","Once the invariance properties are determined, the group generator is used to transform the governing equations from first order, linear, hyperbolic partial differential equations to non-linear, first order, ordinary differential equations.","Classical self-similar motion for a spherical explosion is recovered as a subcase of the general motion. Numerical modeling of these reduced equations is used to validate the analysis.","Knowledge of the invariance properties of the self-similar problem permits the study of a possible equation of state for aluminum, copper, and lead.","Made available in DSpace on 2011-05-07T12:29:25Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9305557.pdf: 5474748 bytes, checksum: fc228a7014230489c64e4239035f0f73 (MD5) Previous issue date: 1992","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:41:42Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:18:04-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9305557","(UMI)AAI9305557","http://hdl.handle.net/2142/20119"],"dc:language":["eng"],"dc:rights":["Copyright 1992 Hrbek, George Michael"],"dc:subject":["Engineering, Nuclear","Physics, Condensed Matter","Physics, Fluid and Plasma"],"dc:title":["Group analysis of shock wave phenomena in solids"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear, Plasma, and Radiological Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:15Z"}