{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115665"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115665","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stochastic green’s function method for the statistical analysis of wave chaotic systems","abstract":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-05-01","abstract_has_math":false,"creators":["Lin, Shen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Peng, Zhen","Jin, Jianming","Bernhard, Jennifer Truman","Zhao, Yang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:54Z","subjects":["Stochastic Green's function","Wave chaos","Electromagnetic coupling","Scalar","Vector","Stochastic integral equation","Statistics","Intentional electromagnetic interfere","MIMO"],"languages":["en","eng"],"rights":["Copyright 2022 Shen Lin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115665","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Peng, Zhen","Jin, Jianming","Bernhard, Jennifer Truman","Zhao, Yang"]},{"key":"dc:creator","label":"Author","values":["Lin, Shen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-03-02"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"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":["Stochastic Green's function","Wave chaos","Electromagnetic coupling","Scalar","Vector","Stochastic integral equation","Statistics","Intentional electromagnetic interfere","MIMO"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Shen Lin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115665"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-05-01","The student, Shen Lin, accepted the attached license on 2022-03-01 at 20:06.","The student, Shen Lin, submitted this Dissertation for approval on 2022-03-01 at 20:32.","This Dissertation was approved for publication on 2022-03-02 at 14:51.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17517 on 2022-11-11 at 12:18:30","There is a long-standing need for the statistical description of complex wave systems displaying ray chaotic dynamics. This thesis presents a stochastic Green’s function (SGF) method for wave interaction within wave-chaotic media, which quantitatively describes generic statistical properties of wave scattering dynamics rather than detailed specifics inside the system. The statistically fluctuating (random) portion of the Green’s function is characterized by random wave model and random matrix theory. The formulation rigorously characterizes coherent and incoherent propagation within a comprehensive form. Built upon the stochastic Green’s function, we have derived a stochastic integral equation method, and a hybrid formulation to incorporate the component-specific attributes. The extensions of the SGF method are discussed next: The vector dyadic SGF approach is proposed to study the correlations of the boundary fields and predict the statistics of vector EM fields; the Broadband SGF approach is developed to investigate spectral-spatial correlations of wave propagation. Finally, we extend the theory of SGF from the spatial domain to the spatio-temporal domain to characterize both spatial and temporal variations and correlations of EM fields in the fully developed wave-chaotic dynamics. The model enables a spatio-temporal statistical analysis of chaotic wave dynamics without the need for detailed knowledge of the complex environment. The proposed models are evaluated and validated through representative experiments."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Stochastic green’s function method for the statistical analysis of wave chaotic systems"]}]}],"canonical_facts":{"dc:contributor":["Peng, Zhen","Jin, Jianming","Bernhard, Jennifer Truman","Zhao, Yang"],"dc:creator":["Lin, Shen"],"dc:date":["2022-05","2022-03-02"],"dc:description":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-05-01","The student, Shen Lin, accepted the attached license on 2022-03-01 at 20:06.","The student, Shen Lin, submitted this Dissertation for approval on 2022-03-01 at 20:32.","This Dissertation was approved for publication on 2022-03-02 at 14:51.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17517 on 2022-11-11 at 12:18:30","There is a long-standing need for the statistical description of complex wave systems displaying ray chaotic dynamics. This thesis presents a stochastic Green’s function (SGF) method for wave interaction within wave-chaotic media, which quantitatively describes generic statistical properties of wave scattering dynamics rather than detailed specifics inside the system. The statistically fluctuating (random) portion of the Green’s function is characterized by random wave model and random matrix theory. The formulation rigorously characterizes coherent and incoherent propagation within a comprehensive form. Built upon the stochastic Green’s function, we have derived a stochastic integral equation method, and a hybrid formulation to incorporate the component-specific attributes. The extensions of the SGF method are discussed next: The vector dyadic SGF approach is proposed to study the correlations of the boundary fields and predict the statistics of vector EM fields; the Broadband SGF approach is developed to investigate spectral-spatial correlations of wave propagation. Finally, we extend the theory of SGF from the spatial domain to the spatio-temporal domain to characterize both spatial and temporal variations and correlations of EM fields in the fully developed wave-chaotic dynamics. The model enables a spatio-temporal statistical analysis of chaotic wave dynamics without the need for detailed knowledge of the complex environment. The proposed models are evaluated and validated through representative experiments."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115665"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Shen Lin"],"dc:subject":["Stochastic Green's function","Wave chaos","Electromagnetic coupling","Scalar","Vector","Stochastic integral equation","Statistics","Intentional electromagnetic interfere","MIMO"],"dc:title":["Stochastic green’s function method for the statistical analysis of wave chaotic systems"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:54Z"}