{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105766"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105766","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A viscoelastic hydrodynamic approach to the density fluctuations in classical liquids","abstract":"The liquid state of matter, an intermediate phase between gas and solid, is ubiquitous on earth. Due to the interplay of strong interatomic potential and large configuration entropy, a liquid exhibits rich patterns of dynamic processes over a wide range of length scales and time scales. Largely for this reason, developing a molecular theory of simple liquids still remains a notoriously challenging topic of statistical mechanics. Fortunately, the advancement of formal theories and experimental techniques over the centuries has directed the current research to focus on the description of time correlation functions which establish a link between microscopic dynamics and macroscopic properties. Previous treatments of the time correlation functions mainly focused on a bottom-up, from microscopic to macroscopic, perspective. This work, instead, investigates the inverse perspective adopted in the generalized hydrodynamics and extends the macroscopic hydrodynamic theory to the shorter-wavelength and higher-frequency regime. Specifically, in this work, a viscoelastic hydrodynamic approach is proposed to describe the density fluctuations in supercooled liquids in the generalized hydrodynamic regime. Based on the generalization of the Navier-Stokes stress-strain constitutive relation, the viscoelastic temporal response and spatial anisotropic effect are integrated into the framework of the hydrodynamic theory with the utilization of a time-dependent fourth-order relaxation tensor. This relaxation tensor provides a unified representation to examine the effects of different viscoelastic mechanisms and anisotropy. Given specific approximations to the relaxation tensor by viscoelastic models, the collective modes responsible for the density and current fluctuations could be derived accordingly at small wavenumbers. Based on the examinations of two fundamental viscoelastic models, namely, the Kelvin-Voigt model and the Maxwell model, it is found that viscoelasticity modifies the number and the values of the collective modes compared to the hydrodynamic results. In particular, depending on specific viscoelastic responses, either transverse excitations or transverse kinetic relaxations may be sustained. Moreover, it is demonstrated that anisotropy naturally leads to a hybrid contribution of longitudinal dynamics and transverse dynamics to the density correlation functions and the current correlation functions. Based on these results, an important perspective is suggested, that is, the puzzling low-frequency boson peak and the beta-relaxation may be different manifestations of the transverse modes in liquids with different fragility. In a parallel manner, the idea of viscoelastic hydrodynamics is also applied to describe the density fluctuations associated with self motions by generalizing the Fick's law with a time-dependent diffusion tensor. To further characterize the underlying modes of time correlation functions outside the hydrodynamic regime, a relaxation-excitation mode analysis is proposed, following the mathematical structure of the hydrodynamic correlation functions. The method projects a time correlation function into a distribution function of relaxation-excitation modes via a joint Fourier-Laplace transform, which could be numerically inverted to extract the most probable modes. Using computer simulations and quasi-elastic neutron scattering measurements, it is demonstrated that this method could serve as an effective numerical scheme to gain insights from the data of complex systems, especially when no appropriate theoretical models are available for the data fitting.","abstract_html":"The liquid state of matter, an intermediate phase between gas and solid, is ubiquitous on earth. Due to the interplay of strong interatomic potential and large configuration entropy, a liquid exhibits rich patterns of dynamic processes over a wide range of length scales and time scales. Largely for this reason, developing a molecular theory of simple liquids still remains a notoriously challenging topic of statistical mechanics. Fortunately, the advancement of formal theories and experimental techniques over the centuries has directed the current research to focus on the description of time correlation functions which establish a link between microscopic dynamics and macroscopic properties. Previous treatments of the time correlation functions mainly focused on a bottom-up, from microscopic to macroscopic, perspective. This work, instead, investigates the inverse perspective adopted in the generalized hydrodynamics and extends the macroscopic hydrodynamic theory to the shorter-wavelength and higher-frequency regime. Specifically, in this work, a viscoelastic hydrodynamic approach is proposed to describe the density fluctuations in supercooled liquids in the generalized hydrodynamic regime. Based on the generalization of the Navier-Stokes stress-strain constitutive relation, the viscoelastic temporal response and spatial anisotropic effect are integrated into the framework of the hydrodynamic theory with the utilization of a time-dependent fourth-order relaxation tensor. This relaxation tensor provides a unified representation to examine the effects of different viscoelastic mechanisms and anisotropy. Given specific approximations to the relaxation tensor by viscoelastic models, the collective modes responsible for the density and current fluctuations could be derived accordingly at small wavenumbers. Based on the examinations of two fundamental viscoelastic models, namely, the Kelvin-Voigt model and the Maxwell model, it is found that viscoelasticity modifies the number and the values of the collective modes compared to the hydrodynamic results. In particular, depending on specific viscoelastic responses, either transverse excitations or transverse kinetic relaxations may be sustained. Moreover, it is demonstrated that anisotropy naturally leads to a hybrid contribution of longitudinal dynamics and transverse dynamics to the density correlation functions and the current correlation functions. Based on these results, an important perspective is suggested, that is, the puzzling low-frequency boson peak and the beta-relaxation may be different manifestations of the transverse modes in liquids with different fragility. In a parallel manner, the idea of viscoelastic hydrodynamics is also applied to describe the density fluctuations associated with self motions by generalizing the Fick's law with a time-dependent diffusion tensor. To further characterize the underlying modes of time correlation functions outside the hydrodynamic regime, a relaxation-excitation mode analysis is proposed, following the mathematical structure of the hydrodynamic correlation functions. The method projects a time correlation function into a distribution function of relaxation-excitation modes via a joint Fourier-Laplace transform, which could be numerically inverted to extract the most probable modes. Using computer simulations and quasi-elastic neutron scattering measurements, it is demonstrated that this method could serve as an effective numerical scheme to gain insights from the data of complex systems, especially when no appropriate theoretical models are available for the data fitting.","abstract_has_math":false,"creators":["Cai, Zhikun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear, Plasma, Radiolgc Engr","degree_department":null,"school":null,"contributors":["Zhang, Yang","Heuser, Brent J","Uddin, Rizwan","Aksimentiev, Aleksei"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:49:16Z","date_published":"2019-11-26T20:49:16Z","updated_at":"2026-07-22T22:24:45Z","subjects":["liquids","generalized hydrodynamics","viscoelasticity","anisotropy","relaxation tensor","transverse modes","collective excitations","beta-relaxation"],"languages":["en"],"rights":["Copyright 2019 Zhikun Cai"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105766","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zhang, Yang","Heuser, Brent J","Uddin, Rizwan","Aksimentiev, Aleksei"]},{"key":"dc:creator","label":"Author","values":["Cai, Zhikun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:49:16Z","2021-11-27T10:15:26Z","2019-07-01","2019-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear, Plasma, Radiolgc 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":["liquids","generalized hydrodynamics","viscoelasticity","anisotropy","relaxation tensor","transverse modes","collective excitations","beta-relaxation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Zhikun Cai"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105766"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The liquid state of matter, an intermediate phase between gas and solid, is ubiquitous on earth. Due to the interplay of strong interatomic potential and large configuration entropy, a liquid exhibits rich patterns of dynamic processes over a wide range of length scales and time scales. Largely for this reason, developing a molecular theory of simple liquids still remains a notoriously challenging topic of statistical mechanics. Fortunately, the advancement of formal theories and experimental techniques over the centuries has directed the current research to focus on the description of time correlation functions which establish a link between microscopic dynamics and macroscopic properties. Previous treatments of the time correlation functions mainly focused on a bottom-up, from microscopic to macroscopic, perspective. This work, instead, investigates the inverse perspective adopted in the generalized hydrodynamics and extends the macroscopic hydrodynamic theory to the shorter-wavelength and higher-frequency regime. Specifically, in this work, a viscoelastic hydrodynamic approach is proposed to describe the density fluctuations in supercooled liquids in the generalized hydrodynamic regime. Based on the generalization of the Navier-Stokes stress-strain constitutive relation, the viscoelastic temporal response and spatial anisotropic effect are integrated into the framework of the hydrodynamic theory with the utilization of a time-dependent fourth-order relaxation tensor. This relaxation tensor provides a unified representation to examine the effects of different viscoelastic mechanisms and anisotropy. Given specific approximations to the relaxation tensor by viscoelastic models, the collective modes responsible for the density and current fluctuations could be derived accordingly at small wavenumbers. Based on the examinations of two fundamental viscoelastic models, namely, the Kelvin-Voigt model and the Maxwell model, it is found that viscoelasticity modifies the number and the values of the collective modes compared to the hydrodynamic results. In particular, depending on specific viscoelastic responses, either transverse excitations or transverse kinetic relaxations may be sustained. Moreover, it is demonstrated that anisotropy naturally leads to a hybrid contribution of longitudinal dynamics and transverse dynamics to the density correlation functions and the current correlation functions. Based on these results, an important perspective is suggested, that is, the puzzling low-frequency boson peak and the beta-relaxation may be different manifestations of the transverse modes in liquids with different fragility. In a parallel manner, the idea of viscoelastic hydrodynamics is also applied to describe the density fluctuations associated with self motions by generalizing the Fick's law with a time-dependent diffusion tensor. To further characterize the underlying modes of time correlation functions outside the hydrodynamic regime, a relaxation-excitation mode analysis is proposed, following the mathematical structure of the hydrodynamic correlation functions. The method projects a time correlation function into a distribution function of relaxation-excitation modes via a joint Fourier-Laplace transform, which could be numerically inverted to extract the most probable modes. Using computer simulations and quasi-elastic neutron scattering measurements, it is demonstrated that this method could serve as an effective numerical scheme to gain insights from the data of complex systems, especially when no appropriate theoretical models are available for the data fitting.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2021-08-01","The student, Zhikun Cai, accepted the attached license on 2019-06-26 at 22:25.","The student, Zhikun Cai, submitted this Dissertation for approval on 2019-06-26 at 23:01.","This Dissertation was approved for publication on 2019-07-01 at 12:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14093 on 2019-11-26 at 13:03:51","Made available in DSpace on 2019-11-26T20:49:16Z (GMT). No. of bitstreams: 3 CAI-DISSERTATION-2019.pdf: 9307786 bytes, checksum: 91bf49749bfe2865122ede23b4e61e36 (MD5) source.zip: 15966483 bytes, checksum: 680eb6931bd4f67da44a12d23b414b20 (MD5) LICENSE.txt: 4207 bytes, checksum: b94a9102e1b58a325e11187a664be11f (MD5) Previous issue date: 2019-07-01","Embargo set by: Seth Robbins for item 112911 Lift date: 2021-11-26T20:49:41Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 112911 on 2021-11-27T10:15:26Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A viscoelastic hydrodynamic approach to the density fluctuations in classical liquids"]}]}],"canonical_facts":{"dc:contributor":["Zhang, Yang","Heuser, Brent J","Uddin, Rizwan","Aksimentiev, Aleksei"],"dc:creator":["Cai, Zhikun"],"dc:date":["2019-11-26T20:49:16Z","2021-11-27T10:15:26Z","2019-07-01","2019-08"],"dc:description":["The liquid state of matter, an intermediate phase between gas and solid, is ubiquitous on earth. Due to the interplay of strong interatomic potential and large configuration entropy, a liquid exhibits rich patterns of dynamic processes over a wide range of length scales and time scales. Largely for this reason, developing a molecular theory of simple liquids still remains a notoriously challenging topic of statistical mechanics. Fortunately, the advancement of formal theories and experimental techniques over the centuries has directed the current research to focus on the description of time correlation functions which establish a link between microscopic dynamics and macroscopic properties. Previous treatments of the time correlation functions mainly focused on a bottom-up, from microscopic to macroscopic, perspective. This work, instead, investigates the inverse perspective adopted in the generalized hydrodynamics and extends the macroscopic hydrodynamic theory to the shorter-wavelength and higher-frequency regime. Specifically, in this work, a viscoelastic hydrodynamic approach is proposed to describe the density fluctuations in supercooled liquids in the generalized hydrodynamic regime. Based on the generalization of the Navier-Stokes stress-strain constitutive relation, the viscoelastic temporal response and spatial anisotropic effect are integrated into the framework of the hydrodynamic theory with the utilization of a time-dependent fourth-order relaxation tensor. This relaxation tensor provides a unified representation to examine the effects of different viscoelastic mechanisms and anisotropy. Given specific approximations to the relaxation tensor by viscoelastic models, the collective modes responsible for the density and current fluctuations could be derived accordingly at small wavenumbers. Based on the examinations of two fundamental viscoelastic models, namely, the Kelvin-Voigt model and the Maxwell model, it is found that viscoelasticity modifies the number and the values of the collective modes compared to the hydrodynamic results. In particular, depending on specific viscoelastic responses, either transverse excitations or transverse kinetic relaxations may be sustained. Moreover, it is demonstrated that anisotropy naturally leads to a hybrid contribution of longitudinal dynamics and transverse dynamics to the density correlation functions and the current correlation functions. Based on these results, an important perspective is suggested, that is, the puzzling low-frequency boson peak and the beta-relaxation may be different manifestations of the transverse modes in liquids with different fragility. In a parallel manner, the idea of viscoelastic hydrodynamics is also applied to describe the density fluctuations associated with self motions by generalizing the Fick's law with a time-dependent diffusion tensor. To further characterize the underlying modes of time correlation functions outside the hydrodynamic regime, a relaxation-excitation mode analysis is proposed, following the mathematical structure of the hydrodynamic correlation functions. The method projects a time correlation function into a distribution function of relaxation-excitation modes via a joint Fourier-Laplace transform, which could be numerically inverted to extract the most probable modes. Using computer simulations and quasi-elastic neutron scattering measurements, it is demonstrated that this method could serve as an effective numerical scheme to gain insights from the data of complex systems, especially when no appropriate theoretical models are available for the data fitting.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2021-08-01","The student, Zhikun Cai, accepted the attached license on 2019-06-26 at 22:25.","The student, Zhikun Cai, submitted this Dissertation for approval on 2019-06-26 at 23:01.","This Dissertation was approved for publication on 2019-07-01 at 12:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14093 on 2019-11-26 at 13:03:51","Made available in DSpace on 2019-11-26T20:49:16Z (GMT). No. of bitstreams: 3 CAI-DISSERTATION-2019.pdf: 9307786 bytes, checksum: 91bf49749bfe2865122ede23b4e61e36 (MD5) source.zip: 15966483 bytes, checksum: 680eb6931bd4f67da44a12d23b414b20 (MD5) LICENSE.txt: 4207 bytes, checksum: b94a9102e1b58a325e11187a664be11f (MD5) Previous issue date: 2019-07-01","Embargo set by: Seth Robbins for item 112911 Lift date: 2021-11-26T20:49:41Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 112911 on 2021-11-27T10:15:26Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/105766"],"dc:language":["en"],"dc:rights":["Copyright 2019 Zhikun Cai"],"dc:subject":["liquids","generalized hydrodynamics","viscoelasticity","anisotropy","relaxation tensor","transverse modes","collective excitations","beta-relaxation"],"dc:title":["A viscoelastic hydrodynamic approach to the density fluctuations in classical liquids"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear, Plasma, Radiolgc Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:45Z"}