This work employs tools and methods from computer science to study clusters comprising a small number N of interacting particles, which are of interest in science, engineering, and nanotechnology. Specifically, the thermodynamics of such clusters is studied using techniques from spectral graph theory (SGT) and machine learning (ML). SGT is used to define the structure of the clusters and ML is used on ensembles of cluster configurations to detect state variables that can be used to model the thermodynamic properties of the system. While the most fundamental description of a cluster is in 3N dimensions, i.e., the Cartesian coordinates of the particles, the ML results demonstrate that sub-spaces of much lower dimension can describe the observed structural motifs. Furthermore, these sub-spaces correlate with meaningful physical variables such as radius of gyration r g and discrete connectivity c, which can be used as state variables in thermodynamic property descriptions. The overarching theme of this thesis is to develop the practice of utilizing data-driven computational techniques to solve problems in natural sciences. Code for this project can be found at https://github.com/AdityaDendukuri/DimReductionThermodynamics.
","abstract_html":"<p>This work employs tools and methods from computer science to study clusters comprising a small number N of interacting particles, which are of interest in science, engineering, and nanotechnology. Specifically, the thermodynamics of such clusters is studied using techniques from spectral graph theory (SGT) and machine learning (ML). SGT is used to define the structure of the clusters and ML is used on ensembles of cluster configurations to detect state variables that can be used to model the thermodynamic properties of the system. While the most fundamental description of a cluster is in 3N dimensions, i.e., the Cartesian coordinates of the particles, the ML results demonstrate that sub-spaces of much lower dimension can describe the observed structural motifs. Furthermore, these sub-spaces correlate with meaningful physical variables such as radius of gyration r g and discrete connectivity c, which can be used as state variables in thermodynamic property descriptions. The overarching theme of this thesis is to develop the practice of utilizing data-driven computational techniques to solve problems in natural sciences. Code for this project can be found at https://github.com/AdityaDendukuri/DimReductionThermodynamics. </p>","abstract_has_math":false,"creators":["Dendukuri, Aditya"],"institution":null,"degree_name":"Master of Science in Computer Science (MS)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Ford, David M.","Luu, Khoa"],"advisors":["Patitz, Matthew J."],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-07-01T07:00:00Z","date_published":"2020-07-01T07:00:00Z","updated_at":"2026-07-24T00:58:53Z","subjects":["Diffusion Maps","Dimensionality Reduction","Neural Networks","Artificial Intelligence and Robotics","Thermodynamics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/3804","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ford, David M.","Luu, Khoa"]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Patitz, Matthew J."]},{"key":"dc:creator","label":"Author","values":["Dendukuri, Aditya"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-02-06T08:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Computer Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Diffusion Maps","Dimensionality Reduction","Neural Networks","Artificial Intelligence and Robotics","Thermodynamics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/3804"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This work employs tools and methods from computer science to study clusters comprising a small number N of interacting particles, which are of interest in science, engineering, and nanotechnology. Specifically, the thermodynamics of such clusters is studied using techniques from spectral graph theory (SGT) and machine learning (ML). SGT is used to define the structure of the clusters and ML is used on ensembles of cluster configurations to detect state variables that can be used to model the thermodynamic properties of the system. While the most fundamental description of a cluster is in 3N dimensions, i.e., the Cartesian coordinates of the particles, the ML results demonstrate that sub-spaces of much lower dimension can describe the observed structural motifs. Furthermore, these sub-spaces correlate with meaningful physical variables such as radius of gyration r g and discrete connectivity c, which can be used as state variables in thermodynamic property descriptions. The overarching theme of this thesis is to develop the practice of utilizing data-driven computational techniques to solve problems in natural sciences. Code for this project can be found at https://github.com/AdityaDendukuri/DimReductionThermodynamics.
"]},{"key":"dc:title","label":"Title","values":["Nonlinear Dimensionality Reduction for the Thermodynamics of Small Clusters of Particles"]}]}],"canonical_facts":{"dc:contributor":["Ford, David M.","Luu, Khoa"],"dc:contributor.advisor":["Patitz, Matthew J."],"dc:creator":["Dendukuri, Aditya"],"dc:date":["2020"],"dc:date.available":["2024-02-06T08:00:00Z"],"dc:description.abstract":["This work employs tools and methods from computer science to study clusters comprising a small number N of interacting particles, which are of interest in science, engineering, and nanotechnology. Specifically, the thermodynamics of such clusters is studied using techniques from spectral graph theory (SGT) and machine learning (ML). SGT is used to define the structure of the clusters and ML is used on ensembles of cluster configurations to detect state variables that can be used to model the thermodynamic properties of the system. While the most fundamental description of a cluster is in 3N dimensions, i.e., the Cartesian coordinates of the particles, the ML results demonstrate that sub-spaces of much lower dimension can describe the observed structural motifs. Furthermore, these sub-spaces correlate with meaningful physical variables such as radius of gyration r g and discrete connectivity c, which can be used as state variables in thermodynamic property descriptions. The overarching theme of this thesis is to develop the practice of utilizing data-driven computational techniques to solve problems in natural sciences. Code for this project can be found at https://github.com/AdityaDendukuri/DimReductionThermodynamics.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/3804"],"dc:subject":["Diffusion Maps","Dimensionality Reduction","Neural Networks","Artificial Intelligence and Robotics","Thermodynamics"],"dc:title":["Nonlinear Dimensionality Reduction for the Thermodynamics of Small Clusters of Particles"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science in Computer Science (MS)"]},"updated_at":"2026-07-24T00:58:53Z"}