{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/80929"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/80929","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Mapped Averaging Methods for Highly Efficient Evaluation of Thermodynamic Properties","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Purohit, Apoorva"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Kofke, David","Chemical and Biological Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-10-29T16:48:14Z","date_published":"2019-10-29T16:48:14Z","updated_at":"2026-07-27T19:05:28Z","subjects":["chemical engineering"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/80929","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kofke, David","Chemical and Biological Engineering"]},{"key":"dc:creator","label":"Author","values":["Purohit, Apoorva"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-10-29T16:48:14Z","2019","2019-08-08 16:36:53"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["chemical engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/80929"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","Mapped averaging is a reformulation of ensemble averages that provides alternative, rigorous expressions for computing equilibrium thermodynamic properties with very high efficiency. The framework uses approximate theoretical results derived from statistical mechanical theory to derive new ensemble averages that represent exactly the error in the theory. This does not require any alteration in how sampling is performed during the simulation, so it may be used with standard Monte Carlo or molecular dynamics methods. For crystalline systems, mapped averaging framework enables molecular simulation to compute directly the anharmonic contribution to the thermodynamic properties, without noise contributed by the analytically-known harmonic behavior. The result is a technique called harmonically-mapped averaging (HMA) for computing crystalline properties with transformative efficiency. This thesis describes the recent advances in formulating and applying mapped averaging methods (both for crystals and fluids), and implementing them in molecular simulation packages. Reformulated ensemble averages for measuring the singlet and pair density distributions have been developed, based on sampling the instantaneous forces acting on the particles instead of the conventional histogram binning approach used so far in literature. The new development yields reduced variance of results, achieving a finite variance even when the bin spacing tends to zero. The approach has been applied to Lennard-Jones (LJ) crystals and fluids; in all the examined cases, mapped averaging provides many times higher computational efficiency than histogramming approach. To allow the practitioners of molecular dynamics to easily exploit the tremendous benefits of mapped averaging for crystalline systems, a new LAMMPS class \"computeHMA\" has been created, which calculates the HMA-based results of energy, pressure and their respective anharmonic contributions, during canonical simulations.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Mapped Averaging Methods for Highly Efficient Evaluation of Thermodynamic Properties"]}]}],"canonical_facts":{"dc:contributor":["Kofke, David","Chemical and Biological Engineering"],"dc:creator":["Purohit, Apoorva"],"dc:date":["2019-10-29T16:48:14Z","2019","2019-08-08 16:36:53"],"dc:description":["Ph.D.","Mapped averaging is a reformulation of ensemble averages that provides alternative, rigorous expressions for computing equilibrium thermodynamic properties with very high efficiency. The framework uses approximate theoretical results derived from statistical mechanical theory to derive new ensemble averages that represent exactly the error in the theory. This does not require any alteration in how sampling is performed during the simulation, so it may be used with standard Monte Carlo or molecular dynamics methods. For crystalline systems, mapped averaging framework enables molecular simulation to compute directly the anharmonic contribution to the thermodynamic properties, without noise contributed by the analytically-known harmonic behavior. The result is a technique called harmonically-mapped averaging (HMA) for computing crystalline properties with transformative efficiency. This thesis describes the recent advances in formulating and applying mapped averaging methods (both for crystals and fluids), and implementing them in molecular simulation packages. Reformulated ensemble averages for measuring the singlet and pair density distributions have been developed, based on sampling the instantaneous forces acting on the particles instead of the conventional histogram binning approach used so far in literature. The new development yields reduced variance of results, achieving a finite variance even when the bin spacing tends to zero. The approach has been applied to Lennard-Jones (LJ) crystals and fluids; in all the examined cases, mapped averaging provides many times higher computational efficiency than histogramming approach. To allow the practitioners of molecular dynamics to easily exploit the tremendous benefits of mapped averaging for crystalline systems, a new LAMMPS class \"computeHMA\" has been created, which calculates the HMA-based results of energy, pressure and their respective anharmonic contributions, during canonical simulations.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/80929"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["chemical engineering"],"dc:title":["Mapped Averaging Methods for Highly Efficient Evaluation of Thermodynamic Properties"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:28Z"}