{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/138271"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/138271","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"First Exit Time Analysis for the Stochastic Reaction Diffusion Process in a One Dimensional Domain","abstract":"Recent advances in modeling stochastic reaction–diffusion (RD) process have focused on particle-based and master equation formulations. While these models offer strong theoretical foundation, a practical challenge remains: how does the choice of spatial discretization affect the accuracy and computational efficiency of simulation results, particularly when estimating first exit times. This thesis addresses this research gap by investigating the accuracy of first exit time estimates in one-dimensional stochastic RD systems. We design and analyze three simplified models using stochastic simulations: (1) model 1: pure diffusion, (2) model 2: diffusion with monomolecular reaction, and (3) model 3: diffusion with bimolecular reaction. We conduct theoretical study for the mean first exit times and evaluate them based on these models. Our results show that strictly following the Gillespie SSA is not necessary to obtain accurate results under certain conditions and a moderate discretizations size (e.g., K ≥ 5) already provides highly accurate estimates for first exit times. Our results can guide efficient and accurate simulation of RD systems.","abstract_html":"Recent advances in modeling stochastic reaction–diffusion (RD) process have focused on particle-based and master equation formulations. While these models offer strong theoretical foundation, a practical challenge remains: how does the choice of spatial discretization affect the accuracy and computational efficiency of simulation results, particularly when estimating first exit times. This thesis addresses this research gap by investigating the accuracy of first exit time estimates in one-dimensional stochastic RD systems. We design and analyze three simplified models using stochastic simulations: (1) model 1: pure diffusion, (2) model 2: diffusion with monomolecular reaction, and (3) model 3: diffusion with bimolecular reaction. We conduct theoretical study for the mean first exit times and evaluate them based on these models. Our results show that strictly following the Gillespie SSA is not necessary to obtain accurate results under certain conditions and a moderate discretizations size (e.g., K ≥ 5) already provides highly accurate estimates for first exit times. Our results can guide efficient and accurate simulation of RD systems.","abstract_has_math":false,"creators":["Zhou, Daodao"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Computer Science & Applications","degree_department":"Computer Science and#38; Applications","school":null,"contributors":[],"advisors":[],"committee_chairs":["Cao, Young"],"committee_members":["Onufriev, Alexey","Sandu, Adrian"],"year":2025,"date_issued":"2025-10-20","date_published":"2025-10-20","updated_at":"2026-07-22T22:19:03Z","subjects":["stochastic simulation","reaction-diffusion processes","first exit time."],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:44772"],"render_values":[{"text":"vt_gsexam:44772","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/138271","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Cao, Young"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Onufriev, Alexey","Sandu, Adrian"]},{"key":"dc:contributor.department","label":"Department","values":["Computer Science and#38; Applications"]},{"key":"dc:creator","label":"Author","values":["Zhou, Daodao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-10-21T08:00:42Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-10-21T08:00:42Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-10-20"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science & Applications"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["stochastic simulation","reaction-diffusion processes","first exit time."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:44772"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/138271"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Recent advances in modeling stochastic reaction–diffusion (RD) process have focused on particle-based and master equation formulations. While these models offer strong theoretical foundation, a practical challenge remains: how does the choice of spatial discretization affect the accuracy and computational efficiency of simulation results, particularly when estimating first exit times. This thesis addresses this research gap by investigating the accuracy of first exit time estimates in one-dimensional stochastic RD systems. We design and analyze three simplified models using stochastic simulations: (1) model 1: pure diffusion, (2) model 2: diffusion with monomolecular reaction, and (3) model 3: diffusion with bimolecular reaction. We conduct theoretical study for the mean first exit times and evaluate them based on these models. Our results show that strictly following the Gillespie SSA is not necessary to obtain accurate results under certain conditions and a moderate discretizations size (e.g., K ≥ 5) already provides highly accurate estimates for first exit times. Our results can guide efficient and accurate simulation of RD systems."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Many natural processes can be described using reaction–diffusion systems. These models often rely on computer simulations to predict when and where particles move or react. One practical question is that: for the computer simulation program, how does the way we divide space or how fine or coarse the grid is affecting the accuracy of the results and the time it takes to compute them? In this thesis, we focus on three simplified models that represent different situations to help answer the question: one with pure diffusion, one where particles can react individually, and one where two types of particles can interact with each other. The results show that simulations do not always need to use the most detailed possible grid to be accurate. Even moderately detailed setups can produce reliable predictions while saving time and computational resources. These findings provide practical guidance for scientists who use computer models to study diffusion and reaction processes efficiently and accurately."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["First Exit Time Analysis for the Stochastic Reaction Diffusion Process in a One Dimensional Domain"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Cao, Young"],"dc:contributor.committeemember":["Onufriev, Alexey","Sandu, Adrian"],"dc:contributor.department":["Computer Science and#38; Applications"],"dc:creator":["Zhou, Daodao"],"dc:date.accessioned":["2025-10-21T08:00:42Z"],"dc:date.available":["2025-10-21T08:00:42Z"],"dc:date.issued":["2025-10-20"],"dc:description.abstract":["Recent advances in modeling stochastic reaction–diffusion (RD) process have focused on particle-based and master equation formulations. While these models offer strong theoretical foundation, a practical challenge remains: how does the choice of spatial discretization affect the accuracy and computational efficiency of simulation results, particularly when estimating first exit times. This thesis addresses this research gap by investigating the accuracy of first exit time estimates in one-dimensional stochastic RD systems. We design and analyze three simplified models using stochastic simulations: (1) model 1: pure diffusion, (2) model 2: diffusion with monomolecular reaction, and (3) model 3: diffusion with bimolecular reaction. We conduct theoretical study for the mean first exit times and evaluate them based on these models. Our results show that strictly following the Gillespie SSA is not necessary to obtain accurate results under certain conditions and a moderate discretizations size (e.g., K ≥ 5) already provides highly accurate estimates for first exit times. Our results can guide efficient and accurate simulation of RD systems."],"dc:description.abstractgeneral":["Many natural processes can be described using reaction–diffusion systems. These models often rely on computer simulations to predict when and where particles move or react. One practical question is that: for the computer simulation program, how does the way we divide space or how fine or coarse the grid is affecting the accuracy of the results and the time it takes to compute them? In this thesis, we focus on three simplified models that represent different situations to help answer the question: one with pure diffusion, one where particles can react individually, and one where two types of particles can interact with each other. The results show that simulations do not always need to use the most detailed possible grid to be accurate. Even moderately detailed setups can produce reliable predictions while saving time and computational resources. These findings provide practical guidance for scientists who use computer models to study diffusion and reaction processes efficiently and accurately."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:44772"],"dc:identifier.uri":["https://hdl.handle.net/10919/138271"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["stochastic simulation","reaction-diffusion processes","first exit time."],"dc:title":["First Exit Time Analysis for the Stochastic Reaction Diffusion Process in a One Dimensional Domain"],"dc:type":["Thesis"],"thesis:degree_discipline":["Computer Science & Applications"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:03Z"}