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A Numerical Study of the Stochastic Reaction-Diffusion Master Equation Using Tensors and Parallelism with Application to Biological Models.

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dc.contributorSun, Min
dc.contributorHalpern, David
dc.contributorRasoulzadeh, Mojdeh
dc.contributorSadkane, Miloud
dc.contributor.advisorSidje, Roger B.
dc.contributor.authorRahman, Md Mustafijur
dc.date.accessioned2025-06-10T16:32:09Z
dc.date.available2025-06-10T16:32:09Z
dc.date.issued2025
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractBiological systems often exhibit both stochasticity in chemical reactions and spatial diffusion of molecules, making their modeling inherently complex. The Reaction-Diffusion Master Equation (RDME) provides a stochastic framework to describe such systems by partitioning space into compartments and considering well-mixed species within each. Compared to the Chemical Master Equation (CME), the RDME introduces a significantly larger state space due to the inclusion of jump processes between compartments. The Stochastic Simulation Algorithm (SSA) is commonly used for CME analysis, but is computationally intensive for large-scale systems, which grow worse in RDME problems. Given this complexity, efficient numerical methods are crucial for analyzing and predicting the dynamics of the systems. In this dissertation, we explore biological models using the RDME formulation and leverage tensor-based techniques to manage the large state space efficiently. Tensors, as multidimensional arrays, offer powerful mechanisms for processing and analyzing data in complex biological systems, making them well-suited for RDME applications. To address the computational challenges associated with simulating RDME trajectories over time with the SSA, we implement a parallelized approach using OpenMP with FORTRAN, distributing computations across multiple processors to enhance efficiency. Building on tensor-based methods and high-performance computing, our study aims to significantly accelerate RDME simulations while maintaining accuracy. Advanced numerical techniques enable more effective modeling of stochastic reaction-diffusion systems, providing deeper insights into the dynamics of biological processes.en_US
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.other1143696
dc.identifier.urihttps://ir.ua.edu/handle/123456789/16719
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectChemical Master Equation
dc.subjectMetapopulation Model
dc.subjectParallel Computing
dc.subjectReaction Diffusion Master Equation
dc.subjectStochastic Simulation Algorithm
dc.subjectTensor Train Decomposition
dc.titleA Numerical Study of the Stochastic Reaction-Diffusion Master Equation Using Tensors and Parallelism with Application to Biological Models.en_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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