Multi-scale behavior in chemical reaction systems: Modeling, applications, and results

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dc.contributor.advisorCox, Dennis D.
dc.creatorTurner, Jesse Hosea, III
dc.date.accessioned2009-06-03T19:50:56Z
dc.date.available2009-06-03T19:50:56Z
dc.date.issued2008
dc.description.abstractFour major approaches model the time dependent behavior of chemical reaction systems: ordinary differential equations (ODE's), the &tgr;-leap algorithm, stochastic differential equations (SDE's), and Gillespie's stochastic simulation algorithm (SSA). ODE's are simulated the most quickly of these, but are often inaccurate for systems with slow rates and molecular species present in small numbers. Under ideal conditions, the SSA is exact, but computationally inefficient. Unfortunately, many reaction systems exhibit characteristics not well captured individually by any of these methods. Therefore, hybrid models incorporating aspects from all four must be employed. The aim is to construct an approach that is close in accuracy to the SSA, useful for a wide range of reaction system examples, and computationally efficient. The Adaptive Multi-scale Simulation Algorithm (AMSA) uses the SSA for slow reactions, SDE's for medium-speed reactions, ODE's for fast reactions, and the tau-leap algorithm for non-slow reactions involving species small in number. This article introduces AMSA and applies it to examples of reaction systems involving genetic regulation. A thorough review of existing reaction simulation algorithms is included. The computational performance and accuracy of AMSA's molecular distributions are compared to those of the SSA, which is used as the golden standard of accuracy. The use of supercomputers can generate much larger data sets than serial processors in roughly the same amount of computational time. Therefore, multi-processor machines are also employed to assess the accuracy of AMSA simulations.
dc.format.extent126 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS STAT. 2008 TURNER
dc.identifier.citationTurner, Jesse Hosea, III. "Multi-scale behavior in chemical reaction systems: Modeling, applications, and results." (2008) Diss., Rice University. <a href="https://hdl.handle.net/1911/22206">https://hdl.handle.net/1911/22206</a>.
dc.identifier.urihttps://hdl.handle.net/1911/22206
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectMathematics
dc.subjectStatistics
dc.subjectPhysical chemistry
dc.titleMulti-scale behavior in chemical reaction systems: Modeling, applications, and results
dc.typeThesis
dc.type.materialText
thesis.degree.departmentStatistics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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