Models of One-Dimensional Transport

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Proposal #0206733PI: Thomas ChouInstitution: University of California at Los AngelesTitle: Models of One-Dimensional TransportABSTRACTThe proposed research explores the mathematical and physical aspects of particle transport in one-dimensional channels. Mean-field analysis of Asymmetric Exclusion Processes (ASEP) will be studied analytically and extended to include spatially varying pore-particle interactions and time-dependent behavior. A three-state ASEP will also be developed for modeling proton conduction along water wires. Mean-field and Monte Carlo simulations will be used to obtain steady-state proton currents as functions of both proton concentration and electric potential differences across the pore. Finally, an analysis of interacting particle transport across periodically structured pores will be performed. Analogies with commensurate-incommensurate phase transitions will be explored within Frenkel-Kontorowa type models. Pore transport is a general process vital for separations and catalysis technologies, electrochemical applications, and cell function. In the limit of small, molecular-sized pores connecting two particle reservoirs, the motions of the transported species can be restricted to one dimension. One-dimensional pores are reasonable models for an enormous number of systems including ion channels in cells (which mediate electrolyte balance) and zeolites (minerals that are used to separate hydrocarbon products and mediate chemical reactions). Therefore, theoretical models that can predict the rate at which molecules enter and react within structured one-dimensional channels will aid in the design of molecularly tailored pores in both the industrial and biological settings. Computational simulations will be used to validate the proposed theoretical models.