Models of One-Dimensional Transport

提案#0206733PI：Thomas ChouInstitution：加州大学洛杉矶分校题目：一维传输的模型摘要拟议的研究探索了一维通道中粒子传输的数学和物理方面。不对称排斥过程的平均场分析(ASEP)将被解析地研究，并扩展到包括空间变化的孔-颗粒相互作用和时间相关的行为。还将开发一个三态ASEP来模拟沿水线的质子传导。平均场和蒙特卡罗模拟将被用来获得作为质子浓度和跨孔电位差的函数的稳态质子电流。最后，将对周期性结构孔隙中相互作用的颗粒传输进行分析。我们将在Frenkel-Kontorowa类型的模型中探索公度-非公度相变的类比。孔传输是一个对分离和催化技术、电化学应用和电池功能至关重要的一般过程。在连接两个颗粒储存库的分子大小的小孔的限制下，所传输的物质的运动可以限制在一个维度上。一维孔是大量系统的合理模型，包括细胞中的离子通道(调节电解质平衡)和沸石(用于分离碳氢化合物和调节化学反应的矿物)。因此，能够预测分子进入结构化一维通道并在其中进行反应的速率的理论模型将有助于在工业和生物环境中设计分子定制的孔。计算模拟将被用来验证所提出的理论模型。

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.