STUDIES IN APPLIED MATHEMATICS AND STATISTICS

应用数学和统计学研究

• 批准号: 5201612
• 负责人: G H WEISS
• 金额: --
• 依托单位: CENTER FOR INFORMATION TECHNOLOGY
• 依托单位国家: 美国
• 资助国家: 美国
• 起止时间: 至
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/5201612
• 关键词: biophysics; capsid; chemical kinetics; chemical models; lasers; light scattering; mathematical model; nuclear magnetic resonance spectroscopy; statistics /biometry; thermodynamics; water

Several problems have been investigated relating to photon migration in a turbid medium. These were suggested by diagnostic applications of laser technology. The research is aimed at finding a way to incorporate anisotropic scattering effects into transport theory that are not computationally intensive, and therefore both easy to implement and able to provide physical insight. An earlier-published theory of anisotropic scattering in an infinite medium in discrete time has been extended to the continuous time domain. Further work, both theoretical and by simulation, has been carried out on utilizing the telegrapher's equation for this purpose, but this has so far proved to be more difficult than anticipated due to problems in framing appropriate boundary conditions. An approximation scheme has been developed for including the effects of pairwise distance constraints between different amino acids in a protein. This is presently being applied to evaluating the accuracy of structures determined from multidimensional NMR experiments. A next step is that of constructing an R factor for NMR, analogous to that used in crystallography. Seemingly anomalous properties of water such as an increase in diffusion constant with increasing pressure have been analyzed both theoretically and by performing molecular dynamics simulations of a lattice model of a physical system. Thermodynamic arguments have been adduced to show that one need not postulate critical behavior in order to explain anomalous properties. A study has been completed with A.M. Berezhkovskii and A. Szabo on models of chemical reaction rates that generalize the commonly-used Smoluchowski model by taking many-body effects into account as well as allowing for the motion of all species of molecules taking part in the reaction. A model of virus capping has been developed together with J. Spouge and A. Szabo. Aspects of the kinetic properties of the model are presently being investigated.

已经研究了与光子迁移有关的几个问题， 混浊的介质 这些是由诊断应用提出的， 激光技术 这项研究旨在找到一种方法， 各向异性散射效应到输运理论， 计算密集型，因此既易于实现， 来提供物理洞察力。 较早发表的各向异性理论 离散时间无限介质中的散射已扩展到 连续时间域。 进一步的工作，包括理论和 利用电报员方程进行了仿真 为此目的，但迄今为止，这已被证明比 这是由于在制定适当的边界条件方面存在问题。 已经开发了一个近似方案来包括以下因素的影响 蛋白质中不同氨基酸之间的成对距离约束。 这是目前正在应用于评估结构的准确性 由多维NMR实验确定。 下一步是， 构建核磁共振的R因子，类似于中使用的R因子 结晶学 水的看似反常的性质，如扩散的增加 从理论上和实验上都分析了 并通过进行晶格模型的分子动力学模拟， 物理系统。 热力学参数已被引证，以表明 人们不需要假设临界行为来解释 反常的性质 与A.M. Berezhkovskii和A. Szabo在模型上 的化学反应速率，推广了常用的Smoluchowski 考虑多体效应，并考虑 所有参与反应的分子的运动。 病毒加帽模型已经与J. Spouge和 A. Szabo. 目前， 正在调查