STUDIES IN MATHEMATICS AND STATISTICS

数学和统计学研究

• 批准号: 3916951
• 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/3916951
• 关键词: chemical kinetics; chemical reaction; density; diffusion; mathematical model; mathematics; model design /development; molecular weight; polymers; solutions; statistics /biometry; viscosity

The two major themes in this project involve transport in disordered media and the development of models for reaction kinetics in chemistry. In addition to work on these, some time was spent on the calculation of the dependence of the relaxation time for the transition from elastic viscosity to plastic viscosity behavior of a polymer on the molecular weight. Together with S. Havlin and R. Kopelman we have investigated the spatial distribution of reactants in one and three dimensions. In one dimension the kinetic properties do not follow classical laws while in three dimensions they do. We show that these effects are due in part to the non-Poisson spatial distribution of reactants in one dimension. Measurements of the dependence of the relaxation time polymer viscosity on the molecular weight deviate from the theoretical prediction that such dependence should go as the inverse third power. Experiments are consistent with the dependence on a power that ranges between -3.3 and -4. Together with J. Bendler, M. Dishon, and H. Kesten we have produced a physical model in which the indicated power is -10/3 which is in much better agreement with the experimental data than earlier theoretical work.

该项目的两个主要主题涉及交通， 无序介质和反应模型的发展 化学中的动力学 除了这些工作，一些时间是 花在弛豫时间依赖性的计算上 对于从弹性粘度到塑性粘度的转变 聚合物的分子量行为。 与S。Havlin和R.科佩尔曼，我们已经调查了 反应物在一维和三维的空间分布。 在 一维动力学性质不遵循经典定律 而在三维空间中则是如此。 我们表明，这些影响是 部分由于反应物的非泊松空间分布 在一个维度上。 弛豫时间与聚合物的关系的测量 粘度对分子量的影响偏离理论 预测这种依赖性应该是逆三分之一 动力. 实验与幂的依赖性是一致的 范围在-3.3到-4之间 与J. Bendler，M. Dishon和H. Kesten，我们已经制作了一个物理模型， 指示功率为-10/3，这与 实验数据比以前的理论工作。