Nonlinear Continuum Mechanics

首席研究员将继续研究DNA弹性棒模型的发展，其目标是：(i)深入了解拓扑异构酶的作用模式，（ii）在自我接触产生的力不可忽略的情况下，找到有效的方法来计算DNA片段和质粒的构型。（三）获得弹性环振动理论的数学结果，这些结果是解释热波动对依赖于DNA质粒三级结构的量（如扭扭）的影响所必需的。在不同领域的研究中，将采用解析和数值方法来研究固体边界表面内曲率驱动的质量扩散所导致的形态变化和不稳定性。要研究的课题包括：(i)曲率驱动扩散理论中轴对称表面和平面曲线的演变和稳定性；（ii）平面薄膜中坑状缺陷的演变。对于已知的与DNA结合并诱导其变形的蛋白质的作用模式，我们还需要了解很多。在某些情况下，人们可以通过将DNA分子视为弹性杆来讨论DNA弯曲蛋白的作用。最近的研究表明，人们可以使用弹性杆平衡方程的精确解来研究DNA片段的结构对其端点施加条件的依赖性质。以这种方式研究的一些问题对理解基因调控的机制很重要。在固体边界表面曲率驱动的质量扩散的研究有望在材料科学中有重要的应用。随着尺寸变小，表面扩散的影响越来越重要，这种扩散理论可以应用于以下研究领域：热槽的形成，即加热金属中晶界处表面压痕的发展；场射极、微电子电路中互连元件和微机电装置中运动部件的稳定性；金属复合材料中纤维球化的研究以及薄膜在晶界顶点处的点蚀。

9705016 Coleman The principal investigator will continue his work on the development of the elastic rod model for DNA with the goals of (i) attaining insight into the mode of action of topoisomerases, (ii) finding efficient ways to calculate configurations of DNA segments and plasmids in circumstances in which the forces arising from self-contact are not negligible, and (iii) obtaining mathematical results in the theory of vibrations of elastic rings that are needed to account for the effects of thermal fluctuations on quantities, such as writhe, that depend on the tertiary structure of DNA plasmids. In research in a different area, analytical and numerical methods will be employed to study the morphological changes and instabilities that result from curvature driven mass diffusion within the bounding surfaces of solid bodies. Among the topics to be investigated are (i) the evolution and stability of axisymmetric surfaces and of planar curves in the theory of curvature driven diffusion and (ii) the evolution of pit-like defects in otherwise flat films. Much is yet to be learned about the modes of action of proteins that are known to bind to and induce deformations in DNA. There are cases in which one can discuss the action of DNA bending proteins by treating a DNA molecule as an elastic rod. Recent research has shown that one can use exact solutions of the equations of equilibrium for elastic rods to investigate the nature of the dependence of the configuration of a segment of DNA on conditions imposed at its end points. Several of the problems that are investigated in this way are important for understanding mechanisms of gene regulation. The work on curvature driven mass diffusion within the bounding surfaces of solids is expected to have significant applications in materials science. As the effects of surface diffusion increase in importance as dimensions become small, the theory of such diffusion can be applied to obtain insight and quan titative results in the following research areas: the formation of thermal grooves, i.e., the development of surface indentations at grain boundaries in heated metals; the stability of field-emitter cathodes, of interconnecting elements in microelectronic circuits, and of moving parts in micro-electromechanical devices; fiber spheroidization in metallic composites; and the pitting of thin films at grain boundary vertices.