Nonlinear Continuum Mechanics

9705016科尔曼 首席研究员将继续致力于DNA弹性杆模型的开发，目标是（i）深入了解拓扑异构酶的作用模式，（ii）找到有效的方法来计算DNA片段和质粒的配置在自接触产生的力不可忽视的情况下，以及（iii）获得弹性环振动理论中的数学结果，所述弹性环振动理论需要解释热波动对依赖于DNA质粒的三级结构的量（例如扭动）的影响。在不同领域的研究中，将采用分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导致的形态变化和不稳定性。 其中要调查的主题是（一）的轴对称表面和平面曲线的曲率驱动扩散理论的演变和稳定性和（ii）在其他平坦的薄膜坑状缺陷的演变。 关于已知与DNA结合并诱导DNA变形的蛋白质的作用模式，还有很多东西有待了解。在有些情况下，我们可以把DNA分子当作弹性杆来讨论DNA弯曲蛋白质的作用。 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片段的构型对其端点处施加的条件的依赖性。 以这种方式研究的几个问题对于理解基因调控机制是重要的。曲率驱动的固体边界表面内的质量扩散的工作预计将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，这种扩散的理论可以应用于以下研究领域以获得洞察力和定量结果：热凹槽的形成，即，加热金属中晶界处表面压痕的发展;场发射阴极、微电子电路中互连元件和微机电设备中移动部件的稳定性;金属复合材料中的纤维球化;以及晶界顶点处薄膜的点蚀。

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.