Mathematical Problems from Materials Science

建议：0313744PI：Robert V.Kohn[Kohn@cims.nyu.edu]机构：纽约大学标题：材料科学的数学问题摘要这个项目致力于数学、物理和材料科学之间的交界处的主题，特别是(A)晶界中能量驱动的图案形成，以及(B)相混合物和缺陷的能量驱动粗化。关于前者：PI将使用基于最小化非相干能量的新观点来研究扭曲晶界中的图案形成。关于后者：PI将使用基于耗散和等周不等式论的新观点，研究相分离、晶体生长和涡旋湮灭问题。能量驱动的图案形成在许多不同的物理系统中，例如第二类超导体中的涡旋晶格，晶界中的位错图案，以及相分离产生的迷宫结构。这个项目寻求一种理解--对于特定的、被广泛研究的系统--为什么形成某些模式而不是其他模式。这样的理解对于解释实验观测是至关重要的，也就是从对系统形成的模式的观测中得出关于系统物理的推断。

Proposal: 0313744PI: Robert V. Kohn [kohn@cims.nyu.edu]Institution: New York UniversityTitle: Mathematical Problems from Materials ScienceABSTRACTThis project addresses topics at the interface between mathematics, physics, and materials science, particularly (a) energy-driven pattern formation in crystalline grain boundaries, and (b) energy-driven coarsening of phase mixtures and defects. Concerning the former: the PI will investigate pattern formation in twist grain boundaries, using a new viewpoint based on minimization of incoherence energy. Concerning the latter: the PI will investigate problems from phase separation, grain growth, and vortex annihilation, using a new viewpoint based on dissipation and isoperimetric inequalities.Energy-driven pattern formation occurs in many different physical systems; examples include vortex lattices in type-II superconductors, dislocation patterns in grain boundaries, and labyrinthine structures created by phase separation. This project seeks an understanding -- for specific, widely studied systems -- why certain patterns form rather than others. Such understanding is crucial for interpreting experimental observations, i.e. for drawing inferences about the physics of a system from observations of the patterns it forms.