Mathematical Problems from Materials Science

提案：0313744 PI：Robert V. Kohn [kohn@cims.nyu.edu]机构：纽约大学材料科学中的数学问题摘要本项目主要研究数学、物理和材料科学之间的界面问题，特别是（a）能量驱动的晶粒边界图案形成，（B）能量驱动的相混合物和缺陷的粗化。 关于前者：PI将使用基于非相干能量最小化新观点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的新观点，研究从相分离、晶粒生长和涡旋湮灭的问题。能量驱动的图案形成发生在许多不同的物理系统中;例子包括II型超导体中的涡旋晶格、晶界中的位错图案和由相分离产生的螺旋结构。 这个项目寻求理解-对于特定的，广泛研究的系统-为什么某些模式形成而不是其他模式。这种理解对于解释实验观察至关重要，即对于从对系统形成的模式的观察中推断系统的物理性质至关重要。

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.