Mathematical Sciences: Variational Methods and Applications

小行星9302318 研究人员研究流体力学，场论，化学和天文学中某些问题的变分原理的构造，分析和数值模拟。 他还研究了某些极大极小问题和发展的算法的数值解的非凸极值问题。 这里要研究的问题包括使用量子化学方程模拟原子和分子的算法的分析和开发。 类似的方法也适用于研究流体中的涡旋方程（这在研究飓风和龙卷风中很重要）以及旋转恒星和行星的模型。 这些都是由系统的非线性偏微分方程所产生的“非凸”变分原理。 该建议研究了这些问题的数学方面，以及通过计算解决这些问题的算法开发问题。 ***

9302318 Auchmuty The investigator studies the construction, analysis and numerical simulation of variational principles for certain problems in fluid mechanics, field theories, chemistry and astronomy. He also studies certain minimax problems and the development of algorithms for the numerical solution of nonconvex extremal problems. The problems to be studied here include the analysis and development of algorithms for modeling atoms and molecules using the equations of quantum chemistry. Similar methods also apply in studying the equations for vortices in fluids (which are important in studying hurricanes and tornadoes) and models of rotating stars and planets. These are all described by systems of nonlinear partial differential equations which arise from "nonconvex" variational principles. This proposal studies aspects of the mathematics of such problems and also questions of developing algorithms for solving these problems computationally. ***