Mathematical Sciences: Nonlinear Continuum Mechanics

在这个项目中，首席研究员将继续研究非线性连续介质力学中的各种问题。特别是，他将研究三维弹性棒的动力学，粘弹性纤维中“颈”的形成和演化，周期相的平衡热力学，以及向列液晶的最小能态。这项工作具有巨大的理论和技术意义。越来越多的人发现，技术进步是由非线性材料理论的改进和该理论的成功应用所驱动的。在这个项目中，首席研究员将继续他在各种弹性、粘弹性和结晶材料基础上的数学和物理学的重要研究。这项工作已应用于生产高强度聚合物和不同形状液晶的最新问题。

In this project the principal investigator will continue his work on various problems in nonlinear continuum mechanics. In particular, he will look at the dynamics of elastic rods in three dimensions, the formation and evolution of "necks" in viscoelastic fibers, the equilibrium thermodynamics of periodic phases, and the minimum energy states of nematic liquid crystals. This work has enormous theoretical and technological implications. More and more one finds that technological advances are driven by improvements in the theory of nonlinear materials and the successful applications of that theory. In this project the principal investigator will continue his important studies of the mathematics and the physics that underlie various types of elastic, viscoelastic and crystalline materials. This work has applications to state-of-the-art problems in the production of high-strength polymers and liquid crystals of different shapes.