Mathematical Sciences: Nonlinear Continuum Mechanics

在这个项目中，首席研究员将继续他的 研究非线性连续介质力学中的各种问题。 在 特别是，他将在三个弹性杆的动力学 尺寸，“脖子”的形成和演变， 粘弹性纤维，周期性热力学平衡 相，和最低能量状态的液晶。 这项工作具有巨大的理论和技术 影响 越来越多的人发现，技术进步 在非线性材料理论的改进的推动下， 这一理论的成功应用。 本工程 首席研究员将继续他的重要研究， 数学和物理是各种类型的 弹性、粘弹性和结晶材料。 这项工作 应用到生产中的最先进的问题， 高强度聚合物和不同形状的液晶。

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.