Interactions in Crystals by a Lagrangian Approach

9712885近年来，资深PI纳尔逊参与了(A)发展介电晶体中长波长现象的拉格朗日公式，(B)使用该公式来推导和阐明高阶非线性相互作用，并纠正了经典理论中长期存在的误解，以及(C)使用反对易变量的格拉斯曼代数将磁现象纳入他的公式中。在上一次获奖取得一系列成功之后，这笔赠款继续支持他的工作。这项资助还包括关于广义能量守恒定律和新的Poynting矢量的工作，然后应用于光孤子的性质。这位资深PI因其对激光物理的贡献而广为人知。在这笔续期拨款中，他继续研究电磁波在绝缘材料中传播的复杂数学公式。在这次更新中，他特别想要推广该公式，以包括材料的磁性。***

9712885 Nelson The senior PI, in recent years, has been involved in (a) the development of a Lagrangian formulation of long wavelength phenomena in dielectric crystals, (b) using this formulation to derive and elucidate high-order nonlinear interactions and correcting widely held long standing misconceptions in classical theories and (c) incorporation of magnetic phenomena in his formulation using Grassmann algebra of anticommuting variables. This grant continues to support his work following a string of successes in the previous award. This grant also includes work on a generalized energy conservation law and a new Poynting vector, followed by application to the properties of an optical soliton. %%% This senior PI is well known for his contributions to Laser Physics. In this renewal grant, he continues his work on a sophisticated mathematical formulation of electromagnetic wave propagation in an insulating material. In this renewal he specifically wants to generalize the formulation to include magnetic properties of materials. ***