Interactions in Crystals by a Lagrangian Approach

9712885纳尔逊高级PI，近年来，一直参与（a）电介质晶体中长波长现象的拉格朗日公式的开发，（B）使用该公式推导和阐明高阶非线性相互作用，并纠正经典理论中广泛存在的长期误解，以及（c）在他的公式中加入磁现象，使用反交换变量的格拉斯曼代数。 这项赠款继续支持他的工作后，在前一个奖项的一系列成功。 该补助金还包括广义能量守恒定律和一个新的坡印廷矢量的工作，其次是应用到光孤子的性质。 这位资深PI因其对激光物理学的贡献而闻名。 在这个更新的补助金，他继续他的工作在一个复杂的数学公式的电磁波传播的绝缘材料。 在这次更新中，他特别希望将该公式推广到包括材料的磁性。 ***

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. ***