The Symmetry of Crystals

9531430 Mermin这笔赠款延续了PI关于(周期晶体的)对称性分类的推广到包括非周期晶体的公认工作。一些具体的项目包括张量序参数的情况，公度-非公度相变的对称性变化以及新发现的四面体准晶。此外，诺维科夫、皮尤金和康威最近在数学文献中的工作与PI的分类方案之间的关系也存在疑问。直到80年代初准晶被发现之前，周期晶体的科学观点已经确立了100多年，并在教科书中得到了描述。非周期或准周期结构挑战了这一框架，在PI的一项开创性工作中，对称分类被推广到包括新的发展。这笔赠款进一步探索了丰富新的分类办法的方法。还计划研究其他人的工作并与之建立关系。***

9531430 Mermin This grant continues on the well recognized work of the PI on the generalization of symmetry classification (of periodic crystals) to include aperiodic crystals. Some specific items include the case of tensorial order parameter, symmetry changes at commensurate-incommensurate phase transition and the newly discovered tetrahedral quasicrystals. In addition, there are questions of the relationship between the recent work in the mathematical literature by Novikov, Piunikhin and Conway and the PI's classification scheme. %%% Until the discovery of quasicrystals in the early eighties, the scientific view of a periodic crystal had been well established for more than 100 years and had been described in the textbooks. The aperiodic or quasiperiodic structures challenged that framework and, in a seminal work by the PI, the symmetry classification has been generalized to include the new developments. The present grant further explores ways of enriching the new classification scheme. There are also plans to study and establish relationships with the work of others. ***