The Symmetry of Crystals

9531430 Mermin这项资助继续进行PI在对称性分类（周期晶体）的推广方面的公认工作，以包括非周期晶体。 具体内容包括张量序参量的情况、对称性在无公度相变中的变化以及新发现的四面体准晶。 此外，诺维科夫、Piunikhin和Conway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问题。 直到80年代初准晶的发现，周期晶体的科学观点已经确立了100多年，并在教科书中有所描述。 非周期性或准周期性结构挑战了这一框架，在PI的开创性工作中，对称性分类已被推广到包括新的发展。 现时的拨款进一步探讨如何丰富新的分类制度。 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. ***