Mathematical Sciences: Continuum and Aperiodic Lattice Models of Statistical Mechanics

瓦基利安教授的项目涉及统计力学中的许多问题。其中一组讨论了分层非周期伊辛模型的比热。这个问题的解决可能会导致发现介于无规和准晶之间的一种新的物质相。其他问题涉及非周期动力系统的迹映射和一维非周期薛定谔算子。瓦基利安教授的主要研究领域是数学物理。在这个研究项目中，首席研究人员将专注于物质模型的数学方面，这些模型不是规则的，也不是完全随机的。这类物质以最近在自然界中发现的准晶形式为代表。

Professor Vakilian's project involves a number of problems in statistical mechanics. One set deals with the specific heat for layered aperiodic Ising models. The solution of this problem could lead to the discovery of a new phase of matter intermediate between random and quasicrystalline forms. Additional problems deal with trace maps of aperiodic dynamical systems and one-dimensional aperiodic Schrodinger operators. The general area of research of Professor Vakilian is mathematical physics. In this research project, the principal investigator will concentrate on the mathematical aspects of models of matter which are not regular but not completely random. This type of matter is typified by the quasicrystalline forms recently found in nature.