Hyperuniformity and non-hyperuniformity of quasicrystals

点过程二阶统计量的（非）超均匀性

(Non-)Hyperuniformity of Second Order Statistics of Point Processes

研究投影核行列式点过程和超稳定对相互作用吉布斯点过程的二阶统计量方差渐近行为，发现两者均呈非超均匀性，并应用于统计力学逆Henderson问题。

无公度共生化合物和准晶的非线性流体力学

Non-linear hydrodynamics of incommensurate intergrowth compounds and quasicrystals

构造了无公度共生化合物（IIC）和准晶（IQ）非线性流体力学的哈密顿结构。本文还讨论了相子性质的内耗的计算方法。我们证明了IIC和IQ中自作用力的存在不仅是本构问题，而且与SO（3）不变性问题有关。分析了准周期结构中不连续面的协变机制。注意力主要集中在“扩散”晶界和尖锐的不连续性（移动可能）表面之间的相互作用。

Existence results in the linear dynamics of quasicrystals with phason diffusion and non-linear gyroscopic effects

Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic flips necessary to match quasi-periodicity under the action of the external environment. Here we discuss the mechanics of quasicrystals, commenting the shift from its initial formulation, as standard elasticity in a space with dimension twice the ambient one, to a more elaborated setting avoiding physical inconveniences of the original proposal. In the new sett…

准晶问题——从统计力学视角看非周期结构的刚性

Quasicrystal problem -- on rigidity of non-periodic structures from statistical mechanics point of view

本文从统计力学角度研究准晶及非周期结构的稳定性，提出严格边界条件这一均匀性要求是保证非周期基态在小扰动和热涨落下稳定的必要条件。

Quasicrystals

Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic alloys which brought this subject into the limelight. These fascinating materials, now called quasicrystals, are characterised by the coexistence of long-range atomic order and 'forbidden' symmetries which are incompatible with periodic arrangements in three-dimensional space. In the first part of this review, we summarise the main properties of quasicrystals, and describe how their structures relate to non-periodic t…