Colour symmetry double point groups

Thirty four distinct composition series arising out of the 32 crystallographic double point groups are employed to re-derive in a simple and elegant fashion all the 169 distinct colour symmetry groups generated by the 32 double point groups, exploiting the idea of colour generators. The advantage of the method employed and some possible applications of these colour groups are discussed. The resulting colour groups are tabulated.     

On the analyticity of the pressure in the hierarchical dipole gas

The convergence of the Mayer expansion is proved by estimating directly the convergence radius.     

Three-dimensional integrable models and associated tangle invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.     

Synthesis of resonant cavities having continuum spectra by genetic algorithm

This paper proposes a novel method for generating continuum spectra with possible applications in WDM access networks. This new method would allow the development of a simple continuum laser structure with better performances in terms of cost and simplicity than those of present supercontinuum sources. In this aim, we will analyze the possibility to broaden the resonant modes of a Fabry–Perot cavity by operating only on the design of one of the cavity's Bragg mirrors. Firstly we considered the conditions which a Bragg grating must satisfy in order to broaden the resonant modes of a resonant cavity. Because an exact solution is not physical possible, the genetic algorithm is the best available tool for the design of such a grating. An active medium is then added inside the cavity and its behavior below threshold is simulated. The spectra thus simulated are continuum over 5–15 nm.     

Multi-mode Spiral Wave in a Coupled Oscillatory Medium

Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve could be nonmonotonic depending on the coupling strength. It may also lead to the coexistence of different wave numbers within one system. Direct numerical observations in 1-d and 2-d systems conform to the prediction of dispersion relation analysis. Our findings indicate that the wave grouping can also be observed in oscillatory media without tip meandering and waves with negative group velocity can occur without inhomogeneity.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

学生培养中交叉课程设置的一些思考和建议

就"教育部高等学校光电信息科学与工程专业教学指导分委员会及协作委员会2007年全体会议"内容,阐明了学科交叉对该学科教学模式和课程设置提出的诉求。从培养方案的知识体系结构入手,分析了现有教学模式存在缺乏纵向衔接和横向贯通的问题,并通过设置"交叉课程",成立关联课程"学科组"、开设"系统设计"课程和加强创新性实验四个方面入手,提出了改善培养模式,提高教学质量的建议。     

The Renormalization Group and Optimization of Entropy

We illustrate the possible connection that exists between the extremal properties of entropy expressions and the renormalization group (RG) approach when applied to systems with scaling symmetry. We consider three examples: (1) Gaussian fixed-point criticality in a fluid or in the capillary-wave model of an interface; (2) Lévy-like random walks with self-similar cluster formation; and (3) long-ranged bond percolation. In all cases we find a decreasing entropy function that becomes minimum under an appropriate constraint at the fixed point. We use an equivalence between random-walk distributions and order-parameter pair correlations in a simple fluid or magnet to study how the dimensional anomaly at criticality relates to walks with long-tailed distributions.