论文标题
半晶聚合物结构中光异常扩散的数值研究
Numerical study of anomalous diffusion of light in semi-crystalline polymer structures
论文作者
论文摘要
从大气中污染物的扩散到养分在细胞膜中的传播，在天然系统中，异常扩散过程无处不在。理解和控制指导各种规模过程的机制的能力在材料科学，金融，医学和能量学方面具有重要的应用。在这里，我们提出了一项通过半晶聚合物结构进行异常扩散的数值研究，其中传输由随机疾病和非局部相互作用引导。该数值技术通过Anderson型哈密顿量的频谱检查了一维（1D）空间的扩散性能，该频谱具有离散的分数拉普拉斯运算符（-δ）^s，0 <s <2和随机分布和无序分布。结果表明，对于大多数检查的病例，S <1（超扩散）的运输增强和S> 1（子扩散）的定位增强。本研究的一个重要发现是，在次划分的情况下，可以在关键的空间尺度上增强运输，在这种情况下，通常所有状态通常被预期用于（1D）无序系统。
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such processes across various scales has important application to research in materials science, finance, medicine, and energetics. Here we present a numerical study of anomalous diffusion of light through a semi-crystalline polymer structure where transport is guided by random disorder and nonlocal interactions. The numerical technique examines diffusion properties in one-dimensional (1D) space via the spectrum of an Anderson-type Hamiltonian with a discrete fractional Laplacian operator (-Δ)^s, 0<s<2 and a random distribution of disorder. The results show enhanced transport for s<1 (super-diffusion) and enhanced localization for s>1 (sub-diffusion) for most examined cases. An important finding of the present study is that transport can be enhanced at key spatial scales in the sub-diffusive case, where all states are normally expected to be localized for a (1D) disordered system.
