Model coupling in multiscale mathematics and properties of nanostructures

应用程序提供了许多物理和生物系统的例子，其特性本质上依赖于大量的空间和时间尺度。在纳米尺度上对这类系统及其性质的研究特别有趣，如果没有数学模型，就不可能解决现代应用数学中一些最具挑战性的问题。许多这样的系统已经并将继续给我们的日常生活带来巨大的变化。今天，我们无法想象没有利用纳米结构激光的电信系统，没有无处不在的纳米结构电子设备，从卫星电视系统到几乎每个家庭的CD播放机，我们的生活将会怎样。结合这种纳米结构的太阳能电池已经广泛应用于太空和地面项目，是绿色能源开发项目的重要组成部分，而纳米结构在生物成像、生物传感、化妆品和个人护理产品等领域的应用也在不断增长。

Applications provide many examples of physical and biological systems whose properties depend inherently on a multitude of spatial and temporal scales. Studies of such systems and their properties at the nanoscale are particularly intriguing and would be impossible without mathematical models leading to some of the most challenging problems in modern applied mathematics. Many such systems have brought and will be bringing tremendous changes in our everyday lives. Today, we cannot imagine our life without telecommunications systems utilizing nanostructure lasers, without nanostructure-based electron devices encountered everywhere, from satellite television systems to virtually every home as part of CD players. Solar cells incorporating such nanostructures are already used extensively in space and terrestrial programs and are essential component of green-energy development programs, while the usage of nanostructures in the areas ranging from bioimaging and biosensing to cosmetics and personal care products continue to grow.