First-principle determination of landscape and the unifying concept for glass transition

1.在自由能景观的基础上，发现了一个统一的理解玻璃化转变的概念，它与朗道相变理论中的自由能具有相同的作用。提出了一种利用大势的密度泛函计算自由能格局的新方法。通过对得到的自由能图的分析，我们发现弦的运动是一个共同的慢弛豫基本过程，并且存在两种类型的协同重排区域。利用主成分分析方法计算了分子模拟数据的自由能格局。提出了一种相互作用的分子动力学模拟和快速构建Voronoi镶嵌的方法。利用这些方法计算了协同重排区域的温度依赖性。利用微观理论，我们证明了跳跃率分布服从幂律函数。在自由能图的框架内得到了模型玻璃原料器比热的温度依赖关系，并表明玻璃转变的冷却速率依赖关系可以用景观图来解释。在自由能全景图的基础上，定义了一阶和二阶频率相关（复）比热，并在玻璃化转变点和Vogel-Fulcher温度附近发现了它们的异常行为。在整个参数空间中得到了二进制硬盘的填充分数，发现填充分数作为半径比的函数有一个最小值。

1.A unifying concept for understanding glass transition was found on the basis of the free energy landscape which plays the same role as the free energy in the Landau theory of phase transitions.2.A novel method to calculate the free energy landscape was found using the density functional of the grand potential. Analyzing the free energy landscape obtained, we showed that the string motion is a common elementary process of the slow relaxation and that there are two kinds of the cooperatively rearranging regions.3.The principal component analysis was utilized to calculate the free energy landscape from the molecular simulation data.4.An interactive molecular dynamics simulation and a fast method to construct the Voronoi tessellation were developed. These methods were exploited to calculate the temperature dependence of the cooperatively rearranging region.5.Using a microscopic theory we showed that the jump rate distribution obeys a power law function.6.The temperature dependence of the specific heat of a model glass former was obtained within the frame work of the free energy landscape and it was shown that the cooling rate dependence of the glass transition can be explained by the landscape picture.7.On the basis of the free energy landscape picture, the first and second order frequency-dependent (complex) specific heats were defined and their anomalous behavior was found around the glass transition point and the Vogel-Fulcher temperature.8.Packing fraction of binary hard discs was obtained in the entire parameter space and it was found that the packing fraction has a minimum as a function of the ratio of radii.