Dynamics of Fokker-Planck Equation with Logarithmic Coefficients and Its Application in Econophysics

We demonstrate that Fokker Planck equations with logarithmic factors in diffusion and drift terms can be straightforwardly derived from the class of ＂constant elasticity of variance＂ stochastic processes without appealing to any symmetry argument, Analytical closed-form solutions are available for some special cases of this class of Fokker-Planck equations. The dynamics of the underlying stochastic variables are examined. These Fokker-Planck equations have found a rather wide range of applications in various contexts. In particular, in the field of econophysics we have demonstrated their immediate relevance to modelling the exchange rate dynamics in a target zone, e.g. the linked exchange rate system of the Hong Kong dollar. Furthermore, the knowledge of exact solutions in some special cases can be useful as a benchmark to test approximate numerical or analytical procedures.     

基于偏斜度、陡峭度特征的光纤布拉格光栅冲击载荷定位

针对复合材料结构上低速冲击载荷位置识别问题,通过构建分布式光纤布拉格光栅(FBG)传感网络,分析了光纤布拉格光栅传感器感知的冲击响应信号时间序列的偏斜度、陡峭度与到传感器之间距离的关系。通过不同位置传感器感知的冲击响应信号的偏斜度和陡峭度对冲击载荷所在的区域和到各个传感器之间的距离进行了辨识,采用加权质心定位算法实现了冲击载荷位置的坐标定位。实验结果表明:在碳纤维复合材料板上240mm×240mm的监测区域内随机选取16个测试样本点进行低速冲击定位识别,实现了所有冲击实验点的区域辨识,坐标定位的平均误差为20.7mm。研究结果为碳纤维复合材料板的低速冲击定位提供了一种可靠的方法。