论文标题
非debye放松：拉伸指数vs Mittag-Leffler的比赛的起伏
Non-Debye relaxations: The ups and downs of the stretched exponential vs Mittag-Leffler's matchings
论文作者
论文摘要
收集的实验数据是根据两个不同的方案获得有关介电弛豫现象的信息的信息：一个可以测量地下电流的时间衰变或使用宽带介电光谱的方法。两组数据通常都由时间或频率依赖性基本功能拟合，这些功能又可以使用Laplace Transform进行分析转换并相互比较。这导致了有关结果可比性的问题，使用了刚刚提到的实验程序。如果我们想在时间域中这样做，我们必须超越广泛接受的kohlrausch-williams-watts近似，并使用Mittag-Leffler功能熟悉描述。为了说服读者，后者并不难理解，我们建议从位于随机过程中心的物体的角度看待问题。这些是从标准的非偏僻频率依赖模式中读取的特征指数。特征函数似乎是用基本功能表示的，这些功能很简单。这为比较用来描述非替代松弛的功能的行为开辟了新的可能性。使用Mittag-Leffler功能的强大设备的计算可以充分证实这种完成比较的结果。
Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are got according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadband dielectric spectroscopy. Both sets of data are usually fitted by time or frequency dependent elementary functions which in turn may be analytically transformed among themselves using the Laplace transform and compared each other. This leads to the question on comparability of results got using just mentioned experimental procedures. If we would like to do that in the time domain we have to go beyond widely accepted Kohlrausch-Williams-Watts approximation and get acquainted with description using the Mittag-Leffler functions. To convince the reader that the latter is not difficult to understand we propose to look at the problem from the point of view of objects sitting in the heart of stochastic processes approach to relaxation. These are the characteristic exponents which are read out from the standard non-Debye frequency dependent patterns. Characteristic functions appear to be expressed in terms of elementary functions which asymptotic analysis is simple. This opens new possibility to compare behavior of functions used to describe non-Debye relaxations. Results of such done comparison are fully confirmed by calculations which use the powerful apparatus of the Mittag-Leffler functions.
