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首页> 外文期刊>Journal of Modern Physics >Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor
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Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

机译：重新审视Curie-Von Schweidler法律，用于介电松弛和抛光函数的放松率作为Zipf的电力法和电容器分数微分方程的表现

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The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations; and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
机译：经典的电力法放松，即通过时间偏移的时间的电流逆的电流放松电流的电流 - 被凭经质地衍生，并且在几个放松实验中观察到自晚后的各种电介质研究中的几个松弛实验19世纪。这种放松法也被认为是介电放宽的“普遍法”;并且也被称为权力法。然后，这种经验居里-Von魁克服克莱宽度释放定律来衍生描述电容器组成表达的分数微分方程。在本文中，我们提供了简单的数学待遇，从而源到这个富利 - 冯·施韦勒法的放松率分布，并表明松弛率遵循ZIPF的电力法分布。我们还展示了这里开发的方法为Zipfian电力法分布提供放松时间常数。然后，我们将显示在数学上校正这可能，但是从所获得的时间常数分布的物理解释与Zipfian速率松弛分布相矛盾。在本文中，我们开发了可能的解释，即为什么ZIPFIAN分配放松率的分布出现在Curie-Von Schweidler Love中，并将这一法律涉及时间变化的放松率。在本文中，我们在使用ZipfianPower法分布的同时导出了分数衍生的外观，这为Curie-Von Schweidler弛豫现象提供了规模依赖性放松率函数的概念。本文给出了分析方法，以了解非德德休闲的洞察力，并为特别是使用尤其多的经验丰富的豪瑞施韦勒（普遍）放松法提供了新的待遇。

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