, 93:5 | Cite as

RETRACTED ARTICLE: Singular vs. non-singular memorised relaxation for basic relaxation current of the capacitor

  • Shantanu DasEmail author


We express the basic relaxation current of capacitor dynamics by using convolution operation of memory kernal function (that we choose as singular and non-singular) with rate of change of applied voltage. We have studied singular and non-singular types of memory kernels in this convolution expression. With these, we form constitutive equations for capacitor dynamics. We conclude that, mathematically, we can use the non-singular kernel now although this does not give much useful practically or physically realisable results and interpretations. It may be that we are unable to interpret these constitutive expressions of capacitor relaxation with non-singular memory kernel. Therefore, we have a question: Do natural relaxation dynamics for dielectrics have a singular memory kernel and is the relaxation current function singular in nature? Is the singular relaxation function for capacitor dynamics with singular memory kernel remains the universal law for dielectric relaxation? However, we are not questioning the researchers modelling the relaxation of dielectric via non-singular functions, but we are hinting about the complexity of basic constituent equation of the capacitor dynamics thus obtained by considering non-singular relaxations.


Convolution memory kernel fractional calculus power law Mittag-Leffler function stretched exponential function 


84.32.Tt 77.22.Gm 02.30.Gp 02.30.Yy 


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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Reactor Control Systems Design Section, Electronics and Instrumentation GroupBhabha Atomic Research CentreMumbaiIndia
  2. 2.Condensed Matter Physics Research Centre, Department of PhysicsJadavpur UniversityKolkataIndia

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