Showing papers by "Shantanu Das published in 2019"

Analytical Formulation for Power, Energy, and Efficiency Measurement of Ultracapacitor Using Fractional Calculus

Abstract: Reliability of any electrical system heavily depends on the accuracy of the model used for representing the integrated device components. The design of renewable power sources and energy management systems using ultracapacitor demands adoption of precise mathematical representation of ultracapacitor dynamics. An appropriate model of ultracapacitor not only allows an accurate assessment of its charge/discharge characteristics but also provides a precise estimation of energy storage and power delivery capabilities. However, due to the lack in the usability of data/information provided by the manufacturer, conventional calculus-based ultracapacitor modeling and energy estimation approach often leads to its inaccurate and inefficient utility. In this regard, this paper has focused on fractional calculus-based analytical formulation for power, energy, and efficiency measurement of ultracapacitor and has deployed an upgraded model of the ultracapacitor, which in turn provides a better estimation of its energy efficiency. The work presented in this paper has been supported by extensive experimentation with the ultracapacitor under different input excitations, considering the dependence of energy storage (state of energy) and power delivery capacity of ultracapacitor on the charge/discharge profile. Furthermore, the hybrid optimization-based analysis recommends the requirement and challenges for the design and development of optimal charging/discharging of ultracapacitors for achieving higher energy efficiency.

Nanofiller-Induced Ionic Conductivity Enhancement and Relaxation Property Analysis of the Blend Polymer Electrolyte Using Non-Debye Electric Field Relaxation Function

Abstract: The enhancement of conductivity of a composite polymer as a dielectric material is an essential requirement for electrostatic storage devices. We have modified the microstructure of the polymer mat...

Higher-dimensional fractional time-independent Schrödinger equation via fractional derivative with generalised pseudoharmonic potential

Abstract: In this paper, we obtain approximate bound-state solutions of N-dimensional time-independent fractional Schrodinger equation for the generalised pseudoharmonic potential which has the form $$V(r^{\alpha })=a_1r^{2\alpha } + ({a_2}/{r^{2\alpha }})+a_3$$ . Here $$\alpha \;(0<\alpha <1)$$ acts like a fractional parameter for the space variable r. The entire study consists of the Jumarie-type fractional derivative and the elegance of Laplace transform. As a result, we can successfully express the approximate bound-state solution in terms of Mittag–Leffler function and fractionally defined confluent hypergeometric function. Our study may be treated as a generalisation of all previous works carried out on this topic when $$\alpha =1$$ and N arbitrary. We provide numerical result of energy eigenvalues and eigenfunctions for a typical diatomic molecule for different $$\alpha $$ close to unity. Finally, we try to correlate our work with a Cornell potential model which corresponds to $$\alpha = {1}$$ $$/$$ $${2}$$ with $$a_3=0$$ and predicts the approximate mass spectra of quarkonia.

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

Abstract: 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.

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

Abstract: 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.