Abstract

Abstract

It is well known that fractals pervade nature. For example obsereved pathof a quantum mechanical particle or Brownian and Fractional Browniantrajectories are known to be fractals and are continuous butnon-differentiable. I will present a new calculus on fractal curves suchas the von-Koch curve. This will include a Riemann-like integral along afractal curve called the F^alpha-integral, where alpha denotes thedimension of the fractal curve. Also, a corresponding derivative, calledF^alpha-derivative will be introduced. I will discuss various aspects andresults of this Calculus. The second part of the talk will consist of theapplication of this Calculus to Fokker-Planck equation on Fractal Curves.I will start with a Chapmann-Kolmogorov equation on fractal curves andtalk about fractal diffusion and drift coefficients for a suitabletransition probability. In this process, a diffusion equation on fractalcurves will be obtained and finally I will show, how the probabilitydistribution shows deviation from ordinary diffusive behaviour due tounderlying fractal space.

Abstract

Recently there is tremendous interest in transparent conducting oxides(TCOs) in general and p-type TCOs in particular. Development of p-typetransparent conducting oxides are essential for the oxide electronics andits applications. Although significant advancement has taken place overthe past few years in this field, still a long way is to go to use thesematerials in actual devices. In my research work, I have tried to developsome route for the synthesis of two prototype p-type TCO materials,namely, NiO and CuAlO2. Also one of the major aims is to understand andexplain some experimental findings such as band gap narrowing in NiO dueto heavy doping etc. The synthesized films were characterized by varioustechniques like XRD, SEM, HRTEM, XPS etc. In this presentation, I shallemphasize on the synthesis and characterizations of nickel oxide thin filmas a p-type material.

Abstract

Abstract