Electrical Characterisation of Polypyrrole Thin Film Conducting Polymer

It is known that organic acids doped Polypyrrole (PPy) will conduct electricity, and the electrical characteristics of the polymer is presented in this paper. The PPy is deposited on a glass substrate using a spin coater, resulted in a thin film with of 0.0823 μm thickness. The I/V characteristics of the PPy thin film were measured using two-point and four-point probe at room temperature. The finding shows that the I/V characteristic is nonlinear. Comparison between these two methods is further explored, and statistically it shows that there is no mean difference between the two methods. Hence, it helps in designing future experiment to measure I/V characteristics at elevated temperature.

A Common Fixed Point Theorem for Nonlinear Quasi-Contractions on b -Metric Spaces with Application in Integral Equations

In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results.

Initial problems for neutral functional differential equations with unbounded delay

General theorems on the existence, uniqueness and convergence of successive approximations for classical solutions of the Cauchy problem are given. Results are based on a comparison method and on the axiomatic approach to equations with unbounded delay. The nonlinear comparison operator is investigated. Examples of nonlinear comparison problems and phase spaces are given.

Upper and lower bounds for the overall properties of a nonlinear composite dielectric. II. Periodic microgeometry

The study of the effective properties of a nonlinear composite dielectric begun in the companion to this paper is continued in the context of a simple cubic array of inclusions embedded in a matrix. Use of a nonlinear comparison material in the nonlinear Hashin-Shtrikman variational principles permits the generation of both upper and lower bounds for any composite. It is straightforward to apply the new approach to the simple composite considered here as the trial electric field which is substituted into the Hashin-Shtrikman variational principle is finite everywhere. The results obtained indicate the likely improvement over the simple classical bounds that can be obtained using the Hashin-Shtrikman principles.

Upper and lower bounds for the overall properties of a nonlinear composite dielectric. I. Random microgeometry

The direct extension of the Hashin-Shtrikman methodology to nonlinear composite problems generally produces at most one new bound - either an upper bound or a lower bound - and in some cases produces no new bound at all. This paper is devoted to the construction of bounds, of generalized Hashin-Shtrikman type, for any nonlinear composite whose behaviour can be characterized in terms of a convex potential function. The construction relies on the use of a nonlinear comparison medium’ and trial fields with the property of ‘bounded mean oscillation’. This permits the exercise of control over the size of the penalty incurred from the use of a nonlinear, as opposed to linear, comparison medium. In cases where a linear comparison medium is adequate, the already established bounds of Hashin-Shtrikman type are reproduced. The exposition is presented in the context of bounding the properties of a nonlinear dielectric, for which a single bound was obtained previously by one of the authors. The approach, however, is applicable more generally.