It is shown that the self-duality constraint on the scalar field (combined with the equations of motion) by itself leads to the critical forms for the potential that minimizes the energy functional in the Chern-Simons-Higgs (CSH) system. If we have only the Chern-Simons (CS) term in the SL (2, R) gauge group one obtains a formalism that yields the equations of motion of a variety on non-linear models in two dimensions when the curvature is set equal to zero.
A new equation for microbial growth has been proposed and its implications discussed. The proposed equation has a distinct advantage over Bertalanffy’s in being an explicit relationship between growth parameter and time. Attempt has been made to read the proposed equation in the light of Hinshelwood’s auto-synthetic model. The constants occurring in the proposed equation have been shown to be intimately related to the kinetic constants in the Hinshelwood’s model.
Structural changes accompanying thermal transformation in Na-montmorillonite samples up to a temperature of 500°C have been investigated by X-ray line profile analysis. The method of Fourier initial slope and variance analysis of X-ray line profiles have been used to calculate the different microstructural parameters like crystallite size, r.m.s. strain (<e2>1/2), variation of inter layer spacing (g), fraction of planes affected by such defects (γ), etc. at different stages of the dehydration process. The dehydration mechanism also has been explained based on thermogravimetric analysis (TGA).