We invoke various tools from physics and mathematics to arrive at a mathematical model of a real life system. We make use of the softcomputing algorithms like artificial neural networks, genetic algorithms, fuzzy logic technique for the simulation of various real life systems.

The problems of fundamental interest in control theory are that of controllability, observability and optimal control. We investigate these problems by using efficient tools from the theory of Differential equations and Functional Analysis. We deal with both linear and nonlinear problems.

When the thickness of the elastic body is small, lower dimensional theories have been proposed, depending on mechanical and geometrical nature of the body, as approximations of usual three-dimensional theory. But it is not evident which is the model most suited to a particular case in mind. Consequently, before approximating the exact solution of a given lower dimensional model, we should first know whether it is “close enough” to the exact solution of the three-dimensional model it is intended to approximate. Thus one is lead to the question of mathematically justifying lower-dimensional models starting from the three-dimensional model.

Studying the effects of particle and fluid inertia for prolate spheroids at low Reynolds numbers under the action of a periodic external force field. In future this work can be extended for the oblate spheroids. The possibility of chaos in the dynamics can be examined. The results of this problem may provide insight into the development of fluids whose rheological properties can be controlled with small changes in controllable parameters. Planned to study the effects of particle and fluid inertia for prolate spheroids in a uniform true dependent flow field at low field at low Reynolds numbers under the action of a periodic external force field.

Presently working in the area of analysis and modeling of naturally occurring series from Ionospheric and Magnetospheric data. Investigating the chaotic dynamics of the time series of Total Electron Content (TEC), the geomagnetic horizontal Intensity (H) and the ring current index (Dst). The analysis based on the calculation of the invariant characteristics such as Lyapunov exponent, Correlation dimension, etc. and of the surrogate data test established the existence of a low dimensional deterministic chaotic system in all cases.