Information geometry is a branch of Mathematics that applies the techniques of differential geometry to the field of probability theory. The family of probability distributions which constitutes a statistical model has a rich geometric structure as a manifold with Riemannian metric and dual connections. Using this geometric interpretation one can obtain new insight into the framework of statistical inference and can develop new techniques for inference.

We first consider thin piezoelectric shallow shells with variable thickness and show that the eigenvalues of the three dimensional problem are order square of thickness the corresponding scaled eigensolutions converge to the eigensolutions of a two dimensional model.

Dynamics of micro particles in fluids and the change in rheological parameters due to particle dynamics occur across many industries including many processes relevant to space programs. We developed solutions for some of the problems and the study will be continued. A set of ordinary differential equations governing the migration of an arbitrary forced spheroid in quiescent/ simple-shear/ uniform/ oscillating/ oscillating-shear flows at low Reynolds number is formulated and discussed, assuming a sufficiently diluted suspension to neglect the particle-particle interactions.

To understand the dynamics of WSB trajectories and develop algorithms to obtain WSB trajectories from Earth to Moon and Mars. The role of periodic orbits (PO) and manifolds associated with them in ballistic lunar capture is studied. As a first step towards orbiter missions, planar fly-by trajectories to the Moon were studied in the framework of Restricted three-body problem (RTBP). We attempt the construction of a WSB trajectory toMoon in the restricted four-body problem (RFBP) and its dynamics. An algorithm is developed to obtain WSB trajectories to the moon in a full force model.

Various types of stability analysis of nonlinear dynamical systems in connection with continuous neural network systems are investigated. The LMI tools and the method of Lyapunov functionals are being employed for the analysis.

Controllability is one of the fundamental properties of control systems which guarantees the ability of the system to be steered from any initial state to a desired final state by using suitable control functions. Controllability analysis for stand-alone systems linear systems has been extensively carried out in the literature. However, for nonlinear systems as well as systems with various other effects like delay, impulses, noises, fuzziness etc in state or control are to be explored for investigation.

A robust and dynamic supply chain can be developed using advanced digital technologies, enabling real-time information sharing. This study provides a conceptual framework for effective supply chain digitalization by considering the key decision-making factors and interrelationships. The key decision-making factors affecting the digitalization process are identified from the literature and consultation with industry and academia experts. A conceptual framework is developed using the integrated systems model approach and DIKW (Data, Information, Knowledge, and Wisdom) hierarchy.

Digital twin and physical internet adoption based on advanced digital technologies is gaining significance in the recent times. Digital twin is one of the enabling technologies that link actual physical system with its virtual depiction using advanced digital technologies. In order to leverage its potential, firms have instigated to adopt digital twin and physical internet for real-world applications.