Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Studies on the systematics, biology and fishery of rainbow sardines, dussumieria spp., from Indian waters

Rainbow sardines of the genus belonging to the family Dueenaieriidae. are small pelagic fishes forming a fairly good, though not abundant. seasonal fishery all along the coasts of India inhabiting the coastal waters. There have been some earlier reports on such individual aspects as their systematic, distribution, abundance. Ostecology and a few biological factors but no attempt has been made towards a comprehensive study on this group. Two species of rainbow sardines are known to occur in the Indian seas and while a knowledge about their biology would be useful from the fishery point of view. it was also thought a study of their systematic position, especially regarding the identity or the two species which had raised doubts among earlier workers would lead to a better understanding or the group as a whole. This thesis is mainly based on studies during the period from April 1969 to march 1971 with a continued investigation of fishhery aspects till December 1975. from the Gulf of manar: and the Palk Bay around mandapam area. on the south-east coast of India. Thus the work deals with the systemtics, biology and fishery of rainbow sardines of Indian seas.

Knowledge Management: Creating Competitive Intelligence for the Future

In this knowledge era, the value of corporations, academic organizations and individuals is directly related to their knowledge and intellectual capital(IC). A newand potentially paradigm shift focus in the intersection between knowledge and intelligence is the recognition of the importance of understanding the intellectual capital of organizations. This paper explains how Cochin University of Science and Technology (CUSAT) is identifying and managing its intellectual capital for creating competitive advantage for the future. This paper also explores the different cost effective knowledge management strategies applied at CUSAT for managing its intellectual capital