Studies on Some Aspects of the Physics of the Early Universe Using Gravitationally Coupled Scalar Field –

This thesis deals with some aspects of the Physics of the early universe, like phase transitions, bubble nucleations and premodial density perturbations which lead to the formation structures in the universe. Quantum aspects of the gravitational interaction play an essential role in retical high-energy physics. The questions of the quantum gravity are naturally connected with early universe and Grand Unification Theories. In spite of numerous efforts, the various problems of quantum gravity remain still unsolved. In this condition, the consideration of different quantum gravity models is an inevitable stage to study the quantum aspects of gravitational interaction. The important role of gravitationally coupled scalar field in the physics of the early universe is discussed in this thesis. The study shows that the scalar-gravitational coupling and the scalar curvature did play a crucial role in determining the nature of phase transitions that took place in the early universe. The key idea in studying the formation structure in the universe is that of gravitational instability.

Studies on planktonic ostracods of the northern indian ocean

Planktonic ostracod of the Indian Ocean have not been studied in detail although extensive studies have been made on them from other oceans, particularly Atlantic. with this view, the present study was undertaken, to throw; some light on the systematics and distribution oi’ planktonic ostracods in this region, This study provides iniormation regarding the distribution or each species in the Northern Indian Ocean, specially in the Bay of Bengal which is the least explored, as far as planlctunio ostracods are concerned. It may also furnish us with the data regarding the nature of ostracod production in this area, which directly reflects on the total productivity as they play an important role in the rapid recycling or organic substances, iaecal pellets and even flocculants In the present study the main objectives are; (1) Proper detemination of the species or planktonic Ostraooda that occur in the area or investigation, (2) to explain the pattern oi’ distribution, (3) to estimate their abundance and to some extent seasonal variation, and (4) to correlate their distribution with the physics-chemical factors of the environment

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

physics of the Web

Science is search for the laws of underlying phenomena of the nature. Engineering constructs the nature as we wish. Interestingly the huge engineering infrastructure like world wide web has grown in such a complex structure such that we need to see the fundamental science behind the structure and behaviour of these networks. This talk covers the science behind the complex networks like web, biological, social etc. The talk aim to discuss the basic theories that govern the static as well as the dynamics of such interesting networks

On the generalized obnoxious center problem: antimedian subsets

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes