Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Legal Control of Industrial Pollution

Industries constitute the main spring of development. Without industrial development no country could reach a stage in which a decent living for its citizens would be achieved. Increasing production to meet the basic needs of society augmented scientific invention and machine oriented industrial order.Environmental pollution ls a burning global issue. It is more serious and dangerous than terrorism. Started with the discovery of fire and development of civilization. Pollution went unnoticed throughout the centuries of human growth until its adverse effects on human environment become explicit.National concern tor environment started in our country only atter the cause of protection of environment received global attention. At present legal control ot industrial pollution is in a scattered framework of piece meal processes with overlapping provisions and authorities.Environmental protection- should be an item not only in the concurrent list of schedule 7 to the Constitution but also in the list of matters entrusted to the panchayati institutions in the Schedule 11. It is heartening to note that so far as municipalities are concerned the Constitution of India lives up to the expectation. In the wake of New Industrial Policy based on liberalisation a long list of small scale industries fall outside the purview of environmental clearance. The Indian concept of environmental im»act assessment introduced under the Environment Act by notification excludes the entire gamut of small scale industries and r.elates only to scheduled industries covered by the notifica~ion. Most of them are subjected to ETA only it the investment goes above ~.50 crores. This provision dilutes the impact assessment considerably A mandatory impact assessment with public partiCipation and with provision for a review by specialized environmental courts will eliminate the possible evils of this judicial passiveness.

A study of the information seeking bebavior of science and technology teachers and researchers of Cocbin University of Science and Technology and University of Kerala in the cbanged library environment

Information communication technology (IC T) has invariably brought about fundamental changes in the way in which libraries gather. preserve and disseminate information. The study was carried out with an aim to estimate and compare the information seeking behaviour (ISB) of the academics of two prominent universities of Kerala in the context of advancements achieved through ICT. The study was motivated by the fast changing scenario of libraries with the proliferation of many high tech products and services. The main purpose of the study was to identify the chief source of information of the academics, and also to examine academics preference upon the form and format of information source. The study also tries to estimate the adequacy of the resources and services currently provided by the libraries.The questionnaire was the central instrument for data collection. An almost census method was adopted for data collection engaging various methods and tools for eliciting data.The total population of the study was 957, out of which questionnaire was distributed to 859 academics. 646 academics responded to the survey, of which 564 of them were sound responses. Data was coded and analysed using Statistical Package for Social Sciences (SPSS) software and also with the help of Microsofl Excel package. Various statistical techniques were engaged to analyse data. A paradigm shift is evident by the fact that academies push themselves towards information in internet i.e. they prefer electronic source to traditional source and the very shift is coupled itself with e-seeking of information. The study reveals that ISB of the academics is influenced priman'ly by personal factors and comparative analysis shows that the ISB ofthc academics is similar in both universities. The productivity of the academics was tested to dig up any relation with respect to their ISB, and it is found that productivity of the academics is extensively related with their ISB. Study also reveals that the users ofthe library are satisfied with the services provided but not with the sources and in conjunction, study also recommends ways and means to improve the existing library system.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Coastal regulation zone rules in coastal panchayats (villages) of Kerala, India vis-a` -vis socio-economic impacts from the recently introduced peoples’ participatory program for local self-governance and sustainable development

Coastal Regulation Zone (CRZ) notification was issued by the Ministry of Environment and Forest of Government of India in February 1991 as a part of the Environmental Protection Act of 1986 to protect the coast from eroding and to preserve its natural resources. The initial notification did not distinguish the variability and diversity of various coastal states before enforcing it on the various states and Union Territories. Impact assessments were not carried out to assess its impact on socio-economic life of the coastal population. For the very same reason, it was unnoticed or rather ignored till 1994 when the Supreme Court of India made a land mark judgment on the fate of the coastal aquaculture which by then had established as an economically successful industry in many South Indian States. Coastal aquaculture in its modern form was a prohibited activity within CRZ. Lately, only various stakeholders of the coast realized the real impact of the CRZ rules on their property rights andbusiness. To overcome the initial drawbacks several amendments were made in the regulation to suit regional needs. In 1995, another great transformation took place in the State of Kerala as a part of the reorganization of the local self government institutions into a decentralized three tier system called ‘‘Panchayathi Raj System’’. In 1997, the state government also decided to transfer the power with the required budget outlay to the grass root level panchayats (villages) and municipalities to plan and implement the various projects in their localities with the full participation of the local people by constituting Grama Sabhas (Peoples’ Forum). It is called the ‘‘Peoples’ Planning Campaign’’(Peoples’ Participatory Programme—PPP for Local Level Self-Governance). The management of all the resources including the local natural resources was largely decentralized to the level of local communities and villages. Integrated, sustainable coastal zone management has become the concern of the local population. The paper assesses the socio-economic impact of the centrally enforced CRZ and the state sponsored PPP on the coastal community in Kerala and suggests measures to improve the system and living standards of the coastal people within the framework of CRZ.