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.

Synthesis of Bio-Compatible SPION–based Aqueous Ferrofluids and Evaluation of RadioFrequency Power Loss for Magnetic Hyperthermia

Bio-compatible magnetic fluids having high saturation magnetization find immense applications in various biomedical fields. Aqueous ferrofluids of superparamagnetic iron oxide nanoparticles with narrow size distribution, high shelf life and good stability is realized by controlled chemical co-precipitation process. The crystal structure is verified by X-ray diffraction technique. Particle sizes are evaluated by employing Transmission electron microscopy. Room temperature and low-temperature magnetic measurements were carried out with Superconducting Quantum Interference Device. The fluid exhibits good magnetic response even at very high dilution (6.28 mg/cc). This is an advantage for biomedical applications, since only a small amount of iron is to be metabolised by body organs. Magnetic field induced transmission measurements carried out at photon energy of diode laser (670 nm) exhibited excellent linear dichroism. Based on the structural and magnetic measurements, the power loss for the magnetic nanoparticles under study is evaluated over a range of radiofrequencies.

Environmentally compatible phyto-chemical larvicides for mosquito control

In the last decades considerable headway has been made in research and development of phyto-chemical pesticides. The most notable recent success is the commercial development of neem products for insect control. The present investigation on Environmentally Compatible Phyto-Chemical Larvicides for Mosquito Control was undertaken to identify plants of the locality with potential larvicidal activity on mosquito larvae. This has been achieved by screening 17 plant species against four mosquito species. The observation and data are compiled in six chapters .

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.

Investigations on novel polymer nano composites and bio-compatible manganese doped ZnS nanocrystals for photonic and bio-imaging applications

Fluorescence is a powerful tool in biological research, the relevance of which relies greatly on the availability of sensitive and selective fluorescent probes. Nanometer sized fluorescent semiconductor materials have attracted considerable attention in recent years due to the high luminescence intensity, low photobleaching, large Stokes’ shift and high photochemical stability. The optical and spectroscopic features of nanoparticles make them very convincing alternatives to traditional fluorophores in a range of applications. Efficient surface capping agents make these nanocrystals bio-compatible. They can provide a novel platform on which many biomolecules such as DNA, RNA and proteins can be covalently linked. In the second phase of the present work, bio-compatible, fluorescent, manganese doped ZnS (ZnS:Mn) nanocrystals suitable for bioimaging applications have been developed and their cytocompatibility has been assessed. Functionalization of ZnS:Mn nanocrystals by safe materials results in considerable reduction of toxicity and allows conjugation with specific biomolecules. The highly fluorescent, bio-compatible and water- dispersible ZnS:Mn nanocrystals are found to be ideal fluorescent probes for biological labeling

Detergent compatible alkaline lipase produced by marine Bacillus smithii BTMS 11

Bacillus smithii BTMS 11, isolated from marine sediment, produced alkaline and thermostable lipase. The enzyme was purified to homogeneity by ammonium sulfate precipitation and ion exchange chromatography which resulted in 0.51 % final yield and a 4.33 fold of purification. The purified enzyme was found to have a specific activity of 360 IU/mg protein. SDS-PAGE analyses, under non-reducing and reducing conditions, yielded a single band of 45 kDa indicating the single polypeptide nature of the enzyme and zymogram analysis using methylumbelliferyl butyrate as substrate confirmed the lipolytic activity of the protein band. The enzyme was found to have 50 C and pH 8.0 as optimum conditions for maximal activity. However, the enzyme was active over wide range of temperatures (30–80 C) and pH (7.0–10.0). Effect of a number of metal salts, solvents, surfactants, and other typical enzyme inhibitors on lipase activity was studied to determine the novel characteristics of the enzyme. More than 90 % of the enzyme activity was observed even after 3 h of incubation in the presence of commercial detergents Surf, Sunlight, Ariel, Henko, Tide and Ujala indicating the detergent compatibility of B. smithii lipase. The enzyme was also found to be efficient in stain removal from cotton cloths. Further it was observed that the enzyme could catalyse ester synthesis between fatty acids of varying carbon chain lengths and methanol with high preference for medium to long chain fatty acids showing 70 % of esterification. Results of the study indicated scope for application of this marine bacterial lipase in various industries