Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

Studies on Some Simple and Zeolite-Y Encapsulated 3d-Transition Metal Complexes of Schiff Bases Derived From 2-Aminobenzothiazole

In this regard Schiff base complexes have attracted wide attention. Furthermore, such complexes are found to play important role in analytical chemistry, organic synthesis, metallurgy, refining of metals, electroplating and photography. Many Schiff base complexes are reported in literature. Their properties depend on the nature of the metal ion as well as on the nature of the ligand. By altering the ligands it is possible to obtain desired electronic environment around the metal ion. Thus there is a continuing interest in the synthesis of simple and zeolite encapsulated Schiff base complexes of metal ions. Zeolites have a number of striking structural similarities to the protein portion of natural enzymes. Zeolite based catalysts are known for their remarkable ability of mimicking the chemistry of biological systems. In view of the importance of catalysts in all the areas of modern chemical industries, an effort has been made to synthesize some simple Schiff base complexes, heterogenize them by encapsulating within the supercages of zeoliteY cavities and to study their applications. The thesis deals with studies on the synthesis and characterization of some simple and zeoliteY encapsulated Mn(II), Fe(III), Co(II), Ni(II) and Cu(II) complexes and on the catalytic activity of these complexes on some oxidation reactions. Simple complexes were prepared from the Schiff base ligands SBT derived from 2-aminobenzothiazole and salicylaldehyde and the ligand VBT derived from 2-aminobenzothiazole and vanillin (4-hydroxy-3- methoxybenzaldehyde). ZeoliteY encapsulated Mn(II), Fe(III), Co(II), Ni(II) and Cu(II) complexes of Schiff base ligands SBT and VBT and also of 2-aminobenzothiazole were synthesized. All the prepared complexes were characterized using the physico-chemical techniques such as chemical analysis (employing AAS and CHN analyses), magnetic moment studies, conductance measurements and electronic and FTIR spectra. EPR spectra of the Cu(II) complexes were also carried out to know the probable structures and nature of Cu(II) complexes. Thermogravimetric analyses were carried out to obtain the information regarding the thermal stability of various complexes. The successful encapsulations of the complexes within the cavities of zeoliteY were ascertained by XRD, surface area and pore volume analysis. Assignments of geometries of simple and zeoliteY encapsulated complexes are given in all the cases. Both simple and zeoliteY encapsulated complexes were screened for catalytic activity towards oxidation reactions such as decomposition of hydrogen peroxide, oxidation of benzaldehyde, benzyl alcohol, 1-propanol, 2-propanol and cyclohexanol.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Studies on the universal parameters and onset of chaos in dissipative systems

It has become clear over the last few years that many deterministic dynamical systems described by simple but nonlinear equations with only a few variables can behave in an irregular or random fashion. This phenomenon, commonly called deterministic chaos, is essentially due to the fact that we cannot deal with infinitely precise numbers. In these systems trajectories emerging from nearby initial conditions diverge exponentially as time evolves)and therefore)any small error in the initial measurement spreads with time considerably, leading to unpredictable and chaotic behaviour The thesis work is mainly centered on the asymptotic behaviour of nonlinear and nonintegrable dissipative dynamical systems. It is found that completely deterministic nonlinear differential equations describing such systems can exhibit random or chaotic behaviour. Theoretical studies on this chaotic behaviour can enhance our understanding of various phenomena such as turbulence, nonlinear electronic circuits, erratic behaviour of heart and brain, fundamental molecular reactions involving DNA, meteorological phenomena, fluctuations in the cost of materials and so on. Chaos is studied mainly under two different approaches - the nature of the onset of chaos and the statistical description of the chaotic state.

Molecular Approaches For Characterization And Determination Of Pathogenicity Of Vibrios With Special Reference To Vibrio Harveyi From Penaeus Monodon Larval Production Systems

The present study focuses on vibrios especially Vibrio harveyi isolated from shrimp (P. monodon) larval production systems from both east and west coasts during times of mortality. A comprehensive approach has been made to work out their systematics through numerical taxonomy and group them based on RAPD profiling and to segregate the virulent from non- virulent isolates based on the presence of virulent genes as well as their phenotypic expression. The information gathered has helped to develop a simple scheme of identification based on phenotypic characters and segregate the virulent from non virulent strains of V. harveyi.

Development of nitrifying bacterial consortia for immobilizing in nitrifying bioreactors designed for penaeid and non-penaeid larval rearing systems in the tropics

Two ammonia oxidizing (AMOPCU-1 and AMONPCU-1) and two nitrite oxidizing (NIOPCU-1 and NIONPCU-1) consortia for activating nitrifying bioreactors and thereby establishing nitrification in penaeid and non-penaeid hatchery systems were developed by enrichment. For further amplification of the consortia a simple medium having seawater (either salinity 30 ‰ or 15 ‰) as base, supplemented with NH4+-N/NO2--N and PO4- and pH adjusted to 8 was identified. During the amplification in a fermentor the consortia exhibited excessive wall growth and diminished their yield coefficient posing difficulty in harvesting the cells completely. The consortia consisted of both Gram negative and Gram-positive bacterial cells embedded in a mucilaginous matrix of glycocalyx - like material presumably composed of polysaccharides. The consortia besides being useful in activating nitrifying bioreactors developed for shrimp/prawn hatchery systems can also be used as bioaugmentors in the bioremediation of ammonia and nitrite toxicity in aquaculture systems.