Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

Investigations on the biology of Indian Mackerel Rastrelliger kanagurta (Cuvier) along the Central Kerala coast with special reference to maturation, feeding and lipid dynamics

Dept. of Marine Biology, Microbiology & Biochemistry, Cochin University of Science and Technology

Implications of Hydrobiology and Nutrient dynamics on trophic structure and interactions in Cochin backwaters

In the present thesis entitled” Implications of Hydrobiology and Nutrient dynamics on Trophic structure and Interactions in Cochin backwaters”, an attempt has been made to assess the influence of general hydrography, nutrients and other environmental factors on the abundance, distribution and trophic interactions in Cochin backwater system. The study was based on five seasonal sampling campaigns carried out at 15 stations spread along the Cochin backwater system. The thesis is presented in the following 5 chapters. Salient features of each chapter are summarized below: Chapter 1- General Introduction: Provides information on the topic of study, environmental factors, back ground information, the significance, review of literature, aim and scope of the present study and its objectives.Chapter 2- Materials and Methods: This chapter deals with the description of the study area and the methodology adopted for sample collection and analysis. Chapter 3- General Hydrograhy and Sediment Characteristics: Describes the environmental setting of the study area explaining seasonal variation in physicochemical parameters of water column and sediment characteristics. Data on hydrographical parameters, nitrogen fractionation, phosphorus fractionation and biochemical composition of the sediment samples were assessed to evaluate the trophic status. Chapter 4- Nutrient Dynamics on Trophic Structure and Interactions: Describes primary, secondary and tertiary production in Cochin backwater system. Primary production related to cell abundance, diversity of phytoplankton that varies seasonally, concentration of various pigments and primary productivitySecondary production refers to the seasonal abundance of zooplankton especially copepod abundance and tertiary production deals with seasonal fish landings, gut content analysis and proximate composition of dominant fish species. The spatiotemporal variation, interrelationships and trophic interactions were evaluated by statistical methods. Chapter 5- Summary: The results and findings of the study are summarized in the fifth chapter of the thesis.

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.

Studies on Selected Myctophid Fishes in Arabian Sea with respect to their Status in Deep Sea Trawl Bycatch, Length-Weight Relationship, Reproductive Biology and Population Dynamics

Available information on abundance of myctophids and their utilisation indicate that there is excellent scope for development of myctophid fisheries in Indian Ocean. Most of the conventional fish stocks have reached a state of full exploitation or over-exploitation. Hence there is need to locate new and conventional fishery resources in order to fill in the supply-demand gap, in the face of increasing demand for fish. Information on length-weight relationship, age and growth, spawning season, fecundity and age at maturity and information on bycatch discards are required for sustainable utilization of myctophid resource in the Indian Ocean

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.