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

Influence of short term climatic fluctuations on the agricultural land use in Kerala

In the present study, the land use over Kerala State and its spatial and temporal variations, spatio-temporal variations of water budget elements, climatic shifts, incidence of droughts and the influence of inter-annual fluctuations of rainfall on area. production and yield of selected crops, have been studied in detail. The thesis consists of seven chapters including the introduction. The first section of the Second Chapter deals with the importance of agrocliinatological studies in general and its application in agricultural land use in particular. It also gives an overview of the short term climatic fluctuations, water balance studies, crop weather relationships, land use patterns and various agricultural indices. This includes a detailed review of available literature in this field. The basic concepts. data used and the methodology adopted in the study forms, the second section of this Chapter. The Third Chapter gives the details of the physical features of the State such as the relief, geology, geomorphologysoils, drainage, and vegetation. The agroclimatology of the State is discussed in detail in Chapter Four. The first Section presents annual and seasonal variations of temperature and rainfall of the State along with a discussion on the water balance of the State. The secondSection of this Chapter deals with the influence of rainfall and water balance elements on various crops. The district-wise general land use pattern of theState and its spatio-temporal variations are discussed in Chapter Five. The first Section of Chapter Six gives an overview of the agricultural land use pattern of the State, cropping patterns, cropping intensity, crop combination and their spatio-temporal variations. The inter-annual variability of water balances of various stations of the State computed using the method of Thornthwaite (1948) and Thornthwaite & Mather (1955) is presented in the second Section of Chapter Six. This also includes a discussion of how the climatic shifts have occurred over the State and the influence of variations of climatic and water balance elements on the crops. The Seventh Chapter gives the summary of the work carried out and the results obtained from the study. Interpretations of the results, conclusions and suggestions made,based on the observations of the study are incorporated in this Chapter.

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.