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

Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Thermal degradation studies on Edible Oil during Deep Fat Frying Process

Deep fat frying process is one of the widely followed cooking practices throughout the world. Cooking oils serve as a medium for frying food for transferring heat and makes fried food tasty and palatable. Frying process is a most complex process involving numerous physicochemical changes which are complicated to understand. Frying leads to thermal degradation of oil through thermo-oxidation, hydrolysis, and polymerization. Hydrolysis results in formation of free fatty acids whereas oxidation process produces hydroperoxides and small molecular carbonyl compounds. This whole process leads to the formation of polar compounds and degradation of antioxidants that further degrades frying oil. Eventually, through mass transfer process these degradation products accumulate into fried food and reduce the nutritional quality of both oil and food. Thus, the frying process is of research interest calls for detailed systematic study which is chosen for the present study. The primary objective of this study is to understand the mechanism of degradation and characterization ofdegraded products which helps in arriving at the limits for frying oil utilization in terms of number of frying cycles. The mechanistic studies and the knowledge on the degraded products help to understand the way to retard the deterioration of oil for stability and enhancement of frying cycles. The study also explores the formation of the predominant polar compounds and their structural elucidation through mass spectrometry. Oxidation of oil is another important factor that ignites the degradation phenomena. One of the best ways to increase thermal stability of any oil is addition of potent antioxidants. But, most of the natural and synthetic antioxidants are unstable and ineffective at frying temperatures. Therefore, it is necessary to screen alternative antioxidants for their activity in the refined oils which are devoid of any added antioxidants. In this context, this study discussed the efficacy of several natural and synthetic antioxidants to retard the formation of polar compounds and thermooxidation during prolonged frying conditions. Similarly, the advantage of blending of two different oils to improve the thermal stability was explored. The present study brings out the total picture on the type of degradation products formed during frying and the ways of retarding the determination to improve upon the stability of the oil and enhancement of frying cycles.

Studies on grain refinement and alloying additions on the microstructure and mechanical properties of Mg-8Zn-4Al alloy

MAGNESIUM ALLOYS have strong potential for weight reduction in a wide range of technical applications because of their low density compared to other structural metallic materials. Therefore, an extensive growth of magnesium alloys usage in the automobile sector is expected in the coming years to enhance the fuel efficiency through mass reduction. The drawback associated with the use of commercially cheaper Mg-Al based alloys, such as AZ91, AM60 and AM50 are their inferior creep properties above 100ºC due to the presence of discontinuous Mg17A112 phases at the grain boundaries. Although rare earth-based magnesium alloys show better mechanical properties, it is not economically viable to use these alloys in auto industries. Recently, many new Mg-Al based alloy systems have been developed for high temperature applications, which do not contain the Mg17Al12 phase. It has been proved that the addition of a high percentage of zinc (which depends upon the percentage of Al) to binary Mg-Al alloys also ensures the complete removal of the Mg17Al12 phase and hence exhibits superior high temperature properties.ZA84 alloy is one such system, which has 8%Zn in it (Mg-8Zn-4Al-0.2Mn, all are in wt %) and shows superior creep resistance compared to AZ and AM series alloys. These alloys are mostly used in die casting industries. However, there are certain large and heavy components, made up of this alloy by sand castings that show lower mechanical properties because of their coarse microstructure. Moreover, further improvement in their high temperature behaviour through microstructural modification is also an essential task to make this alloy suitable for the replacement of high strength aluminium alloys used in automobile industry. Grain refinement is an effective way to improve the tensile behaviour of engineering alloys. In fact, grain refinement of Mg-Al based alloys is well documented in literature. However, there is no grain refiner commercially available in the market for Mg-Al alloys. It is also reported in the literature that the microstructure of AZ91 alloy is modified through the minor elemental additions such as Sb, Si, Sr, Ca, etc., which enhance its high temperature properties because of the formation of new stable intermetallics. The same strategy can be used with the ZA84 alloy system to improve its high temperature properties further without sacrificing the other properties. The primary objective of the present research work, “Studies on grain refinement and alloying additions on the microstructure and mechanical properties of Mg-8Zn-4Al alloy” is twofold: 1. To investigate the role of individual and combined additions of Sb and Ca on the microstructure and mechanical properties of ZA84 alloy. 2. To synthesis a novel Mg-1wt%Al4C3 master alloy for grain refinement of ZA84 alloy and investigate its effects on mechanical properties.

An integrated study on the hydrogeology of Bharathapuzha river basin, South West coast of India

The present work deals with the An integrated study on the hydrogeology of Bharathapuzha river basin ,south west coast of india. To study the spatial and temporal behaviour of the groundwater system of the Bharathapuzha river basin.To discover the sub-surface parameter by ground resistivity surveys.T o determine the groundwater quality of the Bharathapuzha river basin for the different seasons {pre monsoon and post monsoon with reference to the domestic and irrigational water quality standards.Present study will provide a good database on the hydrogeological aspects within the river basin.The study area covers l7 block Panchayats. Of these, Chitoor block is ‘over exploited’, Kollengode, Trithala, and Palakkad are ‘critical’ in category and Kuttippuram and Sreekrishnapuram blocks are ‘semi critical’ in terms of groundwater development.Comparison of Geomorphology map with drainage map shows that the geomorphology has a clear control on the drainage net work of the basin. The structural hill area shows a highest drainage network, where as pediment shows lowest drainage network.There are many discontinuous lineament in the Bharathapuzha river basin which can be connected by a straight line.Ground water flow directions are generally towards the western portions of the study area. From the northern region Water flows towards the central and also water from the eastern and southern side confluences at the centre and move towards western side of the basin.The positive correlation of transmissivity and storativity values show good aquifer conditions exists in the present study area .

Studies on the ecology of zooplankton of cochin backwaters(a tropical estuary)

Ecology is the study of systems at a level in which individuals or whole organisms may be considered elements of interaction, either among themselves, or with a loosely organised environmental matrix. Systems at this level are named ecosystems, and ecology, of course, is the biology of ecosystems" (Hargalef, 1968). This thesis includes principally, a study on the ecology of zooplankton of the Cochin backwaters conducted during the years 1971-72. This monsoonal estuarine system is particularly interesting, since it exhibits a wide range of variations in its environmental conditions which is naturally reflected in the fauna also. Several publications on various aspects of its hydrobiology have come out in the recent past. But studies on the zooplankton of the estuary have mostly been discontinuous either in space or time or restricted to its groups

Predictability Of Share Prices In India: A Study Of The Applicability Of Technical Analysis

In spite of the far longed practices of technical analysis by many participants in Indian stock market, none have arrived at the exact position of technical analysis as a tool for foretelling share prices. There is no evidence supporting that one has established its definite role in predicting the behaviour of share price and also to see the extent of validity (how far reliable) of technical tools in Indian stock market. The problem is the vacuum in the arena of securities market analysis where an unrecognised tool is practised, i.e., whether to hold on to technical analysis or to drop it. Again, as already stated in this chapter, its validity need not continue forever. It may become futile as happened in developed markets. Continuous practice of a tool, which is valid only during discontinuous times is also an error. The efficacy of different market phenomena in terms of their ability to foretell the extent and direction of the price movements and reliability thereof remain as not yet proved in. This requires further study in this area so that this controversy may be settled. A solution to the problem requires enquiring and establishing the applicability of technical analysis, if any, there is in the Indian stock market. The study has the following two broad objectives for the purpose of confirming the applicability, if any, of technical analysis in the Indian stock market. The first objective is to ascertain the current validity of ‘traditional holding with respect to patterns’ and the second objective is to ascertain the ‘consistent superiority’, if any, of technical indicators over non-signal strategies in return generation. The study analyses the five patterns, which are widely known and commonly found in publications. They are: (1) Symmetrical Triangles, (2) Rising Wedges, (3) Falling Wedges, (4) Head and Shoulders Top and (5) Head and Shoulders Bottom.