Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Studies on the littoral processes in relation to stability of beaches around Cchin

The coastal and nearshore areas have played vital role in the trade and economic development of coastal nations since ancient times. In recent years, the demands for utilization of these areas have increased for purposes of navigation, setting up of offshore structures for oil industry, exploitation of the available fishery and mineral resources, and to provide recreational facilities along the coast as a part of the coastal zone management. It is in this context the studies on nearshore processes receive greater priorities. Stability of beaches is controlled by the interaction of various physical parameters such as winds, waves, currents, tides and the nature and constituents of the beaches. The results of studies carried out by the author on the dynamical effects of these environmental parameters on the shoreline processes along the beaches around Cochin are presented in this thesis. The section of the coast investigated is about 57 km of shore from Azhikode to Anthakaranazhi situated on the central Kerala coast. Four regions namely Narakkal, Malipuram, Fort Cochin and Anthakaranazhi were chosen for detailed study

On Truncated Versions of Certain Measures of Inequality and Stability

The present study focuses attention on defining certain measures of income inequality for the truncated distributions and characterization of probability distributions using the functional form of these measures, extension of some measures of inequality and stability to higher dimensions, characterization of bivariate models using the above concepts and estimation of some measures of inequality using the Bayesian techniques. The thesis defines certain measures of income inequality for the truncated distributions and studies the effect of truncation upon these measures. An important measure used in Reliability theory, to measure the stability of the component is the residual entropy function. This concept can advantageously used as a measure of inequality of truncated distributions. The geometric mean comes up as handy tool in the measurement of income inequality. The geometric vitality function being the geometric mean of the truncated random variable can be advantageously utilized to measure inequality of the truncated distributions. The study includes problem of estimation of the Lorenz curve, Gini-index and variance of logarithms for the Pareto distribution using Bayesian techniques.

Polystyrene Anchored Vanillin Schiff Base—Complexation and Ion Removal Studies

A set of six new polystyrene anchored metal complexes have been synthesized by the reaction of the metal salt with the polystyrene anchored Schiff base of vanillin. These complexes were characterized by elemental analyses, Fourier transform infrared spectroscopy, diffuse reflectance studies, thermal studies, and magnetic susceptibility measurements. The elemental analyses suggest a metal : ligand ratio of 1 : 2. The ligand is unidentate and coordinates through the azomethine nitrogen. The Mn(II), Fe(III), Co(II), Ni(II), and Cu(II) complexes are all paramagnetic while Zn(II) is diamagnetic. The Cu(II) complex is assigned a square planar structure, while Zn(II) is assigned a tetrahedral structure and Mn(II), Fe(III), Co(II), and Ni(II) are all assigned octahedral geometry. The thermal analyses were done on the ligand and its complexes to reveal their stability. Further, the application of the Schiff base as a chelating resin in ion removal studies was investigated. The polystyrene anchored Schiff base gave 96% efficiency in the removal of Ni(II) from a 20-ppm solution in 15 min, without any interference from ions such as Mn(II), Co(II), Fe(III), Cu(II), Zn(II), U(VI), Na , K , NH4 , Ca2 , Cl , Br , NO3 , NO2 ,and CH3CO2 . The major advantage is that the removal is achieved without altering the pH.

Studies on natural rubber-bound diphenylamine antioxidants

Diphenylamine was chemically attached to depolymerised natural rubber by photochemical reaction. The rubber-bound diphenylamine was characterised by TLC, HNMR, IR and TGA. The efficiency and permanence of the bound diphenylamine was compared with conventional amine type antioxidant in natural rubber vulcanizates. The rubber-bound diphenylamine was found to be less volatile and less extractable compared to the conventional antioxidant. The vulcanizates showed improved ageing resistance in comparison to vulcanizates containing conventional antioxidant . Also, the presence of liquid rubber-bound diphenylamine reduces the amount of plasticiser required for compounding.

Studies on the curing of short polyester fiber-polyurethane elastomer composite with different interfacial bonding agents

The cure characteristics of short fiber-polyurethane elastomer were studied with respect to different fiber-matrix bonding agents. A hexamethylenetetramine- resorcinol -hydrated silica based bonding agent was found to affect the stability of the composite. A new bonding agent, TP resin, based on polymeric toluenediisocyanate and polypropylene glycol has been developed. Cure characteristics of the composite with and without TP resin at different fiber loadings were also compared. Minimum torque, scorch time and optimum cure time increased with fiber content. Maximum torque was consistently higher with TP resin at all fiber loadings.

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.

Sediment Budgeting Studies for the Kollam Coast

The Sediment budgeting studies are done to bring out the coastal processes at work, to understand the beach-innershelf sedimentary dynamics and to assess the stability of any coastal stretch. There is a dearth of such studies as far as the Indian coast is concerned. The Chavara coast of Kollam district, Kerala, is world famous for its rich heavy mineral resources. These mineral resources are being commercially mined by the Indian Rare Earths Ltd. (IREL) and Kerala Minerals and Metals Ltd. (KMML), two Public Sector Undertakings located in the area. The impact of mining on stability of the beach has been a point of debate among the local people as well as researchers. The coastal stretch of 22km length from Neendakara to Kayamkulam which is referred to as the Chavara coast. The tidal, wind driven and continental shelf currents, there could also be the contribution of coastal trapped waves and baroclinic flow associated with the plumes of fresh water coming from the estuaries. The main objectives of the study are the hydrodynamic processes and mechanism involved in the sediment movement along the Chavara coast, Identify the different sources and sinks of beach sand along the coast, Quantify the sediment input/output into/from the coast and assess the erosion/accretion scenario of the coast.

Studies on Fluxon Dynamics in Coupled Josephson Junctions

The thesis deals with detailed theoretical analysis of fluxon dynamics in single and in coupled Josephson junctions of different geometries under various internal and external conditions. The main objective of the present work is to investigate the properties of narrow Long Josephson junctions (LJJs) and to discuss the intriguing physics. In this thesis, Josephson junctions of three types of geometries, viz, rectangular, semiannular and quarter annular geometries in single and coupled format are studied to implement various fluxon based devices. Studies presented in this thesis reveal that mulistacked junctions are extremely useful in the fabrication of various super conducting electronic devices. The stability of the dynamical mode and therefore the operational stability of the proposed devices depend on parameters such as coupling strength, external magnetic fields, damping parameters etc. Stacked junctions offer a promising way to construct high-TC superconducting electronic components. Exploring the complex dynamics of fluxons in coupled junctions is a challenging and important task for the future experimental and theoretical investigations

Seasonal Studies on Primary Production and Associated Environmental Parameters in the Indian EEZ

The thesis describes the importance of Indian EEZ, definition and the various factors affecting primary production, general account of phytoplankton and its importance in marine ecosystem etc. In review of literature, general oceanography of Arabian Sea and Bay of Bengal and hydrography of eastern Arabian Sea and western Bay of Bengal. It deals with the distribution patterns of primary production, chlorophyll a, phytoplankton composition and particulate organic carbon in the eastern Arabian Sea and western Bay of Bengal during different seasons. Factors that affect primary productivity are irradiance, temperature, stability of the surface waters, nutrients and zooplankton grazing. The differential biological response of eastern Arabian Sea and western Bay of Bengal to monsoonal regimes. A precise estimation on the primary production of the entire EEZ of India on a regional basis and on a seasonal scale would be the only way to achieve any kind of predictive assessment on the fish stock and their sustainable yield. This study mainly envisages the qualitative and quantitative aspects on the magnitude of phytoplankton standing crop and production of organic carbon and their relationship to environmental characteristics during summer monsoon, Inter monsoon and winter monsoon periods in the east and west coasts of the Indian EEZ.This study revealed that the seasonality exerts a great impact on the biological production in the eastern Arabian Sea and western Bay of Bengal. High biological production may be the reason why most of the fish landings are Concentrated in the west coast of India than east coast. The present data on Phytoplankton production rate and the species composition will provide a meaningful ground for evaluations of exploitable renewable resources of the IndianEEZ

STUDIES ON SCATTERING AND QUASI-NORMAL MODES IN BLACK HOLE SPACE-TIMES

The question of stability of black hole was first studied by Regge and Wheeler who investigated linear perturbations of the exterior Schwarzschild spacetime. Further work on this problem led to the study of quasi-normal modes which is believed as a characteristic sound of black holes. Quasi-normal modes (QNMs) describe the damped oscillations under perturbations in the surrounding geometry of a black hole with frequencies and damping times of oscillations entirely fixed by the black hole parameters.In the present work we study the influence of cosmic string on the QNMs of various black hole background spacetimes which are perturbed by a massless Dirac field.

Studies on the Utilisation of Rubber Reclaim in Elastomers

The thesis describes utilisation of reclaimed rubber, Whole Tyre Reclaim (WTR) produced from bio non- degradable solid pollutant scrap and used tyres. In this study an attempt has made to optimize the substitution of virgin rubber with WTR in both natural and synthetic rubber compounds without seriously compromising the important mechanical properties. The WTR is used as potent source of rubber hydrocarbon and carbon black filler. Apart from natural rubber (NR), Butadiene rubber (BR), Styrene butadiene rubber (SBR), Acrylonitrile butadiene rubber (NBR) and Chloroprene rubber (CR) were selected for study, being the most widely used general purpose and specialty rubbers. The compatibility problem was addressed by functionalisation of WTR with maleic anhydride and by using a coupling agent Si69.The blends were systematically evaluated with respect to various mechanical properties. The thermogravimetric analyses were also carried out to evaluate the thermal stability of the blends.Mechanical properties of the blends were property and matrix dependant. Presence of reinforcing carbon black filler and curatives in the reclaimed rubber improved the mechanical properties with the exception of some of the elastic properties like heat build up, resilience, compression set. When WTR was blended with natural rubber and synthetic rubbers, as the concentration of the low molecular weight, depolymerised WfR was increased above 46-weight percent, the properties deteriorates.When WTR was blended with crystallizing rubbers such as natural rubber and chloroprene rubber, properties like tensile strength, ultimate elongation were decreased in presence of WTR. Where as in the case of blends of WTR with non-crystallizing rubbers reinforcement effect was more prominent.The effect of functionalisation and coupling agent was studied in three matrices having different levels of polarity(NBR, CR and SBR).The grafting of maleic anhydride on to WTR definitely improved the properties of its blends with NBR, CR and SBR, the effect being prominent in Chloroprene rubber.Improvement in properties of these blends could also achieved by using a coupling agent Si69. With this there is apparent plasticizing effect at higher loading of the coupling agent. The optimum concentration of Si69 was 1 phr for improved properties, though the improvements are not as significant as in the case of maleic anhydride grafting.Thermal stability of the blend was increased by using silane-coupling agent.

Studies on short Nylon-6 fiber - elastomer composites with epoxy resin as bonding agent

The thesis describes the development and evaluation of epoxy resin as interfacial bonding agent for short Nylon-6 fiber elastomer composites. Epoxy resin is well known for its adhesive property. The potential use of it as interfacial bonding agent in short fiber composite is not explored yet. Three rubbers viz., acrylonitrile butadiene rubber (NBR), Neoprene rubber (CR) and styrene butadiene rubber (SBR) were selected and different fiber loading were tried. The resin concentration was optimized for each fiber loading with respect to cure characteristics and mechanical properties. Rheological characteristics and thermal degradation of the composites containing different fiber loading and different resin concentrations were studied in detail to find the effect of epoxy resin bonding system. The mechanical properties were studied in detail. The short Nylon -6 fiber improved most of the mechanical properties of all the three rubbers. Tensile strength showed a dip at 10 phr fiber loading in the case of CR while it was continuously increased with fiber loading in the case of NBR and SBR. All the composites showed anisotropy in mechanical properties. The epoxy resin is an effective bonding agent for short Nylon -6 fiber reinforced NBR and CR composites. Epoxy resin improved tensile strength, abrasion resistance and modulus of these composites. SEM studies confirmed the improved bonding of fiber and matrix in the presence of epoxy bonding agent. Epoxy resin was not effective as bonding agent in the case of short Nylon fiber- SBR composite. From the rheological studies of the composites with and without bonding agent it was observed that all the composite exhibited pseudoplasticity, which decreased with temperature. At higher shear rates all the mixes showed plug flow. SEM pictures showed that maximum orientation of fibers occured at a shear rate, just before the onset of plug flow. The presence of fiber reduced the temperature sensitivity of the flow at a given shear rate. Die swell was reduced in the presence of fiber. Shear viscosity of the composite was increased in the presence of resin. Die swell was increased in the presence of epoxy resin for composites at all shear rates. The thermal degradation of NBR and SBR composites with and without bonding agent followed single step degradation pattern. Thermal stability of the composites was improved in the presence of bonding agent. The degradation of virgin elastomer and the composites followed first order kinetics.