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.

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.

Stability of Random Sums and Extremes

This study is about the stability of random sums and extremes.The difficulty in finding exact sampling distributions resulted in considerable problems of computing probabilities concerning the sums that involve a large number of terms.Functions of sample observations that are natural interest other than the sum,are the extremes,that is , the minimum and the maximum of the observations.Extreme value distributions also arise in problems like the study of size effect on material strengths,the reliability of parallel and series systems made up of large number of components,record values and assessing the levels of air pollution.It may be noticed that the theories of sums and extremes are mutually connected.For instance,in the search for asymptotic normality of sums ,it is assumed that at least the variance of the population is finite.In such cases the contributions of the extremes to the sum of independent and identically distributed(i.i.d) r.vs is negligible.

Effect of the Vulcanization Time and Storage on the Stability and Physical Properties of Sulfur-Prevulcanized Natural Rubber Latex

Prevulcanized natural rubber latex was prepared by the heating of the latex compound at 55°C for different periods of time (2, 4, 6, 8, and 10 h). The changes in the colloidal stability and physical properties were evaluated during the course of prevulcanization. The prevulcanized latex compounds were stored for 300 days, and the properties were monitored at different storage intervals (0, 20, 40, 60, 120, 180, 240, and 300 days). During prevulcanization, the mechanical stability time increased, and the viscosity remained almost constant. The tensile strength increased during storage for a period of 20 days. The degree of crosslinking, modulus, elongation at break, and chloroform number were varied with the time of storage.

Hydrodynamic Study of Swirling Fluidized Bed and the Role of Distributor

The study aims to the hydrodynamic characteristics of swirling fluidized bed, using large particles (Geldart D-type) selected from locally available agricultural produce (coffee beans and black pepper). The important variables considered in the present study include percentage area of opening, angle of air injection and the percentage useful area of the distributor. A total of seven distributors have been designed and fabricated for a bed column of 300 mm, namely single row vane type distributors (15˚ and 20˚ vane angle), inclined hole type distributors (15˚ and 20˚ vane angle) and perforated plate distributors. The useful area of distributor of single row vane type, three now vane-type and inclined hole-type distributors are respectively 64%,91% and 94%. The hydrodynamic parameters considered in the present study include distributor pressure drop, air velocity, minimum fluidizing velocity, bed pressure drop, bed height and the bed behaviour. It has been observed that, in general, the distributor pressure drop decreases with an increase in the percentage area of opening, Further, and increase in the area of opening above 17% will not considerably reduce the distributor pressure drop. In the present study, for the distributor with an area of opening 17%, and corresponding to the maximum measured superficial velocity of 4.33 m/s, the distributor pressure drop obtained was 55.25mm of water. The study on the bed behavior revealed that, in a swirling fluidized bed, once swirl motion starts, the bed pressure drop increases with superficial velocity in the outer region and it decreases in the inner region. This means that, with higher superficial velocity, the air might get by-passed through the inner boundary of the bed (around the cone). So, depending on the process for which the bed is used, the maximum superficial velocity is to be limited to have an optimum bed performance.

Biochemical Investigations on the Stability of Biological Membranes

In this project, an attempt has been made to study the stability of erythrocyte and lysosomal membranes biochemically. Erythrocytes were chosen for the study because of their ready availability and relative simplicity. Biological membranes forming closed boundaries between compartments of varying composition consist mainly of proteins and lipids. They are asymmetric, fluid structures that are thermodynamically stable and metabolically active. Normal cellular function begins with normal membrane structure and any variation in it may upset the normal functions. The degree of fluidity of a membrane depends on the chain length of its lipids and degree of unsaturation of constituent fatty acids. In response to environmental changes, many cells can regulate composition of their membranes to maintain the overall semi fluid environment necessary for many membrane associated functions. The assembly and Maintenance of membrane structures in cells is a dynamic process. The components are not only synthesized and inserted into a growing membrane but are also continuously degraded at a slower rate. This turnover process varies with each individual molecule.Lysosomes are important in the catabolic processes occurring in the cell. Lysosomes contain hydrolytic enzymes and are stable under normal conditions. In certain pathological conditions, the lysosomal membrane may rupture, releasing the hydrolytic enzymes into the cell and digestion of cell takes place as a whole. This is very dangerous. In normal life processes of multi cellular organisms, lysosomes rupture following the death of a cell and it may have some value as a built in mechanism for selfremoval of dead cells.An attempt has also been made in this project towards developing lysosome membrane stability as an index of fish spoilage during storage. Different membranes within the cell and between cells have different compositions as reflected in the ratio of protein to lipid. The difference is not surprising given the very different functions of membranes

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.

Influence of Processing Variables on Protein Quality and Frozen Storage Stability of Two Commercially Important Species of Squid (Loligo duvaucelii and Doryteuthis sibogae )

Cephalopods are utilized as an important food item in various countries because of its delicacy as raw consumed food. Mainly sepia and loligo are consumed raw by Japanese and Russians. The freshness of the products is very important when the product is consumed raw. The major species that dominate our squid catch are Loligo duvaucelii and Doryteuthis sibogae. There is a noticeable difference in the quality of both the species. The needle squid (Doryteuthis sibogae ) contributes about 35% of the total squid landing. Due to the fast deterioration , a major portion of the needle squid, which is caught during the first few hauls, is thrown back to sea. The catch in the last hauls only are taken to the landing centers. At present the needle squid is processed as blanched rings and the desired quality is not obtained if it is processed as whole, whole cleaned or as tubes. In this study an attempt is made to investigate the biochemical characteristics in both the species of squid in relation to their quality and, the process control measures to be adopted. The effect of various treatments on their quality and the changes in proteolytic and lysosomal enzymes under various processing conditions are also studied in detail.Thus this study can provide the seafood industry with relevant suggestions and solutions for effective utilization of both the species of squid with emphasis on needle squid.

Acid activated montmorillonite: an efficient immobilization support for improving reusability, storage stability and operational stability of enzymes

Three enzymes, α-amylase, glucoamylase and invertase, were immobilized on acid activated montmorillonite K 10 via two independent techniques, adsorption and covalent binding. The immobilized enzymes were characterized by XRD, N2 adsorption measurements and 27Al MAS-NMR spectroscopy. The XRD patterns showed that all enzymes were intercalated into the clay inter-layer space. The entire protein backbone was situated at the periphery of the clay matrix. Intercalation occurred through the side chains of the amino acid residues. A decrease in surface area and pore volume upon immobilization supported this observation. The extent of intercalation was greater for the covalently bound systems. NMR data showed that tetrahedral Al species were involved during enzyme adsorption whereas octahedral Al was involved during covalent binding. The immobilized enzymes demonstrated enhanced storage stability. While the free enzymes lost all activity within a period of 10 days, the immobilized forms retained appreciable activity even after 30 days of storage. Reusability also improved upon immobilization. Here again, covalently bound enzymes exhibited better characteristics than their adsorbed counterparts. The immobilized enzymes could be successfully used continuously in the packed bed reactor for about 96 hours without much loss in activity. Immobilized glucoamylase demonstrated the best results.

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

Stability of periodic orbits of coupled-map lattices

We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.

A study of hydrodynamic turbulence using laser transmission

Using laser transmission, the characteristics of hydrodynamic turbulence is studied following one of the recently developed technique in nonlinear dynamics. The existence of deterministic chaos in turbulence is proved by evaluating two invariants viz. dimension of attractor and Kolmogorov entropy. The behaviour of these invariants indicates that above a certain strength of turbulence the system tends to more ordered states.

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