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 electroluminescence using Powder and thin film devices

The subject of electroluminescence has currently acquired great importance because of its potential applications in display systems of a wide variety. A large number of scientists working in commercial, governmental as well as academic institutions all over the world are at present engaged in the intense effort to develop new and efficient phosphor materials and electroluminescent devices. This thesis presents the work carried out by the author in this field during the past few years. The studies discussed in this thesis are mostly confined to the development of some new phosphor materials, their uses in powder and thin film electroluminescent devices and to their electrical and spectral characteristics. Care has been taken to bring' out the physics involved in all the above aspects of the phenomenon

Development of a Technique for Estimating Rain Parameters from Rain Noise Measurements

The measurement of global precipitation is of great importance in climate modeling since the release of latent heat associated with tropical convection is one of the pricipal driving mechanisms of atmospheric circulation.Knowledge of the larger-scale precipitation field also has important potential applications in the generation of initial conditions for numerical weather prediction models Knowledge of the relationship between rainfall intensity and kinetic energy, and its variations in time and space is important for erosion prediction. Vegetation on earth also greatly depends on the total amount of rainfall as well as the drop size distribution (DSD) in rainfall.While methods using visible,infrared, and microwave radiometer data have been shown to yield useful estimates of precipitation, validation of these products for the open ocean has been hampered by the limited amount of surface rainfall measurements available for accurate assessement, especially for the tropical oceans.Surface rain fall measurements(often called the ground truth)are carried out by rain gauges working on various principles like weighing type,tipping bucket,capacitive type and so on.The acoustic technique is yet another promising method of rain parameter measurement that has many advantages. The basic principle of acoustic method is that the droplets falling in water produce underwater sound with distinct features, using which the rainfall parameters can be computed. The acoustic technique can also be used for developing a low cost and accurate device for automatic measurement of rainfall rate and kinetic energy of rain.especially suitable for telemetry applications. This technique can also be utilized to develop a low cost Disdrometer that finds application in rainfall analysis as well as in calibration of nozzles and sprinklers. This thesis is divided into the following 7 chapters, which describes the methodology adopted, the results obtained and the conclusions arrived at.

High resolution optogalvanic study in nitrogen discharge

Doppler limited high resolution spectrum in the wavelength region 17224 to 17236 cm−1 of the first positive system (B 3Π g −A 3Σ u + ) of the N2 molecule is recorded by optogalvanic spectroscopic technique using a single mode ring dye laser. It is observed that the intensity and line width of the rotational line increase with the discharge current. Dependence of the collision broadening coefficient on the current was also evaluated.

Systematics, Life history traits, abundance andstock assessment of cobia, Rachycentron canadum ( Linnaeus, 1766) occurring in Indian waters with special reference to the north west coast in India

This thesis entitled Systematics,life history traits ,abundance and stock assessment of cobia rachycentron canadum (linnaeus ,1766) occurring in indian waters with special reference to the northwest coast of india.Cobia, Rachycentron canadum is a fast growing pelagic fish belonging to the monotypic family Rachycentridae. They show worldwide distribution in tropical and sub tropical waters. Cobia is exploited commercially in various countries like Taiwan, Pakistan, India, United State of America, Australia, Gulf of Mexico and the Caribbean. Recreational fishery of Cobia exists in different parts of the world. In India Cobia is caught as bycatch of trawlers, gillnet and hook and line fishery.This study also focuses on to bring out the distribution pattern and also to assess the biomass and estimate sustainable yield of Cobia inhabiting in Indian EEZ. In addition to above, present study standardised live collection methods and also reviewed culture prospects.Results of osteological study and morphological studies indicate its close resemblance to Remora and support the view that Cobia was evolved from Dolphin fishes and remoras followed it. Study also confirmed that Cobia does not have any relative or similar species and is a monotypic species belonging to the family Rachycentridae. Re description of the species was done based on the characters identified. In this study, feeding intensity was also assessed following methods like Gastrosomatic index, Mean index of feeding intensity and Index of fullness. Sex wise, month wise and length group wise fluctuations in the feeding intensity also were studied. Cobia actively fed during post monsoon period. In general, adult fed actively than the juveniles. Trophic level value estimated (4.36) indicates that Cobia occupy top level position in the food chain.

Studies on the production management in the seafood processing industry in Kerala

Kerala was the pioneer in modern seafood processing and exporting. But now the industry is Iacingalot of problems due to low productivity and deterioration in the quality of the products. only about 17% of the installed freezing capacity in sea food processing industry was reported to be utilised during 1979-80. The price of the export commodities its decided by the buyers based on international supply and demand pattern and based on the strength and weakness of dollar/yen. The only way to increase the profitability of the processors is to reduce the cost of production to the possible extent. The individual processors find it difficult to continue in this field due to low productivity and quality problems. The main objectives of the research are to find out how the production is being managed in the seafood processing(freezing) 17industry in Kerala and the reasons for low productivity and poor quality of the products. The study includes a detailed analysis of Location of the factories. Layout Purchase, production and storage patterns. Production planning and scheduling. Work Measurement of the processing of important products. Quality Control and Inspection. Management Information System