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.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.

Influence of Selected Dietary Micronutrient Elements on Growth and Biochemistry of Farmed Prawns

From the present study, it is clear that all the three metals, selenium, molybdenum and cobalt have significant effect on the antioxidant status of the shrimps. Selenium and molybdenum were observed to induce peroxidative damage at elevated levels. But at the same level, cobalt did not show such an effect. Selenium was found to be growth promoting at lower levels of dietary supplementation. Even though low levels of dietary selenium had a protective effect against the lipid peroxidation, the present study indicates that high levels of dietary selenium could promote lipid peroxidation. The selenium-dependent antioxidant enzyme, GPx behaved differently in muscle and hepatopancreas. A high concentration of selenium was required for the active expression of the enzyme in the muscle, where as in hepatopancreas maximum activity was observed at lower selenium concentration. Selenium supplementation had a positive effect on GSH concentration. The other antioxidant enzymes such as GST, SOD and CAT showed enhanced activity at higher concentration of selenium. Molybdenum supplementation significantly reduced the free radical scavenger enzymes SOD and CAT. This resulted in enhanced lipid peroxidation in tissues. The activity of antioxidant enzyme GPx and the concentration of the substrate for the enzyme, GSH also were lower at elevated levels of molybdenum supplementation. In addition to this amino acids and fatty acids were also altered in molybdenum supplemented groups. In trace amounts, dietary molybdenum exerts a beneficial effect on the growth and also in the activities of the enzymes XO and SO. At the same time it also indicates a possibility of oxidative damage as a result of the peroxidation caused by the activities of the enzymes SO and XO at elevated concentrations of molybdenum is also indicated. The absorption of various trace elements was also altered by molybdenum supplementation.Among the three metals studied, cobalt was the least toxic one at the administered levels. But this metal has a significant effect on the lipid content, amino acid composition, cholesterol levels and phospholipid levels. Increased growth was also observed as a result of cobalt supplementation in shrimps. The antioxidant system of the animal was activated by dietary cobalt. Tissue levels of the trace metals were also found to be altered in cobalt supplemented groups of shrimps.These studies, thus shows that influence of dietary trace metals calls for more detailed studies in farmed shrimp. They may hold the key to growth and even disease resistance in shrimp. But this still remains as a virgin field which demands more attention, especially in view of the increasing importance of shrimp farming.

Biology, population characteristics and fishery of the speckled shrimp Metapenaeus monoceros (Fabricius, 1798) along the Kerala coast

Crustaceans comprising numerous edible species of prawns, lobsters and crabs inhabiting different ecosystem form significant portion of the aquatic food resources of the world. Among the crustaceans, prawns are the most commercially exploited group and hold premier rank by virtue of their importance as an esteemed food of gourmet and on account of their high export value. Met-ape-naeus manoceras (Fabricius, 1798) which is known IS,Speckled shrimp’ (FAD name) and ‘Brown shrimp’ ( common nameused in the industry) is one of the commercially important marine penaeid prawns of India. During 1995, M. monaceros catch constituted 7.5 Z of the all India marine penaeid prawn landings. M. monoceros attains a maximum length of about 200 mm and has high export potential.Thus realising the growing importance of M. monoceros in the capture fisheries, it was felt, that it would be ideal to carry out detailed study on this species for rational exploitation and management of its fishery. Hence, the present work entitled, “Biology, population characteristics and fishery of the speckled shrimp Hetapenaeus monoceros (Fabricius, 1798) along Kerala coast“ was undertaken by the author. The thesis is laid out in seven chapters comprising TAXONOMY, FOOD AND FEEDING HABITS, AGE AND GROWTH, REPRODUCTION,LENGTH-WEIGHT RELATIONSHIP, FISHERY and POPULATION DYNAMICS

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

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.

‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Efficacy of fermented prawn shell waste as a feed ingredient for Indian white prawn, Fenneropenaeus indicus

Prawn shell waste collected from shrimp-processing plants in Cochin, India, was subjected to fermentation using 20 chitinoclastic and proteolytic/non-proteolytic bacterial strains. The products generated were analysed for protein, lipid, total sugars, N-acetyl glucosamine, free amino acids and ash. Shrimp diets were prepared using these 20 fermented products and a control diet using raw prawn shell waste. Feeding experiment was conducted with postlarvae (PL21) of Indian white prawn, Fenneropenaeus indicus for a period of 21 days. Biogrowth parameters such as mean weight gain, feed conversion ratio, specific growth rate and protein efficiency ratio were estimated and the animals were challenged with white spot virus orally via diet. Enhanced growth could be observed in prawns fed F134 and F124, incorporated with the fermentation products generated using Bacillus spp., C134 and C124 respectively. The percentage survival of prawns after 7 days of challenge was found to be highest for groups fed diet F111 incorporated with fermentation product generated using Bacillus sp. These products of bacterial fermentation hold promise as growth enhancers and immunostimulants in aquaculture. KEY WORDS: biogrowth parameters, feed

Efficient Watermarking Schemes for Speaker Verification Guaranteeing Non-repudiation

Presently different audio watermarking methods are available; most of them inclined towards copyright protection and copy protection. This is the key motive for the notion to develop a speaker verification scheme that guar- antees non-repudiation services and the thesis is its outcome. The research presented in this thesis scrutinizes the field of audio water- marking and the outcome is a speaker verification scheme that is proficient in addressing issues allied to non-repudiation to a great extent. This work aimed in developing novel audio watermarking schemes utilizing the fun- damental ideas of Fast-Fourier Transform (FFT) or Fast Walsh-Hadamard Transform (FWHT). The Mel-Frequency Cepstral Coefficients (MFCC) the best parametric representation of the acoustic signals along with few other key acoustic characteristics is employed in crafting of new schemes. The au- dio watermark created is entirely dependent to the acoustic features, hence named as FeatureMark and is crucial in this work. In any watermarking scheme, the quality of the extracted watermark de- pends exclusively on the pre-processing action and in this work framing and windowing techniques are involved. The theme non-repudiation provides immense significance in the audio watermarking schemes proposed in this work. Modification of the signal spectrum is achieved in a variety of ways by selecting appropriate FFT/FWHT coefficients and the watermarking schemes were evaluated for imperceptibility, robustness and capacity char- acteristics. The proposed schemes are unequivocally effective in terms of maintaining the sound quality, retrieving the embedded FeatureMark and in terms of the capacity to hold the mark bits. Robust nature of these marking schemes is achieved with the help of syn- chronization codes such as Barker Code with FFT based FeatureMarking scheme and Walsh Code with FWHT based FeatureMarking scheme. An- other important feature associated with this scheme is the employment of an encryption scheme towards the preparation of its FeatureMark that scrambles the signal features that helps to keep the signal features unreve- laed. A comparative study with the existing watermarking schemes and the ex- periments to evaluate imperceptibility, robustness and capacity tests guar- antee that the proposed schemes can be baselined as efficient audio water- marking schemes. The four new digital audio watermarking algorithms in terms of their performance are remarkable thereby opening more opportu- nities for further research.

Community Participation in Ecotourism: An Inclusive Development Option for Kerala

The inferences obtained from the study are presented in coherent area-specific levels so as to understand the ecotourism and its sub-sector areas for the researchers and policy makers about the issues, importances and potentialities of the sector. An analysis of the tourism sector in Kerala has shown tremendous growth both in terms of tourist arrivals and in terms of revenue generation from direct and indirect sources. The foreign tourist visitors in Kerala in 2014 was 9,23,336 which shows 7.60 percent increase from the last year and the domestic tourist visitors were 1,16,95,411 which again shows 7.71 percent increase, is a clear evidence of its potential. In 2014 the industry contributed revenue of 24885.44 crores from direct and indirect sources giving rise to an increase of 12.11 percent from the last year. A dichotomy of tourists and ecotourists shows that tourists in the ecotourism destinations come to 42.6 percent of the total, shows the scope, significance and its potential. Correlation of zone-wise tourist arrivals based on the ecotourism destinations highlights the fact that with only 19 of the 64 destinations that come in the central zone are the most preferred centres (around 54 percent) for the domestic as well as foreign tourists. The north zone encompassing 6 districts with rich biodiversity shows that the tourists‟ arrival patterns exhibit less promising results. Though the north zone has 31 ecotourism destinations of the state receives only 6.19 percent of the foreign visitors. The ecotourism activities in the state are primarily managed by the Eco-Development Committees (EDCs) and the Vana Samrakshana Samithies (VSS) under the Forest Development Agency of Kerala. Social class-wise categorization of membership shows that 13142 families have membership in 190 EDCs with SC (28 percent), ST (33 percent) and other marginalised communities (39 percent). But this in the VSS shows that 400 VSS have 59085 members actively engaged in ecotourism activities and social category of the VSS makes clear that majority are from the other marginalized fringe households with 62 percent where as the participation of SC is 12 percent and ST is 26 percent. An evaluation of the socio-economic and demographic matrix of the community members involved in ecotourism activities brings out region specific differences. About 75.70 percent of the respondents are males and the rest are females. Majority of the respondents (about 60 percent) are in the age group of 20 to 40 years, followed by the age group of 40-50 (20 percent). The average age of respondents in the three zones is between 35 and 37 years. The majority of the respondents are married, a few are unmarried. Average family size is 4-5 members and differences are identified among zones. Average number of adults per household is 3 and child per household is 2. Majority have an education of 10th class and below i.e. about 60 percent of the sample have only basic school education like primary, secondary and high school (i.e. up to SSLC but not passed) level. About 18 percent are SSLC passed, 10 percent are undergraduates whereas 6 percent constitute respondents having qualification of graduation and above. Majority of the „graduates and above‟ are from south and central zone. Inter-zone differences in educational profile are also identified with lesser number of „graduates and above‟ are identified in the north zone compared to the other two zones. Investigating into the income and livelihood options of the respondents gives insight about the prominence of ecotourism as an employment and livelihood option for the community members, as more than 90 percent of the respondents have cited tourism sector as their main employment option. Most (49.30 percent) of respondents get 100 percent income from tourism related activities, followed by 37.30 percent of community members have income between 75-99 percent from tourism whereas the rest (13 percent) have less than 74 percent of their income from tourism and there exists difference between zones and percentage of income. Financial habit shows that about 49.7 percent hold active bank accounts, 61 percent have savings behaviour and 73.8 percent have indebtedness. Analysis about the ownership of house brings to light that 37 percent of respondents live in their own house followed by 25.7 percent in government funded/provided house and 21 percent in their parent‟s house and 3.5 percent in rented house. About 12 percent of the respondents have other kinds of accommodation facilities such as staff quarters, etc. But in the case of north zone majority i.e. 52 percent primarily depend on the government funded house indicating the effectiveness of government housing programme. Standard of living measured in SLI frameworks shows that majority of the respondents have medium SLI values (42.3 percent); the remaining 47.7 percent have low SLI and 10 percent have high SLI. The community members have been benefitted immensely from forest and its resources. Since the ecotourism destinations are located amidst the wildlife settings, majority of them depend on forest for their livelihood. The information on the tourist‟s demographic characteristics like age, sex, educational qualification and annual income show that the age category of domestic and foreign tourists falls below the age group of less than 35 years (about 65 percent), whereas only 16 percent of tourists are aged above 46 years. The age group below 25 years consists of more international tourists (31.3 percent) compared to the proportion of domestic tourists (12.5 percent). Male-female ratio shows that the males constitute 56 percent of the sample and females with 44 percent. The factors determining the impact of ecotourism programmes in the community was evaluated with the aid of a factor analysis with 12 selected statements. The worries and concerns of the community members about the impact of ecotourism on the environment are well understood from this analysis. It can be drawn that environment protection and the role of ecotourism in improving the income and livelihood options of the local communities is the most important factor concerning the community members.