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.

Dielectric Behavior of Natural Rubber Composites in Microwave Fields

In this article, we report the preparation of conducting natural rubber (NR) with polyaniline (Pani). NR was made into a conductive material by the compounding of NR with Pani in powder form. NR latex was made into a conductive material by the in situ polymerization of aniline in the presence of NR latex. Different compositions of Pani- NR semi-interpenetrating networks were prepared, and the dielectric properties of all of the samples were determined in microwave frequencies. The cavity perturbation techpique was used for this study. A HP8510 vector network analyzer with a rectangular cavity resonator was used for this study. S bands 2-4 GHz in frequency were used. Thermal studies were also carried out with thermogravimetric analysis and differential scanning calorimetry.

Dielectric Behavior of Natural Rubber Composites in Microwave Fields

In this article, we report the preparation of conducting natural rubber (NR) with polyaniline (Pani). NR was made into a conductive material by the compounding of NR with Pani in powder form. NR latex was made into a conductive material by the in situ polymerization of aniline in the presence of NR latex. Different compositions of Pani- NR semi-interpenetrating networks were prepared, and the dielectric properties of all of the samples were determined in microwave frequencies. The cavity perturbation techpique was used for this study. A HP8510 vector network analyzer with a rectangular cavity resonator was used for this study. S bands 2-4 GHz in frequency were used. Thermal studies were also carried out with thermogravimetric analysis and differential scanning calorimetry.

Alkaline Protease from a Non-toxigenic Vibrio sp.(V26) and its Applications

The thesis presents a detailed account of the alkaline protease produced by Vibrio sp.(V26) a mangrove isolate,and the application of this enzyme in different fields.The protease producer strain was identified on the basis of biochemical characteristice,putative virulence traits and 16S rRNA gene sequencing.The purification and characterization of the protease has been carried out. Along with this, an attempt has been made to identifiy the protease gene. The physical parameters as well as the media components influencing protease production were optimized using Response Surfce Methodology(RSM).The scale up of the application of the protease from Vibrio sp.(V26) in the dissociation of cells in animal cell culture,in the recovery of silver from used X-ray films as well as an ingredient in commercial detergents were investigated.

Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

Occurrence of filamentous algae and soil characteristics in the paddy fields of Kuttanad and Kole lands of Kerala

The present work is the study of filamentous algae in the paddy fields of Kuttanad and Kole lands of Kerala. This investigation was initiated by sampling of filamentous algae in Kuttanad during December 2010 to February 2011. A second phase of sampling was done from November 2011 to February 2012. The sampling periodicity corresponded to the crop growth starting from field preparation through sowing, and continued till the harvest. Sampling locations were selected from the active paddy cultivation regions of the six agronomic zones of Kuttanad. The numbers of sampling locations were proportional to the area of each zone. Algae of the Kole lands were collected during from October 2011 to January 2012. It was observed that blue-green algae dominated in both Kuttanad and Kole lands. Thirty two species of blue-green algae and eight species of green algae were identified from Kuttanad. The highest number of algal species was observed from Kayal lands in Kuttanad throughout the cropping season. Among the thirty two species of blue-green algae twenty five species are nonheterocystous and seven species are heterocystous. Twenty eight species of blue-green and six species of green algae were identified from Kole lands, and highest number of species was observed in Palakkal throughout the cropping season. Among the twenty eight species of blue-green algae collected from Kole lands twenty one species are non-heterocystous, and only seven species are heterocystous filamentous algae. Blooms of Spirogyra were observed during the second phase of sampling in Kuttanad and also in the Kole lands. The results of the germination study revealed that the extract of Spirogyra sp. inhibited seed germination and reduced seedling vigour. The growth of the treated seedlings was evaluated by pot experiments. The results clearly showed that Spirogyra sp. can negatively affect the seed germination, seedling vigour, and the yield of rice.

Soft Computing Approach for Optimization of siRNA Efficiency Prediction for Post-transcriptional Gene Silencing

Post-transcriptional gene silencing by RNA interference is mediated by small interfering RNA called siRNA. This gene silencing mechanism can be exploited therapeutically to a wide variety of disease-associated targets, especially in AIDS, neurodegenerative diseases, cholesterol and cancer on mice with the hope of extending these approaches to treat humans. Over the recent past, a significant amount of work has been undertaken to understand the gene silencing mediated by exogenous siRNA. The design of efficient exogenous siRNA sequences is challenging because of many issues related to siRNA. While designing efficient siRNA, target mRNAs must be selected such that their corresponding siRNAs are likely to be efficient against that target and unlikely to accidentally silence other transcripts due to sequence similarity. So before doing gene silencing by siRNAs, it is essential to analyze their off-target effects in addition to their inhibition efficiency against a particular target. Hence designing exogenous siRNA with good knock-down efficiency and target specificity is an area of concern to be addressed. Some methods have been developed already by considering both inhibition efficiency and off-target possibility of siRNA against agene. Out of these methods, only a few have achieved good inhibition efficiency, specificity and sensitivity. The main focus of this thesis is to develop computational methods to optimize the efficiency of siRNA in terms of “inhibition capacity and off-target possibility” against target mRNAs with improved efficacy, which may be useful in the area of gene silencing and drug design for tumor development. This study aims to investigate the currently available siRNA prediction approaches and to devise a better computational approach to tackle the problem of siRNA efficacy by inhibition capacity and off-target possibility. The strength and limitations of the available approaches are investigated and taken into consideration for making improved solution. Thus the approaches proposed in this study extend some of the good scoring previous state of the art techniques by incorporating machine learning and statistical approaches and thermodynamic features like whole stacking energy to improve the prediction accuracy, inhibition efficiency, sensitivity and specificity. Here, we propose one Support Vector Machine (SVM) model, and two Artificial Neural Network (ANN) models for siRNA efficiency prediction. In SVM model, the classification property is used to classify whether the siRNA is efficient or inefficient in silencing a target gene. The first ANNmodel, named siRNA Designer, is used for optimizing the inhibition efficiency of siRNA against target genes. The second ANN model, named Optimized siRNA Designer, OpsiD, produces efficient siRNAs with high inhibition efficiency to degrade target genes with improved sensitivity-specificity, and identifies the off-target knockdown possibility of siRNA against non-target genes. The models are trained and tested against a large data set of siRNA sequences. The validations are conducted using Pearson Correlation Coefficient, Mathews Correlation Coefficient, Receiver Operating Characteristic analysis, Accuracy of prediction, Sensitivity and Specificity. It is found that the approach, OpsiD, is capable of predicting the inhibition capacity of siRNA against a target mRNA with improved results over the state of the art techniques. Also we are able to understand the influence of whole stacking energy on efficiency of siRNA. The model is further improved by including the ability to identify the “off-target possibility” of predicted siRNA on non-target genes. Thus the proposed model, OpsiD, can predict optimized siRNA by considering both “inhibition efficiency on target genes and off-target possibility on non-target genes”, with improved inhibition efficiency, specificity and sensitivity. Since we have taken efforts to optimize the siRNA efficacy in terms of “inhibition efficiency and offtarget possibility”, we hope that the risk of “off-target effect” while doing gene silencing in various bioinformatics fields can be overcome to a great extent. These findings may provide new insights into cancer diagnosis, prognosis and therapy by gene silencing. The approach may be found useful for designing exogenous siRNA for therapeutic applications and gene silencing techniques in different areas of bioinformatics.