Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Anisotropy in elastic properties of lithium sodium sulphate hexahydrate single crystal—An ultrasonic study

The double sulfate family (ABSO4), where A and B are alkali metal cations, is the object of great interest owing to the complexity and richness of its sequence of phase transition induced by temperature variation. A new sulfate salt characterized by the presence of water molecule in the unit cell with the chemical formula, Li2Na3(SO4)2⋅6H2O (LSSW), was obtained. The ultrasonic velocity measurement was done with pulse echo overlap technique [PEO]. All the six second order elastic stiffness constants, C11 = C22, C33, C44 = C55, C12, C14 and C13 = C23 are reported for the first time. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the polar plots of phase velocity, slowness, Young’s modulus and linear compressibility in a–b and a–c planes.

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.

Phase Transitions Of Trace Metals In The Aquatic Environment Of Kuttanad, Kerala

Environmental persistence, fate and interactive effects with living organisms - beneficial or toxic - of trace elements are directly related to the physico-chemical forms in which they occur. Knowledge on the association of trace metals with different environmental compartments in an aquatic system are, therefore, essential for monitoring the trace metal pollution as well as transport, fate and bio-geochemical cycles of trace metals. This thesis is a modest attempt in assessing the trace metal levels and their behaviour in the aquatic environment of Kuttanad, an aquatic system that is severely affected by man's intervention on natural processes, by seriously evaluating the levels of trace metals in dissolved and particulate phases and also in the different chemical fractions of the sediments.

Analytical Study of Typographical Errors in OPACS and Corrective Measures

The present study is an attempt to highlight the problem of typographical errors in OPACS. The errors made while typing catalogue entries as well as importing bibliographical records from other libraries exist unnoticed by librarians resulting the non-retrieval of available records and affecting the quality of OPACs. This paper follows previous research on the topic mainly by Jeffrey Beall and Terry Ballard. The word “management” was chosen from the list of likely to be misspelled words identified by previous research. It was found that the word is wrongly entered in several forms in local, national and international OPACs justifying the observations of Ballard that typos occur in almost everywhere. Though there are lots of corrective measures proposed and are in use, the study asserts the fact that human effort is needed to get rid of the problem. The paper is also an invitation to the library professionals and system designers to construct a strategy to solve the issue

Analytical Study of Typographical Errors in OPACS and Corrective Measures

The present study is an attempt to highlight the problem of typographical errors in OPACS. The errors made while typing catalogue entries as well as importing bibliographical records from other libraries exist unnoticed by librarians resulting the non-retrieval of available records and affecting the quality of OPACs. This paper follows previous research on the topic mainly by Jeffrey Beall and Terry Ballard. The word “management” was chosen from the list of likely to be misspelled words identified by previous research. It was found that the word is wrongly entered in several forms in local, national and international OPACs justifying the observations of Ballard that typos occur in almost everywhere. Though there are lots of corrective measures proposed and are in use, the study asserts the fact that human effort is needed to get rid of the problem. The paper is also an invitation to the library professionals and system designers to construct a strategy to solve the issue

Characterization of radio frequency plasma using Langmuir probe and optical emission spectroscopy

The radio frequency plasma generated during the sputtering of Indium Tin Oxide target using Argon was analyzed by Langmuir probe and optical-emission spectroscopy. The basic plasma parameters such as electron temperature and ion density were evaluated. These studies were carried out by varying the RF power from 20 to 50 W. A linear increase in ion density and an exponential decrease in electron temperature with rf power were observed. The measured plasma parameters were then correlated with the properties of ITO thin films deposited under similar plasma conditions.

A Chloride Ion-Selective Potentiometric Sensor Based on a Polymeric Schiff Base Complex

This paper describes the fabrication of an ion-selective electrode in which a polymeric Schiff base complex of cobalt(II) is used as the ionophore.The main advantage of the electrode is that it is mechanically stable upto 3 months..The electrode shows a linear response in the range of 2.5 × 10-5-0.5 × 10-1 mol dm-3. The response time of the electrode is 30 s.The pH range at which the electrode works is 3.8 to 6.8. The electrode was found to be selective towards chloride ion in the presence of ions like Na+, Ca2+, Mn2+, ,Fe3+, Co2+, Ni2+, Cu2+, Zn2+, CH3COO-, NO3-, SO42- ,Br- and NO2-.

Elastic constant measurements of super ionic LiKSO4:Na single crystals

Elastic properties of sodium doped Lithium potassium sulphate, LiK0.9Na0.1SO4, crystal has been studied by ultrasonic Pulse Echo Overlap [PEO] technique and are reported for the first time. The controversy regarding the type of crystal found while growth is performed at 35 °C with equimolar fraction of Li2SO4H2O, K2SO4 and Na2SO4 has been resolved by studying the elastic properties. The importance of this crystal is that it exhibits pyroelectric, ferroelectric and electro optic properties. It is simultaneously ferroelastic and superionic. The elastic properties of LiK0.9Na0.1SO4 crystal are well studied by measuring ultrasonic velocity in the crystal in certain specified crystallographic directions and evaluating the elastic stiffness constants, compliance constants and Poisson’s ratios. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the surface plots of phase velocity, slowness and linear compressibility in a-b and a-c planes.

Marine yeasts — a review

Yeasts are ubiquitous in their distribution and populations mainly depend on the type and concentration of organic materials. The distribution of species, as well as their numbers and metabolic characteristics were found to be governed by existing environmental conditions. Marine yeasts were first discovered from the Atlantic Ocean and following this discovery, yeasts were isolated from different sources, viz. seawater, marine deposits, seaweeds, fish, marine mammals and sea birds. Nearshore environments are usually inhabited by tens to thousands of cells per litre of water, whereas low organic surface to deep-sea oceanic regions contain 10 or fewer cells/litre. Aerobic forms are found more in clean waters and fermentative forms in polluted waters. Yeasts are more abundant in silty muds than in sandy sediments. The isolation frequency of yeasts fell as the depth of the sampling site is increased. Major genera isolated in this study were Candida, Cryptococcus, Debaryomyces and Rhodotorula. For biomass estimation ergosterol method was used. Classification and identification of yeasts were performed using different criteria, i.e. morphology, sexual reproduction and physiological/biochemical characteristics. Fatty acid profiling or molecular sequencing of the IGS and ITS regions and 28S gene rDNA ensured accurate identification.

Studies on the Deep - Water Crab Charybdis (Goniohellenus ) Smithii Macleay From the Seas Around India

The present study deals with a general introduction which outlines the objective of the study providing an exhaustive review of works on crabs with particular reference to deep-sea forms. In the first section, Taxonomy and Geographical disribution of the crab are dealt with. The species is described in detail based on several male and female specimens obtained from the pelagic and bottom collections, and its identity in Indian waters is established. It is also distinguished from a closely allied species so far not reported from Indian waters. The second section comprises the biology of the species and it is dealt with under four subheading, namely Habit and Habitats, Reproduction, Food and feeding and Proximate composition. The different habitats occupied by juveniles, subadults and adults of the species have been described and discussed in the light of available information on differential distribution of other related species. The reproductive biology is described in various details touching on gross anatomy and histology of the reproductive systems, spermatogenesis, oogenesis, size at maturity, ovarian maturation process, fecundity, egg carriage and breeding. The food and feeding habits of the species have been studied with reference to the different life stages such as juveniles, subadults and adults during the different phases of life based on stomach content analysis. The percentage of meat recovery and protein, carbohydrate and lipid content of meat have been described in the section dealing with proximate composition. In section three the distribution and abundance of the crab for the entire Indian EEZ and some contiguous ares have been described and illustrated in detail separately for pelagic and benthic realms. The size frequency disrtibution, sex ratios, length weight relationship and relative abundance of breeding population in the experimental catches have been dealt with in detail and discussed.

Development of Electrochemical Sensors for Various Pharmaceuticals

The development of electrochemical sensors is currently one of the active areas of research in analytical chemistry.Voltammetric sensors as an important class of electrochemical sensors are extensively used in pharmaceutical applications.In voltammetric analysis,many active compounds in dosage forms,in contrast to excipients,can be readily oxidised or reduced at the electrode surface by applying a potential.Chemically modified electrodes have great significance in the electrochemical determination of pharmaceuticals.The modification of electrode results in efficient determination of electroactive species at very lower potential without any major interferences.The present study involves the fabrication of 8 voltammetric sensors for the drugs Metronidazole Benzoate, Sulfamethoxazole, Acyclovir, Pam Chloride , Trimethoprim , Tamsulosin Hydrochloride and Ceftriaxone Sodium.Two sensors were developed for the drug tamsulosin hydrochloride while one sensor each was developed for the other drugs.

A study on the Effect of Psychological Empowerment on Job Satisfaction and Job Related Stress Among the Bank Employees

The present research is carried out to understand how psychological empowerment, job satisfaction and job related stress are related.In banking sector, employees are less satisfied and less motivated than employees in other lines of work (Kelley, 1990; Bajpai, Naval and Deepak, 2004). The banking industry also suffers from high employee turnover rate (Branham, 2005; Nelson, 2007) and high level of stress (Chen and Lien, 2008). There are no adequate studies linking psychological empowerment and job satisfaction, stress, turnover etc. among employees of banking sector. Lack of psychological empowerment could be a reason for these problems faced by banking sector. Further majority of studies in psychological empowerment are carried out in manufacturing sector and studies in service sector are concentrated on hotel industry and hospitals. Empowerment takes different forms in different contexts (Zimmerman, 1995). In the light of above discussion, the present research is directed to explore the dimensions of psychological empowerment of employees in banking sector and to find out whether high psychological empowerment can increase job satisfaction and reduce job related stress among employees in banking sector

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.