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.

Sol-Gel Nanocrystalline Catalytic Titania Powders and Functional Coatings

In the present work Titania bulk powders and coatings were prepared by subjecting titanium isopropoxide solution to a controlled hydrolysis-condensation process. The powders were characterized using techniques such as FTIR for their chemical interactions, TG-DTA for the thermal decomposition features, XRD for the phase assemblage, BET specific surface area analysis for the textural features. The study discusses the preparation methods and the characterization techniques employed and a detailed discussion on the physico-chemical characterization of the prepared systems. The influence of dopants and leaching on the physico-chemical properties as well as their influence on photo activity is also included. The structural/functional coatings of different Titania compositions includes in this study. Coatings on pre-treated glass surfaces with the best compositions prepared showed 90 % transmittance in the visible region.

Chemical Modification of Blends of Poly (Vinyl Chloride) With Linear Low Density Polyethylene

The effects of modifying blends of poly(vinyl chloride) (PVC) with linear low density polyethylene (LLDPE) by means of acrylic acid, maleic anhydride, phenolic resins and p-phenylene diamine were investigated. Modification by acrylic acid and maleic anhydride in the presence of dicumyl peroxide was found to be the most useful procedure for improving the mechanical behaviour and adhesion properties of the blend. The improvement was found to be due mainly to the grafting of the carboxylic acid to the polymer chains; grafting was found to be more effective in LLDPE/PVC blends than in pure LLDPE.

Decreased GABAA Receptors Functional Regulation 3 in the Cerebral Cortex and Brainstem of Hypoxic Neonatal Rats: 4 Effect of Glucose and Oxygen Supplementation

Hypoxia in neonates can lead to biochemical and molecular alterations mediated through changes in neurotransmitters resulting in permanent damage to brain. In this study, we evaluated the changes in the receptor status of GABAA in the cerebral cortex and brainstem of hypoxic neonatal rats and hypoxic rats supplemented with glucose and oxygen using binding assays and gene expression of GABAAa1 and GABAAc5. In the cerebral cortex and brainstem of hypoxic neonatal rats, a significant decrease in GABAA receptors was observed, which accounts for the respiratory inhibition. Hypoxic rats sup- plemented with glucose alone and with glucose and oxygen showed, respectively, a reversal of the GABAA receptors, andGABAAa1 and GABAAc5 gene expression to control. Glucose acts as an immediate energy source thereby reducing the ATP-depletion-induced increase in GABA and oxygenation, which helps in encountering anoxia. Resuscitation with oxygen alone was less effective in reversing the receptor alterations. Thus, the results of this study suggest that reduction in the GABAA receptors functional regulation during hypoxia plays an important role in mediating the brain damage. Glucose alone and glucose and oxygen supplementation to hypoxic neonatal rats helps in protecting the brain from severe hypoxic damage.

The tautomerism, solvatochromism and non-linear optical properties of fluorescent 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine

The Schiff base, 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine, was synthesized by the condensation of 3-hydroxyquinoxaline-2-carboxaldehyde with 4-aminoantipyrine. HPLC, FT-IR and NMR spectral data revealed that the compound exists predominantly in the amide tautomeric form and exhibits both absorption and fluorescence solvatochromism, large stokes shift, two electron quasireversible redox behaviour and good thermal stability, with a glass transition temperature of 104oC. The third-order non-linear optical character was studied using open aperture Z-scan methodology employing 7 ns pulses at 532 nm. The third-order non-linear absorption coefficient, b, was 1.48 x 10-6 cm W-1 and the imaginary part of the third-order non-linear optical susceptibility, Im c(3), was 3.36 x10-10 esu. The optical limiting threshold for the compound was found to be 340 MW cm-2.

The tautomerism, solvatochromism and non-linear optical properties of fluorescent 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine

The Schiff base, 3-hydroxyquinoxaline-2-carboxalidine-4-aminoantipyrine, was synthesized by the condensation of 3-hydroxyquinoxaline-2-carboxaldehyde with 4-aminoantipyrine. HPLC, FT-IR and NMR spectral data revealed that the compound exists predominantly in the amide tautomeric form and exhibits both absorption and fluorescence solvatochromism, large stokes shift, two electron quasireversible redox behaviour and good thermal stability, with a glass transition temperature of 104 oC. The third-order non-linear optical character was studied using open aperture Z-scan methodology employing 7 ns pulses at 532 nm. The third-order non-linear absorption coefficient, b, was 1.48 x 10-6 cm W-1 and the imaginary part of the third-order non-linear optical susceptibility, Im c(3), was 3.36x10-10 esu. The optical limiting threshold for the compound was found to be 340 MW cm-2.

Sol-Gel Mesoporous Silica Aerogels and Bio Hybrids for Functional Applications

The thesis covers a systematic investigation on the synthesis of silica aerogels and microspheres with tailored porosity, at ambient conditions by varying the experimental parameters as well as using organic templates. Organically modified silica-gelatin and silica-chitosan hybrids were developed for the first time using alkylalkoxysilanes such as MTMS and VTMS. Application of novel silica-biopolymer antiwetting coatings on different substrates such as glass, leather and textile is also demonstrated in the thesis.

DETECTION OF BILIARY FUNCTIONAL PROBLEMS USING MICROWAVES

This article reports a new in vitro bile analysis based on the measurement of the dielectric properties at microwave frequencies. The measurements were made using rectangular cavity perturbation technique at the S-band of microwave frequency with the different samples of bile obtained from healthy persons as well as from patients. It is observed that an appreciable change in the dielectric properties of patient’s samples with the normal healthy samples and these measurements were in good agreement with clinical analysis. These results prove an alternative in-vitro method of detecting bile abnormalities based on the measurement of the dielectric properties of bile samples using microwaves without surgical procedure.

DOPAMINE D2 RECEPTOR FUNCTIONAL REGULATION : cAMP AND IP3 ROLE IN PANCREATIC REGENERATION

The present study deals with the differential regulation of Dopamine content in pancreas and functional regulation of Dopamine D2 receptor in brain regions such as hypothalamus, brain stem, cerebral cortex and corpus striatum play an important role during pancreatic islets cell proliferation and insulin secretion. Though may reports are there implicating the functional interaction between DA receptor and pancreatic islets cell insulin secretion, the involvement of specific DA D2 receptors and changes in second messenger system during insulin secretion and pancreatic islets cell proliferation were not given emphasis. Down regulation of DA content in brain regions and pancreatic islets were observed during pancreatic regeneration. Up regulation of DA content in plasma and adrenals down regulated sympathetic activity in pancreas which cause an increase in insulin secretion and pancreatic islets cell proliferation during pancreatic regeneration. There was a differential regulation of DA D2 receptor in brain regions. The pancreatic islets DA D2 receptors were lip regulated during pancreatic regeneration. DA D2 receptor activation at specific concentration has accounted for increased pancreatic islets cell proliferation. In vitro experiments have proved the differential regulation of DA on insulin synthesis and pancreatic islets cell proliferation. Inhibitory effect of DA on cAMP and stimulatory effect of DA on IP3 through DA D2 receptors were observed in in vitro cell culture system. These effects are correlating with the DA, cAMP and IP3 content during pancreatic regeneration and islets cell proliferation. Up regulation of intracellular Ca2+ was also observed at 10-8 M DA, a specific concentration of DA which showed maximum increase of IP3 content in pancreatic islets through DA D2 receptor activation in in vitro culture. These in vitro data was highly correlating with the changes in DA, cAMP and IP3 content in pancreas during pancreatic regeneration and insulin secretion. Thus we conclude that there is a differential functional regulation of DA and DA D2 receptors in brain and pancreas during pancreatic regeneration. In vitro studies confirmed a concentration depend functional regulation of DA through DA D2 receptors on pancreatic islets cell proliferation and insulin secretion mediated through increased cAMP, IP3 and intracellular Ca2+ level. This will have immense clinical significance in the management in diabetes mellitus.

Influence of residual cations (Na+, K+ and Mg2+) in the alkylation activity of benzene with 1-octene over rare earth metal ion exchanged FAU–Y zeolite

The effect of residual cations in rare earth metal modified faujasite–Y zeolite has been monitored using magic angle spinning NMR spectral analysis and catalytic activity studies. The second metal ions being used are Na+, K+ and Mg+. From a comparison of the spectra of different samples, it is concluded that potassium and magnesium exchange causes a greater downfield shift in the 29Si NMR peaks. Also, lanthanum exchanged samples show migration behavior from large cages to small cages, which causes the redistribution of second counter cations. It is also observed that Mg2+ causes the most effective migration of lanthanum ions due to its greater charge. The prepared systems were effectively employed for the alkylation of benzene with 1-octene in the vapor phase. From the deactivation studies it is observed that the as-exchanged zeolites possess better stability towards reaction condition over the pure HFAU zeolite.

A simple linear magnetic field sweep generator for magnetic resonance experiments

A simple and inexpensive linear magnetic field sweep generating system suitable for magnetic resonance experiments is described. The circuit, utilising a modified IC bootstrap configuration, generates field sweep over a wide range of sweep durations with excellent sweep linearity.

Sol-Gel Alumina Nano Composites for Functional Applications

The thesis entitled "Sol-Gel Alumina Nano Composites for Functional Applications" investigate sol-gel methods of synthesis of alumina nanocomposites special reference to alumina-aluminium titanate and alumina-lanthanum phosphate composites. The functional properties such as thermal expansion coefficient and thermal shock resistance, machinability of composites as well as thermal protection are highlighted in addition to novel approach in synthesis of composites.A general introduction of alumina matrix composites materials, followed by brief coverage of alumina-aluminium titanate and alumina-lanthanum phosphate composites is highlight of the first chapter. The second chapter deals with the sol-gel synthesis of aluminium titanate and alumina-aluminium titanate composite. The synthesis of machinable substrate, based on alumina and lanthanum phosphate forms the basis of the third chapter. The fourth chapter describes the sol-gel coating of mullite on SiC substrate for the possible gas filtration application.