Fluid mechanics-non-linear waves studies on korteweg-de vries equations

In this thesis the author has presented qualitative studies of certain Kdv equations with variable coefficients. The well-known KdV equation is a model for waves propagating on the surface of shallow water of constant depth. This model is considered as fitting into waves reaching the shore. Renewed attempts have led to the derivation of KdV type equations in which the coefficients are not constants. Johnson's equation is one such equation. The researcher has used this model to study the interaction of waves. It has been found that three-wave interaction is possible, there is transfer of energy between the waves and the energy is not conserved during interaction.

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.

Structural Characterization and Non-linear Optical Properties of Metal Complexes of Some Donor-Acceptor Substituted N-salicylidene-N' -aroylhydrazine Ligands

The present work deals with the complexation of Schiff bases of aroylhydrazines with various transition metal ions. The hydrazone systems selected for study have long 7I:-delocalized chain in the ligand molecule itself, which get intensified due to metal-to-ligand or ligand-to-metal charge transfer excitations upon coordination. Complexation with metal ions like copper, nickel, cobalt, manganese, iron, zinc and cadmium are tried. Various spectral techniques are employed for characterization. The structures of some complexes have been well established by single crystal X-ray diffraction studies. The nonIinaer optical studies of the ligands and complexes synthesized have been studied by hyper-Rayleigh scattering technique.The work is presented in seven chapters and the last one deals with summary and conclusion. One of the hydrazone system selected for study proved that it could give rise to polymeric metal complexes. Some of the copper, nickel, zinc and cadmium complexes showed non-linear optical activity. The NLO studies of manganese and iron showed negative result, may be due to the inversion centre of symmetry within the molecular lattice.

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.

Design and Synthesis of Donor-Acceptor Low Band Gap Copolymers for Photoconductive and Non-linear Optical Applications

The main focus of the present study was to develop ideal low band gap D-A copolymers for photoconducting and non-linear optical applications. This chapter summarizes the overall research work done. Designed copolymers were synthesized via direct arylation or Suzuki coupling reactions. Copolymers were characterized by theoretical and experimental methods. The suitability of these copolymers in photoconducting and optical limiting devices has been investigated.The results suggest that the copolymers investigated in the present study have a good non-linear optical response and are comparable to or even better than the D-A copolymers reported in the literature and hence could be chosen as ideal candidates with potential applications for non-linear optics. The results also show that the structures of the polymers have great impact on NLO properties. Copolymers studied here exhibits good optical limiting property at 532 nm wavelength due to two-photon absorption (TPA) process. The results revealed that the two copolymers, (P(EDOT-BTSe) and P(PH-TZ)) exhibited strong two-photon absorption and superior optical power limiting properties, which are much better than that of others.

Strategies for Inverse Profiling of Two Dimensional Dielectric Scatterers Using Electromagnetic Illumination

Electromagnetic tomography has been applied to problems in nondestructive evolution, ground-penetrating radar, synthetic aperture radar, target identification, electrical well logging, medical imaging etc. The problem of electromagnetic tomography involves the estimation of cross sectional distribution dielectric permittivity, conductivity etc based on measurement of the scattered fields. The inverse scattering problem of electromagnetic imaging is highly non linear and ill posed, and is liable to get trapped in local minima. The iterative solution techniques employed for computing the inverse scattering problem of electromagnetic imaging are highly computation intensive. Thus the solution to electromagnetic imaging problem is beset with convergence and computational issues. The attempt of this thesis is to develop methods suitable for improving the convergence and reduce the total computations for tomographic imaging of two dimensional dielectric cylinders illuminated by TM polarized waves, where the scattering problem is defmed using scalar equations. A multi resolution frequency hopping approach was proposed as opposed to the conventional frequency hopping approach employed to image large inhomogeneous scatterers. The strategy was tested on both synthetic and experimental data and gave results that were better localized and also accelerated the iterative procedure employed for the imaging. A Degree of Symmetry formulation was introduced to locate the scatterer in the investigation domain when the scatterer cross section was circular. The investigation domain could thus be reduced which reduced the degrees of freedom of the inverse scattering process. Thus the entire measured scattered data was available for the optimization of fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of Symmetry formulation could also be applied to the practical problem of limited angle tomography, as in the case of a buried pipeline, where the ill posedness is much larger. The formulation was also tested using experimental data generated from an experimental setup that was designed. The experimental results confirmed the practical applicability of the formulation.