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.

Electron Donating Property and Catalytic Activity of Perovskite-type Mixed Oxides (ABO3 ) Consisting of Rare Earth and 3d Transition Metals

The catalytic activity of Perovskite-type mixed oxides (LaCo03 . PrCo03 and SmCo03 ) for the reduction of cyclohexanone to cyclohexanol with 2-propanol (Meerwein-Ponndorf-Verley reduction) has been studied. The data have been correlated with the surface electron donor properties of these mixed oxides.

Investigation of nonlinear absorption and aggregation in aqueous solutions of rhodamine B using thermal lens technique

Thermal lensing effect was studied in aqueous solutions of rhodamine B using 532 nm, 9 ns pulses from a Nd:YAG laser. A low intensity He-Ne laser beam was used for probing the thermal lens. Results obtained show that it is appropriate to use this technique for studying nonlinear absorption processes like two photon absorption or excited state absorption and for analyzing dimerization equilibria.

Studies of nonlinear absorption and aggregation in aqueous solutions of rhodamine 6G using a transient thermal lens technique

Dual-beam transient thermal lens studies were carried out in aqueous solutions of rhodamine 6G using 532 nm pulses from a frequency-doubled Nd:YAG laser. The analysis of the observed data showed that the thermal lens method can effectively be utilized to study the nonlinear absorption and aggregation which are taking place in a dye medium.

Experimental investigation of optical limiting and thermal lensing in toluene solutions of C70

Optical limiting and thermal lensing studies are carried out in C70–toluene solutions. The measurements are performed using 9-ns pulses generated from a frequencydoubled Nd:YAG laser at 532 nm. Optical limiting studies in fullerene molecules lead to the conclusion that reverse saturable absorption is the major mechanism for limiting. Analysis of thermal lensing measurements showed a quadratic dependence of thermal lens signal on incident laser energy, which also supports the view that optical limiting in C70 arises due to sequential two-photon absorption via excited triplet state (reverse saturable absorption).

Characteristics of two-photon absorption in methanol solutions of Rhodamine 6G using laser induced pulsed photoacoustics

Two-photon absorption in methanol solutions of Rhodamine 6G is investigated by photoacoustics using the second harmonic of a pulsed Nd:YAG laser. Competition between one-photon and two-photon processes is observed, depending critically on the sample concentration and input light flux.

Stability of periodic orbits of coupled-map lattices

We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.

Nanosecond optical limiting response of sandwich-type neodymium dyphthalocyanine in a co-polymer host

The nanosecond optical limiting characteristics of sandwich-type neodymium diphthalocyanine in a co-polymer matrix of polymethyl methacrylate (PMMA) and methyl-2-cyanoacrylate have been studied for the first time. The measurements were performed using 9 ns laser pulses generated from a frequency-doubled Nd:YAG laser at 532 nm wavelength. The optical limiting performance of neodymium diphthalocyanine in co-polymer host was studied at different linear transmission. Laser damage threshold was also measured for the doped and undoped co-polymer samples. The optical limiting response is attributed to reverse saturable absorption which is due to excited-state absorption.

Growth and characterisation of p-type delafossite transparent conducting thin films for heterojunction applications

In the present studies, various copper delafossite materials viz; CuAlO2, CuGaO2, CuFeO2 , CuGa1-xFexO2, CuYO2 and CuCaxY1-xO2 were synthesised by solid state reaction technique. These copper delafossite materials were grown in thin film form by rf magnetron sputtering technique. In general copper delafossites exhibit good optical transparency. The conductivity of the CuYO2 could be improved by Ca doping or by oxygen intercalation by annealing the film in oxygen atmosphere. It has so far been impossible to improve the p-type conductivity of CuGaO2 significantly by doping Mg or Ca on the Ga site. The ptype conductivity is presumed to be due to oxygen doping or Cu Vacancies [6]. Reports in literature show, oxygen intercalation or divalent ion doping on Ga site is not possible for CuGaO2 thin films to improve the p-type conductivity. Sintered powder and crystals of CuFeO2 have been reported as the materials having the highest p-type conductivity [14, 15] among the copper and silver delafossites. However the CuFeO2 films are found to be less transparent in the visible region compared to CuGaO2. Hence in the present work, the solid solution between the CuGaO2 and CuFeO2 was effected by solid state reaction, varying the Fe content. The CuGa1-xFexO2 with Fe content, x=0.5 shows an increase in conductivity by two orders, compared to CuGaO2 but the transparency is only about 50% in the visible region which is less than that of CuGaO2 The synthesis of α−AgGaO2 was carried out by two step process which involves the synthesis of β-AgGaO2 by ion exchange reaction followed by the hydrothermal conversion of the β-AgGaO2 into α-AgGaO2. The trace amount of Ag has been reduced substantially in the two step synthesis compared to the direct hydrothermal synthesis. Thin films of α-AgGaO2 were prepared on silicon and Al2O3 substrates by pulsed laser deposition. These studies indicate the possibility of using this material as p-type material in thin film form for transparent electronics. The room temperature conductivity of α-AgGaO2 was measured as 3.17 x 10-4 Scm-1and the optical band gap was estimated as 4.12 eV. A transparent p-n junction thin film diode on glass substrate was fabricated using p-type α-AgGaO2 and n-ZnO.AgCoO2 thin films with 50% transparency in the visible region were deposited on single crystalline Al2O3 and amorphous silica substrates by RF magnetron sputtering and p type conductivity of AgCoO2 was demonstrated by fabricating transparent p-n junction diode with AgCoO2 as p-side and ZnO: Al as n-side using sputtering. The junction thus obtained was found to be rectifying with a forward to reverse current of about 10 at an applied voltage of 3 V.The present study shows that silver delafossite thin films with p-type conductivity can be used for the fabrication of active devices for transparent electronics applications.

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.

Development of p-type transparent semiconducting oxides for thin film transistor applications

Semiconductor physics has developed significantly in the field of re- search and industry in the past few decades due to it’s numerous practical applications. One of the relevant fields of current interest in material science is the fundamental aspects and applications of semi- conducting transparent thin films. Transparent conductors show the properties of transparency and conductivity simultaneously. As far as the band structure is concerned, the combination of the these two properties in the same material is contradictory. Generally a trans- parent material is an insulator having completely filled valence and empty conduction bands. Metallic conductivity come out when the Fermi level lies within a band with a large density of states to provide high carrier concentration. Effective transparent conductors must nec- essarily represent a compromise between a better transmission within the visible spectral range and a controlled but useful electrical con- ductivity [1–6]. Generally oxides like In2O3, SnO2, ZnO, CdO etc, show such a combination. These materials without any doping are insulators with optical band gap of about 3 eV. To become a trans- parent conductor, these materials must be degenerately doped to lift the Fermi level up into the conduction band. Degenerate doping pro- vides high mobility of extra carriers and low optical absorption. The increase in conductivity involves an increase in either carrier concen- tration or mobility. Increase in carrier concentration will enhance the absorption in the visible region while increase in mobility has no re- verse effect on optical properties. Therefore the focus of research for new transparent conducting oxide (TCO) materials is on developing materials with higher carrier mobilities.

Raman and FTIR studies of the structural aspects of Nasicon-type crystals; AFeTi(PO4)3 [A ¼ Ca, Cd]

Raman and FTIR spectra of CaFeTi(PO4)3 and CdFeTi(PO4)3 are recorded and analyzed. The observed bands are assigned in terms of vibrations of TiO6 octahedra and PO4 tetrahedra. The symmetry of TiO6 octrahedra and PO4 tetrahedra is lowered from their free ion symmetry. The presence of Fe3+ ion disrupts the Ti–O–P–O–Ti chain and leads to the distortion of TiO6 octrahedra and PO4 tetrahedra. The PO4 3 tetrahedra in both crystals are linearly distorted. The covalency bonding factor of PO4 3 polyanion of both the crystals are calculated from the Raman spectra and compared to that of other Nasicon-type systems. The numerical values of covalency bonding factor indicates that there is a reduction in redox energy and cell voltage and is attributed to strong covalency of PO4 3 polyanionin

FT-IR and FT-Raman study of Nasicon type phosphates, ASnFe(PO4)3 [A=Na2, Ca, Cd]

FT-Raman and FT-IR spectra of ASnFe(PO4)3 [A=Na2, Ca, Cd] were recorded and analyzed. The bands were assigned in terms of the vibrational group frequencies of SnO6 octahedral and PO4 tetrahedral. The spectral analysis shows that the symmetry of corner shared octahedral (SnO6) and the tetrahedral (PO4) are lowered from their free ion symmetry state. The presence of Fe3+ ions disrupts the S–N–O–S–N chain in the structure. This causes distortion of SnO6 and PO4 in the structure of all the compounds. Also it is seen that there are two distinct PO4 tetrahedra of different P–O bond lengths. One of these tetrahedra is linearly distorted in all the title compounds. The PO4 frequencies and bond lengths are calculated theoretically and are in agreement with the experimental values. The presence of PO4 polyanion in the structure can reduce the redox energy and hence reduce the metal oxygen covalency strength in the structure