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.

Swift heavy ion induced surface and microstructural evolution in metallic glass thin films

Swift heavy ion induced changes in microstructure and surface morphology of vapor deposited Fe–Ni based metallic glass thin films have been investigated by using atomic force microscopy, X-ray diffraction and transmission electron microscopy. Ion beam irradiation was carried out at room temperature with 103 MeV Au9+ beam with fluences ranging from 3 1011 to 3 1013 ions/cm2. The atomic force microscopy images were subjected to power spectral density analysis and roughness analysis using an image analysis software. Clusters were found in the image of as-deposited samples, which indicates that the film growth is dominated by the island growth mode. As-deposited films were amorphous as evidenced from X-ray diffraction; however, high resolution transmission electron microscopy measurements revealed a short range atomic order in the samples with crystallites of size around 3 nm embedded in an amorphous matrix. X-ray diffraction pattern of the as-deposited films after irradiation does not show any appreciable changes, indicating that the passage of swift heavy ions stabilizes the short range atomic ordering, or even creates further amorphization. The crystallinity of the as-deposited Fe–Ni based films was improved by thermal annealing, and diffraction results indicated that ion beam irradiation on annealed samples results in grain fragmentation. On bombarding annealed films, the surface roughness of the films decreased initially, then, at higher fluences it increased. The observed change in surface morphology of the irradiated films is attributed to the interplay between ion induced sputtering, volume diffusion and surface diffusion

Structural, topographical and magnetic evolution of RF-sputtered Fe-Ni alloy based thin films with thermal annealing

Metglas 2826 MB having a nominal composition of Fe40Ni38Mo4B18 is an excellent soft magnetic material and finds application in sensors and memory heads. However, the thin-film forms of Fe40Ni38Mo4B18 are seldom studied, although they are important in micro-electro-mechanical systems/nano-electromechanical systems devices. The stoichiometry of the film plays a vital role in determining the structural and magnetic properties of Fe40Ni38Mo4B18 thin films: retaining the composition in thin films is a challenge. Thin films of 52 nm thickness were fabricated by RF sputtering technique on silicon substrate from a target of nominal composition of Fe40Ni38Mo4B18. The films were annealed at temperatures of 400 °C and 600 °C. The micro-structural studies of films using glancing x-ray diffractometer (GXRD) and transmission electron microscope (TEM) revealed that pristine films are crystalline with (FeNiMo)23B6 phase. Atomic force microscope (AFM) images were subjected to power spectral density analysis to understand the probable surface evolution mechanism during sputtering and annealing. X-ray photoelectron spectroscopy (XPS) was employed to determine the film composition. The sluggish growth of crystallites with annealing is attributed to the presence of molybdenum in the thin film. The observed changes in magnetic properties were correlated with annealing induced structural, compositional and morphological changes

Evolution of structural and magnetic properties of Co–Fe based metallic glass thin films with thermal annealing

Ultra thin films based on CoFe were prepared from a composite target employing thermal evaporation. The microstructure of the films was modified by thermal annealing. The relationship between microstructure and magnetic properties of the films was investigated using techniques like glancing angle X-ray diffraction (GXRD), transmission electron microscopy (TEM) and vibrating sample magnetometry (VSM). The GXRD and TEM investigations showed an onset of crystallization of CoFe at around 373 K. The magnetic softness of the films improved with thermal annealing but at higher annealing temperature it is found to be deteriorating. Annealing inducedmodification of surface morphology of the alloy thin filmswas probed by atomic force microscopy (AFM). Surface smoothening was observed with thermal annealing and the observed magnetic properties correlate well with surface modifications induced by thermal annealing