Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Studies on Non-Resonant Multiphoton Processes in Atomic Hydrogen

In the present thesis we have formulated the Dalgarno-Lewis procedure for two-and three-photon processes and an elegant alternate expressions are derived. Starting from a brief review on various multiphoton processes we have discussed the difficulties coming in the perturbative treatment of multiphoton processes. A small discussion on various available methods for studying multiphoton processes are presented in chapter 2. These theoretical treatments mainly concentrate on the evaluation of the higher order matrix elements coming in the perturbation theory. In chapter 3 we have described the use of Dalgarno-Lewis procedure and its implimentation on second order matrix elements. The analytical expressions for twophoton transition amplitude, two-photon ionization cross section, dipole dynamic polarizability and Kramers-Heiseberg are obtained in a unified manner. Fourth chapter is an extension of the implicit summation technique presented in chapter 3. We have clearly mentioned the advantage of our method, especially the analytical continuation of the relevant expressions suited for various values of radiation frequency which is also used for efficient numerical analysis. A possible extension of the work is to study various multiphoton processcs from the stark shifted first excited states of hydrogen atom. We can also extend this procedure for studying multiphoton processes in alkali atoms as well as Rydberg atoms. Also, instead of going for analytical expressions, one can try a complete numerical evaluation of the higher order matrix elements using this procedure.

Photoacoustic thermal characterization of Al2O3–Ag ceramic nanocomposites

Laser-induced nondestructive photoacoustic (PA) technique has been employed to determine the thermal diffusivity of nanometal (Ag) dispersed ceramic alumina matrix sintered at different temperatures. The thermal diffusivity values are evaluated by knowing the transition frequency from the amplitude spectrum of PA signal using the one-dimensional heat flow model of Rosencwaig and Gersho. Analysis of the data shows that heat transport and hence the thermal diffusivity value is greatly affected by the influence of incorporation of foreign atom. It is also seen that sintering temperature affects the thermal diffusivity value in a substantial manner. The results are interpreted in terms of variation in porosity and carrier-assisted heat transport mechanism in nanometal dispersed ceramics.