In nature we find many instances of complex behavior for example the dynamics of stock markets, power grids, internet networks, highway traffic, social networks, heartbeat dynamics, neural dynamics, dynamics of living organisms, etc. The study of these complex systems involves the use of tools of non-linear dynamics and non-equilibrium statistical physics. This dissertation is devoted to understanding two different sources of complex behavior – non-poissonian renewal events also called crucial events and infinite memory of fractional Brownian motion. They both generate 1/f noise frequency spectrum. Thus, we studied examples of both processes and also their joint action. We also tried to establish the role of crucial events in biological and physiological processes like biophoton emission during the germination of seeds, the dynamics of heartbeat and neural dynamics. Using a statistical method of analyzing the time series of bio signals we were able to quantify the complexity associated with the underlying dynamics of these processes. Finally, we adopted a model that unifies both crucial events and memory fluctuations to study the rhythmic behavior observed in heart rate variability of people during meditation. We were able to also quantify the level of stress reduction during meditation. The work presented in this dissertation …

The main goals of this research were to fabricate magnetic cobalt nanoparticles and study their structural, crystal structure, optical, and magnetic properties. Cobalt nanoparticles with average particle size 8.7 nm were fabricated by the method of high temperature reduction of cobalt salt utilizing trioctylphosphine as a surfactant, oleic acid as a stabilizer, and lithium triethylborohydride as a reducing reagent. Energy-dispersive X-ray spectroscopy (EDX) analysis confirmed the formation of cobalt nanoparticles. High resolution transmission electron microscopy images show that Co NPs form both HCP and FCC crystal structure. The blocking temperature of 7.6 nm Co NPs is 189 K. Above the blocking temperature, Co NPs are single domain and hence showed superparamagnetic behavior. Below the blocking temperature, Co NPs are ferromagnetic. Cobalt nanoparticles with a single-domain crystal structure support a sharp plasmon resonance at 280 nm. Iron nanoparticles with average particle size 4.8 nm were fabricated using chemical reduction method show plasmon resonance at 266 nm. Iron nanoparticles are ferromagnetic at 6 K and superparamagnetic at 300 K.