The dynamic approach to fractional Brownian motion (FBM) establishes a link between non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a non-vanishing memory of their past time evolution. It is well known that the recrossing times of the origin by an ordinary 1D diffusion trajectory generates a distribution of time distances between two consecutive origin recrossing times with an inverse power law with index m=1.5. However, with theoretical and numerical arguments, it is proved that this is the special case of a more general condition, insofar as the recrossing times produced by the dynamic FBM generates process with m=2-H. Later, the model of ballistic deposition is studied, which is as a simple way to establish cooperation among the columns of a growing surface, to show that cooperation generates memory properties and, at same time, non-Poisson renewal events. Finally, the connection between trajectory and density memory is discussed, showing that the trajectory memory does not necessarily yields density memory, and density memory might be compatible with the existence of abrupt jumps resetting to zero the system's memory.

A resonant cavity operating in TE011 mode was used to study the adsorption response of single walled carbon nanotubes (SWCNTs) and other nanomaterials for different types of gas molecules. The range of the frequency signal as a probe was chosen as geometry dependent range between 9.1 -9.8 GHz. A highly specific range can be studied for further experiments dependent on the type of molecule being investigated. It was found that for different pressures of gases and for different types of nanomaterials, there was a different response in the shifts of the probe signal for each cycle of gassing and degassing of the cavity. This dissertation suggests that microwave spectroscopy of a complex medium of gases and carbon nanotubes can be used as a highly sensitive technique to determine the complex dielectric response of different polar as well as non-polar gases when subjected to intense electromagnetic fields within the cavity. Also, as part of the experimental work, a range of other micro-porous materials was tested using the residual gas analysis (RGA) technique to determine their intrinsic absorption/adsorption characteristics when under an ultra-high vacuum environment. The scientific results obtained from this investigation, led to the development of a chemical biological sensor prototype. …