Sharif Digital Repository

In this thesis, we studied the oscillation of neutrino flavors and the measurement of mixing parameters through the detection of cosmic neutrinos at neutrino telescopes. Most of the astrophysical explosions predict the emission of neutrino flux and kilometer-scale detectors are under construction for the observation of these neutrinos. Detection of astrophysical neutrinos opens a new window to understand the neutrino properties and also the properties of astrophysical sources.In this thesis first we review the phenomenology of neutrino flavor oscillation and characteristics of neutrino mass matrix. By introducing a new class of invariants (under general transformation of lepton fields bases)... 

Excitability is one of the most important characteristics of a neuron. In 1948, Hodgkin identified three different types of excitability of neurons. Excitability an all of its types can be observed in Hodgkin-Huxley model of neuronal dynamics (H-H model) as a four-dimensional system of differential equations and in at least two dimensional reductions of H-H type models. By applying the theory of dynamical systems (e.g. bifurcation theory), one can give a mathematical definition of excitability.Excitability of the neuron is equivalent to that the neuronal model is near a bifurcation through which the state of the system approaches to a stable limit cycle. In this thesis, a two-dimensional... 

Complex systems involve a large number of degrees of freedom and consist of many components. Interactions of these components with each other, or with an external force, play a significant role in the collective behavior of the complex system.We come across complex systems in many different fields of study including neuroscience, climatology, studying stock markets, etc. The non-linearity of the interactions between their components is what they have in common. Interesting macro-scale properties can be observed in a complex system, as a result of the collective behavior of the system components. We usually focus on studying a group of components in a system, rather than a single component,... 

Neutrino flavor oscillations are clear evidence of massive neutrinos. It has been for more than a decade that neutrino physics became one of active topics in the field of particle physics and various experiments started studying the flavor oscillation of neutrinos. Unfortunately, experiments studying the flavor oscillations are only sensitive to the mass square difference, and they are incapable of providing more information about the absolute mass scale of neutrinos. Additionally, sterile neutrinos having non-standard interactions are under vast investigations and studies. Determination of neutrino masses and their effective number is among the most challenging problems by which...