A new type of self-similar potential is used to study a multibarrier system made of graphene. Such potential is based on the traditional middle third Cantor set rule combined with a scaling of the barriers height. The resulting transmission coefficie
nt for charge carriers, obtained using the quantum relativistic Dirac equation, shows a surprising self-similar structure. The same potential does not lead to a self-similar transmission when applied to the typical semiconductors described by the non-relativistic Schrodinger equation. The proposed system is one of the few examples in which a self-similar structure produces the same pattern in a physical property. The resulting scaling properties are investigated as a function of three parameters: the height of the main barrier, the total length of the system and the generation number of the potential. These scaling properties are first identified individually and then combined to find general analytic scaling expressions.
Aging associated brain decline often result in some kind of dementia. Even when this is a complex brain disorder a physical model can be used in order to describe its general behavior. This model is based in first principles. A probabilistic model fo
r the development of dementia is obtained and fitted to some experimental data obtained from the Alzheimers Disease Neuroimaging Initiative. It is explained how dementia appears as a consequence of aging and why it is irreversible.
