Validity of the fractional Leibniz rule on a coarse-grained medium yields a modified fractional chain rule

In this short communication, we show that the validity of the Leibniz rule for a fractional derivative on a coarse-grained medium brings about a modified chain rule, in agreement with alternative versions of fractional calculus. We compare our results to those of a recent article on this matter.Comment: 4 page

On the Zitterbewegung Transient Regime in a Coarse-Grained Space-Time

In the present contribution, by studying a fractional version of Dirac's equation for the electron, we show that the phenomenon of Zitterbewegung in a coarse-grained medium exhibits a transient oscillatory behavior, rather than a purely oscillatory regime, as it occurs in the integer case, $\alpha=1$. Our result suggests that, in such systems, the Zitterbewegung-type term related to a trembling motion of a quasiparticle is tamed by its complex interactions with other particles and the medium. This can justify the difficulties in the observation of this interesting phenomenon. The possibility that the Zitterbewegung be accompanied by a damping factor supports the viewpoint of particle substructures in Quantum Mechanics.Comment: 11 pages, 1 figure. This paper has been published in J. Adv. Phys. 7 (2015) 144

Structural Derivative Model for Tissue Radiation Response

By means of a recently-proposed metric or structural derivative, called scale-q-derivative approach, we formulate differential equation that models the cell death by a radiation exposure in tumor treatments. The considered independent variable here is the absorbed radiation dose D instead of usual time. The survival factor, Fs, for radiation damaged cell obtained here is in agreement with the literature on the maximum entropy principle, as it was recently shown and also exhibits an excellent agreement with the experimental data. Moreover, the well-known linear and quadratic models are obtained. With this approach, we give a step forward and suggest other expressions for survival factors that are dependent on the complex tumor structure.Comment: 6 pages, 2 collumn

A source of terahertz coherent phonons

Resonant tunnelling in a double-barrier heterostructure (DBHS) designed in order to produce an intense coherent emission of phonons is studied theoretically. Thisemission is achieved when the energy difference between the first excited level and the ground state in the well is close to the LO-phonon energy. The LO phonons emitted during the electron transition decay into a pair of (fLO and TA) phonons that leave the well in the [111] direction. These secondary TA phonons are coherent and form a beam that we call a SASER (by analogy with ‘laser’). The circulating current and the populations of phonons and electrons in the well are calculated by solving appropriate kinetic equations. Some possible applications of this system are discussed.(undefined

Generalized Maxwell Relations in Thermodynamics with Metric Derivatives

In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the α -total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe