The spectra of the Dirac quasi-electrons transmission through the Fibonacci quasi-periodical superlattice (SL) are calculated and analyzed in the continuum model with the help of the transfer matrix method. The onedimensional SL based on a monolayer graphene modulated by the Fermi velocity barriers is studied. A new quasi-periodical factor is proposed to be considered. We show that the Fibonacci quasi-periodic modulation in graphene superlattices with the velocity barriers can be effectively realized by virtue of a difference in the velocity barrier values (no additional factor is needed and we keep in mind that not each factor can provide the quasi-periodicity). This fact is true for a case of normal incidence of quasi-electrons on a lattice. In contrast to the case of other types of the graphene SL spectra studied reveal the remarkable property, namely the periodic character over all the energy scale and the transmission coefficient doesn't tend asymptotically to unity at rather large energies. Both the conductance (using the known Landauer-Buttiker formula) and the Fano factor for the structure considered are also calculated and analyzed. The dependence of spectra on the Fermi velocity magnitude and on the external electrostatic potential as well as on the SL geometrical parameters (width of barriers and quantum wells) is analyzed. Using the quasi-periodical SL one can control the transport properties of the graphene structures in a wide range. The obtained results can be used for applications in the graphene-based electronics.

The article evaluates the energy resources of the components of the environment and the prospects for their use on the redistribution with the creation of local zones of cooling and heating. The physical basis of the principle and systems of redistribution and transformations of energy resources of environments with coverage of the role of compensation processes is given. The use of closed energy circuits with intermediate energy sources, which are subject to phase transitions of evaporation and condensation, and data of energy potentials of ambient air, which are practically achievable for use on this basis, is proposed. The article shows the advantages of arranging systems for redistribution of thermal potentials based on the use of phase transitions of material media. Determination of energy balances of energy redistribution systems is carried out with the indication that in the end, such a method is the most energy-efficient. Upon completion of technological tasks, local areas with different energy potentials and temperatures degrade in dissipation processes and transform to the level of environmental indicators. This means interfering with the environment only at the level of energy costs in compensation processes. The article shows the transition to secondary recovery systems of energy resources based on the use of primary energy sources in environmental transformations at the levels of increasing their energy potentials and providing phase transitions with appropriate mathematical formalizations. A regression analysis of the feasibility of using primary energy potentials is given. It is proved that in the heat pump due to the generated mechanical energy the heat return at the level of the lost one. The estimation of the general condition of processes at power effects is given. The offered air pump and system of realization of a refrigerating cycle are considered. The redistribution of energy potentials of natural, forcibly created environments or systems and the synthesis on this basis of powerful heat fluxes in combination with advanced control methods, allows you to control their values of thermodynamic parameters.

The transmission coefficient T of the Dirac quasielectrons through a rectangular potential barrier in the α-T3 model is calculated and analyzed in the continuum approach. The dependence of the transmission rate on para-meter α, which characterizes the degree of coupling of the central atom with the atoms in the vertices of the hexagonal lattice, and parameter β, which is equal to the ratio of Fermi velocities in the barrier and out-of-barrier regions, is analyzed. It was found, for certain quasiparticle energies, the supertunneling phenomenon is observed, which is that the transmission coefficient is equal to one independently of an angle of the particle incidence on the barrier, provided that α = 1. The values of these energies depend on the barrier height and the parameter β. It is shown that for some sets of parameters the function T(α) has maxima in the range 0 < α < 1. For a large range of parameter values, the transmittance increases monotonically with increasing α. For the zero angle of incidence of quasiparticles on the barrier the Klein paradox is observed, i.e., the quantum transparency of the system is ideal, and this is true for any values of parameters α, β, barrier height, and energy of quasiparticles.

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