Modified gravity in a viscous and non-isotropic background

We study the dynamical evolution of an $f(R)$ model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of $f(R)$ gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law $f(R)$ models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of $f(R)$ models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law $f(R)$ models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.Comment: 7 pages, 2 figure

Thermoelectric and Electronic Properties of B-doped Graphene Nanoribbon

The effect of concentration and position of boron atoms as impurities in graphene nanoribbon has been studied through density functional theory (DFT) and Landauer approach. For this purpose, we designed the graphene nanoribbon which has been doped with three different concentrations of boron atoms and finally the Density of States (DOS), electronic current and thermopower have been calculated. The comparison between the DOS curve of the pure graphene and the B-doped graphene shows that presence of boron atoms as impurity in graphene has caused an energy gap near the Fermi energy. Moreover, the study of the Iâ V characteristics shows that not only the current quantization is established but also the reduction in conductivity caused by doping with boron atoms can be observed, however this reduction is not sensitive to the concentration of boron atoms. In addition, the changes of the seebeck coefficient shows that in both pure and B-doped graphene, the curve has a minimum value at the temperature of 10 K, which is decreased to lower value by increasing the concentration of boron atoms. Generally, the result of calculations shows that by increasing the boron concentration, not only the energy gap of graphene is changed, but also several changes appear in its thermoelectric properties that can be attributed to the impurity potential distribution. The results of this study can be effectively used for designing the semiconductor electronic devices based on the graphene nanoribbon.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author