Full linear perturbations and localization of gravity on f(R,T)f(R,T) brane

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.Comment: v3: 8 pages, 2 figures, improved version with minor corrections, accepted by EPJ

Truncation of Unitary Operads

We introduce truncation ideals of a $\Bbbk$-linear unitary symmetric operad and use them to study ideal structure, growth property and to classify operads of low Gelfand-Kirillov dimension

Electronic, mechanical, and thermodynamic properties of americium dioxide

By performing density functional theory (DFT) +$U$ calculations, we systematically study the electronic, mechanical, tensile, and thermodynamic properties of AmO$_{2}$. The experimentally observed antiferromagnetic insulating feature [J. Chem. Phys. 63, 3174 (1975)] is successfully reproduced. It is found that the chemical bonding character in AmO$_{2}$ is similar to that in PuO$_{2}$, with smaller charge transfer and stronger covalent interactions between americium and oxygen atoms. The valence band maximum and conduction band minimum are contributed by 2$p-5f$ hybridized and 5$f$ electronic states respectively. The elastic constants and various moduli are calculated, which show that AmO$_{2}$ is less stable against shear forces than PuO$_{2}$. The stress-strain relationship of AmO$_{2}$ is examined along the three low-index directions by employing the first-principles computational tensile test method. It is found that similar to PuO$_{2}$, the [100] and [111] directions are the strongest and weakest tensile directions, respectively, but the theoretical tensile strengths of AmO$_{2}$ are smaller than those of PuO$_{2}$. The phonon dispersion curves of AmO$_{2}$ are calculated and the heat capacities as well as lattice expansion curve are subsequently determined. The lattice thermal conductance of AmO$_{2}$ is further evaluated and compared with attainable experiments. Our present work integrally reveals various physical properties of AmO$_{2}$ and can be referenced for technological applications of AmO$_{2}$ based materials.Comment: 23 pages, 8 figure