Narrow Results

Considering the Møller energy definition in both Einstein's theory of general relativity and tele-parallel theory of gravity, we find the energy of the universe based on viscous Kasner-type metrics. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories and this result agrees with previous works of Cooperstock and Israelit et al., Banerjee–Sen, Vargas who investigated the problem of the energy in Friedmann–Robertson–Walker universe in Einstein's theory of general relativity and Aydogdu–Saltı who considered the same problem in tele-parallel gravity. In all of these works, they found that the energy of the Friedmann–Robertson–Walker spacetime is zero. Our result is the same as that obtained in the studies of Saltı and Havare. They used the viscous Kasner-type metric and found the total energy and momentum by using Bergmann–Thomson energy–momentum formulation in both general relativity and tele-parallel gravity. The result that the total energy and momentum components of the universe is zero supports the viewpoints of Albrow and Tryon.

The advancement in new materials processing and fabrication techniques has made it possible to better control the atomistic level of structures in a way, which was not feasible only a decade ago. If one can couple this atomic control with a good understanding of the relationship between structure and properties, this will in the future lead to a significant contribution to the synthesizing of tailor-made materials. In this paper we have focused on, the structurally related nanolayered ternary compounds M_N+1AX_N, (MAX) where N = 1, 2 or 3, M is an early transition metal, A is an A-group (mostly IIIA and IVA) element, and X is either C and/or N, which has attracted increasing interest owing to their unique properties. The general relations between the electronic structure and materials properties of MAX phases have been elaborated based on ab initio calculations.

The atomic structure and edge state of zigzag carbon nanoscrolls (ZCNSs) are investigated using first-principles calculations based on density functional theory. The results show a non-monotonic dependence of the total energy of ZCNS on the surface curvature due to a competition between the elasticity and the van der Waals interactions in a scroll. The edge states can be tuned by using different forms of edge hydrogenation and inner radius. It is found that the edge state range of monohydrogenated ZCNSs is smaller than that of monohydrogenated zigzag-edged graphene nanoribbons (ZGNRs), which is also verified using the tight-binding approximation. With the different edge hydrogenations, ZCNSs prefer the $s{p}^2$ hybridization more than the $s{p}^3$ one. Our present study could suggest the possibility of adjusting the electronic properties of ZCNSs and may provide potential applications in the electronic devices.

The deformation structure of the even–even ytterbium, hafnium and tungsten nuclei is investigated in framework of the collective model, the single-particle Schrödinger fluid model and the cranked Nilsson model. Accordingly, we have calculated the rotational and vibrational energies, the nuclear moments of inertia, the total ground-state energy, the quadrupole moment, the liquid drop (LD) energy, the Strutinsky inertia, the LD inertia, the volume conservation factor , the smoothed energy, the Bardeen, Cooper and Schrieffer (BCS) energy and the G-value of the ytterbium: ¹⁷⁰Yb, ¹⁷²Yb and ¹⁷⁴Yb, hafnium: ¹⁷⁶Hf, ¹⁷⁸Hf and ¹⁸⁰Hf and tungsten: ¹⁸²W, ¹⁸⁴W and ¹⁸⁶W nuclei as functions of the deformation parameters β, γ, which are assumed to vary in the ranges (-0.50 ≤ β ≤ 0.50) and (0° ≤ γ ≤ 60°). Also, two polynomials in β are obtained to produce results in good agreement with the corresponding results for the total ground-state energy and the quadrupole moment of the mentioned nine nuclei.

We have investigated the lowest-energy structures and electronic properties of the Cu_n(n = 2–10) nanoclusters based on density functional theory (DFT) in local density approximation. The total energies, binding energies per atom, bond lengths, HOMO-LUMO gaps and ionization potentials have been calculated. The results are compared well with other theoretical and available experimental results.

By means of ab initio calculations, we have estimated stability of 2D Me${}_{2}X$ ($\mathrm{\text{Me}}=\mathrm{\text{Mg}}$, Ca, Sr, Ba and $X=\mathrm{\text{Si}}$, Ge, Sn) in the T and Td phases, which are similar to the ones of 2D transition metal chalcogenides, in addition to their phonon spectra. The T phase is found to be more stable for 2D Ca${}_{2}X$, Sr${}_{2}X$ and Ba${}_{2}X$, whereas the Td phase is predicted to be the ground state for 2D Mg${}_{2}X$. We have also discussed that imaginary frequencies in the calculated phonon spectra of 2D Me${}_{2}X$, which appeared in the vicinity of the $\mathrm{\Gamma }$ point, were not necessarily associated with the dynamic instability.

In this paper, we obtain decay rates for the total energy associated to the linear plate equation with effects of rotational inertia and a fractional damping term depending on a number θ ∈ [0, 1]. We observe that the dissipative structure of the equation with θ = 0 is of the regularity-loss type. This decay structure still remains true in the plate equation with a power of fractional damping θ > 0, but it becomes more weak when θ increase. This means that we can have an optimal decay estimate of solutions under an additional regularity assumption on the initial data. Our results generalize previous results by Luz and Charão and some of recent results due to Sugitani and Kawashima. We use a special method in the Fourier space which we developed in a previous work for the wave equation. So, our approach shows to be very effective to study decay properties for several problems in Rⁿ.

The advancement in new materials processing and fabrication techniques has made it possible to better control the atomistic level of structures in a way, which was not feasible only a decade ago. If one can couple this atomic control with a good understanding of the relationship between structure and properties, this will in the future lead to a significant contribution to the synthesizing of tailor-made materials. In this paper we have focused on, the structurally related nanolayered ternary compounds M_N+1AX_N, (MAX) where N = 1, 2 or 3, M is an early transition metal, A is an A-group (mostly IIIA and IVA) element, and X is either C and/or N, which has attracted increasing interest owing to their unique properties. The general relations between the electronic structure and materials properties of MAX phases have been elaborated based on ab initio calculations.