Spacetimes Admitting Concircular Curvaure Tensor in f(R) Gravity

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

How a projectively flat geometry regulates F(R)-gravity theory?

In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.

Extreme Poisson’s Ratios of Honeycomb, Re-Entrant, and Zig-Zag Crystals of Binary Hard Discs

Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. In contrast to equidiameter HD, which crystallize into a homogeneous solid which is elastically isotropic due to its six-fold symmetry axis, the systems studied in this work contain artificial patterns and can be either isotropic or anisotropic. It turns out that the symmetry of the patterns obtained by the appropriate arrangement of two types of discs strongly influences their elastic properties. The Poisson’s ratio (PR) of each of the considered structures was studied in two aspects: (a) its dependence on the external isotropic pressure and (b) in the function of the direction angle, in which the deformation of the system takes place, since some of the structures are anisotropic. In order to accomplish the latter, the general analytic formula for the orientational dependence of PR in 2D systems was used. The PR analysis at extremely high pressures has shown that for the vast majority of the considered structures it is approximately direction independent (isotropic) and tends to the upper limit for isotropic 2D systems, which is equal to +1. This is in contrast to systems of equidiameter discs for which it tends to 0.13, i.e., a value almost eight times smaller.

The gravitational energy density of the Universe

The teleparallel gravitational energy–momentum tensor density of the Friedmann–Lemaître–Robertson–Walker spacetime is calculated and analyzed: it is decomposed into density, isotropic pressure, non-isotropic pressures, and the heat-flux 4-vector; the antisymmetric part is decomposed into “electric” and “magnetic” components. It is found that the gravitational field obeys a radiation-like equation of state, the antisymmetric part does not contribute to the gravitational energy–momentum; and the total energy density, the non-isotropic pressures and the heat-flux 4-vector vanish for spatially flat universes. Finally, it is verified that the field equations have a well-defined vacuum.

Ultra-wide bandgap semiconductor behavior of NaCaF3 fluoro-perovskite with external static isotropic pressure and its impact on optical properties: First-principles computation

A comprehensive theoretical study to investigate the outcomes of externally applied static isotropic pressure (0 GPa - 50 GPa) on electronic, optical and structural properties of NaCaF3, using density functional theory (DFT) based CASTEP (Cambridge Serial Total Energy Package) code with ultra-soft pseudo-potential USP plane wave and Perdew Burke Ernzerhof (PBE) exchange-correlation functional of Generalized Gradient Approximation (GGA), is reported. The electronic bandgap shows the increasing trend 4.773 eV - 6.203 eV (direct bandgap) with increasing external pressure. The increase in bandgap is significant up to 20 GPa as compared to higher external pressures. The mystery of increasing band gap is nicely decoded by total density of states (TDOS) and elemental partial density of states (EPDOS). Optical properties have been calculated to analyze the impact of increment in band gap on them. We observed that highest peak of energy loss function L(w) shows the blue shift which confirms the increment of band gap. At zero photon energy, for 0 GPa, the static refractive index n(w) has value of 1.4456. After applying external pressure, there is a slight increase in n(w) which favors the semiconducting behavior of ternary compound. The energy points at which the absorption peak is maxima, the refractive index has lowest value.

Seismic waveform modelling and inversion with velocity-deviatoric stress-isotropic pressure formulation

<p>In waveform inversion, most of the existing adjoint-state methods are based on the second-order elastic wave equations subject to displacement. The implementation of the acoustic-elastic coupling problem and free-surface in this formulation is not explicit, especially for arbitrary boundaries. The formulation of velocity-deviatoric stress-isotropic pressure can tackle the above issue. We firstly review the difference between velocity stress equations and velocity-deviatoric stress-isotropic pressure equations. Then the adjoint state of the velocity-stress equations are derived, decomposing stresses into their deviatoric and isotropic parts. To simulate the unbounded wavefield, perfectly matched layers (PML) are embedded into the system of equations. It is modified for cheap computation, which avoids PML-related memory variables by applying complex coordinate stretch to three Cartesian axes in parallel.</p><p>A 3D velocity-deviatoric stress-isotropic stress formulation is implemented with the staggered finite-difference method for several synthetic models (including anisotropic models). And inversions are then performed to reconstruct the model parameters, which is followed by a sensitivity analysis.</p><p>This method has the potential to be used with real data, both for active and passive seismics. However, in its current form, since it does not treat fluid/anisotropic solid interfaces correctly, it is limited to fluid or isotropic solid problems.</p>

A generalization of the Einstein–Maxwell equations

The proposed modifications of the Einstein–Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a four-dimensional, nonlinear electromagnetic constitutive tensor, (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection and (4) the addition of a non-isotropic pressure tensor. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well behaved everywhere. The constitutive tensor introduces two structure fields: One contributes to the mass and the other contributes to the angular momentum. The additional curvature terms couple both to particle solutions and to localized electromagnetic and gravitational wave solutions. The pressure term is needed for the most general spherically symmetric, static metric. It results in a distinction between the Schwarzschild mass and the inertial mass.