From Maximal Force to the Field Equations of General Relativity

We point out that field equations of general relativity are implied by a maximal force given by c4/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.

A First-Principles Study of Structure, Elastic and Electronic Properties of GeTiO3 as Environmentally Innocuous Ferroelectric Perovskites

The structural parameters, elastic properties, spontaneous polarization, electronic band structure, and density of states (DOS) of GeTiO3 in tetragonal phase have been studied computationally using pseudopotential plane-wave (PP-PW) method based on the density functional theory (DFT). The generalized gradient approximation (GGA) was used to estimate the exchange-correlation energies. The equilibrium lattice parameter, unit cell volume, bulk modulus and its derivative are obtained and compared with the available theoretical data. The elastic characteristics such as elastic constants, Poisson’s ratio, elastic modulus, and anisotropy factor are obtained in the pressure range 0–50 GPa. Our computed results of elastic constant satisfy Born’s stability criterion. In view of Pugh’s prediction standard, the material is taken as ductile. Once the elastic constant is calculated, the Debye temperature of GeTiO3 compound is also evaluated from the average sound velocity. The density of states, band structures, and charge-density distribution are discussed and compared with previous computational results. The calculation within Berry’s phase approach indicate a high spontaneous polarization of tetragonal GeTiO3 (1.125 C/m2). Thus, the substance is identifi ed as a promising environmentally friendly ferroelectric material.

The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals

In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model.