Cosmic inhomogeneities and averaged cosmological dynamics

If general relativity (GR) describes the expansion of the Universe, the observed cosmic acceleration implies the existence of a "dark energy." However, while the Universe is on average homogeneous on large scales, it is inhomogeneous on smaller scales. While GR governs the dynamics of the inhomogeneous Universe, the averaged homogeneous Universe obeys modified Einstein equations. Can such modifications alone explain the acceleration? For a simple generic model with realistic initial conditions, we show the answer to be "no." Averaging effects negligibly influence the cosmological dynamics.     

Haldane-like antiferromagnetic spin chain in the large anisotropy limit

We consider the one dimensional, periodic spin chain with N sites, similar to the one studied by Haldane [1], however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude s. For a chain with an even number of sites we show that actually the ground state is non-degenerate and given by a superposition of the two Neél states, due to quantum spin tunnelling. With an odd number of sites, the Neél state must necessarily contain a soliton. The position of the soliton is arbitrary thus the ground state is N-fold degenerate. This set of states reorganizes into a band. We show that this occurs at order 2s in perturbation theory. The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramers' theorem [18].     

An underpinning for spacetime

We argue, that from a background pre spacetime Zero Point Field, physical spacetime emerges on averaging over unphysical Compton scales.     

Self-energy of a charge near a metal surface

A quantum mechanical expression for the self-energy of a charged particle near a metal surface has been derived. The expression incorporates the interaction of the charge with the surface and bulk plasmons including their dispersions in the hydrodynamic model. It is found that the inclusion of the plasmons dispersions gives result for the saturated value of the image potential for copper closer to experiment.     

Constant current coulometric method for the determination of uranium in active process solutions

The determination of uranium in the range of 2.5–5 mg by constant current coulometry is described. The procedure is based on the modified version of the DAVIES—GRAY method, wherein uranium, after the reduction step, is oxidized by adding a known amount of potassium dichromate, and the excess of dichromate is determined by titration with Fe²⁺ solution. Fe²⁺ ions needed for the titration are generated in situ with 100% current efficiency by electrolytic reduction of Fe³⁺. The method is found to be accurate with a coefficient of variation better than 0.2%.