Centaur 1939

Digitised by the Faculty of the Veterinary Scienc

Numerical study of vortex system quantum melting

We report a numerical study of the vortex system in the two dimensional II-type superconductors. We have proposed a phenomenological model that takes into account quantum fluctuations of Abrikosov's vortices. The results of the quantum Monte-Carlo simulations by the SSE algorithm show that the thermal fluctuations are dominated by quantum fluctuations at low temperatures. In particular, we demonstrate the possibility of the quantum melting transition for vortex system in the temperature region where thermal melting transition is improbable

On the reconstruction of planar lattice-convex sets from the covariogram

A finite subset $K$ of $\mathbb{Z}^d$ is said to be lattice-convex if $K$ is the intersection of $\mathbb{Z}^d$ with a convex set. The covariogram $g_K$ of $K\subseteq \mathbb{Z}^d$ is the function associating to each u \in \integer^d the cardinality of $K\cap (K+u)$. Daurat, G\'erard, and Nivat and independently Gardner, Gronchi, and Zong raised the problem on the reconstruction of lattice-convex sets $K$ from $g_K$. We provide a partial positive answer to this problem by showing that for $d=2$ and under mild extra assumptions, $g_K$ determines $K$ up to translations and reflections. As a complement to the theorem on reconstruction we also extend the known counterexamples (i.e., planar lattice-convex sets which are not reconstructible, up to translations and reflections) to an infinite family of counterexamples.Comment: accepted in Discrete and Computational Geometr

Topological Defects in Gravitational Lensing Shear Fields

Shear fields due to weak gravitational lensing have characteristic coherent patterns. We describe the topological defects in shear fields in terms of the curvature of the surface described by the lensing potential. A simple interpretation of the characteristic defects is given in terms of the the umbilical points of the potential surface produced by ellipsoidal halos. We show simulated lensing shear maps and point out the typical defect configurations. Finally, we show how statistical properties such as the abundance of defects can be expressed in terms of the correlation function of the lensing potential.Comment: 17 pages, 4 figure

Fouling in Nanofiltration

According to Koros et al. [1] fouling is “the process resulting in loss of performance of a membrane due to deposition of suspended or dissolved substances on its external surfaces, at its pore openings, or within its pores”. Fouling is also decribed as flux decline which is irreversible and can only be removed by, for example, chemical cleaning [2]. This is different to flux decline due to solution chemistry effects or concentration polarisation which is described in more detail later in this chapter. Those flux declines can be reversed with clean water and are hence not considered as fouling

Critical-point scaling function for the specific heat of a Ginzburg-Landau superconductor

If the zero-field transition in high temperature superconductors such as YBa_2Cu_3O_7-\delta is a critical point in the universality class of the 3-dimensional XY model, then the general theory of critical phenomena predicts the existence of a critical region in which thermodynamic functions have a characteristic scaling form. We report the first attempt to calculate the universal scaling function associated with the specific heat, for which experimental data have become available in recent years. Scaling behaviour is extracted from a renormalization-group analysis, and the 1/N expansion is adopted as a means of approximation. The estimated scaling function is qualitatively similar to that observed experimentally, and also to the lowest-Landau-level scaling function used by some authors to provide an alternative interpretation of the same data. Unfortunately, the 1/N expansion is not sufficiently reliable at small values of N for a quantitative fit to be feasible.Comment: 20 pages; 4 figure

Microlensing by natural wormholes: theory and simulations

We provide an in depth study of the theoretical peculiarities that arise in effective negative mass lensing, both for the case of a point mass lens and source, and for extended source situations. We describe novel observational signatures arising in the case of a source lensed by a negative mass. We show that a negative mass lens produces total or partial eclipse of the source in the umbra region and also show that the usual Shapiro time delay is replaced with an equivalent time gain. We describe these features both theoretically, as well as through numerical simulations. We provide negative mass microlensing simulations for various intensity profiles and discuss the differences between them. The light curves for microlensing events are presented and contrasted with those due to lensing produced by normal matter. Presence or absence of these features in the observed microlensing events can shed light on the existence of natural wormholes in the Universe.Comment: 16 pages, 24 postscript figures (3 coloured), revtex style, submitted to Phys. Rev.

Three-body vs. dineutron approach to two-neutron radiative capture in 6^{6}He

The low-energy behavior of the strength function for the $1^-$ soft dipole excitation in $^{6}$He is studied theoretically. Use of very large basis sizes and well-grounded extrapolation procedures allows to move to energies as small as 1 keV, at which the low-energy asymptotic behavior of the E1 strength function seems to be achieved. It is found that the low-energy behavior of the strength function is well described in the effective three-body "dynamical dineutron model". The astrophysical rate for the $\alpha$+$n$+$n \rightarrow ^6$He+$\gamma$ is calculated. Comparison with the previous calculations is performed.Comment: 6 pages, 9 figure

NMR and NQR Fluctuation Effects in Layered Superconductors

We study the effect of thermal fluctuations of the s-wave order parameter of a quasi two dimensional superconductor on the nuclear spin relaxation rate near the transition temperature Tc. We consider both the effects of the amplitude fluctuations and the Berezinskii-Kosterlitz-Thouless (BKT) phase fluctuations in weakly coupled layered superconductors. In the treatment of the amplitude fluctuations we employ the Gaussian approximation and evaluate the longitudinal relaxation rate 1/T1 for a clean s-wave superconductor, with and without pair breaking effects, using the static pair fluctuation propagator D. The increase in 1/T1 due to pair breaking in D is overcompensated by the decrease arising from the single particle Green's functions. The result is a strong effect on 1/T1 for even a small amount of pair breaking. The phase fluctuations are described in terms of dynamical BKT excitations in the form of pancake vortex-antivortex (VA) pairs. We calculate the effect of the magnetic field fluctuations caused by the translational motion of VA excitations on 1/T1 and on the transverse relaxation rate 1/T2 on both sides of the BKT transitation temperature T(BKT)<Tc. The results for the NQR relaxation rates depend strongly on the diffusion constant that governs the motion of free and bound vortices as well as the annihilation of VA pairs. We discuss the relaxation rates for real multilayer systems where the diffusion constant can be small and thus increase the lifetime of a VA pair, leading to an enhancement of the rates. We also discuss in some detail the experimental feasibility of observing the effects of amplitude fluctuations in layered s-wave superconductors such as the dichalcogenides and the effects of phase fluctuations in s- or d-wave superconductors such as the layered cuprates.Comment: 38 pages, 12 figure