BGS Consultancy : UNICEF IWASH project, Northern Ghana : visit report 25/10-5/11/2010

BGS have been commissioned to investigate the low drilling success rates encountered by the UNICEF IWASH programme in the Northern region of Ghana. The work is split into three phases: (1) situation analysis and information collation on current methods of groundwater development; (2) the development of a preliminary groundwater development map and suggestions for improving siting methods; and (3) a workshop and training course on groundwater development in N region. The project started on October 15th 2010 and is scheduled to finish by February 28th, 2011. Phase 1 involves a visit to Ghana, Phase 2 will occur mainly in the UK; and Phase 3 is scheduled to take place in Ghana during February 2011. This short note reports on the data collection visit 25th October – 5th November 2010. An itinerary, list of contacts and summary of data collected is given in the Appendices

Electrode Polarization Effects in Broadband Dielectric Spectroscopy

In the present work, we provide broadband dielectric spectra showing strong electrode polarization effects for various materials, belonging to very different material classes. This includes both ionic and electronic conductors as, e.g., salt solutions, ionic liquids, human blood, and colossal-dielectric-constant materials. These data are intended to provide a broad data base enabling a critical test of the validity of phenomenological and microscopic models for electrode polarization. In the present work, the results are analyzed using a simple phenomenological equivalent-circuit description, involving a distributed parallel RC circuit element for the modeling of the weakly conducting regions close to the electrodes. Excellent fits of the experimental data are achieved in this way, demonstrating the universal applicability of this approach. In the investigated ionically conducting materials, we find the universal appearance of a second dispersion region due to electrode polarization, which is only revealed if measuring down to sufficiently low frequencies. This indicates the presence of a second charge-transport process in ionic conductors with blocking electrodes.Comment: 9 pages, 6 figures, experimental data are provided in electronic form (see "Data Conservancy"

Macdonald polynomials in superspace: conjectural definition and positivity conjectures

We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity relations, is tested for high degrees. We conjecture a simple form for the norm of the Macdonald polynomials in superspace, and a rather non-trivial expression for their evaluation. We study the limiting cases q=0 and q=\infty, which lead to two families of Hall-Littlewood polynomials in superspace. We also find that the Macdonald polynomials in superspace evaluated at q=t=0 or q=t=\infty seem to generalize naturally the Schur functions. In particular, their expansion coefficients in the corresponding Hall-Littlewood bases appear to be polynomials in t with nonnegative integer coefficients. More strikingly, we formulate a generalization of the Macdonald positivity conjecture to superspace: the expansion coefficients of the Macdonald superpolynomials expanded into a modified version of the Schur superpolynomial basis (the q=t=0 family) are polynomials in q and t with nonnegative integer coefficients.Comment: 18 page

Orbital and spin contributions to the gg-tensors in metal nanoparticles

We present a theoretical study of the mesoscopic fluctuations of $g$-tensors in a metal nanoparticle. The calculations were performed using a semi-realistic tight-binding model, which contains both spin and orbital contributions to the $g$-tensors. The results depend on the product of the spin-orbit scattering time $\tau_{\textrm{\small so}}$ and the mean-level spacing $\delta$, but are otherwise weakly affected by the specific shape of a {\it generic} nanoparticle. We find that the spin contribution to the $g$-tensors agrees with Random Matrix Theory (RMT) predictions. On the other hand, in the strong spin-orbit coupling limit $\delta \tau_{\textrm{\small so}}/\hbar \to 0$, the orbital contribution depends crucially on the space character of the quasi-particle wavefunctions: it levels off at a small value for states of $d$ character but is strongly enhanced for states of $sp$ character. Our numerical results demonstrate that when orbital coupling to the field is included, RMT predictions overestimate the typical $g$-factor of orbitals that have dominant $d$-character. This finding points to a possible source of the puzzling discrepancy between theory and experiment.Comment: 21 pages, 6 figures; accepted for publication in Physical Review

Mixed-State Quasiparticle Spectrum for d-wave Superconductors

Controversy concerning the pairing symmetry of high-$T_c$ materials has motivated an interest in those measurable properties of superconductors for which qualitative differences exist between the s-wave and d-wave cases. We report on a comparison between the microscopic electronic properties of d-wave and s-wave superconductors in the mixed state. Our study is based on self-consistent numerical solutions of the mean-field Bogoliubov-de Gennes equations for phenomenological BCS models which have s-wave and d-wave condensates in the absence of a magnetic field. We discuss differences between the s-wave and the d-wave local density-of-states, both near and away from vortex cores. Experimental implications for both scanning-tunneling-microscopy measurements and specific heat measurements are discussed.Comment: 10 pages, REVTEX3.0, 3 figures available upon reques

Electronic excitations and the tunneling spectra of metallic nanograins

Tunneling-induced electronic excitations in a metallic nanograin are classified in terms of {\em generations}: subspaces of excitations containing a specific number of electron-hole pairs. This yields a hierarchy of populated excited states of the nanograin that strongly depends on (a) the available electronic energy levels; and (b) the ratio between the electronic relaxation rate within the nano-grain and the bottleneck rate for tunneling transitions. To study the response of the electronic energy level structure of the nanograin to the excitations, and its signature in the tunneling spectrum, we propose a microscopic mean-field theory. Two main features emerge when considering an Al nanograin coated with Al oxide: (i) The electronic energy response fluctuates strongly in the presence of disorder, from level to level and excitation to excitation. Such fluctuations produce a dramatic sample dependence of the tunneling spectra. On the other hand, for excitations that are energetically accessible at low applied bias voltages, the magnitude of the response, reflected in the renormalization of the single-electron energy levels, is smaller than the average spacing between energy levels. (ii) If the tunneling and electronic relaxation time scales are such as to admit a significant non-equilibrium population of the excited nanoparticle states, it should be possible to realize much higher spectral densities of resonances than have been observed to date in such devices. These resonances arise from tunneling into ground-state and excited electronic energy levels, as well as from charge fluctuations present during tunneling.Comment: Submitted to the Physical Review

Symmetrized models of last passage percolation and non-intersecting lattice paths

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.Comment: 21 pages, 5 figure

The interaction of a gap with a free boundary in a two dimensional dimer system

Let $\ell$ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let \Cal H be the half plane to the left of $\ell$. We consider lozenge tilings of \Cal H that have a triangular gap of side-length two and in which $\ell$ is a free boundary - i.e., tiles are allowed to protrude out half-way across $\ell$. We prove that the correlation function of this gap near the free boundary has asymptotics $\frac{1}{4\pi r}$, $r\to\infty$, where $r$ is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric charge near a conductor can be obtained by the method of images.Comment: 34 pages, AmS-Te

Negatively Charged Excitons and Photoluminescence in Asymmetric Quantum Well

We study photoluminescence (PL) of charged excitons ($X^-$) in narrow asymmetric quantum wells in high magnetic fields B. The binding of all $X^-$ states strongly depends on the separation $\delta$ of electron and hole layers. The most sensitive is the ``bright'' singlet, whose binding energy decreases quickly with increasing $\delta$ even at relatively small B. As a result, the value of B at which the singlet--triplet crossing occurs in the $X^-$ spectrum also depends on $\delta$ and decreases from 35 T in a symmetric 10 nm GaAs well to 16 T for $\delta=0.5$ nm. Since the critical values of $\delta$ at which different $X^-$ states unbind are surprisingly small compared to the well width, the observation of strongly bound $X^-$ states in an experimental PL spectrum implies virtually no layer displacement in the sample. This casts doubt on the interpretation of PL spectra of heterojunctions in terms of $X^-$ recombination