Discretization and solution of the inhomogeneous Bogoliubov-de Gennes equations

In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

Extracting S-matrix poles for resonances from numerical scattering data: Type-II Pade reconstruction

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [421: Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [451) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H-2 -> HE + H, F + HD : HE + D, Cl + HCI CIH + Cl and H + D-2 -> HD + D reactions. Some detailed examples are given in the text.

Volumetric properties and enthalpies of solution of alcohols CkH2k+1OH (k = 1, 2, 6) in 1-methyl-3-alkylimidazolium bis(trifluoromethylsulfonyl)imide {[C1CnIm][NTf2] n = 2, 4, 6, 8, 10} ionic liquids

We present a study on the effect of the alkyl chain length of the imidazolium ring in 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids, [C1CnIm][NTf2] (n = 2 to 10), on the mixing properties of (ionic liquid + alcohol) mixtures (enthalpy and volume). We have measured small excess molar volumes with highly asymmetric curves as a function of mole fraction composition (S-shape) with more negative values in the alcohol-rich regions. The excess molar volumes increase with the increase of the alkyl-chain length of the imidazolium cation of the ionic liquid. The values of the partial molar excess enthalpy and the enthalpy of mixing are positive and, for the case of methanol, do not vary monotonously with the length of the alkyl side-chain of the cation on the ionic liquid – increasing from n = 2 to 6 and then decreasing from n = 8. This non-monotonous variation is explained by a more favourable interaction of methanol with the cation head group of the ionic liquid for alkyl chains longer than eight carbon atoms. It is also observed that the mixing is less favourable for the smaller alcohols, the enthalpy of mixing decreasing to less positive values as the alkyl chain of the alcohol increases. Based on the data from this work and on the knowledge of the vapour pressure of {[C1CnIm][NTf2] + alcohol} binary mixtures at T = 298 K reported in the literature, the excess Gibbs free energy, excess enthalpy and excess entropy could be then calculated and it was observed that these mixtures behave like the ones constituted by a non-associating and a non-polar component, with its solution behaviour being determined by the enthalpy.

Extracting a more realistic pseudopotential for aluminum, lead, niobium and tantalum from superconductor electron tunnelling spectroscopy data

Electron tunnelling spectroscopy, developed to extract superconductive metals the electron-phonon spectral density, $\alpha^2F(\nu)$, is found to be a powerful tool also for extracting a more realistic pseudopotential from such metals. The pseudopotential so extracted has a range of surprising but physically reasonable properties and regenerates $\alpha^2F(\nu)$ accurately. Free from most of its long-standing uncertainties, thie pseudopotential may be useful in a number of active fields.

PHOTOPERTURBATION OF THE (1)A-][-(5)T SPIN EQUILIBRIUM IN AN IRON(II) COMPLEX IN SOLUTION VIA LIGAND-FIELD EXCITATION

Variable-temperature magnetic susceptibility measurements in the solid state of the bis complex of tris(1-pyrazolyl)-methane with Fe(II), [Fe(tpm)2](ClO4)2, suggest the existence of singlet-quintet spin crossover with the singlet isomer largely favored at room temperature. In acetonitrile solution, measurement of the absorption spectrum as a function of temperature reveals a spin equilibrium with the quintet population varying from ca. 6% at 233 K to ca. 30% at 295 K. When the complex in solution is irradiated with a laser pulse at wavelengths within the ligand field absorption band of the singlet isomer, ground-state depletion occurs within the pulse duration followed by fast recovery to the original absorbance level with a time constant of 25 +/- 5ns. The recovery time is virtually independent of temperature over the range +23 to -43-degrees-C, but the signal:noise ratio of the transient signals increases with decreasing temperature. The effect was observable at several monitoring wavelengths spanning the LF and MLCT absorption regions of the complex but only when the irradiation wavelength fell within the LF absorption region. Irradiation within the MLCT band produced no effect other than that of laser pulse scatter. The observations are interpreted in terms of photoperturbation of the singlet-quintet spin state equilibrium, which in this case occurs solely through excitation in the ligand field absorption region of the complex and is the first reported instance of this type for a spin-crossover complex in solution.

OBSERVATION OF BIPHASIC KINETICS IN LIGHT-INDUCED SPIN-STATE CROSSOVER IN AN IRON(II) COMPLEX IN SOLUTION

Relaxation of the 1A1 half arrow right over half arrow left 5T2 spin equilibrium in acetonitrile of the complex of Fe(II) with the multidentate pyridyl macrocyclic ligand N,N',N''-tris(2-pyridylmethyl)-1,4,7-triazacyclodecane (tp[10]aneN3) after perturbation by a pulsed laser provides the first example of biphasic kinetics for spin crossover in solution with a fast (tau

Technical Note: Assessing a 24/7 solution for monitoring water quality loads in small river catchments

Quantifying nutrient and sediment loads in catchments is dif?cult owing to diffuse controls related to storm hydrology. Coarse sampling and interpolation methods are prone to very high uncertainties due to under-representation of high discharge, short duration events. Additionally, important low-?ow processes such as diurnal signals linked to point source impacts are missed. Here we demonstrate a solution based on a time-integrated approach to sampling with a standard 24 bottle autosampler con?gured to take a sample every 7 h over a week according to a Plynlimon design. This is evaluated with a number of other sampling strategies using a two-year dataset of sub-hourly discharge and phosphorus concentration data. The 24/7 solution is shown to be among the least uncertain in estimating load (inter-quartile range: 96% to 110% of actual load in year 1 and 97% to 104% in year 2) due to the increased frequency raising the probability of sampling storm events and point source signals. The 24/7 solution would appear to be most parsimonious in terms of data coverage and certainty, process signal representation, potential laboratory commitment, technology requirements and the ability to be widely deployed in complex catchments.