A Branched Pore Model Analysis for the Adsorption of Acid Dyes on Activated Carbon

A new branched-pore adsorption model has been developed using an external mass transfer coefficient, K _f, an effective diffusivity, D _eff, a lumped micropore diffusion rate parameter, K _b, and the fraction of macropores, f, to describe sorption kinetic data from initial adsorbent-adsorbate contact to the long-term adsorption phase. This model has been applied to an environmental pollution problem—the removal of two dyes, Acid Blue 80 (AB80) and Acid Red 114 (AR114), by sorption on activated carbon. A computer program has been used to generate theoretical concentration-time curves and the four mass transfer kinetic parameters adjusted so that the model achieves a close fit to the experimental data. The best fit values of the parameters have been determined for different initial dye concentrations and carbon masses. Since the model is specifically applicable to fixed constant values of these four parameters, a further and key application of this project is to see if single constant values of these parameters can be used to describe all the experimental concentration-time decay curves for one dye-carbon system.The error analysis and best fit approach to modeling the decay curves for both dye systems show that the correlation between experimental and theoretical data is good for the fixed values of the four fitted parameters. A significantly better fit of the model predictions is obtained when K _f, K _b and f are maintained constant but D _eff is varied. This indicates that the surface diffusivity may vary as a function of surface coverage.     

Low valent and hydride complexes of NHC coordinated gallium and indium

The reactions of the N-heterocyclic carbene 1,3-dimesitylimidazol-2-ylidene (IMes) with Ga[GaCl(4)], "GaI", InCl(2) and GaBr(3) have been examined. All reactions using a low valent gallium or indium starting material led to species of the form [{MX(2)(IMes)}(2)], where M = Ga, X = Cl (1), I (2); M = In, X = Cl (3), with disproportionation and loss of gallium metal in the case of 2. Reaction of IMes with gallium tribromide yields the air and moisture stable complex [GaBr(3)(IMes)] (4), which has been used as a precursor to the mixed bromohydrides [GaBrH(2)(IMes)] (5) and [GaBr(2)H(IMes)] (6) by (i) ligand redistribution with [GaH(3)(IMes)], (ii) hydride-bromide exchange with triethylsilane, and (iii) alkylation with (n)butyllithium followed by β-hydride elimination (6 only). Attempts to prepare 1, or monovalent analogues such as [{GaCl(IMes)}(n)], by thermally induced reductive elimination of dihydrogen from the chlorohydride congeners of 5 and 6 resulted in isolation of the known compounds [IMesCl][Cl] (IMesCl = 1,3-dimesityl-2-chloroimidazolium), and/or 1,3-dimesityl-2-dihydroimidazole, and gallium metal. Preliminary photochemical NMR spectroscopy and catalytic studies of 5 and 6 aimed at reductive dehydrogenation under milder conditions are reported. Compounds 1 and 4 have been characterised by single crystal X-ray structure determination.     

Determination of uranium in marine sediment pore waters by isotope dilution inductively coupled plasma mass spectrometry

Inductively coupled plasma mass spectrometry (ICP-MS) was used in an isotope dilution mode to assay small-volume (0.25 ml) sediment pore waters for their uranium contents, using ²³⁶U as the spike. The only pretreatment required was a simple dilution by a factor of 20, which gave sufficient volume for three replicate analyses per sample. Rapid and accurate results were obtained for a variety of samples and standards, ranging in concentration from 0.05 to 10 ng U ml^?1. A suite of 30 samples can be analysed in less than 6 h by this method. The relative standard deviation was better than 1.9%, with a detection limit, based on 3σ background, of 2 pg U ml^?1 in solution (40 pg ml^?1 in samples). Sea water is a difficult matrix for ICP-MS and thus the method is generally suitable for uranium determinations in many other sample solutions.     

The Order of Automorphisms of Quasigroups

We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D.  Stones.     

Rectangular-radial drawings of cubic plane graphs

Rectangular drawings and rectangular duals can be naturally extended to other surfaces. In this paper, we extend rectangular drawings and rectangular duals to drawings on a cylinder. The extended drawings are called rectangular-radial drawings and rectangular-radial duals. Rectangular-radial drawings correspond to periodic rectangular tilings of a 1-dimensional strip. We establish a necessary and sufficient condition for plane graphs with maximum degree 3 to have rectangular-radial drawings and a necessary and sufficient condition for triangulated plane graphs to have rectangular-radial duals. Furthermore, we present three linear time algorithms under three different conditions for finding a rectangular-radial drawing for a given cubic plane graph, if one exists.     

A Linear Time Algorithm for Constructing Maximally Symmetric Straight Line Drawings of Triconnected Planar Graphs

Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. To draw graphs symmetrically, we employ two steps. The first step is to find appropriate automorphisms. The second step is to draw the graph to display the automorphisms. Our aim in this paper is to construct maximally symmetric straight line drawings of triconnected planar graphs in linear time. Previously known algorithms run in quadratic time. We show that an algorithm of Fontet can be used to find an embedding in the plane with the maximum number of symmetries, and present a new algorithm for finding a straight line drawing that achieves that maximum. Both algorithms run in linear time.     

Asymptotic enumeration of dense 0-1 matrices with specified line sums

Let s=(s₁,s₂,…,sm) and t=(t₁,t₂,…,tn) be vectors of non-negative integers with . Let B(s,t) be the number of m×n matrices over {0,1} with jth row sum equal to sj for 1?j?m and kth column sum equal to tk for 1?k?n. Equivalently, B(s,t) is the number of bipartite graphs with m vertices in one part with degrees given by s, and n vertices in the other part with degrees given by t. Most research on the asymptotics of B(s,t) has focused on the sparse case, where the best result is that of Greenhill, McKay and Wang (2006). In the case of dense matrices, the only precise result is for the case of equal row sums and equal column sums (Canfield and McKay, 2005). This paper extends the analytic methods used by the latter paper to the case where the row and column sums can vary within certain limits. Interestingly, the result can be expressed by the same formula which holds in the sparse case.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Sussmann's orbit theorem and maps

A map between manifolds which matches up families of complete vector fields is a fiber bundle mapping on each orbit of those vector fields.