Topotactic oxidation of TiGaPO-1, a pyridine-templated titanium gallophosphate with a new octahedral-tetrahedral 3-D framework structure containing Ti-III/Ti-IV

The first 3-D open-framework TiGaPO complex, constructed from (TiO6)-O-III, (TiO6)-O-IV, GaO4, and PO4 polyhedra, contains pyridinium cations in a 1-D pore network and can be oxidized in air at 543 K with retention of the original framework structure.

Tin and tin-titanium as catalyst components for reversible hydrogen storage of sodium aluminium hydride

This paper is concerned with the effects of adding tin and/or titanium dopant to sodium aluminium hydride for both dehydrogenation and re-hydrogenation reactions during their reversible storage of molecular hydrogen. Temperature programmed decomposition (TPD) measurements show that the dehydrogenation kinetics of NaAlH4 are significantly enhanced upon doping the material with 2 mol% of tributyltin hydride, Sn(Bu)(3)H but the tin catalyst dopant is shown to be inferior than titanium. On the other hand, in this preliminary work, a significant synergetic catalytic effect is clearly revealed in material co-doped with both titanium and tin catalysts which shows the highest reversible rates of dehydrogenation and re-hydrogenation (after their hydrogen depletion). The re-hydrogenation rates of depleted Sn/Ti/NaAlH4 evaluated at both 9.5 and 140 bars hydrogen are also found to be favourable compared to the Ti/NaAlH4, which clearly suggest the importance of the catalyst choice. Basing on these results some mechanistic insights for the catalytic reversible dehydrogenation and re-hydrogenation processes of Sn/Ti/NaAlH4 are therefore made. (C) 2006 Elsevier Ltd. All rights reserved.

Antitumour activity of [1,2-di(cyclopentadienyl)-1,2-di(p-N,N-dimethylaminophenyl)-ethanediyl] titanium dichloride in xenografted Ehrlich's ascites tumour

The effects of a new titanocene compound with an ansa ligand in the cyclopentadienyl rings, the 1,2-di(cyclopentadienyl)-1,2-di(p-NNdimethylaminophenyl)-ethanediyl] titanium dichloride (TITANOCENE X), on the growth and differentiation of granulocyte-macrophage progenitor cells [colony-forming unit-granulocyte-macrophage (CFU-GM)] and Natural killer (NK) cell activity in Ehrlich's ascites tumour (EAT)-bearing mice were studied. Myelosuppression concomitant with increased numbers of spleen CFU-GM was observed in tumour-bearing mice. Treatment of these animals with TITANOCENE X (2.5-50mg/kg/day) produced an increase in myelopoicsis, in a dose-dependent manner, and reduced spleen colony formation. In addition, the treatment of EAT-bearing mice with 3 doses of 20 or 50 mg/kg TITANOCENE X restored to normal values the reduced Natural killer cell function observed during tumour growth. In parallel, TITANOCENE X prolonged, in a dose-dependent manner, the survival of mice inoculated with Ehrlich's ascites tumour. The highest dose of 50 mg/kg prolonged in 50% the survival time of EAT-bearing mice, compared to non-treated tumour-bearing controls. In comparison with previous results from our laboratory addressing the effects of titanocenes on haematopoiesis, we observed with TITANOCENE X a similar effective profile as for bis(cyclopentadienyl) dithiocyanate titanium(IV), being both less effective than di(cyclopentadienyl) dichloro titanium(IV), since the latter not only prolonged, but also increased the rate of survival. These differences in efficacy may be due to the nature of the ansa-cyclopentadienyl ligand used in TITANOCENE X, since the C, bridge between the two cyclopentadienyl groups will increase the hydrolytic stability by an organometallic chelate effect. Also, the introduction of two dimethylamino substituents increases the water solubility of TITANOCENE X when compared to titanocene dichloride itself (c) 2006 Elsevier B.V. All rights reserved.

A non-uniform mesh scheme for compressible flow

A non-uniform mesh scheme is presented for the computation of compressible flows governed by the Euler equations of gas dynamics. The scheme is based on flux-difference splitting and represents an extension of a similar scheme designed for uniform meshes. The numerical results demonstrate that little, if any, spurious oscillation occurs as a result of the non-uniformity of the mesh; and importantly, shock speeds are computed correctly.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Fulvalene titanium and zirconium complexes: synthesis and NMR study of phosphanido-, alkyl-, and alkynyl-derivatives. X-ray crystal structures of [{Ti(η5−C5H5)(μ−PPH2)}2{μ−(η5−C5H4−η5−C5H4)}] and [{Zr(η5−C5H5)(μ−C≡CSiMe3)}2{μ−(η5−C5H4−η5−C5H4)}]

Reaction of with one or two equivalents of LiPPh2 afforded the new phosphanidometal(III) complexes . Reaction of 2 with LiC≡CSiMe3 led to the diamagnetic zirconium(III) alkynyl derivative [{Zr(C5H5)(μ−C≡CSiMe3)}2(μ−η5−C5H4−η5−C5H4], 7. Alkylation of 6 with LiCH2CMe2Ph gave [{Zr(η5−C5H5)(CH2CMe2Ph)2}2{μ−(η5−C5H4)}], 8. A detailed NMR study of complexes 3 and 4 allowed the observation of the spectral behaviour of the eight different fulvalene protons through their coupling to the 31P nucleus. The fluxional behaviour of complex 7 was studied by dynamic DNMR, and kinetic parameters for the σ-π-conversion of the alkynyl ligand were determined. The molecular structures of complexes 3 and 7 were determined by X-ray diffraction methods.

Fulvalene cyclopentadienyl titanium and zirconium(III) and -(IV) complexes. X-Ray crystal structure of [{Ti(η5-C5H5) Cl}2 (μ-O)(μ-η5-η5-C10H8)]

The reaction of the fulvalene titanium(III) hydride [{Ti(η5-C5H5)(μ-H)}2(μ-η5-η5-C10H8)] (1) with chlorine leads to [{Ti(η5-C5H5)(μ-Cl)}2(μ-η5-η5-C10H8)] (3) and [{Ti(η5-C5H5)Cl2}2(μ-η5-η5-C10H8)] (4). The reaction of 3 with azobenzene, in wet toluene, gives [{Ti(η5-C5H5)Cl}2(μ-O)(μ-η5-η5-C10H8)] (5) and 1,2-diphenyl hydrazine. The alkylation of 4 and the analogous zirconium complex [{Zr(η5-C5H55)Cl2}2(μ-η5-η5-C10H8)] (2) with LiCH2SiMe3 or LiCH3 permits isolation of the tetraalkyl derivatives [{M(η5-C5H5)(CH2SiMe3)2}2(μ-η5-η5-C10H8)] (M  Ti (6); Zr (8)) and [{Ti(η5-C5H5)(CH3)2}2(μ-η5-η5C10H8)] (7). All the new fulvalene compounds were characterized by IR, and 1H and 13C NMR spectroscope, and mass spectra and 5 by X-ray diffraction. The structure of 5 is very similar to that of the comparable TiIV compound [{Ti(η5-C5H5)2Cl}2(μ-O)] except for the smaller TiOTi angle (159.4° against 173.81°) and a significant deviation from linearity.

Prediction of a typhoon using a fine-mesh NWP model

The ECMWF operational grid point model (with a resolution of 1.875° of latitude and longitude) and its limited area version (with a resolution of !0.47° of latitude and longitude) with boundary values from the global model have been used to study the simulation of the typhoon Tip. The fine-mesh model was capable of simulating the main structural features of the typhoon and predicting a fall in central pressure of 60 mb in 3 days. The structure of the forecast typhoon, with a warm core (maximum potential temperature anomaly 17 K). intense swirling wind (maximum 55 m s-1 at 850 mb) and spiralling precipitation patterns is characteristic of a tropical cyclone. Comparison with the lower resolution forecast shows that the horizontal resolution is a determining factor in predicting not only the structure and intensity but even the movement of these vortices. However, an accurate and refined initial analysis is considered to be a prerequisite for a correct forecast of this phenomenon.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.

Fast three dimensional r-adaptive mesh redistribution

This paper describes a fast and reliable method for redistributing a computational mesh in three dimensions which can generate a complex three dimensional mesh without any problems due to mesh tangling. The method relies on a three dimensional implementation of the parabolic Monge–Ampère (PMA) technique, for finding an optimally transported mesh. The method for implementing PMA is described in detail and applied to both static and dynamic mesh redistribution problems, studying both the convergence and the computational cost of the algorithm. The algorithm is applied to a series of problems of increasing complexity. In particular very regular meshes are generated to resolve real meteorological features (derived from a weather forecasting model covering the UK area) in grids with over 2×107 degrees of freedom. The PMA method computes these grids in times commensurate with those required for operational weather forecasting.