Zero- one- and two-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, nicotinamide and isonicotinamide

The structures of the anhydrous 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, 3-(aminocarboxy) pyridine (nicotinamide) and 4-(aminocarbonyl) pyridine (isonicotinamide), namely 2-aminopyrimidinium 2-carboxy-4,5-dichlorobenzoate C4H6N3+ C8H3Cl2O4- (I), 3-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate C6H7N2O+ C8H3Cl2O4- (II) and the unusual salt adduct 4-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate 2-carboxymethyl-4,5-dichlorobenzoic acid (1/1/1) C6H7N2O+ C8H3Cl2O4-.C9H6Cl2O4 (III) have been determined at 130 K. Compound (I) forms discrete centrosymmetric hydrogen-bonded cyclic bis(cation--anion) units having both R2/2(8) and R2/1(4) N-H...O interactions. In compound (II) the primary N-H...O linked cation--anion units are extended into a two-dimensional sheet structure via amide-carboxyl and amide-carbonyl N-H...O interactions. The structure of (III) reveals the presence of an unusual and unexpected self-synthesized methyl monoester of the acid as an adduct molecule giving one-dimensional hydrogen-bonded chains. In all three structures the hydrogen phthalate anions are

Unusual hydrate stabilization in the two-dimensional layered structure of quinacrinium bis(2-carboxy-4,5-dichlorobenzoate) tetrahydrate, a proton-transfer compound of the drug quinacrine

The crystal structure of the hydrated proton-transfer compound of the drug quinacrine [rac-N'-(6-chloro-2-methoxyacridin-9-yl)-N,N-diethylpentane-1,4-diamine] with 4,5-dichlorophthalic acid, C23H32ClN3O2+ . 2(C8H3Cl2O4-).4H2O (I), has been determined at 200 K. The four labile water molecules of solvation form discrete ...O--H...O--H... hydrogen-bonded chains parallel to the quinacrine side chain, the two N--H groups of which act as hydrogen-bond donors for two of the water acceptor molecules. The other water molecules, as well as the acridinium H atom, also form hydrogen bonds with the two anion species and extend the structure into two-dimensional sheets. Between these sheets there are also weak cation--anion and anion--anion pi-pi aromatic ring interactions. This structure represents only the third example of a simple quinacrine derivative for which structural data are available but differs from the other two in that it is unstable in the X-ray beam due to efflorescence, probably associated with the destruction of the unusual four-membered water chain structures.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Phenyl-ring disorder in the two-dimensional hydrogen-bonded structure of the 1:1 proton-transfer salt of the diazo-dye precursor 4-(phenyldiazenyl)aniline (aniline yellow) with L-tartaric acid

The structure of the 1:1 proton-transfer compound from the reaction of L-tartaric acid with the azo-dye precursor aniline yellow [4-(phenylazo)aniline], 4-(phenyldiazenyl)anilinium hydrogen 2R,3R-tartrate C12H12N3+ . C4H6O6- has been determined at 200 K. The asymmetric unit of the compound contains two independent phenylazoanilinium cations and two hydrogen L-tartrate anions. The structure is unusual in that all four phenyl rings of both cations have identical 50% rotational disorder. The two hydrogen L-tartrate anions form independent but similar chains through head-to-tail carboxylic O--H...O~carboxyl~ hydrogen bonds [graph set C7] which are then extended into a two-dimensional hydrogen-bonded sheet structure through hydroxyl O--H...O hydrogen-bonding links. The anilinium groups of the phenyldiazenyl cations are incorporated into the sheets and also provide internal hydrogen-bonding extensions while their aromatic tails layer in the structure without significant interaction except for weak \p--\p interactions [minimum ring centroid separation, 3.844(3) \%A]. The hydrogen L-tartrate residues of both anions have the common short intramolecular hydroxyl O--H...O~carboxyl~ hydogen bonds. This work has provided a solution to the unusual disorder problem inherent in the structure of this salt as well as giving another example of the utility of the hydrogen tartrate in the generation of sheet substructures in molecular assembly processes.

A two-Dimensional finite volume method for variable density flow and solute transport through saturated-unsaturated media

Extensive groundwater withdrawal has resulted in a severe seawater intrusion problem in the Gooburrum aquifers at Bundaberg, Queensland, Australia. Better management strategies can be implemented by understanding the seawater intrusion processes in those aquifers. To study the seawater intrusion process in the region, a two-dimensional density-dependent, saturated and unsaturated flow and transport computational model is used. The model consists of a coupled system of two non-linear partial differential equations. The first equation describes the flow of a variable-density fluid, and the second equation describes the transport of dissolved salt. A two-dimensional control volume finite element model is developed for simulating the seawater intrusion into the heterogeneous aquifer system at Gooburrum. The simulation results provide a realistic mechanism by which to study the convoluted transport phenomena evolving in this complex heterogeneous coastal aquifer.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Functional heterogeneity as a two-dimensional concept : empirical evidence for new venture teams

Previous research on entrepreneurial teams has failed to settle the controversy over whether team heterogeneity helps or hinders new venture performance. Reconciling this inconsistency, this paper suggests a new conceptual approach to disentangle differential effects of team heterogeneity by modeling two separate heterogeneity dimensions, namely knowledge scope and knowledge disparity. Analyzing unique data on functional experiences of the members of 337 start-up teams, we find support for our contention of team heterogeneity as a two-dimensional concept. Results suggest that knowledge disparity negatively relates to both start-ups’ entrepreneurial and innovative performance. In contrast, we find knowledge scope to positively affect entrepreneurial performance, while it shows an inverse U-shaped relationship to innovative start-up performance.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Two-dimensional coordination polymers in rubidium and caesium complexes with orthanilic acid

The crystal structures of the rubidium and caesium complexes with 2-aminobenzenesulfonic acid (orthanilic acid), [Rb4(C6H6NO3S)4(H2O)]n (1) and [Cs(C6H6NO3S)]n (2) and have been determined at 200 K. Complex 1 has a repeating unit comprising four independent and different Rb coordination centres, (RbO8), (RbO7), (RbN2O4) and (RbO10), each having irregular stereochemistry and involving a number of bidentate chelate sulfonate-O,O’-metal and bridging interactions, giving a two-dimensional polymeric layered structure. Anhydrous complex 2 is also polymeric with the irregular (CsO7) coordination polyhedron comprising six sulfonate oxygen donors from three separate bidentate chelate sulfonate ligands and one monodentate bridging sulfonate oxygen, giving a two-dimensional layered structure.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.