Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

An efficient numerical scheme for the Euler equations

A finite difference scheme based on flux difference splitting is presented for the solution of the Euler equations for the compressible flow of an ideal gas. A linearised Riemann problem is defined, and a scheme based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to the usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. The scheme is applied to a shock tube problem and a blast wave problem. Each approximate solution compares well with those given by other schemes, and for the shock tube problem is in agreement with the exact solution.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Efficient group communication for large-scale parallel clustering

Global communication requirements and load imbalance of some parallel data mining algorithms are the major obstacles to exploit the computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication cost in iterative parallel data mining algorithms. In particular, the analysis focuses on one of the most influential and popular data mining methods, the k-means algorithm for cluster analysis. The straightforward parallel formulation of the k-means algorithm requires a global reduction operation at each iteration step, which hinders its scalability. This work studies a different parallel formulation of the algorithm where the requirement of global communication can be relaxed while still providing the exact solution of the centralised k-means algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real world distributed applications or can be induced by means of multi-dimensional binary search trees. The approach can also be extended to accommodate an approximation error which allows a further reduction of the communication costs.

Precise analysis of array usage in scientific programs

The automatic transformation of sequential programs for efficient execution on parallel computers involves a number of analyses and restructurings of the input. Some of these analyses are based on computing array sections, a compact description of a range of array elements. Array sections describe the set of array elements that are either read or written by program statements. These sections can be compactly represented using shape descriptors such as regular sections, simple sections, or generalized convex regions. However, binary operations such as Union performed on these representations do not satisfy a straightforward closure property, e.g., if the operands to Union are convex, the result may be nonconvex. Approximations are resorted to in order to satisfy this closure property. These approximations introduce imprecision in the analyses and, furthermore, the imprecisions resulting from successive operations have a cumulative effect. Delayed merging is a technique suggested and used in some of the existing analyses to minimize the effects of approximation. However, this technique does not guarantee an exact solution in a general setting. This article presents a generalized technique to precisely compute Union which can overcome these imprecisions.

A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

GDASH: a grid-enabled program for structure solution from powder diffraction data

The simulated annealing approach to structure solution from powder diffraction data, as implemented in the DASH program, is easily amenable to parallelization at the individual run level. Very large scale increases in speed of execution can therefore be achieved by distributing individual DASH runs over a network of computers. The GDASH program achieves this by packaging DASH in a form that enables it to run under the Univa UD Grid MP system, which harnesses networks of existing computing resources to perform calculations.

MDASH: a multi-core-enabled program for structure solution from powder diffraction data

The simulated annealing approach to structure solution from powder diffraction data, as implemented in the DASH program, is easily amenable to parallelization at the individual run level. Modest increases in speed of execution can therefore be achieved by executing individual DASH runs on the individual cores of CPUs.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

The influence of mineral solubility and soil solution concentration on the toxicity of copper to Eisenia fetida Savigny

The OECD 14 d earthworm acute toxicity test was used to determine the toxicity of copper added as copper nitrate (Cu(NO3)(2)), copper sulphate (CuSO4) and malachite (Cu-2(OH)(2)(CO3)) to Eisenia fetida Savigny. Cu(NO3)(2), and CuSO4 were applied in both an aqueous (aq) and solid (s) form, Cu-2(OH)(2)(CO3) was added as a solid. Soil solution was extracted by centrifugation, and analysed for copper. Two extractants [0.01 M CaCl2 and 0.005 M diethylenetriminpentaacetic acid (DTPA)] were used as a proxy of the bioavailable copper fraction in the soil. For bulk soil copper content the calculated copper toxicity decreased in the order nitrate > sulphide > carbonate, the same order as decreasing solubility of the metal compounds. For Cu(NO3)(2) and CuSO4, the LC50s obtained were not significantly different when the compound was added in solution or solid form. There was a significant correlation between the soil solution copper concentration and the percentage earthworm mortality for all 3 copper compounds (P less than or equal to 0.05) indicating that the soil pore water copper concentration is important for determining copper availability and toxicity to E. fetida. In soil avoidance tests the earthworms avoided the soils treated with Cu(NO3)(2) (aq and s) and CuSO4 (aq and s), at all concentrations used (110-8750 mug Cu g(-1), and 600-8750 mug Cu g(-1) respectively). In soils treated with Cu-2(OH2)CO3, avoidance behaviour was exhibited at all concentrations greater than or equal to3500 mug Cu g(-1). There was no significant correlation between the copper extracted by either CaCl2 or DTPA and percentage mortality. These two extractants are therefore not useful indicators of copper availability and toxicity to E. fetida.

Zinc deficiency in selected cultivars of wheat and barley as tested in solution culture

The relative zinc (Zn) efficiencies of 33 wheat and 3 barley cultivars were determined by growing them in chelate-buffered culture solutions. Zn efficiency, determined by growth in a Zn-deficient solution relative to that in a medium containing an adequate concentration of Zn, was found to vary between 10% and 63% among the cultivars tested. Out of the 36 cultivars tested, 12 proved to be Zn efficient, 10 were Zn inefficient, and the remaining 14 varieties were classed as intermediate. The most Zn-efficient cultivars included Bakhtawar, Gatcher S61, Wilgoyne, and Madrigal, and the most Zn inefficient included Durati, Songlen, Excalibur, and Chakwal-86. Zn-efficient cultivars accumulated greater amounts of Zn in their shoots than inefficient cultivars, but the correlation between shoot Zn and shoot dry matter production was poor. All the cultivars accumulated higher concentrations of iron (Fe), copper (Cu), manganese (Mn), and phosphorus (P) at deficient levels of Zn, compared with adequate Zn concentrations. The Zn-inefficient cultivars accumulated higher concentrations of these other elements compared to efficient cultivars.

Morphology, biomass and nutrient status of fine roots of Scots pine (Pinus sylvestris) as influenced by seasonal fluctuations in soil moisture and soil solution chemistry

A field monitoring study was carried out to follow the changes of fine root morphology, biomass and nutrient status in relation to seasonal changes in soil solution chemistry and moisture regime in a mature Scots pine stand on acid soil. Seasonal and yearly fluctuations in soil moisture and soil solution chemistry have been observed. Changes in soil moisture accounted for some of the changes in the soil solution chemistry. The results showed that when natural acidification in the soil occurs with low pH (3.5-4.2) and high aluminium concentration in the soil solution (> 3-10 mg l(-1)), fine root longevity and distribution could be affected. However, fine root growth of Scots pine may not be negatively influenced by adverse soil chemical conditions if soil moisture is not a limiting factor for root growth. In contrast, dry soil conditions increase Scots pine susceptibility to soil acidification and this could significantly reduce fine root growth and increase root mortality. It is therefore important to study seasonal fluctuations of the environmental variables when investigating and modelling cause-effect relationships.