Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Optically driven micromachine elements

We report on a proof of principle demonstration of an optically driven micromachine element. Optical angular momentum is transferred from a circularly polarized laser beam to a birefringent particle confined in an optical tweezers trap. The optical torque causes the particle to spin at up to 350 Hz, and this torque is harnessed to drive an optically trapped microfabricated structure. We describe a photolithographic method for producing the microstructures and show how a light driven motor could be used in a micromachine system. (C) 2001 American Institute of Physics.

Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths. (C) 2001 Elsevier Science B.V. All rights reserved.

The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

Scavenging of siliceous grain-boundary phase of 8-mol%-ytterbia-stabilized zirconia without additive

The grain-boundary conductivity (sigma (gb),) of 8-mol%-ytterbiastabilized zirconia increased markedly with heat treatment between 1000 degrees and 1300 degreesC with a slow heating rate (0.1 degreesC/min) before sintering. The extent of the sigma (gb) improvement was the same or larger than that via Al2O3 addition. The heat treatment did not affect the grain-interior conduction when sintered at 1600 degreesC, while Al2O3-derived scavenging significantly did, given the larger increment of total conductivity in the heat-treated sample. The formation of a silicon-containing phase in a discrete form was suggested as a possible route of scavenging the resistive phase from the correlation between average grain size and sigma (gb).

Amino acid residues in conodont elements

Thermally unaltered conodont elements, brachiopods. and vertebrates were analyzed with reverse phase high profile liquid chromatography to locate and quantify amino acid remnants of the original organic matrix in the fossils. No consistent similarities in amino acid content were found in conodont taxa. and criteria based on organic residues appear to have no taxonomic significance in the fossils tested from these localities. However, hydroxyproline. an amino acid that is found in the collagen molecules of animals. as well as in the glycoproteins in the cell walls and reproductive tissues of certain plants, is represented in most taxa. The organic matter retained in the impermeable crowns of conodont elements might have been derived originally from a form of collagen. Biochemical analyses. correlated with histochemical tests, demonstrate that organic matter is an integral part of the hyaline tissue of the element crown and not the result of surface contamination. Tests of a range of vertebrate and invertebrate fossil hard tissues produced similar results. The analyses indicate that hyaline tissue in the conodont element crown is not a form of vertebrate enamel. which contains no collagen. Albid tissue. with little or no organic content. is not a form of vertebrate bone or dentine, both based on collagen and low in mineral. Although these results do not help to determine the phylogenetic affinities of conodont animals, they indicate teat conodont elements do not contain hard tissues characteristic of vertebrate animals.

Hyaline tissue of thermally unaltered conodont elements and the enamel of vertebrates

Comparison of the ultrastructure of the hyaline tissue of conodont elements and the enamel of vertebrates provides little support for a close phylogenetic relationship between conodonts and vertebrates. Transmission and scanning electron microscopy shows that the mineralised component of the hyaline tissue of Panderodus and of Cordylodus elements consists of large, flat, oblong crystals, arranged in layers that run parallel to the long axis of the conodont. Enamel in the dentition of a living vertebrate, the lungfish Neoceratodus forsteri, has crystals of calcium hydroxyapatite, arranged in layers, and extending in groups from the dentine-enamel junction; the crystals are slender, elongate spicules perpendicular to the surface of the tooth plate, Similar crystal arrangements to those of lungfish are found in other vertebrates, but none resembles the organisation of the hyaline tissue of conodont elements, The crystals of hydroxyapatite in conodont hyaline tissue are exceptionally large, perpendicular or parallel to the surface of the element, with no trace of prisms, unlike the protoprismatic radial crystallite enamel of fish teeth and scales, or the highly organised prismatic enamel of mammals.

Precursor scavenging of resistive grain-boundary phase in 8 mol % ytterbia-stabilized zirconia

The grain-boundary conduction of 8 mol % ytterbia-stabilized zirconia (8YbSZ) was improved markedly by precursor scavenging via the two-stage sintering process. The most significant increase in the grain-boundary conductivity was found when the sample, whose conductivity was higher than that via Al2O3-derived scavenging, was heat-treated at 1250degreesC for greater than or equal to 20 h. The formation of a stable Si-containing phase such as ZrSiO4 during the first-stage heat-treatment was suggested as one probable scavenging route from the optimal heat-treatment temperature (HTT), long duration time (>20 h) at HTT, and the stability of the formed phase up to sintering temperatures (1500degrees C). (C) 2002 The Electrochemical Society.

RNA trafficking and stabilization elements associate with multiple brain proteins

Two of the best understood somatic cell mRNA cytoplasmic trafficking elements are those governing localization of beta-actin and myelin basic protein mRNAs. These cis-acting elements bind the trans-acting factors fibroblast ZBP-1 and hnRNP A2, respectively. It is not known whether these elements fulfil other roles in mRNA metabolism. To address this question we have used Edman sequencing and western blotting to identify six rat brain proteins that bind the beta-actin element (zipcode). All are known RNA-binding proteins and differ from ZBP-1. Comparison with proteins that bind the hnRNP A2 and AU-rich response elements, A2RE/A2RE11 and AURE, showed that AURE and zipcode bind a similar set of proteins that does not overlap with those that bind A2RE11. The zipcode-binding protein, KSRP, and hnRNP A2 were selected for further study and were shown by confocal immunolluorescence microscopy to have similar distributions in the central nervous system, but they were found in largely separate locations in cell nuclei. In the cytoplasm of cultured oligodendrocytes they were segregated into separate populations of cytoplasmic granules. We conclude that not only may there be families of trans-acting factors for the same cis-acting element, which are presumably required at different stages of mRNA processing and metabolism, but independent factors may also target different and multiple RNAs in the same cell.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.