Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

A comparative study of the fluidized-bed coating of cylindrical metal surfaces with various thermoplastic polymer powders

This paper reports the results of an experimental investigation into the fluidized-bed coating of cylindrical metal specimens using two types of thermoplastic powders, Rilsan(R) PA11, a nylon-11 powder produced by Elf Atochem, France and Cotene(TM) 4612, a linear low density polyethylene powder produced by J.R Courtenay (New Zealand). The effects of dipping time, preheat temperature and particle size distribution on coating thickness and surface finish were investigated. Consistent trends in coating thickness growth with dipping time were obtained for both nylon-11 and polyethylene powders with increases in coating thickness with preheat temperature. For the same preheat temperature, the lower melting point of polyethylene results in thicker coatings compared to those of nylon-11. There is a negligible change in the coating thickness for sieved powders compared to that for unsieved powders. A pre-heat temperatures of between 240 degrees C and 300 degrees C is necessary to achieve an acceptable surface finish with both nylon-11 and polyethylene powders. To minimize errors in achieving the desired coating thickness, dipping times shorter than 2 s are not recommended. The use of graphs of coating thickness versus dipping time in combination with the coating surface roughness plots presented in this paper enable the optimal choice of pre-heat temperature and dipping time to achieve acceptable surface finish. (C) 1999 Elsevier Science S.A. All rights reserved.

Freeform fabrication of functional aluminium prototypes using powder metallurgy

Freeform fabrication methods allow the direct formation of parts built layer by layer, under the control of a CAD drawing. Most of these methods form parts in thermoplastic or thermoset polymers, but there would be many applications for freeform fabrication of fully functional metal or ceramic parts. We describe here the freeforming of sinterable aluminium alloys. In addition, the building approach allows different materials to be positioned within a monolithic part for an optimal combination of properties. This is illustrated here with the formation of an aluminium gear with a metal-matrix composite wear surface. (C) 1999 Kluwer Academic Publishers.

Effect of additives on gelatinization, rheological properties and biodegradability of thermoplastic starch

Effect of additives on the starch gelatinization was governed by the processing conditions. The order-disorder transition of starch in water can occur in more than one way and the effect of polar additives on gelatinization can also be in more than one way. The additives appear to be plasticising thermoplastic starches, resulting in improving rheological properties. The thermoplastic starches with the additives are all biodegradable although the rates of biodegradability are slightly different.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

Long-term quantification of the release of monomers from dental resin composites and a resin-modified glass ionomer cement

This study quantified the release of monomers from polymerized specimens of four commercially available resin composites and one glass ionomer cement immersed in water:ethanol solutions. Individual standard curves were prepared from five monomers: (1) triethylene glycol dimethacrylate (TEGDMA), (2) 2-hydroxy-ethyl methacrylate (HEMA), (3) urethane dimethacrylate (UDMA), (4) bisphenol A glycidyl dimethacrylate (BISGMA), and (5) bisphenol A. The concentration of the monomers was determined at Days 1, 7, 30, and 90 with the use of electrospray ionization/mass spectrometry. Data were expressed in mean mumol per mm(2) surface area of specimen and analyzed with Scheffe's test (P < 0.05). The following monomers were found in water: monomers (1) and (2) from Delton sealant, monomer (5) from ScotchBond Multipurpose Adhesive and Delton sealant, monomer (3) from Definite and monomer (4) from Fuji II LC, ScotchBond Multipurpose Adhesive, Synergy and Definite. All these monomers increased in concentration over time, with the exception of monomer (1) from Delton sealant. Monomers (3) and (5) were found in extracts of materials despite their absence from the manufacturer's published composition. All monomers were released in significantly higher concentrations in water:ethanol solutions than in water. The greatest release of monomers occurred in the first day. The effect of the measured concentrations of monomers (1-5) on human genes, cells, or tissues needs to be considered with the use of a biological model. (C) 2002 Wiley Periodicals, Inc.

The interaction of metal ions and Marimastat with matrix metalloproteinase 9

The effect of a range of metal ions on the ability of Marimastat to inhibit matrix metalloproteinase 9 (MMP-9) was examined in a fluorescence based proteolytic assay. Whilst none of the metals examined significantly affected the inhibitory ability of Marimastat, several metal ions did have a significant effect on MMP-9 activity itself. In the absence of Marimastat, Zn(II) and Fe(II) significantly inhibited MMP-9 activity at metal ion concentrations of 10 and 100 muM, respectively. In both the absence and presence of Marimastat, Cd(II) significantly inhibited MMP-9 at 100 muM. In contrast, 1 mM Co(II) significantly upregulated MMP-9 proteolytic activity. (C) 2003 Elsevier Science Inc. All rights reserved.

A new approach to the synthesis of conjugated polymer-nanocrystal composites for heterojunction optoelectronics

We report a simple one pot process for the preparation of lead sulfide (PbS) nanocrystals in the conjugated polymer poly (2-methoxy-5-(2'-ethyl-hexyloxy)-p-phenylene vinylene) (MEH-PPV), and we demonstrate electronic coupling between the two components.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.