Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Fatigue life and failure modes of crowns systems with a modified framework design

Objectives: To evaluate the effect of framework design on the fatigue life and failure modes of metal ceramic (MC, Ni-Cr alloy core, VMK 95 porcelain veneer), glass-infiltrated alumina (ICA, In-Ceram Alumina/VM7), and veneered yttria-stabilized tetragonal zirconia polycrystals (Y-TZP, IPSe.max ZirCAD/IPS e.max,) crowns. Methods: Sixty composite resin tooth replicas of a prepared maxillary first molar were produced to receive crowns systems of a standard (MCs, ICAs, and Y-TZPs, n = 10 each) or a modified framework design (MCm, ICAm, and Y-TZPm, n = 10 each). Fatigue loading was delivered with a spherical steel indenter (3.18 mm radius) on the center of the occlusal surface using r-ratio fatigue (30-300 N) until completion of 10(6) cycles or failure. Fatigue was interrupted every 125,000 cycles for damage evaluation. Weibull distribution fits and contour plots were used for examining differences between groups. Failure mode was evaluated by light polarized and SEM microscopy. Results: Weibull analysis showed the highest fatigue life for MC crowns regardless of framework design. No significant difference (confidence bound overlaps) was observed between ICA and Y-TZP with or without framework design modification. Y-TZPm crowns presented fatigue life in the range of MC crowns. No porcelain veneer fracture was observed in the MC groups, whereas ICAs presented bulk fracture and ICAm failed mainly through the veneer. Y-TZP crowns failed through chipping within the veneer, without core fractures. Conclusions: Framework design modification did not improve the fatigue life of the crown systems investigated. Y-TZPm crowns showed comparable fatigue life to MC groups. Failure mode varied according to crown system. (C) 2010 Elsevier Ltd. All rights reserved.

The strain-driven pyrochlore to "defect fluorite" phase transition in rare earth sesquioxide stabilized cubic zirconias

The relationship between the ordering characteristic of the pyrochlore structure type and that characteristic of the defect fluorite structure type (immediately on either side of two phase regions separating the two structure types) in a range of rare eath sesquioxide stabilized cubic zirconias is investigated via electron diffraction and imaging. Systematic structural change as a function of composition and relative size of the constituent metal ions is highlighted and a multi-q to single-q = 1/2 [111]* model proposed for the observed pyrochlore to defect fluorite phase transition. Strain introduced into the close-packed {111} metal ion planes of the defect fluorite average structure by the local cation and oxygen vacancy distribution is pointed to as the likely origin of the observed behavior. (C) 2001 Academic Press

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Ni(II)-doped CsCdBrCl2: Variation of spectral and structural properties via mixed-halide coordination

A new addition to the family of single-molecule magnets is reported: an Fete cage stabilized with benzoate and pyridonate ligands. Monte Carlo methods have been used to derive exchange parameters within the cage, and hence model susceptibility behavior.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

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.

On surrogate methods for detecting lateral gene transfer

Surrogate methods for detecting lateral gene transfer are those that do not require inference of phylogenetic trees. Herein I apply four such methods to identify open reading frames (ORFs) in the genome of Escherichia coli K12 that may have arisen by lateral gene transfer. Only two of these methods detect the same ORFs more frequently than expected by chance, whereas several intersections contain many fewer ORFs than expected. Each of the four methods detects a different non-random set of ORFs. The methods may detect lateral ORFs of different relative ages; testing this hypothesis will require rigorous inference of trees. (C) 2001 Federation of European Microbiological Societies. Published by Elsevier Science BN. All rights reserved.

Stickiness in foods: A review of mechanisms and test methods

Problems associated with the stickiness of food in processing and storage practices along with its causative factors are outlined. Fundamental mechanisms that explain why and how food products become sticky are discussed. Methods currently in use for characterizing and overcoming stickiness problems in food processing and storage operations are described. The use of glass transition temperature-based model, which provides a rational basis for understanding and characterizing the stickiness of many food products, is highlighted.

'Neighbourhood' size, dispersal and density estimates in the prickly forest skink (Gnypetoscincus queenslandiae) using individual genetic and demographic methods

Dispersal, or the amount of dispersion between an individual's birthplace and that of its offspring, is of great importance in population biology, behavioural ecology and conservation, however, obtaining direct estimates from field data on natural populations can be problematic. The prickly forest skink, Gnypetoscincus queenslandiae, is a rainforest endemic skink from the wet tropics of Australia. Because of its log-dwelling habits and lack of definite nesting sites, a demographic estimate of dispersal distance is difficult to obtain. Neighbourhood size, defined as 4 piD sigma (2) (where D is the population density and sigma (2) the mean axial squared parent-offspring dispersal rate), dispersal and density were estimated directly and indirectly for this species using mark-recapture and microsatellite data, respectively, on lizards captured at a local geographical scale of 3 ha. Mark-recapture data gave a dispersal rate of 843 m(2)/generation (assuming a generation time of 6.5 years), a time-scaled density of 13 635 individuals * generation/km(2) and, hence, a neighbourhood size of 144 individuals. A genetic method based on the multilocus (10 loci) microsatellite genotypes of individuals and their geographical location indicated that there is a significant isolation by distance pattern, and gave a neighbourhood size of 69 individuals, with a 95% confidence interval between 48 and 184. This translates into a dispersal rate of 404 m(2)/generation when using the mark-recapture density estimation, or an estimate of time-scaled population density of 6520 individuals * generation/km(2) when using the mark-recapture dispersal rate estimate. The relationship between the two categories of neighbourhood size, dispersal and density estimates and reasons for any disparities are discussed.