The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Composite auction method for suppressing unreasonable electricity price spikes in a competitive electricity market

The existence of undesirable electricity price spikes in a competitive electricity market requires an efficient auction mechanism. However, many of the existing auction mechanism have difficulties in suppressing such unreasonable price spikes effectively. A new auction mechanism is proposed to suppress effectively unreasonable price spikes in a competitive electricity market. It optimally combines system marginal price auction and pay as bid auction mechanisms. A threshold value is determined to activate the switching between the marginal price auction and the proposed composite auction. Basically when the system marginal price is higher than the threshold value, the composite auction for high price electricity market is activated. The winning electricity sellers will sell their electricity at the system marginal price or their own bid prices, depending on their rights of being paid at the system marginal price and their offers' impact on suppressing undesirable price spikes. Such economic stimuli discourage sellers from practising economic and physical withholdings. Multiple price caps are proposed to regulate strong market power. We also compare other auction mechanisms to highlight the characteristics of the proposed one. Numerical simulation using the proposed auction mechanism is given to illustrate the procedure of this new auction mechanism.

Influence of cavity preparation and curing method on the marginal seal of resin composite restorations: an in vitro evaluation.

OBJECTIVE: To evaluate the influence of cavity design and photocuring method on the marginal seal of resin composite restorations. METHOD AND MATERIALS: Seventy-two bovine teeth were divided into 2 groups: group 1 received box-type cavity preparations, and group 2 received plate-type preparations. Each group was divided into 3 subgroups. After etching and bonding, Z250 resin composite (3M Espe) was applied in 2 equal increments and cured with 1 of 3 techniques: (1) conventional curing for 30 seconds at 650 mW/cm2; (2) 2-step photocuring, in which the first step was performed 14 mm from the restoration for 10 seconds at 180 mW/cm2 and the second step was performed in direct contact for 20 seconds at 650 mW/cm2; or (3) progressive curing using Jetlite 4000 (J. Morita) for 8 seconds at 125 mW/cm2 and then 22 seconds at 125 mW/cm2 up to 500 mW/cm2. The specimens were thermocycled for 500 cycles and then submitted to dye penetration with a 50% silver nitrate solution. Microleakage was assessed using a stereomicroscope. Data were analyzed using analysis of variance and Tukey test (5% level of significance). RESULTS: A statistically significant difference was found between groups when a double interaction between photocuring and cavity preparation was considered (P = .029). CONCLUSIONS: No one type of cavity preparation or photocuring method prevented micro-leakage. The plate-type preparation showed the worst dye penetration when conventional and progressive photocuring methods were used. The best results were found using the 2-step photocuring with the plate-type preparation.

Non-resorbable glass fibre-reinforced composite with porous surface as bone substitute material: Experimental studies in vitro and in vivo focused on bone-implant interface

The development of load-bearing osseous implant with desired mechanical and surface properties in order to promote incorporation with bone and to eliminate risk of bone resorption and implant failure is a very challenging task. Bone formation and resoption processes depend on the mechanical environment. Certain stress/strain conditions are required to promote new bone growth and to prevent bone mass loss. Conventional metallic implants with high stiffness carry most of the load and the surrounding bone becomes virtually unloaded and inactive. Fibre-reinforced composites offer an interesting alternative to metallic implants, because their mechanical properties can be tailored to be equal to those of bone, by the careful selection of matrix polymer, type of fibres, fibre volume fraction, orientation and length. Successful load transfer at bone-implant interface requires proper fixation between the bone and implant. One promising method to promote fixation is to prepare implants with porous surface. Bone ingrowth into porous surface structure stabilises the system and improves clinical success of the implant. The experimental part of this work was focused on polymethyl methacrylate (PMMA) -based composites with dense load-bearing core and porous surface. Three-dimensionally randomly orientated chopped glass fibres were used to reinforce the composite. A method to fabricate those composites was developed by a solvent treatment technique and some characterisations concerning the functionality of the surface structure were made in vitro and in vivo. Scanning electron microscope observations revealed that the pore size and interconnective porous architecture of the surface layer of the fibre-reinforced composite (FRC) could be optimal for bone ingrowth. Microhardness measurements showed that the solvent treatment did not have an effect on the mechanical properties of the load-bearing core. A push-out test, using dental stone as a bone model material, revealed that short glass fibre-reinforced porous surface layer is strong enough to carry load. Unreacted monomers can cause the chemical necrosis of the tissue, but the levels of leachable resisidual monomers were considerably lower than those found in chemically cured fibre-reinforced dentures and in modified acrylic bone cements. Animal experiments proved that surface porous FRC implant can enhance fixation between bone and FRC. New bone ingrowth into the pores was detected and strong interlocking between bone and the implant was achieved.

Notes on Newton-Euler formulation of robotic manipulators

The equations corresponding to Newton-Euler iterative method for the determination of forces and moments acting on the rigid links of a robotic manipulator are given a new treatment using composed vectors for the representation of both kinematical and dynamical quantities. It is shown that Lagrange equations for the motion of a holonomic system are easily found from the composed vectors defined in this note. Application to a simple model of an industrial robot shows that the method developed in these notes is efficient in solving the dynamics of a robotic manipulator. An example is developed, where it is seen that with the application of appropriate control moments applied to each arm of the robot, starting from a given initial position, it is possible to reach equilibrium in a final pre-assigned position.

Volumetric microleakage assessment of glass-ionomer-resin composite hybrid materials

Objective: This study was intended to quantify the marginal leakage of three glass-ionomer-resin composite hybrid materials and compare it with the leakage exhibited by a glass-ionomer cement and a bonded resin composite system. Method and materials: Standardized Class V cavities were prepared on root surfaces of 105 extracted human teeth, randomly assigned to five groups of 21 each, and restored with either Ketac-Fil Aplicap, Z100/Scotchbond Multi-Purpose Plus, Vitremer, Photac-Fil Aplicap, or Dyract. The teeth were thermally stressed for 500 cycles and stained with methylene blue. The microleakage was quantified spectrophotometrically, and the data were statistically analyzed with Friedman's test. Results: There were no significant differences in microleakage among the five groups. Restorations of all tested materials showed some marginal leakage in Class V cavities. Conclusion: The microleakage performance of glass-ionomer-resin composite hybrid materials was similar to those of a conventional glass-ionomer and a bonded resin composite system.

Simulação numérica do comportamento dinâmico de uma laje

Nesta dissertação pretende-se simular o comportamento dinâmico de uma laje de betão armado aplicando o Método de Elementos Finitos através da sua implementação no programa FreeFEM++. Este programa permite-nos a análise do modelo matemático tridimensional da Teoria da Elasticidade Linear, englobando a Equação de Equilíbrio, Equação de Compatibilidade e Relações Constitutivas. Tratando-se de um problema dinâmico é necessário recorrer a métodos numéricos de Integração Directa de modo a obter a resposta em termos de deslocamento ao longo do tempo. Para este trabalho escolhemos o Método de Newmark e o Método de Euler para a discretização temporal, um pela sua popularidade e o outro pela sua simplicidade de implementação. Os resultados obtidos pelo FreeFEM++ são validados através da comparação com resultados adquiridos a partir do SAP2000 e de Soluções Teóricas, quando possível.

Integration methods in dynamic analysis

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Étude numérique des origines hémodynamiques des oscillations dans des réseaux de capillaires

En simulant l’écoulement du sang dans un réseau de capillaires (en l’absence de contrôle biologique), il est possible d’observer la présence d’oscillations de certains paramètres comme le débit volumique, la pression et l’hématocrite (volume des globules rouges par rapport au volume du sang total). Ce comportement semble être en concordance avec certaines expériences in vivo. Malgré cet accord, il faut se demander si les fluctuations observées lors des simulations de l’écoulement sont physiques, numériques ou un artefact de modèles irréalistes puisqu’il existe toujours des différences entre des modélisations et des expériences in vivo. Pour répondre à cette question de façon satisfaisante, nous étudierons et analyserons l’écoulement du sang ainsi que la nature des oscillations observées dans quelques réseaux de capillaires utilisant un modèle convectif et un modèle moyenné pour décrire les équations de conservation de masse des globules rouges. Ces modèles tiennent compte de deux effets rhéologiques importants : l’effet Fåhraeus-Lindqvist décrivant la viscosité apparente dans un vaisseau et l’effet de séparation de phase schématisant la distribution des globules rouges aux points de bifurcation. Pour décrire ce dernier effet, deux lois de séparation de phase (les lois de Pries et al. et de Fenton et al.) seront étudiées et comparées. Dans ce mémoire, nous présenterons une description du problème physiologique (rhéologie du sang). Nous montrerons les modèles mathématiques employés (moyenné et convectif) ainsi que les lois de séparation de phase (Pries et al. et Fenton et al.) accompagnés d’une analyse des schémas numériques implémentés. Pour le modèle moyenné, nous employons le schéma numérique explicite traditionnel d’Euler ainsi qu’un nouveau schéma implicite qui permet de résoudre ce problème d’une manière efficace. Ceci est fait en utilisant une méthode de Newton- Krylov avec gradient conjugué préconditionné et la méthode de GMRES pour les itérations intérieures ainsi qu’une méthode quasi-Newton (la méthode de Broyden). Cette méthode inclura le schéma implicite d’Euler et la méthode des trapèzes. Pour le schéma convectif, la méthode explicite de Kiani et al. sera implémentée ainsi qu’une nouvelle approche implicite. La stabilité des deux modèles sera également explorée. À l’aide de trois différentes topologies, nous comparerons les résultats de ces deux modèles mathématiques ainsi que les lois de séparation de phase afin de déterminer dans quelle mesure les oscillations observées peuvent être attribuables au choix des modèles mathématiques ou au choix des méthodes numériques.

Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Estimating age of mature adults from the degeneration of the sternal end of the clavicle

The sternal end of the clavicle has been illustrated to be useful in aging young adults, however, no studies have investigated what age-related changes occur to the sternal end post epiphyseal fusion. In this study, three morphological features (i.e., surface topography, porosity, and osteophyte formation) were examined and scored using 564 clavicles of individuals of European ancestry (n = 318 males; n = 246 females), with known ages of 40+ years, from four documented skeletal collections: Hamann-Todd, Pretoria, St. Bride's, and Coimbra. An ordinal scoring method was developed for each of the three traits. Surface topography showed the strongest correlation with age, and composite scores (formed by summing the three separate trait scores) indicated progressive degeneration of the surface with increasing chronological age. Linear regression analyses were performed on the trait scores to produce pooled-sample age estimation equations. Blind tests of the composite score method and regression formulae on 56 individuals, aged 40+ years, from Christ Church Spitalfields, suggest accuracies of 96.4% for both methods. These preliminary results display the first evidence of the utility of the sternal end of the clavicle in aging older adult individuals. However, in the current format, these criteria should only be applied to individuals already identified as over 40 years in order to refine the age ranges used for advanced age. These findings do suggest the sternal end of the clavicle has potential to aid age estimates beyond the traditional "mature adult" age category (i.e., 46+ years), and provides several suggestions for future research.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

Simulação numérica da interação entre uma nuvem incidente de vórtices e uma aerofólio através do método dos vórtices

The study of aerodynamic loading variations has many engineering applications, including helicopter rotor blades, wind turbines and turbo machinery. This work uses a Vortex Method to make a lagrangian description of the a twodimensional airfoil/ incident wake vortex interaction. The flow is incompressible, newtonian, homogeneus and the Reynolds Number is 5x105 .The airfoil is a NACA 0018 placed a angle of attack of the 0° and 5°simulates with the Painel Method with a constant density vorticity panels and a generation poit is near the painel. The protector layer is created does not permit vortex inside the body. The vortex Lamb convection is realized with the Euler Method (first order) and Adans-Bashforth (second order). The Random Walk Method is used to simulate the diffusion. The circular wake has 366 vortex all over positive or negative vorticity located at different heights with respect to the airfoil chord. The Lift was calculated based in the algorithm created by Ricci (2002). This simulation uses a ready algorithm vatidated with single body does not have a incident wake. The results are compared with a experimental work The comparasion concludes that the experimental results has a good agrement with this papper