The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Hydraulic modeling of runoff over a rough surface under partial inundation

This study presents a numerical method to derive the Darcy- Weisbach friction coefficient for overland flow under partial inundation of surface roughness. To better account for the variable influence of roughness with varying levels of emergence, we model the flow over a network which evolves as the free surface rises. This network is constructed using a height numerical map, based on surface roughness data, and a discrete geometry skeletonization algorithm. By applying a hydraulic model to the flows through this network, local heads, velocities, and Froude and Reynolds numbers over the surface can be estimated. These quantities enable us to analyze the flow and ultimately to derive a bulk friction factor for flow over the entire surface which takes into account local variations in flow quantities. Results demonstrate that although the flow is laminar, head losses are chiefly inertial because of local flow disturbances. The results also emphasize that for conditions of partial inundation, flow resistance varies nonmonotonically but does generally increase with progressive roughness inundation.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

Vortex state in a mesoscopic flat disk with rough surface

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Early loading of single crowns supported by 6-mm-long implants with a moderately rough surface: a prospective 2-year follow-up cohort study

AimTo evaluate prospectively the clinical and radiographic outcomes after 2 years of loading of 6 mm long moderately rough implants supporting single crowns in the posterior regions.Material and methodsForty SLActive Straumann (R) short (6 mm) implants were placed in 35 consecutively treated patients. Nineteen implants, 4.1 mm in diameter, and 21 implants, 4.8 mm in diameter, were installed. Implants were loaded after 6 weeks of healing. Implant survival rate, marginal bone loss and resonance frequency analysis (RFA) were evaluated at different intervals. The clinical crown/implant ratio was also calculated.ResultsTwo out of 40 implants were lost before loading. Hence, the survival rate before loading was 95%. No further technical or biological complications were encountered during the 2-year follow-up. The mean marginal bone loss before loading was 0.34 +/- 0.38 mm. After loading, the mean marginal bone loss was 0.23 +/- 0.33 and 0.21 +/- 0.39 mm at the 1- and 2-year follow-ups. The RFA values increased between insertion (70.2 +/- 9) and the 6-week evaluation (74.8 +/- 6.1). The clinical crown/implant ratio increased with time from 1.5 at the delivery of the prosthesis to 1.8 after 2 years of loading.ConclusionShort implants (6 mm) with a moderately rough surface loaded early (after 6 weeks) during healing yielded high implant survival rates and moderate loss of bone after 2 years of loading. Longer observation periods are needed to draw more definite conclusions on the reliability of short implants supporting single crowns.To cite this article:Rossi F, Ricci E, Marchetti C, Lang NP, Botticelli D. Early loading of single crowns supported by 6-mm-long implants with a moderately rough surface: a prospective 2-year follow-up cohort study.Clin. Oral Impl. Res. 21, 2010; 937-943.doi: 10.1111/j.1600-0501.2010.01942.x.

On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Early loading of 6-mm-short implants with a moderately rough surface supporting single crowns: a prospective 5-year cohort study

AimTo evaluate prospectively the clinical and radiographic outcomes after 5years of early loading of 6-mm implants with a moderately rough (SLActive((R))) surface supporting single crowns in the posterior regions.Material and methodsThirty-five consecutive patients received 40 SLActive((R)) (Straumann) 6-mm implants with a diameter of 4.1mm (n=19) or 4.8mm (n=21). Insertion torque and resonance frequency analysis (RFA) were measured at implant installation. RFA was also measured at abutment connection. SynOcta abutments were tightened with 35Ncm after 6weeks of healing, and single porcelain fuse to metal crowns was cemented within 1week. Implant survival rate and marginal bone loss were evaluated at various time intervals until 5years after loading. The clinical crown/implant ratio was calculated as well.ResultsTwo of 40 implants were lost before loading (incorporation rate 95%), and no further implant loss or technical complications were encountered during the 5-year follow-up period. A mean marginal bone loss of 0.70.6mm was found after 5years of function. The clinical crown/implant ratio increased with time from 1.6 at the delivery of the prosthesis to 2 after 5years of loading.ConclusionSix millimeter implants with a SLActive((R)) moderately rough surface supporting single crowns in the posterior region and loaded after 6-7weeks maintained full function for at least 5year with low marginal bone resorption.

Histomorphometric analysis of pure titanium implants with porous surface versus rough surface

The purpose of this study was to analyze the bone repair around commercially pure titanium implants with rough and porous surface, fabricated using powder metallurgy technique, after their insertion in tibiae of rabbits. Seven male rabbits were used. Each animal received 3 porous-surface implants in the left tibia and 3 rough-surface implants in the right tibia. The rabbits were sacrificed 4 weeks after surgery and fragments of the tibiae containing the implants were submitted to histological and histomorphometric analyses to evaluate new bone formation at the implant-bone interface. Means (%) of bone neoformation obtained in the histomorphometric analysis were compared by Student's t-test for paired samples at 5% significance level.. The results of the histological analysis showed that osseointegration occurred for both types of implants with similar quality of bone tissue. The histomorphometric analysis revealed means of new bone formation at implant-bone interface of 79.69 ± 1.00% and 65.05 ± 1.23% for the porous- and rough-surface implants, respectively. Statistically significant difference was observed between the two types of implants with respect to the amount new bone formation (p<0.05). In conclusion, the porous-surface implants contributed to the osseointegration because they provide a larger contact area at implant-bone interface.

Bacterial Adhesion on Smooth and Rough Titanium Surfaces After Treatment With Different Instruments

Background: Newly formed biofilm after implant debridement may challenge the long-term stability of peri-implant therapy. This in vitro study aimed to assess the roughness and adherence of Streptococcus sanguinis after treatment of smooth and rough titanium surfaces with an erbium-doped: yttrium, aluminum, and garnet (Er:YAG) laser, metal and plastic curets, and an air-powder abrasive system. Methods: Forty titanium disks with smooth-machined surfaces and 40 with sand-blasted and acid-etched surfaces were divided into the following treatment groups: Er:YAG laser; plastic curet; metal curet, and air-powder abrasive system. The surface roughness (roughness average [Raj) before and after treatments was determined using a profilometer. S. sanguinis (American Type Culture Collection 10556) was grown on treated and untreated specimens, and the amounts of retained bacteria on the surfaces were measured by the culture method. Rough and smooth surfaces with and without a suspension of S. sanguinis were also analyzed using scanning electron microscopy (SEM). Results: For smooth surfaces, the roughest surfaces were produced by metal curets (repeated - measures analysis of variance [ANOVA] and Tukey test; P<0.05). The rough-surface profile was not altered by any of the treatments (repeated-measures ANOVA; P>0.05). Rough surfaces treated with metal curets and air-powder abrasion showed the lowest level of bacteria] adhesion (two-way ANOVA and Tukey test; P<0.05). SEM analysis revealed distinct surface profiles produced by all devices. Conclusions: Metal curets are not recommended for smooth titanium surface debridement due to severe texture alteration. Rough surfaces treated with a metal curet and the air-powder abrasive system were less susceptible to bacterial adhesion, probably due to texture modification and the presence of abrasive deposits. J Periodontol 2009;80: 1824-1832.

High concentration of residual aluminum oxide on titanium surface inhibits extracellular matrix mineralization

In the present study we characterized titanium (Ti) surfaces submitted to different treatments and evaluated the response of osteoblasts derived from human alveolar bone to these surfaces. Five different surfaces were evaluated: ground (G), ground and chemical etched (G1-HF for 60 s), sand blasted (SB-Al2O3 particles 65 pm), sand blasted and chemical etched (SLA1-HF for 60 s and SLA2-HF for 13 s). Surface morphology was evaluated under SEM and roughness parameters by contact scanning instrument. The presence of Al2O3 was detected by EDS and the amount calculated by digital analyses. Osteoblasts, were cultured on these surfaces and it was evaluated: cell adhesion, proliferation, and viability, alkaline phosphatase activity, total protein content, and matrix mineralization formation. Physical and chemical treatments produced very different surface morphologies. Al2O3 residues were detected on SB and SLA2 surfaces. Only matrix mineralization formation was affected by different surface treatments, being increased on rough surface (SLA1) and reduced on surface with high amount of Al2O3 residues (SB). On the basis of these findings, it is possible to conclude that high concentration of residual Al2O3 negatively interfere with the process of matrix mineralization formation in contact with Ti implant surfaces. (C) 2008 Wiley Periodicals, Inc. J Biomed Mater Res 87A: 588-597, 2008