A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Morphology induced spinodal decomposition at the surface of symmetric diblock copolymer films

Atomic force microscopy is used to study the ordering dynamics of symmetric diblock copolymer films. The films order to form a lamellar structure which results in a frustration when the film thickness is incommensurate with the lamellae. By probing the morphology of incommensurate films in the early ordering stages, we discover an intermediate phase of lamellae arranged perpendicular to the film surface. This morphology is accompanied by a continuous growth in amplitude of the film surface topography with a characteristic wavelength, indicative of a spinodal process. Using selfconsistent field theory, we show that the observation of perpendicular lamellae suggests an intermediate state with parallel lamellae at the substrate and perpendicular lamellae at the free surface. The calculations confirm that the intermediate state is unstable to thickness fluctuations, thereby driving the spinodal growth of surface structures.

Control and analysis of oriented thin films of lipid inverse bicontinuous cubic phases using grazing incidence small-angle X‑ray scattering

Lipid cubic phases are complex nanostructures that form naturally in a variety of biological systems, with applications including drug delivery and nanotemplating. Most X-ray scattering studies on lipid cubic phases have used unoriented polydomain samples as either bulk gels or suspensions of micrometer-sized cubosomes. We present a method of investigating cubic phases in a new form, as supported thin films that can be analyzed using grazing incidence small-angle X-ray scattering (GISAXS). We present GISAXS data on three lipid systems: phytantriol and two grades of monoolein (research and industrial). The use of thin films brings a number of advantages. First, the samples exhibit a high degree of uniaxial orientation about the substrate normal. Second, the new morphology allows precise control of the substrate mesophase geometry and lattice parameter using a controlled temperature and humidity environment, and we demonstrate the controllable formation of oriented diamond and gyroid inverse bicontinuous cubic along with lamellar phases. Finally, the thin film morphology allows the induction of reversible phase transitions between these mesophase structures by changes in humidity on subminute time scales, and we present timeresolved GISAXS data monitoring these transformations.

Creep and recovery of magnetorheological fluids: experiments and simulations

A direct comparative study on the creep-recovery behavior of conventional MR fluids is carried out using magnetorheometry and particle-level simulations. Two particle concentrations are investigated (ϕ=0.05 and 0.30) at two different magnetic field strengths (53 kA•m-1 and 173 kA•m-1) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: i) In the initial viscoelastic region, the chain-like (at ϕ=0.05) or percolated three-dimensional network (at ϕ=0.30) structures fill up the gap and the average cluster size remains constant; ii) Above a critical strain of 10 %, in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheet-like or thick lamellar structures, depending on the particle concentration; iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Predicting sizes of hexagonal and gyroid metal nanostructures from liquid crystal templating

We describe a method to predict and control the lattice parameters of hexagonal and gyroid mesoporous materials formed by liquid crystal templating. In the first part, we describe a geometric model with which the lattice parameters of different liquid crystal mesophases can be predicted as a function of their water/surfactant/oil volume fractions, based on certain geometric parameters relating to the constituent surfactant molecules. We demonstrate the application of this model to the lamellar (LR), hexagonal (H1), and gyroid bicontinuous cubic (V1) mesophases formed by the binary Brij-56 (C16EO10)/water system and the ternary Brij-56/hexadecane/water system. In this way, we demonstrate predictable and independent control over the size of the cylinders (with hexadecane) and their spacing (with water). In the second part, we produce mesoporous platinum using as templates hexagonal and gyroid phases with different compositions and show that in each case the symmetry and lattice parameter of the metal nanostructure faithfully replicate those of the liquid crystal template, which is itself in agreement with the model. This demonstrates a rational control over the geometry, size, and spacing of pores in a mesoporous metal.

Control of nanomaterial self-assembly in ultrasonically levitated droplets

We demonstrate that acoustic trapping can be used to levitate and manipulate droplets of soft matter, in particular, lyotropic mesophases formed from selfassembly of different surfactants and lipids, which can be analyzed in a contact-less manner by X-ray scattering in a controlled gas-phase environment. On the macroscopic length scale, the dimensions and the orientation of the particle are shaped by the ultrasonic field, while on the microscopic length scale the nanostructure can be controlled by varying the humidity of the atmosphere around the droplet. We demonstrate levitation and in situ phase transitions of micellar, hexagonal, bicontinuous cubic, and lamellar phases. The technique opens up a wide range of new experimental approaches of fundamental importance for environmental, biological, and chemical research.

Equilibrium behavior of symmetric ABA triblock copolymer melts

Melts of ABA triblock copolymer molecules with identical end blocks are examined using self-consistent field theory (SCFT). Phase diagrams are calculated and compared with those of homologous AB diblock copolymers formed by snipping the triblocks in half. This creates additional end segments which decreases the degree of segregation. Consequently, triblock melts remain ordered to higher temperatures than their diblock counterparts. We also find that middle-block domains are easier to stretch than end-block domains. As a result, domain spacings are slightly larger, the complex phase regions are shifted towards smaller A-segment compositions, and the perforated-lamellar phase becomes more metastable in triblock melts as compared to diblock melts. Although triblock and diblock melts exhibit very similar phase behavior, their mechanical properties can differ substantially due to triblock copolymers that bridge between otherwise disconnected A domains. We evaluate the bridging fraction for lamellar, cylindrical, and spherical morphologies to be about 40%–45%, 60%–65%, and 75%–80%, respectively. These fractions only depend weakly on the degree of segregation and the copolymer composition.

Hard tissue formation adjacent to implants of various size and configuration immediately placed into extraction sockets: an experimental study in dogs

Objectives To evaluate the influence of implant size and configuration on osseointegration in implants immediately placed into extraction sockets. Material and methods Implants were installed immediately into extraction sockets in the mandibles of six Labrador dogs. In the control sites, cylindrical transmucosal implants (3.3 mm diameter) were installed, while in the test sites, larger and conical (root formed, 5 mm diameter) implants were installed. After 4 months of healing, the resorptive patterns of the alveolar crest were evaluated histomorphometrically. Results With one exception, all implants were integrated in mineralized bone, mainly composed of mature lamellar bone. The alveolar crest underwent resorption at the control as well as at the test implants. This resorption was more pronounced at the buccal aspects and significantly greater at the test (2.7 +/- 0.4 mm) than at the control implants (1.5 +/- 0.6 mm). However, the control implants were associated with residual defects that were deeper at the lingual than at the buccal aspects, while these defects were virtually absent at test implants. Conclusions The installment of root formed wide implants immediately into extraction sockets will not prevent the resorption of the alveolar crest. In contrast, this resorption is more marked both at the buccal and lingual aspects of root formed wide than at standard cylindrical implants. To cite this article:Caneva M, Salata LA, de Souza SS, Bressan E, Botticelli D, Lang NP. Hard tissue formation adjacent to implants of various size and configuration immediately placed into extraction sockets: an experimental study in dogs.Clin. Oral Impl. Res. 21, 2010; 885-895.doi: 10.1111/j.1600-0501.2010.01931.x.

In Vivo Comparison of Hard Tissue Regeneration with Human Mesenchymal Stem Cells Processed with Either the FICOLL Method or the BMAC Method

Objective: To compare new bone formation in maxillary sinus augmentation procedures using biomaterial associated with mesenchymal stem cells (MSCs) separated by two different isolation methods. Background: In regenerative medicine open cell concentration systems are only allowed for clinical application under good manufacturing practice conditions. Methods: Mononuclear cells, including MSCs, were concentrated with either the synthetic poylsaccharid (FICOLL) method (classic open system-control group, n = 6 sinus) or the bone marrow aspirate concentrate (BMAC) method (closed system-test group, n = 12 sinus) and transplanted in combination with biomaterial. A sample of the cells was characterized by their ability to differentiate. After 4.1 months (SD +/- 1.0) bone biopsies were obtained and analyzed. Results: The new bone formation in the BMAC group was 19.9% (90% confidence interval [CI], 10.9-29), and in the FICOLL group was 15.5% (90% CI, 8.6-22.4). The 4.4% difference was not significant (90% CI, -4.6-13.5; p = 0.39). MSCs could be differentiated into osteogenic, chondrogenic, and adipogenic lineages. Conclusion: MSCs harvested from bone marrow aspirate in combination with bovine bone matrix particles can form lamellar bone and provide a reliable base for dental implants. The closed BMAC system is suited to substitute the open FICOLL system in bone regeneration procedures.

Influence of implant positioning in extraction sockets on osseointegration: histomorphometric analyses in dogs

Aim To evaluate the influence of implant positioning into extraction sockets on osseointegration. Material and methods Implants were installed immediately into extraction sockets in the mandibles of six Labrador dogs. In the control sites, the implants were positioned in the center of the alveolus, while in the test sites, the implants were positioned 0.8 mm deeper and more lingually. After 4 months of healing, the resorptive patterns of the alveolar crest were evaluated histomorphometrically. Results All implants were integrated in mineralized bone, mainly composed of mature lamellar bone. The alveolar crest underwent resorption at the control as well as at the test sites. After 4 months of healing, at the buccal aspects of the control and test sites, the location of the implant rough/smooth limit to the alveolar crest was 2 +/- 0.9 mm and 0.6 +/- 0.9 mm, respectively (P < 0.05). At the lingual aspect, the bony crest was located 0.4 mm apically and 0.2 mm coronally to the implant rough/smooth limit at the control and test sites, respectively (NS). Conclusions From a clinical point of view, implants installed into extraction sockets should be positioned approximately 1 mm deeper than the level of the buccal alveolar crest and in a lingual position in relation to the center of the alveolus in order to reduce or eliminate the exposure above the alveolar crest of the endosseous (rough) portion of the implant. To cite this article:Caneva M, Salata LA, de Souza SS, Baffone G, Lang NP, Botticelli D. Influence of implant positioning in extraction sockets on osseointegration: histomorphometric analyses in dogs.Clin. Oral Impl. Res. 21, 2010; 43-49.

Tissue response around silicon nitride implants in rabbits

The chemical and dimensional stability associated with suitable fracture toughness and propitious tribological characteristics make silicon nitride-based ceramics potential candidates for biomedical applications, mainly as orthopedic implants. Considering this combination of properties, silicon nitride components were investigated in relation to their biocompatibility. For this study, two cylindrical implants were installed in each tibia of five rabbits and were kept in the animals for 8 weeks. During the healing time, tissue tracers were administrated in the animals so as to evaluate the bone growth around the implants. Eight weeks after the surgery, the animals were euthanized and histological analyses were performed. No adverse reactions were observed close to the implant. The osteogenesis process occurred during the entire period defined by the tracers. However, this process occurred more intensely 4 weeks after the surgery. In addition, the histological analyses showed that bone growth occurred preferentially in the cortical areas. Different kinds of tissue were identified on the implant surface, characterized by lamellar bone tissue containing osteocytes and osteons, by a noncalcified matrix containing osteoblasts, or by the presence of collagen III, which may change to collagen I or remain as a fibrous tissue. The results demonstrated that silicon nitride obtained according to the procedure proposed in this research is a biocompatible material. (c) 2007 Wiley Periodicals, Inc.

Phase behavior of the orange essential oil/sodium bis(2-ethylhexyl)sulfosuccinate/water system

The ternary phase diagram for the orange essential oil (OEO)/sodium bis(2-ethylhexyl)sulfosuccinate (AOT)/water system was constructed at 25 degrees C. It indicates a large single phase region, comprising an isotropic water-in-oil (W/O) microemulsion (ME) phase (L(2)), a liquid crystal (LC) (lamellar or hexagonal) and a large unstable emulsion phase that separates in two phases of normal and reverse micelles (L(1) and L(2)). In this communication the properties of the ME are investigated by viscosity, electric conductivity and small angle X-ray scattering (SAXS) indicating that the isotropic ME phase exhibits different behaviors depending on composition. At low water content low viscous ""dry"" surfactant structures are formed, whereas at higher water content higher viscous water droplets are formed. The experimental data allow the determination of the transition from ""dry"" to the water droplet structures within the L(2) phase. SAXS analyses have also been performed for selected LC samples. (C) 2009 Elsevier B.V. All rights reserved.