Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

New insights on growth mechanisms of protein clusters at surfaces: an AFM and simulation study

Despite its relevance to a wide range of technological and fundamental areas, a quantitative understanding of protein surface clustering dynamics is often lacking. In inorganic crystal growth, surface clustering of adatoms is well described by diffusion-aggregation models. In such models, the statistical properties of the aggregate arrays often reveal the molecular scale aggregation processes. We investigate the potential of these theories to reveal hitherto hidden facets of protein clustering by carrying out concomitant observations of lysozyme adsorption onto mica surfaces, using atomic force microscopy. and Monte Carlo simulations of cluster nucleation and growth. We find that lysozyme clusters diffuse across the substrate at a rate that varies inversely with size. This result suggests which molecular scale mechanisms are responsible for the mobility of the proteins on the substrate. In addition the surface diffusion coefficient of the monomer can also be extracted from the comparison between experiments and simulations. While concentrating on a model system of lysozyme-on-mica, this 'proof of concept' study successfully demonstrates the potential of our approach to understand and influence more biomedically applicable protein-substrate couples.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Liberation or limitation? Understanding Iyengar Yoga as a practice of the self

This article explores the Foucauldian notions of practices of the self and care of the self, read via Deleuze, in the context of Iyengar yoga (one of the most popular forms of yoga currently). Using ethnographic and interview research data the article outlines the Iyengar yoga techniques which enable a focus upon the self to be developed, and the resources offered by the practice for the creation of ways of knowing, experiencing and forming the self. In particular, the article asks whether Iyengar yoga offers possibilities for freedom and liberation, or whether it is just another practice of control and management. Assessing Iyengar yoga via a ‘critical function’, a function of ‘struggle’ and a ‘curative and therapeutic function’, the article analyses whether the practice might constitute a mode of care of the self, and what it might offer in the context of the contemporary need to live better, as well as longer.

Multilayered hydrogel coatings covalently-linked to glass surfaces showing a potential to mimic mucosal tissues

Multilayered hydrogel coatings can be developed on the surface of glass slides via layer-by-layer deposition of hydrogen-bonded interpolymer complexes formed by poly(acrylic acid) and methylcellulose. Chemical modification of the glass surface with (3-aminopropyl)triethoxysilane with subsequent layer-by-layer deposition and cross-linking of interpolymer complexes by thermal treatment allows fabrication of ultrathin hydrogel coatings, not detachable from the substrate. The thickness of these coatings is directly related to the number of deposition cycles and cross-linking conditions. An unusual dependence of the hydrogel swelling properties on the sample thickness is observed and can be interpreted by gradual transitions between two- and three-dimensional networks. The hydrogels exhibit pH-responsive swelling behaviour, achieving higher swelling degrees at pH > 6.0. These coatings can be used as model substrates to study the adhesive properties of pharmaceutical tablets and can potentially mimic the total work of adhesion observed for the detachment of mucoadhesives from porcine buccal mucosa but fail to exhibit identical detachment profiles.

Hiatal surfaces from the Miocene Globigerina Limestone Formation of Malta: Biostratigraphy, sedimentology, trace fossils and early diagenesis

The Miocene Globigerina Limestone of the Maltese islands contains widespread omission surfaces with very different characteristics and origins. The terminal Lower Globigerina Limestone hardground (TLGLHg) formed during a period of falling sea level. Coccolith assemblages suggest shallowness. Sedimentary structures and trace fossil assemblages, indicate increasing frequency of storm events and erosional episodes, towards the surface. Calcite cementation which took place around Thalassinoides burrows and formed irregular nodules was followed by dissolution of aragonite. It is suggested that lithification was linked to microbial reactions involving organic matter. In contrast two later surfaces, the terminal Middle Globigerina Limestone omissionground (TMGLOg), which marks the Lower to Middle Miocene boundary, and the Fomm-ir-Rih local hardground (FiRLHg) both contain early diagenetic dolomite. Lithification took place in two phases. The dolomite is interpreted to have formed beneath the sea floor: it was subsequently exhumed and partially corroded as the precipitation of calcitic and phosphatic cements took place around burrows open to the circulation of sea water. (C) 2008 Elsevier B.V. All rights reserved.

Weathering microenvironments on feldspar surfaces: implications for understanding fluid-mineral reactions in soils

The mechanisms by which coatings develop on weathered grain surfaces, and their potential impact on rates of fluid-mineral interaction, have been investigated by examining feldspars from a 1.1 ky old soil in the Glen Feshie chronosequence, Scottish highlands. Using the focused ion beam technique, electron-transparent, foils for characterization by transmission electron microscopy were cut from selected parts of grain surfaces. Some parts were bare whereas others had accumulations, a few micrometres thick, of Weathering products, often mixed with mineral and microbial debris. Feldspar exposed at bare grain surfaces is crystalline throughout and so there is no evidence for the presence of the amorphous 'leached layers' that typically form in acid-dissolution experiments and have been described from some natural Weathering contexts. The weathering products comprise sub-mu m thick crystallites of an Fe-K aluminosilicate, probably smectite, that have grown within an amorphous and probably organic-rich matrix. There is also evidence for crystallization of clays having been mediated by fungal hyphae. Coatings formed within Glen Feshie soils after similar to 1.1 ky are insufficiently continuous or impermeable to slow rates Of fluid-feldspar reactions, but provide valuable insights into the complex Weathering microenvironments oil debris and microbe-covered mineral surfaces.

Characterization of mineral surfaces using FIB and TEM: a case study of naturally weathered alkali feldspars

Using a focused ion beam (FIB) instrument, electron-transparent samples (termed foils) have been cut from the naturally weathered surfaces of perthitic alkali feldspars recovered from soils overlying the Shap granite, northwest England. Characterization of these foils by transmission electron microscopy (TEM) has enabled determination of the crystallinity and chemical composition of near-surface regions of the feldspar and an assessment of the influence of intragranular microtextures on the microtopography of grain surfaces and development of etch pits. Damage accompanying implantation of the 30 kV Ga+ ions used for imaging and deposition of protective platinum prior to ion milling creates amorphous layers beneath outer grain surfaces, but can be overcome by coating grains with > 85 nm of gold before FIB work. The sidewalls of the foil and feldspar surrounding original voids are also partially amorphized during later stages of ion milling. No evidence was found for the presence of amorphous or crystalline weathering products or amorphous "leached layers" immediately beneath outer grain surfaces. The absence of a leached layer indicates that chemical weathering of feldspar in the Shap soils is stoichiometric, or if non-stoichiometric, either the layer is too thin to resolve by the TEM techniques used (i.e., <=similar to 2.5 nm) or an insufficient proportion of ions have been leached from near-surface regions so that feldspar crystallinity is maintained. No evidence was found for any difference in the mechanisms of weathering where a microbial filament rests on the feldspar surface. Sub-micrometer-sized steps on the grain surface have formed where subgrains and exsolution lamellae have influenced the propagation of fractures during physical weathering, whereas finer scale corrugations form due to compositional or strain-related differences in dissolution rates of albite platelets and enclosing tweed orthoclase. With progressive weathering, etch pits that initiated at the grain surface extend into grain interiors as etch tubes by exploiting preexisting networks of nanopores that formed during the igneous history of the grain. The combination of FIB and TEM techniques is an especially powerful way of exploring mechanisms of weathering within the "internal zone" beneath outer grain surfaces, but results must be interpreted with caution owing to the ease with which artifacts can be created by the high-energy ion and electron beams used in the preparation and characterization of the foils.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard 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. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.