The reactivity of basal surfaces, steps and edges of muscovite was studied by imaging surface precipitates of PbCl2 using atomic force microscopy (AFM). We reacted PbCl2 solution with freshly cleaved muscovite surfaces and found that PbCl2 precipitates were formed on the basal surfaces, steps and edges. It was observed that PbCl2 precipitated preferentially along the steps compared to the basal surfaces and that PbCl2 precipitates at multiple-layer edges were needle-shaped and oriented in different directions. One of the muscovite samples we cleaved had muscovite fragments sitting on the freshly cleaved surfaces. These fragments resulted from previously formed cracks. Thus, we were able to compare the reactivity of the weathered surfaces with that of freshly cleaved surfaces. It was found that PbCl2 was not precipitated along the edges of previously cracked muscovite fragments. These results clearly demonstrated that the edges of freshly cleaved muscovite are the most reactive surface sites, whereas the edges of weathered muscovite are not as reactive. We believe that the surface reactivity of the edges of freshly cleaved muscovite is likely due to terminal or Al-OH1/2− groups on these crystalline surfaces, which favor adsorption of Pb2+ ions and the subsequent nucleation and precipitation reactions. We also investigated the effect of drying rate on the morphology of the surface precipitates. Fast drying resulted in a nearly complete covered surface with a leaflike morphology, whereas slow drying resulted in more isolated surface clusters.

We obtain a complete topological classification of $k$-folding map-germs on generic surfaces in $\mathbb {R}^3$, discover new robust features of surfaces and recover, in a unified way, many of the robust features that were obtained previously by considering the contact of a surface with lines, planes or spheres.

The effects of mechano-chemical treatment on the surface characteristics and sorption properties of hydrotalcite were studied. Non-milled (crushed) and milled samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), particle size analysis and specific area. A milling time of 2 h decreased the particle size of the hydrotalcite samples from 21 to 8.0 nm, the specific area from 97 to 5.7 m2 g–1 and the total pore volume from 0.41 to 0.01 cm3. After the crushed and milled samples had been separately calcined at 500ºC, they were agitated with 10–2 M Na2MoO4 aqueous solutions for 48 h. The molybdate ion content in the regenerated non-milled hydrotalcite samples (HTc-MoO4) was found to be 6.0 meq g–1 while in the milled hydrotalcite (HTm-MoO4) samples this content was 2.5 meq g–1. The lower molybdate content was thought to be a result of compaction and, hence, reduced reactivity of the milled HT samples.

We introduce a new affinely invariant structure on smooth surfaces in ℝ3 by defining a family of reflections in all points of the surface. We show that the bifurcation set of this family has a special structure at ‘ points’, which are not detected by the flat geometry of the surface. These points (without an associated structure on the surface) have also arisen in the study of the centre symmetry set; using our technique we are able to explain how the points are created and annihilated in a generic family of surfaces. We also present the bifurcation set in a global setting.

Surface properties affect the attachment of micro- and macroscopic marine organisms. The current study examined the settlement response of the mussel Mytilus coruscus plantigrades to natural biofilms formed on surfaces of different wettability. The percentages of plantigrade settlement were not influenced by the biofilms formed on variously wettable surfaces in the short term, but after 10 days, the plantigrade settlement rates decreased on biofilms formed on lower wettability surfaces. In general, lower wettability of the surfaces resulted in the decrease of the dry weight, bacterial and diatom density and the thickness of natural biofilms when compared to high wettability surfaces. In contrast, chlorophyll-a concentration in biofilms was independent of the initial wettability of the surfaces. Comparative cluster analysis of bacterial denaturing gradient gel electrophoresis patterns revealed that high variability existed between the bacterial community on high wettability surfaces and that on low wettability surfaces. Thus, surface wettability affects the formation of natural biofilms, and this variation in biofilms developed on different wettability surfaces may explain the discrepancy in their corresponding inducing activities on M. coruscus plantigrade settlement. This finding provides new insight into interactions between mussel settlement, biofilm characteristics and surface properties.

We report a new simple but effective method to extract the weak surface signals from a “thickness series” of recorded electron energy-loss spectra. Using precise thickness measurements and energy-loss near-edge structures measured at increasing thicknesses, we are able to extract the surface and bulk components in the series. The electronic structure and bonding information from SrTiO3 (001) reconstructed surfaces have been successfully obtained by applying this approach. This approach can be applied to study many other cases including absorbed monolayers and beam-sensitive interfaces.

In this paper, we introduce two quantities defined on a surface in a contact manifold. The first one is called degree of transversality $(\text{DOT})$, which measures the transversality between the tangent spaces of a surface and the contact planes. The second quantity, called curvature of transversality $(\text{COT})$, is designed to give a comparison principle for $\text{DOT}$ along characteristic curves under bounds on $\text{COT}$. In particular, this gives estimates on lengths of characteristic curves, assuming $\text{COT}$ is bounded below by a positive constant.

We show that surfaces with constant $\text{COT}$ exist, and we classify all graphs in the Heisenberg group with vanishing $\text{COT}$. This is accomplished by showing that the equation for graphs with zero $\text{COT}$ can be decomposed into two first order PDEs, one of which is the backward invisicid Burgers’ equation. Finally we show that the p-minimal graph equation in the Heisenberg group also has such a decomposition. Moreover, we can use this decomposition to write down an explicit formula of a solution near a regular point.

Visual motion, i.e. the pattern of changes on the retinae caused by the motion of objects or the observer through the environment, contains important cues for the accurate perception of the three-dimensional layout of the visual scene. In this study, we investigate if neurons in the visual system, specifically in area MT of the macaque monkey, are able to differentiate between various velocity gradients. Our stimuli were random dot patterns designed to eliminate stimulus variables other than the orientation of a velocity gradient. We develop a stimulus space (“deformation space”) that allows us to easily parameterize our stimuli. We demonstrate that a substantial proportion of MT cells show tuned responses to our various velocity gradients, often exceeding the response evoked by an optimized flat velocity profile. This suggests that MT cells are able to represent complex aspects of the visual environment and that their properties make them well suited as building blocks for the complex receptive-field properties encountered in higher areas, such as area MST to which many cells in area MT project.

The physical properties of NEOs and other asteroids are mostly obtained with photometry. The resulting models describe the shapes, spin states, scattering properties and surface structure of the targets, and are the solutions of inverse problems involving comprehensive mathematical analysis. We review what can and cannot be obtained from photometric (and complementary) data, and how all this is done in practice. The role of photometry will become completely dominating with the advent of large-scale surveys capable of producing calibrated brightness data. Due to their quickly changing geometries with respect to the Earth, NEOs are the population that can be mapped the fastest.

Let X be a smooth complex projective surface and let C(X) denote the field of rational functions on X. In this paper, we prove that for any m > M(X), there exists a rational dominant map $f \colon X \to Y$, which is generically finite of degree m, into a complex rational ruled surface Y, whose monodromy is the alternating group Am. This gives a finite algebraic extension C(X): C(x1, x2) of degree m, whose normal closure has Galois group Am.

Isometric deformations of immersed surfaces in Euclidean 3-space are studied by means of the drehriss. When the immersion is of constant mean curvature and the deformation preserves the mean curvature, we determine the drehriss explicitly in terms of the immersion and its Gauss map. These methods are applied to obtain an alternative classification of the Smyth surfaces, i.e. constant mean curvature immersions of the plane into Euclidean 3-space which admit the action of $S^1$ as a non-trivial group of internal isometries.

Let $\mathcal{E}$ be a rank-2 bundle over a smooth complex projective surface X. Whenever the subscheme of zeros of a global section of $\mathcal{E}$ is zero-dimensional, it gives a geometric realization of the second Chern class $c_2(\mathcal{E})$. Taking the incidence correspondence

\[\xymatrix{{\mathcal{Z} =\{(x,[e]) \in X\times \bf{P} (H^0(\mathcal{E}))\mid e(x)= 0\}} \ar[r]^>>>>>{p_2}& {\bf{P} (H^0(\mathcal{E}))}}\]

and considering the Zariski open subset $U_f \subset \bf{P} (H^0(\mathcal{E}))$ over which the morphism p2 is finite, we have

\[\mathcal{Z}_f = p^{-1}_2(U_f)\longrightarrow U_f,\]

a family of zero-dimensional subschemes of X of length $\deg (c_2(\mathcal{E}))$. This can be viewed as a distinguished geometric representative of $c_2(\mathcal{E})$.

We define a new invariant of $\mathcal{E}$ which can be viewed as a ‘lifting’ of $c_2(\mathcal{E})$ to Uf. This invariant is a sequence of sections of some coherent sheaves on Uf. These sheaves are built from the following cohomology cup-products:

\begin{align}\gamma_1 &: H^1 (\mathcal{E}^{\ast}) \otimes H^0 (\mathcal{E}) \longrightarrow H^1 (\mathcal{O}_X),\\ \gamma_2&: S^2 H^1 (\mathcal{E}^{\ast})\longrightarrow H^2 (\mathcal{O}_X (\det(\mathcal{E}^{\ast})) ).\end{align}

The main property of our invariant is as follows: either it determines the family $\mathcal{Z}_f \stackrel{p_2}{\longrightarrow} U_f$, or the vector bundle $\mathcal{E}$ is ‘special’. The speciality is expressed in terms of the special geometry of zero-loci of global sections of $\mathcal{E}$ and the special geometry of X.

The sequence of sections entering the definition of our invariant is obtained by starting with the one defined by the cup-product $\gamma_2$ and deriving others inductively by using a geometric interpretation of a part of the cup-product $\gamma_1$ together with the Grothendieck residue map. So one can view our invariant as $\gamma_2$ together with some kind of higher-order cohomology cup-products.

The emergence of these higher-order cohomology cup-products is explained conceptually as higher-order derivatives of a natural deformation of $\gamma_2$ associated to a certain ‘natural’ deformation of the complex structure on $\mathcal{E}$. The variety of these natural deformations of $\mathcal{E}$ has all the features of the classical Jacobian of curves: it carries a distinguished divisor which either determines the family $\mathcal{Z}_f \stackrel{p_2}{\longrightarrow} U_f$ or ‘sees’ that $\mathcal{E}$ is special in the aforementioned sense. An essentially new feature of this Jacobian of $\mathcal{E}$ is that it also carries a variation of Hodge-like structures which arises naturally from our invariant.

Obtaining an X-ray laser emission from plasmas, created and driven by an intense IR laser, has been pursued at the Laboratoire de Spectroscopie Atomique et Ionique (LSAI) for several years. At present, we operate various types of X-ray lasers driven by IR laser pulses of different durations (600 ps, 100 ps, and 600 ps/1 ps). A review of different techniques used at the LSAI to produce a strongly amplified emission using the collisional excitation pumping is presented. In the second part of this paper, to illustrate the potential of the X-ray lasers for applications, we present the main results obtained with an X-ray laser emitting at 21.2 nm in a study of surface defects of a niobium cathode, induced by strong electrical fields. We also describe a novel imaging interferometry device using an X-ray laser as a source and designed as a tool for high-resolution diagnostic of dense plasmas.

We study the geometry of surfaces in $\mathbb{R}^4$ associated to contact with hyperplanes. We list all possible transitions that occur on the parabolic and so-called $A_3$-set, and analyse the configurations of the asymptotic curves and their bifurcations in generic one-parameter families.

AMS 2000 Mathematics subject classification: Primary 58C27. Secondary 53A05

Travelling wave solutions to the vortex filament flow generated by elastica produce surfaces in ${{\mathbb{R}}^{3}}$ that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classified in the special cases where the helices are all congruent or are all generated by a single screw motion. The first case yields a new characterization for the Bäcklund transformation for constant torsion curves in ${{\mathbb{R}}^{3}}$, previously derived fromthe well-known transformation for pseudospherical surfaces. A similar investigation for surfaces in ${{H}^{3}}$ or ${{S}^{3}}$ leads to a new transformation for constant torsion curves in those spaces that is also derived from pseudospherical surfaces.

Elevated temperature scanning tunneling microscopy is used to study oxides that are room temperature insulators but become sufficiently electrically conducting at higher temperatures to allow imaging to be performed. Atomic resolution images of NiO, CoO, and UO2 have been obtained in this fashion which allow surface structure and defect determination. To complement the experiments, modeling of the electronic surface structure reveals which atomic sites give rise to the contrast observed in the images. Low voltage scanning electron microscopy is used to image small equilibrium pores in UO2 single crystals to evaluate the surface energy ratio of the (111) to (001) surfaces.

Isotopic labeling experiments have revealed correlations between hydrogen reactions, Ga desorption, and ammonia decomposition in GaN CVD. Low energy electron diffraction (LEED) and temperature programmed desorption (TPD) were used to demonstrate that hydrogen atoms are available on the surface for reaction after exposing GaN(0001) to deuterium at elevated temperatures. Hydrogen reactions also lowered the temperature for Ga desorption significantly. Ammonia did not decompose on the surface before hydrogen exposure. However, after hydrogen reactions altered the surface, N15H3 did undergo both reversible and irreversible decomposition. This also resulted in the desorption of N2 of mixed isotopes below the onset of GaN sublimation. This suggests that the driving force of the high nitrogen-nitrogen bond strength (226 kcal/mol) can lead to the removal of nitrogen from the substrate when the surface is nitrogen rich. Overall, these findings indicate that hydrogen can influence GaN CVD significantly, being a common factor in the reactivity of the surface, the desorption of Ga, and the decomposition of ammonia.