Blackfolds, plane waves and minimal surfaces

Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.

Polar Nature of Biomimetic Fluorapatite/Gelatin Composites: A Comparison of Bipolar Objects and the Polar State of Natural Tissue

The correspondence of the state of alignment of macromolecules in biomimetic materials and natural tissues is demonstrated by investigating a mechanism of electrical polarity formation: An in vitro grown biomimetic FAp/gelatin composite is investigated for its polar properties by second harmonic (SHGM) and scanning pyroelectric microscopy (SPEM). Hexagonal prismatic seed crystals formed in gelatin gels represent a monodomain polar state, due to aligned mineralized gelatin molecules. Later growth stages, showing dumbbell morphologies, develop into a bipolar state because of surface recognition by gelatin functionality: A reversal of the polar alignment of macromolecules, thus, takes place close to that basal plane of the seed. In natural hard tissues (teeth and bone investigated by SPEM) and the biomimetic FAp/gelatin composite, we find a surprising analogy in view of growth-induced states of polarity: The development of polarity in vivo and in vitro can be explained by a Markov-type mechanism of molecular recognition during the attachment of macromolecules.

Effectiveness of Fluorescence-based Methods in Monitoring Progression of Noncavitated Caries-like Lesions on Smooth Surfaces

Although there has been a significant decrease in caries prevalence in developed countries, the slower progression of dental caries requires methods capable of detecting and quantifying lesions at an early stage. The aim of this study was to evaluate the effectiveness of fluorescence-based methods (DIAGNOdent 2095 laser fluorescence device [LF], DIAGNOdent 2190 pen [LFpen], and VistaProof fluorescence camera [FC]) in monitoring the progression of noncavitated caries-like lesions on smooth surfaces. Caries-like lesions were developed in 60 blocks of bovine enamel using a bacterial model of Streptococcus mutans and Lactobacillus acidophilus . Enamel blocks were evaluated by two independent examiners at baseline (phase I), after the first cariogenic challenge (eight days) (phase II), and after the second cariogenic challenge (a further eight days) (phase III) by two independent examiners using the LF, LFpen, and FC. Blocks were submitted to surface microhardness (SMH) and cross-sectional microhardness analyses. The intraclass correlation coefficient for intra- and interexaminer reproducibility ranged from 0.49 (FC) to 0.94 (LF/LFpen). SMH values decreased and fluorescence values increased significantly among the three phases. Higher values for sensitivity, specificity, and area under the receiver operating characteristic curve were observed for FC (phase II) and LFpen (phase III). A significant correlation was found between fluorescence values and SMH in all phases and integrated loss of surface hardness (ΔKHN) in phase III. In conclusion, fluorescence-based methods were effective in monitoring noncavitated caries-like lesions on smooth surfaces, with moderate correlation with SMH, allowing differentiation between sound and demineralized enamel.

Influence of contact points on the performance of caries detection methods in approximal surfaces of primary molars: an in vivo study

This in vivo study aimed to evaluate the influence of contact points on the approximal caries detection in primary molars, by comparing the performance of the DIAGNOdent pen and visual-tactile examination after tooth separation to bitewing radiography (BW). A total of 112 children were examined and 33 children were selected. In three periods (a, b, and c), 209 approximal surfaces were examined: (a) examiner 1 performed visual-tactile examination using the Nyvad criteria (EX1); examiner 2 used DIAGNOdent pen (LF1) and took BW; (b) 1 week later, after tooth separation, examiner 1 performed the second visual-tactile examination (EX2) and examiner 2 used DIAGNOdent again (LF2); (c) after tooth exfoliation, surfaces were directly examined using DIAGNOdent (LF3). Teeth were examined by computed microtomography as a reference standard. Analyses were based on diagnostic thresholds: D1: D 0 = health, D 1 –D 4 = disease; D2: D 0 , D 1 = health, D 2 –D 4 = disease; D3: D 0 –D 2 = health, D 3 , D 4 = disease. At D1, the highest sensitivity/specificity were observed for EX1 (1.00)/LF3 (0.68), respectively. At D2, the highest sensitivity/ specificity were observed for LF3 (0.69)/BW (1.00), respectively. At D3, the highest sensitivity/specificity were observed for LF3 (0.78)/EX1, EX2 and BW (1.00). EX1 showed higher accuracy values than LF1, and EX2 showed similar values to LF2. We concluded that the visual-tactile examination showed better results in detecting sound surfaces and approximal caries lesions without tooth separation. However, the effectiveness of approximal caries lesion detection of both methods was increased by the absence of contact points. Therefore, regardless of the method of detection, orthodontic separating elastics should be used as a complementary tool for the diagnosis of approximal noncavitated lesions in primary molars.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Fatty acids and intact polar lipids of laminated microbial sediments from St. Peter Ording, German Wadden Sea

Hidden for the untrained eye through a thin layer of sand, laminated microbial sediments occur in supratidal beaches along the North Sea coast. The inhabiting microbial communities organize themselves in response to vertical gradients of light, oxygen or sulfur compounds. We performed a fine-scale investigation on the vertical zonation of the microbial communities using a lipid biomarker approach, and assessed the biogeochemical processes using a combination of microsensor measurements and a 13C-labeling experiment. Lipid biomarker fingerprinting showed the overarching importance of cyanobacteria and diatoms in these systems, and heterocyst glycolipids revealed the presence of diazotrophic cyanobacteria even in 9 to 20 mm depth. High abundance of ornithine lipids (OL) throughout the system may derive from sulfate reducing bacteria, while a characteristic OL profile between 5 and 8 mm may indicate presence of purple non-sulfur bacteria. The fate of 13C-labeled bicarbonate was followed by experimentally investigating the uptake into microbial lipids, revealing an overarching importance of cyanobacteria for carbon fixation. However, in deeper layers, uptake into purple sulfur bacteria was evident, and a close microbial coupling could be shown by uptake of label into lipids of sulfate reducing bacteria in the deepest layer. Microsensor measurements in sediment cores collected at a later time point revealed the same general pattern as the biomarker analysis and the labeling experiments. Oxygen and pH-microsensor profiles showed active photosynthesis in the top layer. The sulfide that diffuses from deeper down and decreases just below the layer of active oxygenic photosynthesis indicates the presence of sulfur bacteria, like anoxygenic phototrophs that use sulfide instead of water for photosynthesis.