Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

New geometries for black hole horizons

We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D ≥ 6.

Untersuchungen über Minimaldoppelflächen /

Thesis--Westf. Wilhelms-Universität.

Bestimmung einer speciellen periodischen minimalfläche,

Mode of access: Internet.

Funzioni BV e disuguaglianze isoperimetriche

All'interno della mia tesi verrà introdotta la teoria delle funzioni in R^{n} a variazione limitata (BV), seguendo le presentazioni di Lawrence C.Evans e Ronald F.Gariepy nel libro Measure Theory and Fine Properties of Functions e di Enrico Giusti nell'opera Minimal Surfaces and Functions of Bounded Variation. Le funzioni BV sono funzioni le cui derivate prime deboli sono misure di Radon, ossia misure di Borel regolari finite sui compatti. In particolare verranno anche analizzati gli insiemi E che hanno perimetro finito, ossia tali che la funzione indicatrice dell’insieme E sia una funzione BV. Nello specifico, nel primo capitolo verranno date le definizioni di funzioni BV e insiemi di perimetro finito, sia in una versione globale che in una locale, verrà enunciato un primo importante teorema per le funzioni BV e verrà analizzata la relazione tra funzioni di Sobolev e funzioni BV. Nel secondo capitolo, invece, verranno analizzate la semicontinuità inferiore, l'approssimazione con funzioni lisce e la compattezza di funzioni BV, mentre nel terzo capitolo verranno elencati alcuni risultati sulle funzioni BV riguardanti la Traccia, l'Estensione e la formula di Coarea. Infine, nel quarto ed ultimo capitolo, verranno studiate le disuguaglianze di Sobolev e Poincaré e le disuguaglianze isoperimetriche per funzioni BV.

Pollutant characteristics on roof surfaces for evaluation as a stormwater harvesting catchment

This paper presents the outcomes of a study which focused on evaluating roof surfaces as stormwater harvesting catchments. Build-up and wash-off samples were collected from model roof surfaces. The collected build-up samples were separated into five different particle size ranges prior to the analysis of physico-chemical parameters. Study outcomes showed that roof surfaces are efficient catchment surfaces for the deposition of fine particles which travel over long distances. Roof surfaces contribute relatively high pollutant loads to the runoff and hence significantly influence the quality of the harvested rainwater. Pollutants associated with solids build-up on roof surfaces can vary with time, even with minimal changes to total solids load and particle size distribution. It is postulated that this variability is due to changes in distant atmospheric pollutant sources and wind patterns. The study highlighted the requirement for first flush devices to divert the highly polluted initial portion of roof runoff. Furthermore, it is highly recommended to not to harvest runoff from small intensity rainfall events since there is a high possibility that the runoff would contain a significant amount of pollutants even after the initial runoff fraction.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Analysis of susceptibility profile of Pseudomonas spp. and prevalence of bacterial samples from the surfaces of dental consulting-rooms

The aim of this research was to evaluate the susceptibility profile of Pseudomonas spp. and the prevalence of bacterial samples isolated from horizontal surfaces surrounding wash-basins used by dentists in several adjoined consulting-rooms, at points next to and at a distance from the basin, before and after surgical procedures. Our results showed a high percentage of Gram-positive cocci and Gram-negative bacilli; 34.66% were Staphylococcus spp. and 30.12% were non-fermentative Gram-negative bacilli among which Pseudomonas spp. (40.90%) was the commonest genus. Analysis of the susceptibility profile of Pseudomonas spp. isolates by determining the minimal inhibitory concentration (MIC) of 14 antibiotics showed a great variation among the strains and high rates of resistance to cefazolin, ceftazidime and aztreonan. Of the 14 antibiotics tested, 59.03% were found to be active against all the environmental isolates. Strains were resistant to aztreonan (62.82%), while susceptibility to third generation cephalosporins was variable.

Minimal alterations on the enamel surface by micro-abrasion: in vitro roughness and wear assessments

Objective: To evaluate the in vitro changes on the enamel surface after a micro-abrasion treatment promoted by different products. Material and Methods: Fifty (50) fragments of bovine enamel (15 mm × 5 mm) were randomly assigned to five groups (n=10) according to the product utilized: G1 (control)= silicone polisher (TDV), G2= 37% phosphoric acid (3M/ESPE) + pumice stone (SS White), G3= Micropol (DMC Equipment), G4= Opalustre (Ultradent) and G5= Whiteness RM (FGM Dental Products). Roughness and wear were the responsible variables used to analyze these surfaces in four stages: baseline, 60 s and 120 s after the micro-abrasion and after polishing, using a Hommel Tester T1000 device. After the tests, a normal distribution of data was verified, with repeated ANOVA analyses (p?0.05) which were used to compare each product in different stages. One-way ANOVA and Tukey tests were applied for individual comparisons between the products in each stage (p?0.05). Results: Means and standard deviations of roughness and wear (µm) after all the promoted stages were: G1=7.26(1.81)/13.16(2.67), G2=2.02(0.62)/37.44(3.33), G3=1.81(0.91)/34.93(6.92), G4=1.92(0.29)/38.42(0.65) and G5=1.98(0.53)/33.45(2.66). At 60 seconds, all products tended to produce less surface roughness with a variable gradual decrease over time. After polishing, there were no statistically significant differences between the groups, except for G1. Independent of the product utilized, the enamel wear occurred after the micro-abrasion. Conclusions: In this in vitro study, enamel micro-abrasion presented itself as a conservative approach, regardless of the type of the paste compound utilized. These products promoted minor roughness alterations and minimal wear. The use of phosphoric acid and pumice stone showed similar results to commercial products for the micro-abrasion with regard to the surface roughness and wear.

Three distinct molecular surfaces in ephrin-A5 are essential for a functional interaction with EphA3

Eph receptor tyrosine kinases (Ephs) function as molecular relays that interact with cell surface-bound ephrin ligands to direct the position of migrating cells. Structural studies revealed that, through two distinct contact surfaces on opposite sites of each protein, Eph and ephrin binding domains assemble into symmetric, circular heterotetramers. However, Eph signal initiation requires the assembly of higher order oligomers, suggesting additional points of contact. By screening a random library of EphA3 binding-compromised ephrin-A5 mutants, we have now determined ephrin-A5 residues that are essential for the assembly of high affinity EphA3 signaling complexes. In addition to the two interfaces predicted from the crystal structure of the homologous EphB2 center dot ephrin-B2 complex, we identified a cluster of 10 residues on the ephrin-A5 E alpha-helix, the E-F loop, the underlying H beta-strand, as well as the nearby B - C loop, which define a distinct third surface required for oligomerization and activation of EphA3 signaling. Together with a corresponding third surface region identified recently outside of the minimal ephrin binding domain of EphA3, our findings provide experimental evidence for the essential contribution of three distinct protein-interaction interfaces to assemble functional EphA3 signaling complexes.

Do ‘passive’ medical titanium surfaces deteriorate in service in the absence of wear?

Globally, more than 1000 tonnes of titanium (Ti) is implanted into patients in the form of biomedical devices on an annual basis. Ti is perceived to be ‘biocompatible’ owing to the presence of a robust passive oxide film (approx. 4 nm thick) at the metal surface. However, surface deterioration can lead to the release of Ti ions, and particles can arise as the result of wear and/or corrosion processes. This surface deterioration can result in peri-implant inflammation, leading to the premature loss of the implanted device or the requirement for surgical revision. Soft tissues surrounding commercially pure cranial anchorage devices (bone-anchored hearing aid) were investigated using synchrotron X-ray micro-fluorescence spectroscopy and X-ray absorption near edge structure. Here, we present the first experimental evidence that minimal load-bearing Ti implants, which are not subjected to macroscopic wear processes, can release Ti debris into the surrounding soft tissue. As such debris has been shown to be pro-inflammatory, we propose that such distributions of Ti are likely to effect to the service life of the device.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.