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.

Carbon surfaces for the oxidative quantification of pravastatin: glassy-carbon vs. screen-printed carbon electrodes

The electrooxidative behavior of pravastatin (PRV) in aqueous media was studied by square-wave voltammetry at a glassycarbon electrode (GCE) and at a screen-printed carbon electrode (SPCE). Maximum peak current intensities in a pH 5.0 buffer were obtained at +1.3 V vs. AgCl/Ag and +1.0 V vs. Ag for the GCE and SPCE surface respectively. Validation of the developed methodologies revealed good performance characteristics and confirmed their applicability to the quantification of PRV in pharmaceutical products, without significant sample pretreatment. A comparative analysis between the two electrode types showed that SPCEs are preferred as an electrode surface because of their higher sensitivity and the elimination of the need to clean the electrode’s surface for its renewal, which frequently is, if not always, the rate-limiting step in voltammetric analysis.

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.

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.

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

EFFECTS OF ION LIMITING CONDITIONS ON THE BEHAVIOR OF MICROFLUIDIC DEVICES

Finite numbers of ions are present in microfluidic devices. This leads to ion limiting effects in microfluidic channels and electrode surfaces. These effects include electrode surface changes and ion concentration gradient formation across microfluidic channels, and can influence microfluidic device behavior. A literature survey on the use of electrochemical analysis techniques in micro- and nanofluidic devices was carried out, which puts into perspective the importance of electrode surface changes with regards to analytical microfluidic applications. Surface changes in Pt wire electrodes under various physiological buffer and electric field conditions were investigated using cyclic voltammetry (CV), SEM-EDS and XPS. Effects of surface changes on electrochemical analysis performance of Pt wire and thin film electrodes were investigated. Electrode surfaces were subjected to varying phosphate buffer and electric field conditions, and their CV performance was monitored. Electrode surfaces were also studied with SEM-EDS. Two studies of ion concentration gradient formation in microfluidic channels were conducted. In the first, concentration gradients of H+ and OH- ions generated on electrode surfaces were found to cause significant pH decreases in certain buffer and electric field conditions, which was also found to play a key role in iDEP manipulation of proteins. The role of electrode surface reactions in this case shows the importance of understanding electrode surface changes in microfluidic devices. In the second study of ion concentration gradient formation, Cl- ion concentration gradient formation was attempted to be quantified upon electric field application across a KCl solution. Electrokinetic transport of the Cl- indicating fluorophore MQAE contributed significantly to the fluorescence microscopy signals collected, complicating Cl- quantification as a function of position and time. It was shown that a dielectric coating on electrode surfaces is effective at preventing MQAE electrokinetic transport.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Electronic And Structural Study Of Pt-modified Au Vicinal Surfaces: A Model System For Pt-au Catalysts.

Two single crystalline surfaces of Au vicinal to the (111) plane were modified with Pt and studied using scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS) in ultra-high vacuum environment. The vicinal surfaces studied are Au(332) and Au(887) and different Pt coverage (θPt) were deposited on each surface. From STM images we determine that Pt deposits on both surfaces as nanoislands with heights ranging from 1 ML to 3 ML depending on θPt. On both surfaces the early growth of Pt ad-islands occurs at the lower part of the step edge, with Pt ad-atoms being incorporated into the steps in some cases. XPS results indicate that partial alloying of Pt occurs at the interface at room temperature and at all coverage, as suggested by the negative chemical shift of Pt 4f core line, indicating an upward shift of the d-band center of the alloyed Pt. Also, the existence of a segregated Pt phase especially at higher coverage is detected by XPS. Sample annealing indicates that the temperature rise promotes a further incorporation of Pt atoms into the Au substrate as supported by STM and XPS results. Additionally, the catalytic activity of different PtAu systems reported in the literature for some electrochemical reactions is discussed considering our findings.

Analysis Of The Fluorescence Of Body Fluids On Different Surfaces And Times.

The use of screening techniques, such as an alternative light source (ALS), is important for finding biological evidence at a crime scene. The objective of this study was to evaluate whether biological fluid (blood, semen, saliva, and urine) deposited on different surfaces changes as a function of the age of the sample. Stains were illuminated with a Megamaxx™ ALS System and photographed with a Canon EOS Utility™ camera. Adobe Photoshop™ was utilized to prepare photographs for analysis, and then ImageJ™ was used to record the brightness values of pixels in the images. Data were submitted to analysis of variance using a generalized linear mixed model with two fixed effects (surface and fluid). Time was treated as a random effect (through repeated measures) with a first-order autoregressive covariance structure. Means of significant effects were compared by the Tukey test. The fluorescence of the analyzed biological material varied depending on the age of the sample. Fluorescence was lower when the samples were moist. Fluorescence remained constant when the sample was dry, up to the maximum period analyzed (60 days), independent of the substrate on which the fluid was deposited, showing the novelty of this study. Therefore, the forensic expert can detect biological fluids at the crime scene using an ALS even several days after a crime has occurred.

Visual demonstration of the ionic strength effect in the classroom: the Debye-Hückel limiting law

The effects of ionic strength on ions in aqueous solutions are quite relevant, especially for biochemical systems, in which proteins and amino acids are involved. The teaching of this topic and more specifically, the Debye-Hückel limiting law, is central in chemistry undergraduate courses. In this work, we present a description of an experimental procedure based on the color change of aqueous solutions of bromocresol green (BCG), driven by addition of electrolyte. The contribution of charge product (z+|z-|) to the Debye-Hückel limiting law is demonstrated when the effects of NaCl and Na2SO4 on the color of BCG solutions are compared.

Influence of implant surfaces on osseointegration

The biological fixation between the dental implant surfaces and jaw bones should be considered a prerequisite for the long-term success of implant-supported prostheses. In this context, the implant surface modifications gained an important and decisive place in implant research over the last years. As the most investigated topic in, it aided the development of enhanced dental treatment modalities and the expansion of dental implant use. Nowadays, a large number of implant types with a great variety of surface properties and other features are commercially available and have to be treated with caution. Although surface modifications have been shown to enhance osseointegration at early implantation times, for example, the clinician should look for research evidence before selecting a dental implant for a specific use. This paper reviews the literature on dental implant surfaces by assessing in vitro and in vivo studies to show the current perspective of implant development. The review comprises quantitative and qualitative results on the analysis of bone-implant interface using micro and nano implant surface topographies. Furthermore, the perspective of incorporating biomimetic molecules (e.g.: peptides and bone morphogenetic proteins) to the implant surface and their effects on bone formation and remodeling around implants are discussed.

Enhanced bone apposition to Brazilian microrough titanium surfaces

It has recently been reported that machined and microrough (micro) Brazilian titanium (Ti) implants have good production standards. The aim of this study was to evaluate in vivo bone formation around 2 different implant surfaces placed in dog's mandible. Thirty-two screw-typed Ti implants were used in this study. Mandibular premolars were extracted in 8 dogs and, after 12 weeks, 2 machined (Neodent Titamax, Brazil) and 2 micro implants (Neodent Titamax Porous, Brazil) were placed in each animal. Biopsies were taken at 3 and 8 weeks post-implantation and stained with Stevenel's blue and Alizarin red for histomorphometric measurements of bone-to-implant contact (BIC), bone area between threads (BABT) and bone area within the mirror area (BAMA). Data were analyzed statistically by two-way ANOVA (α=0.05). While at 3 weeks micro implants exhibited significantly more BIC than machined ones (55 ± 12.5% and 35.6 ± 15%, p<0.05), no significant difference in such parameter was detected at 8 weeks (51.2 ± 21% and 48.6 ± 18.1%, p>0.05). There were no significant differences in BABT and BAMA between the implants. Micro surfaces promoted higher contact osteogenesis. These data indicate that this commercial micro Ti implant surface enhances contact osteogenesis at an early post-implantation period when compared to the machined one.

Characterization of thiol-functionalised silica films deposited on electrode surfaces

Thiol-functionalised silica films were deposited on various electrode surfaces (gold, platinum, glassy carbon) by spin-coating sol-gel mixtures in the presence of a surfactant template. Film formation occurred by evaporation induced self-assembly (EISA) involving the hydrolysis and (co)condensation of silane and organosilane precursors on the electrode surface. The characterization of such material was performed by IR spectroscopy, thermogravimetry (TG), elemental analysis (EA), atomic force microscopy (AFM), scanning electron microscopy (SEM) and cyclic voltammetry (CV).

Shoulder Muscular Activity During Isometric Three-Point Kneeling Exercise on Stable and Unstable Surfaces

The purpose of this study was to determine if performing isometric 3-point kneeling exercises on a Swiss ball influenced the isometric force output and EMG activities of the shoulder muscles when compared with performing the same exercises on a stable base of support. Twenty healthy adults performed the isometric 3-point kneeling exercises with the hand placed either on a stable surface or on a Swiss ball. Surface EMG was recorded from the posterior deltoid, pectoralis major, biceps brachii, triceps brachii, upper trapezius, and serratus anterior muscles using surface differential electrodes. All EMG data were reported as percentages of the average root mean square (RMS) values obtained in maximum voluntary contractions for each muscle studied. The highest load value was obtained during exercise on a stable surface. A significant increase was observed in the activation of glenohumeral muscles during exercises on a Swiss ball. However, there were no differences in EMG activities of the scapulothoracic muscles. These results suggest that exercises performed on unstable surfaces may provide muscular activity levels similar to those performed on stable surfaces, without the need to apply greater external loads to the musculoskeletal system. Therefore, exercises on unstable surfaces may be useful during the process of tissue regeneration.

Nd:YAG Laser Improves Biocompatibility of Human Dental Root Surfaces

Objective: Our goal was to compare the in vivo biocompatibility of dental root surfaces submitted to four different treatments after tooth avulsion followed by implantation into rat subcutaneous tissue. Background Data: Dental root surface preparation prior to replanting teeth remains a challenge for endodontists. Root surface changes made by Nd:YAG irradiation could be an alternative preparation. Methods: Forty-eight freshly extracted human dental roots were randomly divided into four treatment groups prior to implantation into rat subcutaneous tissue: G1, dry root, left in the environment up to 3 h; G2, the same treatment as G1, followed by a soaking treatment in a 2.4% sodium fluoride solution (pH 5.5); G3, root soaked in physiologic saline after avulsion for 72 h; G4, the same treatment as G1, followed by Nd:YAG laser irradiation (2.0 W, 20 Hz, 100 mJ, and 124.34 J/cm(2)). The animals were sacrificed 1, 7, and 45 d later. Histological and scanning electron microscopy analyses were done. Results: All dental roots were involved and in intimate contact with connective tissue capsules of variable thicknesses. Differences were observed in the degree of inflammation and in connective tissue maturation. In G3 the inflammatory infiltrate was maintained for 45 d, whereas the Nd:YAG laser irradiation (G4) led to milder responses. The overall aspects of the root surfaces were similar, except by the irradiated roots, where fusion and resolidification of the root surface covering the dentinal tubules were observed. Conclusion: Nd:YAG laser irradiation improves the biocompatibility of dental root and thus could be an alternative treatment of dental root prior to replantation.