Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Population

2000 Mathematics Subject Classification: primary 60J80; secondary 60J85, 92C37.

Fourth-root summation of contrast over area:no end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat

Measurements of area summation for luminance-modulated stimuli are typically confounded by variations in sensitivity across the retina. Recently we conducted a detailed analysis of sensitivity across the visual field (Baldwin et al, 2012) and found it to be well-described by a bilinear “witch’s hat” function: sensitivity declines rapidly over the first 8 cycles or so, more gently thereafter. Here we multiplied luminance-modulated stimuli (4 c/deg gratings and “Swiss cheeses”) by the inverse of the witch’s hat function to compensate for the inhomogeneity. This revealed summation functions that were straight lines (on double log axes) with a slope of -1/4 extending to ≥33 cycles, demonstrating fourth-root summation of contrast over a wider area than has previously been reported for the central retina. Fourth-root summation is typically attributed to probability summation, but recent studies have rejected that interpretation in favour of a noisy energy model that performs local square-law transduction of the signal, adds noise at each location of the target and then sums over signal area. Modelling shows our results to be consistent with a wide field application of such a contrast integrator. We reject a probability summation model, a quadratic model and a matched template model of our results under the assumptions of signal detection theory. We also reject the high threshold theory of contrast detection under the assumption of probability summation over area.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Nanoscratch and nanowear testing of TiN coatings on M42 steel

Constant load, progressive load and multipass nanoscratch (nanowear) tests were carried out on 500 and 1500 nm TiN coatings on M42 steel chosen as model systems. The influences of film thickness, coating roughness, scratch direction relative to the grinding grooves on the critical load in the progressive load test and number of cycles to failure in the wear test have been determined. Progress towards the development of a suitable methodology for determining the scratch hardness from nanoscratch tests is discussed. © 2011 W. S. Maney & Son Ltd.

Comprehensive process maps for synthesizing high density aluminum oxide-carbon nanotube coatings by plasma spraying for improved mechanical and wear properties

Plasma sprayed aluminum oxide ceramic coating is widely used due to its outstanding wear, corrosion, and thermal shock resistance. But porosity is the integral feature in the plasma sprayed coating which exponentially degrades its properties. In this study, process maps were developed to obtain Al2O3-CNT composite coatings with the highest density (i.e. lowest porosity) and improved mechanical and wear properties. Process map is defined as a set of relationships that correlates large number of plasma processing parameters to the coating properties. Carbon nanotubes (CNTs) were added as reinforcement to Al2O 3 coating to improve the fracture toughness and wear resistance. Two novel powder processing approaches viz spray drying and chemical vapor growth were adopted to disperse CNTs in Al2O3 powder. The degree of CNT dispersion via chemical vapor deposition (CVD) was superior to spray drying but CVD could not synthesize powder in large amount. Hence optimization of plasma processing parameters and process map development was limited to spray dried Al2O3 powder containing 0, 4 and 8 wt. % CNTs. An empirical model using Pareto diagram was developed to link plasma processing parameters with the porosity of coating. Splat morphology as a function of plasma processing parameter was also studied to understand its effect on mechanical properties. Addition of a mere 1.5 wt. % CNTs via CVD technique showed ∼27% and ∼24% increase in the elastic modulus and fracture toughness respectively. Improved toughness was attributed to combined effect of lower porosity and uniform dispersion of CNTs which promoted the toughening by CNT bridging, crack deflection and strong CNT/Al2O3 interface. Al2O 3-8 wt. % CNT coating synthesized using spray dried powder showed 73% improvement in the fracture toughness when porosity reduced from 4.7% to 3.0%. Wear resistance of all coatings at room and elevated temperatures (573 K, 873 K) showed improvement with CNT addition and decreased porosity. Such behavior was due to improved mechanical properties, protective film formation due to tribochemical reaction, and CNT bridging between the splats. Finally, process maps correlating porosity content, CNT content, mechanical properties, and wear properties were developed.

Hydroxyapatite-nanotube composites and coatings for orthopedic applications

Hydroxyapatite (HA) has received wide attention in orthopedics, due to its biocompatibility and osseointegration ability. Despite these advantages, the brittle nature and low fracture toughness of HA often results in rapid wear and premature fracture of implant. Hence, there is a need to improve the fracture toughness and wear resistance of HA without compromising its biocompatibility. ^ The aim of the current research is to explore the potential of nanotubes as reinforcement to HA for orthopedic implants. HA- 4 wt.% carbon nanotube (CNT) composites and coatings are synthesized by spark plasma sintering and plasma spraying respectively, and investigated for their mechanical, tribological and biological behavior. CNT reinforcement improves the fracture toughness (>90%) and wear resistance (>66%) of HA for coating and free standing composites. CNTs have demonstrated a positive influence on the proliferation, differentiation and matrix mineralization activities of osteoblasts, during in-vitro biocompatibility studies. In-vivo exposure of HA-CNT coated titanium implant in animal model (rat) shows excellent histocompatibility and neobone integration on the implant surface. The improved osseointegration due to presence of CNTs in HA is quantified by the adhesion strength measurement of single osteoblast using nano-scratch technique. ^ Considering the ongoing debate about cytotoxicity of CNTs in the literature, the present study also suggests boron nitride nanotube (BNNT) as an alternative reinforcement. BNNT with the similar elastic modulus and strength as CNT, were added to HA. The resulting composite having 4 wt.% BNNTs improved the fracture toughness (∼85%) and wear resistance (∼75%) of HA in the similar range as HA-CNT composites. BNNTs were found to be non-cytotoxic for osteoblasts and macrophages. In-vitro evaluation shows positive role of BNNT in osteoblast proliferation and viability. Apatite formability of BNNT surface in ∼4 days establishes its osseointegration ability.^

Nanostructured Metal Oxide Coatings for Electrochemical Energy Conversion and Storage Electrodes

The realization of an energy future based on safe, clean, sustainable, and economically viable technologies is one of the grand challenges facing modern society. Electrochemical energy technologies underpin the potential success of this effort to divert energy sources away from fossil fuels, whether one considers alternative energy conversion strategies through photoelectrochemical (PEC) production of chemical fuels or fuel cells run with sustainable hydrogen, or energy storage strategies, such as in batteries and supercapacitors. This dissertation builds on recent advances in nanomaterials design, synthesis, and characterization to develop novel electrodes that can electrochemically convert and store energy.

Chapter 2 of this dissertation focuses on refining the properties of TiO2-based PEC water-splitting photoanodes used for the direct electrochemical conversion of solar energy into hydrogen fuel. The approach utilized atomic layer deposition (ALD); a growth process uniquely suited for the conformal and uniform deposition of thin films with angstrom-level thickness precision. ALD’s thickness control enabled a better understanding of how the effects of nitrogen doping via NH3 annealing treatments, used to reduce TiO2’s bandgap, can have a strong dependence on TiO2’s thickness and crystalline quality. In addition, it was found that some of the negative effects on the PEC performance typically associated with N-doped TiO2 could be mitigated if the NH3-annealing was directly preceded by an air-annealing step, especially for ultrathin (i.e., < 10 nm) TiO2 films. ALD was also used to conformally coat an ultraporous conductive fluorine-doped tin oxide nanoparticle (nanoFTO) scaffold with an ultrathin layer of TiO2. The integration of these ultrathin films and the oxide nanoparticles resulted in a heteronanostructure design with excellent PEC water oxidation photocurrents (0.7 mA/cm2 at 0 V vs. Ag/AgCl) and charge transfer efficiency.

In Chapter 3, two innovative nanoarchitectures were engineered in order to enhance the pseudocapacitive energy storage of next generation supercapacitor electrodes. The morphology and quantity of MnO2 electrodeposits was controlled by adjusting the density of graphene foliates on a novel graphenated carbon nanotube (g-CNT) scaffold. This control enabled the nanocomposite supercapacitor electrode to reach a capacitance of 640 F/g, under MnO2 specific mass loading conditions (2.3 mg/cm2) that are higher than previously reported. In the second engineered nanoarchitecture, the electrochemical energy storage properties of a transparent electrode based on a network of solution-processed Cu/Ni cores/shell nanowires (NWs) were activated by electrochemically converting the Ni metal shell into Ni(OH)2. Furthermore, an adjustment of the molar percentage of Ni plated onto the Cu NWs was found to result in a tradeoff between capacitance, transmittance, and stability of the resulting nickel hydroxide-based electrode. The nominal area capacitance and power performance results obtained for this Cu/Ni(OH)2 transparent electrode demonstrates that it has significant potential as a hybrid supercapacitor electrode for integration into cutting edge flexible and transparent electronic devices.

TILTED COLUMNAR THIN FILM COATINGS WITH ANISOTROPIC LIGHT SCATTERING PROPERTIES FOR SOLAR ENERGY APPLICATIONS

The main goal of this thesis is to show the versatility of glancing angle deposition (GLAD) thin films in applications. This research is first focused on studying the effect of select deposition variables in GLAD thin films and secondly, to demonstrate the flexibility of GLAD films to be incorporated in two different applications: (1) as a reflective coating in low-level concentration photovoltaic systems, and (2) as an anode structure in dye-sensitized solar cells (DSSC). A particular type of microstructure composed of tilted micro-columns of titanium is fabricated by GLAD. The microstructures form elongated and fan-like tilted micro-columns that demonstrate anisotropic scattering. The thin films texture changes from fiber texture to tilted fiber texture by increasing the vapor incidence angle. At very large deposition angles, biaxial texture forms. The morphology of the thin films deposited under extreme shadowing condition and at high temperature (below recrystallization zone) shows a porous and inclined micro-columnar morphology, resulting from the dominance of shadowing over adatom surface diffusion. The anisotropic scattering behavior of the tilted Ti thin film coatings is quantified by bidirectional reflectance distribution function (BRDF) measurements and is found to be consistent with reflectance from the microstructure acting as an array of inclined micro-mirrors that redirect the incident light in a non-specular reflection. A silver-coating of the surface of the tilted-Ti micro-columns is performed to enhance the total reflectance of the Ti-thin films while keeping the anisotropic scattering behavior. By using such coating is as a booster reflector in a laboratory-scale low-level concentration photovoltaic system, the short-circuit current of the reference silicon solar cell by 25%. Finally, based on the scattering properties of the tilted microcolumnar microstructure, its scattering effect is studied as a part of titanium dioxide microstructure for the anode in DSSCs. GLAD-fabricated TiO2 microstructures for the anode in a DSSC, consisting of vertical micro-columns, and combined vertical topped with tilted micro-columns are compared. The solar cell with the two-part microstructure shows the highest monochromatic incident photon to current efficiency with 20% improvement compared to the vertical microstructure, and the efficiency of the cell increases from 1.5% to 2% due to employing the scattering layer.

Fibronectin/phosphorylcholine coatings on fluorocarboned surfaces: a study upon adsorption and grafting processes

Depuis ces dernières décennies, le domaine des biomatériaux a connu un essor considérable, évoluant de simples prothèses aux dispositifs les plus complexes pouvant détenir une bioactivité spécifique. Outre, le progrès en science des matériaux et une meilleure compréhension des systèmes biologiques a offert la possibilité de créer des matériaux synthétiques pouvant moduler et stimuler une réponse biologique déterminée, tout en améliorant considérablement la performance clinique des biomatériaux. En ce qui concerne les dispositifs cardiovasculaires, divers recouvrements ont été développés et étudiés dans le but de modifier les propriétés de surface et d’améliorer l’efficacité clinique des tuteurs. En effet, lorsqu’un dispositif médical est implanté dans le corps humain, son succès clinique est fortement influencé par les premières interactions que sa surface établit avec les tissus et les fluides biologiques environnants. Le recouvrement à la surface de biomatériaux par diverses molécules ayant des propriétés complémentaires constitue une approche intéressante pour atteindre différentes cibles biologiques et orienter la réponse de l’hôte. De ce fait, l’élucidation de l’interaction entre les différentes molécules composant les recouvrements est pertinente pour prédire la conservation de leurs propriétés biologiques spécifiques. Dans ce travail, des recouvrements pour des applications cardiovasculaires ont été créés, composés de deux molécules ayant des propriétés biologiques complémentaires : la fibronectine (FN) afin de promouvoir l’endothélialisation et la phosphorylcholine (PRC) pour favoriser l’hémocompatibilité. Des techniques d’adsorption et de greffage ont été appliquées pour créer différents recouvrements de ces deux biomolécules sur un polymère fluorocarboné déposé par traitement plasma sur un substrat en acier inoxydable. Dans un premier temps, des films de polytétrafluoroéthylène (PTFE) ont été utilisés en tant que surface modèle afin d’explorer l’interaction de la PRC et de la FN avec les surfaces fluorocarbonées ainsi qu’avec des cellules endothéliales et du sang. La stabilité des recouvrements de FN sur l’acier inoxydable a été étudiée par déformation, mais également par des essais statiques et dynamiques sous-flux. Les recouvrements ont été caractérisés par Spectroscopie Photoéléctronique par Rayons X, immunomarquage, angle de contact, Microscopie Électronique de Balayage, Microscopie de Force Atomique et Spectrométrie de Masse à Ionisation Secondaire à Temps de Vol (imagerie et profilage en profondeur). Des tests d’hémocompatibilité ont été effectués et l’interaction des cellules endothéliales avec les recouvrements a également été évaluée. La FN greffée a présenté des recouvrements plus denses et homogènes alors que la PRC quant à elle, a montré une meilleure homogénéité lorsqu’elle était adsorbée. La caractérisation de la surface des échantillons contenant FN/PRC a été corrélée aux propriétés biologiques et les recouvrements pour lesquels la FN a été greffée suivie de l’adsorption de la PRC ont présenté les meilleurs résultats pour des applications cardiovasculaires : la promotion de l’endothélialisation et des propriétés d’hémocompatibilité. Concernant les tests de stabilité, les recouvrements de FN greffée ont présenté une plus grande stabilité et densité que dans le cas de l’adsorption. En effet, la pertinence de présenter des investigations des essais sous-flux versus des essais statiques ainsi que la comparaison des différentes stratégies pour créer des recouvrements a été mis en évidence. D’autres expériences sont nécessaires pour étudier la stabilité des recouvrements de PRC et de mieux prédire son interaction avec des tissus in vivo.

Inhomogeneous cloud coverage through the Coulomb explosion of dust in substellar atmospheres

Context. Recent observations of brown dwarf spectroscopic variability in the infrared infer the presence of patchy cloud cover. Aims. This paper proposes a mechanism for producing inhomogeneous cloud coverage due to the depletion of cloud particles through the Coulomb explosion of dust in atmospheric plasma regions. Charged dust grains Coulomb-explode when the electrostatic stress of the grain exceeds its mechanical tensile stress, which results in grains below a critical radius a < a Coul crit being broken up. Methods. This work outlines the criteria required for the Coulomb explosion of dust clouds in substellar atmospheres, the effect on the dust particle size distribution function, and the resulting radiative properties of the atmospheric regions. Results. Our results show that for an atmospheric plasma region with an electron temperature of Te = 10 eV (≈105 K), the critical grain radius varies from 10−7 to 10−4 cm, depending on the grains’ tensile strength. Higher critical radii up to 10−3 cm are attainable for higher electron temperatures. We find that the process produces a bimodal particle size distribution composed of stable nanoscale seed particles and dust particles with a ≥ a Coul crit , with the intervening particle sizes defining a region devoid of dust. As a result, the dust population is depleted, and the clouds become optically thin in the wavelength range 0.1–10 μm, with a characteristic peak that shifts to higher wavelengths as more sub-micrometer particles are destroyed. Conclusions. In an atmosphere populated with a distribution of plasma volumes, this will yield regions of contrasting radiative properties, thereby giving a source of inhomogeneous cloud coverage. The results presented here may also be relevant for dust in supernova remnants and protoplanetary disks.