Mid-infrared sub-wavelength grating mirror design: tolerance and influence of technological constraints

High polarization selective Si/SiO2 mid-infrared sub-wavelength grating mirrors with large bandwidth adapted to VCSEL integration are compared. These mirrors have been automatically designed for operation at \lambda = 2.3 $\mu$m by an optimization algorithm which maximizes a specially defined quality factor. Several technological constraints in relation with the grating manufacturing process have been imposed within the optimization algorithm and their impact on the optical properties of the mirror have been evaluated. Furthermore, through the tolerance computation of the different dimensions of the structure, the robustness with respect to fabrication errors has been tested. Finally, it appears that the increase of the optical performances of the mirror imposes a less tolerant design with severer technological constraints resulting in a more stringent control of the manufacturing process.Comment: The final publication is available at http://iopscience.iop.org/2040-8986/13/12/125502

Tarski monoids: Matui's spatial realization theorem

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui on a class of \'etale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147

Systematic construction of efficient six-stage fifth-order explicit Runge-Kutta embedded pairs without standard simplifying assumptions

This thesis examines methodologies and software to construct explicit Runge-Kutta (ERK) pairs for solving initial value problems (IVPs) by constructing efficient six-stage fifth-order ERK pairs without standard simplifying assumptions. The problem of whether efficient higher-order ERK pairs can be constructed algebraically without the standard simplifying assumptions dates back to at least the 1960s, with Cassity's complete solution of the six-stage fifth-order order conditions. Although RK methods based on the six-stage fifth-order order conditions have been widely studied and have continuing practical importance, prior to this thesis, the aforementioned complete solution to these order conditions has no published usage beyond the original series of publications by Cassity in the 1960s. The complete solution of six-stage fifth-order ERK order conditions published by Cassity in 1969 is not in a formulation that can easily be used for practical purposes, such as a software implementation. However, it is shown in this thesis that when the order conditions are solved and formulated appropriately using a computer algebra system (CAS), the generated code can be used for practical purposes and the complete solution is readily extended to ERK pairs. The condensed matrix form of the order conditions introduced by Cassity in 1969 is shown to be an ideal methodology, which probably has wider applicability, for solving order conditions using a CAS. The software package OCSage developed for this thesis, in order to solve the order conditions and study the properties of the resulting methods, is built on top of the Sage CAS. However, in order to effectively determine that the constructed ERK pairs without standard simplifying assumptions are in fact efficient by some well-defined criteria, the process of selecting the coefficients of ERK pairs is re-examined in conjunction with a sufficient amount of performance data. The pythODE software package developed for this thesis is used to generate a large amount of performance data from a large selection of candidate ERK pairs found using OCSage. In particular, it is shown that there is unlikely to be a well-defined methodology for selecting optimal pairs for general-purpose use, other than avoiding poor choices of certain properties and ensuring the error coefficients are as small as possible. However, for IVPs from celestial mechanics, there are obvious optimal pairs that have specific values of a small subset of the principal error coefficients (PECs). Statements seen in the literature that the best that can be done is treating all PECs equally do not necessarily apply to at least some broad classes of IVPs. By choosing ERK pairs based on specific values of individual PECs, not only are ERK pairs that are 20-30% more efficient than comparable published pairs found for test sets of IVPs from celestial mechanics, but the variation in performance between the best and worst ERK pairs that otherwise would seem to have similar properties is reduced from a factor of 2 down to as low as 15%. Based on observations of the small number of IVPs of other classes in common IVP test sets, there are other classes of IVPs that have different optimal values of the PECs. A more general contribution of this thesis is that it specifically demonstrates how specialized software tools and a larger amount of performance data than is typical can support novel empirical insights into numerical methods

Integrating-factor-based 2-additive Runge-Kutta methods for advection-reaction-diffusion equations

There are three distinct processes that are predominant in models of flowing media with interacting components: advection, reaction, and diffusion. Collectively, these processes are typically modelled with partial differential equations (PDEs) known as advection-reaction-diffusion (ARD) equations. To solve most PDEs in practice, approximation methods known as numerical methods are used. The method of lines is used to approximate PDEs with systems of ordinary differential equations (ODEs) by a process known as semi-discretization. ODEs are more readily analysed and benefit from well-developed numerical methods and software. Each term of an ODE that corresponds to one of the processes of an ARD equation benefits from particular mathematical properties in a numerical method. These properties are often mutually exclusive for many basic numerical methods. A limitation to the widespread use of more complex numerical methods is that the development of the appropriate software to provide comparisons to existing numerical methods is not straightforward. Scientific and numerical software is often inflexible, motivating the development of a class of software known as problem-solving environments (PSEs). Many existing PSEs such as Matlab have solvers for ODEs and PDEs but lack specific features, beyond a scripting language, to readily experiment with novel or existing solution methods. The PSE developed during the course of this thesis solves ODEs known as initial-value problems, where only the initial state is fully known. The PSE is used to assess the performance of new numerical methods for ODEs that integrate each term of a semi-discretized ARD equation. This PSE is part of the PSE pythODE that uses object-oriented and software-engineering techniques to allow implementations of many existing and novel solution methods for ODEs with minimal effort spent on code modification and integration. The new numerical methods use a commutator-free exponential Runge-Kutta (CFERK) method to solve the advection term of an ARD equation. A matrix exponential is used as the exponential function, but CFERK methods can use other numerical methods that model the flowing medium. The reaction term is solved separately using an explicit Runge-Kutta method because solving it along with the diffusion term can result in stepsize restrictions and hence inefficiency. The diffusion term is solved using a Runge-Kutta-Chebyshev method that takes advantage of the spatially symmetric nature of the diffusion process to avoid stepsize restrictions from a property known as stiffness. The resulting methods, known as Integrating-factor-based 2-additive Runge-Kutta methods, are shown to be able to find higher-accuracy solutions in less computational time than competing methods for certain challenging semi-discretized ARD equations. This demonstrates the practical viability both of using CFERK methods for advection and a 3-splitting in general

Structural and Lithological Models of Ilmenite Placer Deposits in Ukraine

Since the 1950s, a large number of geological prospecting and exploration works have been carried out on the territory of Ukraine, dedicated to the search and exploration of placer titanium deposits. As a result, a powerful titanium raw material base has been created, in particular, titanium ore deposits with reserves and resources exceeding the total titanium reserves of all other countries of the world have been explored and prepared for exploration. The most promising deposits began to be developed and became the basis for the creation of the Irshanskiy mining and processing plant (Zhytomyr region) and the Vilnohirsk mining and metallurgical plant (Dnipropetrovsk region). The relevance of the presented subject is conditioned upon the need to use the latest information support tools to improve the quality of processing and presentation of geological information. The paper presents a summary lithostratigraphic scheme, features of the  genesis and distribution of ore material (ilmenite) of the Krasnokutsk, Zlobychi, and Birzuliv deposits. These deposits are located in different parts (according to the tectonic division) of Ukraine, they have a diversified lithostratigraphy, geological and genetic types. Structural-lithological modelling of these objects is carried out. According to the presented structural and lithological models and paleogeographic reconstructions of the time of deposit formation, the change in ilmenite distribution depending on the type of placer formation is shown

Ore content of Avramivske and Zakhidne deposits (Novomyrhorod gabbro-anorthosite massif)

The geological structure and ore content of the Avramivske and Zakhidne phosphate-titanium deposits located in the southern part of the Korsun-Novomyrhorod pluton are characterized. Within these deposits, phosphate-titanium mineralization is contained in crystalline basement rocks, their weathered crust and Aptian–Lower Albian (Zakhidne deposit) and Middle Eocene (Avramivske deposit) continental formations. The rocks overlying these sediments are less ore-bearing. Based on the coordinates, description and results of well testing of the productive formations of these deposits, a target database was created, on the basis of which cartographic constructions were carried out. The results of studies of the spatial distribution of the bottom, of the top and of the thickness of the weathering crust, of the Aptian-Lower Albian deposits, of the sands and of the redeposited kaolins of the Middle Eocene of these fields are presented. The lateral distribution of the average content of ilmenite, apatite, rutile, zircon and correlations between them in the weathering crust, Aptian-Lower Albian and Middle Eocene sediments of these deposits were studied. The distribution of content and correlations of these minerals in the vertical section of the wells are studied and the corresponding mapping is presented. Information on the chemical composition of ilmenite is presented and the lateral distribution of ilmenite with different oxide content in the weathering crusts of the Avramivske and Zakhidne deposits is studied. The obtained results confirm and supplement the results of previous studies on ore content and prospects for increasing the mineral resource base of critical raw materials within the Novomyrhorod massif

Structural and lithological model of the Velykogadomynetske deposit of eluvial kaolins

Information on the geological structure of the Velykogadomynetske deposit of eluvial kaolins, zonation and material composition of the weathering crust is presented. Data on the mineral composition and physical and chemical characteristics of eluvial kaolins are presented. On the basis of the data of coordinates, description, results of well sampling drilled in different years by production geological organizations, chemical analysis of rocks and determination of their whiteness index, a target attributive electronic database was created (coordinates, description and data of well sampling, results of laboratory studies of rocks) on the basis of which structural (absolute elevations of the top and bottom of sediments, relief of the top and of the bottom and thickness of sediments) and material (material composition, content of iron and titanium oxides, whiteness) rock parameters of different weathering crustal zones and redeposited kaolins were studied. Cartographic constructions were made that visualize the structural (isohypses of the surface of the top and bottom, isopachites of the thickness of the disintegration and leaching zone, kaolinite-hydro-mica zone, pelicanite zone, alkaline kaolin zone, normal kaolin zone) and qualitative parameters (content of iron and titanium oxides and their lateral distribution) of the deposit rocks. The direction and strength of correlations between the surface of the top and the bottom of sediments and between their thickness, between the content of Fe₂O₃ and TiO₂ were studied and between the whiteness index and the content of iron and titanium oxides. It was found that the kaolin deposit has a complex occurrence and complex morphology, which are expressed in significant fluctuations in the absolute elevations of its top and bottom, changes in thickness, in the presence of substandard kaolin and are due to the geological and tectonic features of the deposit and the erosion section. The created structural-lithological model of the Velykogadomynetske deposit of eluvial kaolin reveals the cause-and-effect relationships between the geological and tectonic structure of the territory; structure, material composition, zonation and thickness of the weathering crust and its individual zones in particular; conditions of occurrence, material composition, thickness and spatial and vertical variability of qualitative indicators (whiteness indicator, content of harmful impurities of iron and titanium oxides) of the kaolin deposit

Correcting for enzyme immunoassay changes in long term monitoring studies

Enzyme immunoassays (EIAs) are a common tool for measuring steroid hormones in wildlife due to their low cost, commercial availability, and rapid results. Testing technologies improve continuously, sometimes requiring changes in protocols or crucial assay components. Antibody replacement between EIA kits can cause differences in EIA sensitivity, which can hinder monitoring hormone concentration over time. The antibody in a common cortisol EIA kit used for long-term monitoring of stress in wildlife was replaced in 2014, causing differences in cross reactivity and standard curve concentrations. Therefore, the objective of this study was to develop a method to standardize results following changes in EIA sensitivity. We validated this method using cortisol concentrations measured in the hair of brown bears (Ursus arctos). • We used a simple linear regression to model the relationship between cortisol concentrations using kit 1 and kit 2. • We found a linear relationship between the two kits (R2 = 0.85) and used the regression equation (kit2 = (0.98 × kit1) + 1.65) to predict cortisol concentrations in re-measured samples. • Mean predicted percent error was 16% and 72% of samples had a predicted percent error <20%, suggesting that this method is well-suited for correcting changes in EIA sensitivity.publishedVersio