Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics

Geometric Representation Learning

Vector embedding models are a cornerstone of modern machine learning methods for knowledge representation and reasoning. These methods aim to turn semantic questions into geometric questions by learning representations of concepts and other domain objects in a lower-dimensional vector space. In that spirit, this work advocates for density- and region-based representation learning. Embedding domain elements as geometric objects beyond a single point enables us to naturally represent breadth and polysemy, make asymmetric comparisons, answer complex queries, and provides a strong inductive bias when labeled data is scarce. We present a model for word representation using Gaussian densities, enabling asymmetric entailment judgments between concepts, and a probabilistic model for weighted transitive relations and multivariate discrete data based on a lattice of axis-aligned hyperrectangle representations (boxes). We explore the suitability of these embedding methods in different regimes of sparsity, edge weight, correlation, and independence structure, as well as extensions of the representation and different optimization strategies. We make a theoretical investigation of the representational power of the box lattice, and propose extensions to address shortcomings in modeling difficult distributions and graphs

Special Libraries, January 1966

Volume 57, Issue 1https://scholarworks.sjsu.edu/sla_sl_1966/1000/thumbnail.jp

Controlling Plasma Reactivity Transfer to Gases, Solids and Liquids

Plasma discharges at atmospheric pressure enable efficient conversion of the kinetic energy of electrons to chemical reactivity. In the process of breaking of bonds of molecular gases, plasmas produce high densities of reactive species. These species can then be utilized to treat flue gases and waste water. However, currently deployed systems suffer from poor energy efficiencies and throughputs, largely due to the lack of understanding of the underlying physics and chemistries. In this work, computational modeling was performed to investigate the transfer of reactivity (relative capacity to undergo or produce a chemical reaction) from plasmas to gases (via Packed Bed Reactors (PBRs)), solids (metallic catalysts, porous media) and liquid (micron-scale aerosols). The work was performed using the plasma hydrodynamics model – nonPDPSIM. Necessary changes and additions to the code included addition of source terms to the surface heating module, implementation of an updated mesh generator, and parallelization of radiation transport routines. The evolution and properties of plasmas in PBRs were characterized. Three plasma modalities were shown to exist, each leading to different rates of production of reactive species. Chemical selectivity could be achieved by choosing the packing fraction and materials that lead to preferential formation of one of the modalities over others – for example, formation of Surface Ionization Waves in air preferentially increases dissociation of nitrogen over oxygen. When metallic catalysts were added to the PBR, the discharge modalities changed, causing increased fluxes of charged species to the surfaces of the catalysts. This was, in part, due to realignment of charges within the metallic particles, which induced high local electric fields, and electric field emission of electrons. The high fluxes could lead to heating and self-cleaning of the catalysts, which would explain some of the plasma-catalytic synergies observed in experimental literature. Lastly, the interactions of liquid aerosols with Dielectric Barrier Discharges were investigated. The diameter of the droplets was shown to address diffusion transport limits of both ions and neutrals by maximizing the surface-to-volume ratio. Large surface areas enable rapid solvation from the gas-phase while small volume led to fast saturation of liquid-phase reactive species. Different species were shown to have different saturation time-scales, depending on the droplet size, pointing to an additional control mechanism of liquid-chemistry and selectivity. For example, for a 10 μm droplet, ozone (Henry’s law constant, h0 ≈ 0.3) saturates within one tenth of a millisecond. On the other hand, hydrogen peroxide (h0 ≈ 1.9×106) requires up to 10 seconds to saturate a droplet of the same size.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169745/1/jkrusze_1.pd

X-ray computed microtomography applications for complex geometries and multiphase flow

In all fields, fundamental and applied research seek to produce experimental measurements without causing interferences to the process being observed. This capability is of paramount importance, since small perturbations of the phenomenon can alter it to the point of producing biased or even incorrect results. Xray techniques, based on synchrotron or laboratory X-ray sources, have attracted the attention of the research and industrial R&D community thanks to their characteristic of having little to no detectable influence on the subject under study. Moreover, if declined as tomography, this technique can provide localized full volume information at the micrometre scale, from which arbitrary shaped geometries and material densities can be deduced. During this thesis an X-ray microtomography instrument, based on a laboratory X-ray source, has been exploited to gain three main objectives. The first one is the analysis of how a liquid drop, of water or glycol, adapts its shape to reach an equilibrium state when gently deposed on a flat or patterned surface. So far this has been done using 2D techniques but introducing the knowledge of the third dimension and being able to see the drop shape even in not optically accessible locations, opens new possibilities to better understand the physics that regulate it. The second one is the reconstruction of the internal geometries of automotive diesel injectors with high resolution to detect and highlight differences between nominal and real geometries, key information to produce more realistic CFD simulations of the flow inside production grade injectors geometries. A scaled -up model made of PEEK was also studied, producing successive tomographies, to detect small geometrical changes induced by part usage, giving an in-depth view of the locations more prone to be damaged by cavitation flow. The third one is the study of a multiphase flow inside the same scaled-up model injection channel with flowing conditions exhibiting cavitation. The geometry of the non-axisymmetric model mimics the flow pattern of a real diesel injection channel and automotive grade diesel was consequently selected as fluid. Understanding the dependence of cavitation development on flow characteristics in a three-dimensional way, through the determination of the localized void fraction of the multiphase flow, can lead to improvements in the knowledge of such a phenomenon that can guide the design of future fuel injection equipment

Numerical study of transonic buffet on supercritical airfoil with different boundary layer states

Accurate numerical simulations of flow over airfoils play an increasingly important role in the design of aircraft major components such as wings and turbo- machinery blades. These lifting devices often operate in demanding aerodynamic conditions for optimum performances, and may experience the presence of shock waves in operating conditions. Shocks may become unsteady under specific conditions, undergoing a large-scale, low-frequency periodic motion, which affects the entire flow-field. This unsteady phenomenon, named transonic buffet, is the subject of the present numerical investigation, with an oscillating shock over the suction side of the airfoil. In this study, a range of transonic Mach numbers and angles of incidence are considered, but the bulk of the analysis is carried out for flow conditions at free- stream Mach number M∞ = 0.7 and angle of incidence α = 7°, which show well established buffet. Large-eddy simulations (LES) with natural and forced transition carried out at chord Reynolds number Re = 3000000 clearly highlight the effects of the incoming boundary-layer state on the shock oscillations. While a laminar upstream boundary layer yields weak oscillations of the shock, a turbulent incoming boundary layer yields significant buffet. The LES database has been used to establish veracity (or not) of suggested buffet pathways, mainly based on the alleged existence of an acoustic feedback loop. This mechanism is actually found to consist of two separate patterns: coherent pressure disturbances convected from the shock to the trailing edge, and acoustic waves scattered at the trailing edge, feeding the shock motion. Additional exploration of the pressure side role in the unsteadiness reveals that is has but marginal effect on the phenomenon. Direct numerical simulations (DNS) at lower Reynolds number (Re = 300000) suggest a reversal in the previously observed trend. In this case, a laminar incoming boundary layer yields stronger buffet as compared to its turbulent counterpart, highlighting strong dependence of the buffet phenomenon on the Reynolds number when natural transition is considered. In order to passively control buffet, we consider devices whose design is similar to large-eddy break-up devices (LEBU), consisting of a thin circular-arc airfoil placed between shock and trailing edge, with the main goal of: i) breaking the eddies originating at the shock, responsible for the acoustic scattering at the trailing edge; ii) manipulating the acoustic field in the aft part of the airfoil. RANS simulations show potential for this kind of device for complete stabilization of buffet. On the other hand, DNS shows that the device is able to curtail the buffet, but not to eliminate it. Additional tests are needed in order to assess the effectiveness of the control device, whose practical impact might be very larg

A Fuzzy Inference System Approach for Evaluating the Feasibility of Product Remanufacture

In the recent past, efforts have been made in enhancing sustainable manufacturing aimed at protecting the environment and saving natural resources. Among the efforts that have been explored include strategies to ensure responsible end-of-life product management so as reduce the impact on the environment and achieve effective use of resources. Towards this end, reduce, reuse and recycle product disposal strategies have found a lot of consideration in manufacturing. Of the product reuse strategies, remanufacturing has been widely applied owing to its unique feature of rendering the remanufactured product as good as new. For remanufacturers, this strategy leads to provision of quality products comparable to new their new counterparts at a reduced cost. Remanufacturing also leads to a sustainable environment through energy and material savings, as well as minimized solid wastes. Remanufacturing however, poses challenges related to collection of the returns or cores, manufacturing process planning, resource allocation, warranty estimation and redistribution. These challenges are due to product and process complexities, customer requirements, and uncertainties associated with product take back and the remanufactured products’ market-base. Key among these challenges is the remanufacturing process which is complicated, labor intensive with varying process times. In most cases the routing of these processes is stochastic in nature, based on the condition of the returned product. There is also the negative perception among consumers that remanufactured products are less superior to new ones, which calls for the need to allocate preferably longer warranty periods for the remanufactured product to induce confidence in the consumer while at the same time keeping the warranty costs low. The objectives of this study were informed by challenges faced by a local remanufacturing firm. They include: (1) a detailed study of the current remanufacturing process of the firm’s products; (2) identification of bottlenecks in the process to make recommendations for improvement; (3) develop a decision support system for assessing product remanufacture; (4) assess warranty allocation options for remanufactured product reuse. The study revealed that there are bottlenecks in the current remanufacturing process and suggested an improvement to enhance efficiency. This bottlenecks include overutilization of some of the process centers such as the diagnostic testing and the after-repair testing centers which lead to the product spending more time in the system than necessary. To improve the system performance the capacities of the bottleneck centers were increased which yielded significant reduction in the time the product spends in the system. The key contribution of this dissertation is the development of a decision support system based on a bi-level fuzzy linguistic computing approach. This model integrates qualitative and quantitative product attributes in determining the remanufacturability of a product. The fuzzy-based model established remanufacturability metric, herein referred to as an index, is applied to assess the feasibility of remanufacturing two products that were used as a case study. A number of warranty scenarios are considered to ascertain the impact of different warranty periods on the cost of warranty. The results show that the additional warranty cost for product reuse is a function of the period of first use and the residual life of the produc