A geometric approach to the embedding calculus knot invariants

In this thesis we consider two homotopy theoretic approaches to the study of spaces of knots: the theory of finite type invariants of Vassiliev and the embedding calculus of Goodwillie and Weiss, and address connections between them. Our results confirm that the knot invariants evn produced by the embedding calculus for (long) knots in a 3-manifold M are surjective for all n ≥ 1. On one hand, this solves certain remaining open cases of the connectivity estimates of Goodwillie and Klein, and on the other hand, confirms a part of the conjecture by Budney, Conant, Scannell and Sinha that for the case of classical knots evn are universal additive Vassiliev invariants over Z. There are two crucial ingredients for this result. Firstly, we study the so-called Taylor tower of the embedding calculus more generally for long knots in any manifold with dim(M) ≥ 3 and develop a geometric understanding of its layers (fibres between two consecutive spaces in the tower). In particular, we describe their first non-vanishing homotopy groups in terms of groups of decorated trees. Secondly, we give an explicit interpretation of evn when dim(M)=3 using capped grope cobordisms. These objects were introduced by Conant and Teichner in a geometric approach to the finite type theory, but turn out to exactly describe certain points in the layers. Our main theorem then states that the first possibly non-vanishing embedding calculus invariant of a knot which is grope cobordant to the unknot is precisely the equivalence class of the underlying decorated tree of the grope in the homotopy group of the layer. The surjectvity of evn onto the components of the Taylor tower follows from this immediately. As another corollary we obtain a sufficient condition for the mentioned conjecture to hold over a certain coefficient group A. Namely, it is enough that the spectral sequence for the homotopy groups of the Taylor tower, tensored with A, collapses along the diagonal. In particular, such a collapse result is known for A = Q, confirming that the embedding calculus invariants are universal rational additive Vassiliev invariants, and that they factor configuration space integrals through the Taylor tower. It also follows that they are universal over the p-adic integers in a range depending on the prime p, using recent results of Boavida de Brito and Horel. Moreover, the surjectivity of evn implies that any two group structures on the path components of the tower, which are compatible with the connected sum of knots, must agree. Finally, we also discuss the geometric approach to the finite type theory in terms of the Gusarov–Habiro filtration of the set of isotopy classes of knots in a 3-manifold. We extend some known techniques to prove that the associated graded quotients of this filtration are abelian groups, and study the map which relates these groups to certain graph complexes

Interdependence of fundamental and applied research in material science

Development of materials with desirable properties essentially depends on realization of interdependence: natural science ⇔ technical sciences. Taking this into account, in order to develop of new advanced materials it is essential to determine principles that characterize this interdependency. Therefore, in this article the principles of fundamental research and the importance of obtained results are considered and implemented in the field of technical realizations

Static-dynamic model for endpoint control used in Smederevo's BOF shop

This paper describes the computer model for BOF control that was in use at Smederevo, Serbia, during the period 1994-2006. The model was developed at the Institute of Metallurgy of the Smederevo Steelwork in mid-1994 and was motivated by the fact that the plant in Smederevo, by that time, had many years of experience in endpoint control using Intermediate Stop Practice (ISP). The vision for the model was to continuously improve and adapt to the working conditions of production through self-learning and adjustments. The model belongs to the well-known family of Static-Dynamic models (SDMs). It is aimed to reduce the "oxygen off-to-start tap" time and thus increase productivity and reduce production costs. The paper briefly describes the metallurgical software, operator operations and provides some information on the model's effectiveness

Effect of temperature on the physical changes and drying kinetics in plum (Prunus domestica L.) Požegača variety

In this study, drying kinetics of autochthonous variety Požegača plum was examined in a laboratory dryer at three temperatures. The whole plum fruits, together with the kernels were subjected to the drying process. The effect of drying has been examined at temperatures of 55, 60 and 75 °C, with a constant air velocity of 1.1 m s-1. The corresponding experimental results were tested using six nonlinear regression models. Coefficient of determination (R2), standard regression error (SSE), model correlation coeficient (Vy), as well as the maximum absolute error (ΔY) showed that the logaritmic model was in good agreement with the experimental data obtained. During drying of plums, the effective diffusivity was found to be between 5.6×10-9 for 55 °C and 8.9×10-9 m2 s-1 at 75 °C, respectively. The physical characteristics of fresh (length 39.64 mm and width 29.15 mm) and dried (length 37.52 mm and width 22.85 mm) plum fruit were determined. Finally, by chemical analysis, the contents of micro- and macro-elements (Fe, Mn, Cu, B and N, F, K, Ca, Mg and S) in the skin and flesh of the dried product, prunes, has been established

Mechanical-chemical synthesis Ba0.77Sr0.23TiO3

Barium-Strontium-Titanate Ba0.77Sr0.23TiO3 was prepared from starting materials BaCO3, SrCO3 and TiO2 through solid-state reactions. Mixtures of these oxides are mechanically activated in a high-energy planetary ball mill at different time intervals from 0 to 120 minutes. In order to obtain information on phase composition, crystal structure was determent by X-ray diffraction. It was observed that after 80 minutes in process synthesis Ba0.77Sr0.23TiO3 started Thermal analyzes were performed in order to determine the characteristic temperatures of the processes that occur in the solid phase. Particle size distribution, together with electron microscopy scanning has given us very useful information about the morphology of the powder

Rhinoplasty: The Nasal Bones - Anatomy and Analysis

Background: The analysis of nasal anatomy, and especially the nasal bones including the osseocartilaginous vault, is significant for functional and aesthetic reasons. Objectives: The objective was to understand the anatomy of the nasal bones by establishing new descriptions, terms, and definitions because the existing parameters were insufficient. Adequate terminology was employed to harmonize the anthropometric and clinical measurements. Methods: A two-part harvest technique consisting of resecting the specimen and then creating a replica of the skull was performed on 44 cadavers to obtain specific measurements. Results: The nasal bones have an irregular, variable shape, and three distinct angles can be found along the dorsal profile line beginning with the nasion angle (NA), the dorsal profile angulation (DPA) and the kyphion angulation (KA). In 12% of cases, the caudal portion of the nasal bones was straight and without angulation resulting in a "V-shape" configuration. In 88% of cases, the caudal portion of the bone was angulated, which resulted in an "S-shape" nasal bone configuration. The intervening cephalic bone, nasion to sellion (N-S), represents the radix while the caudal bone, sellion to r (S-R), represents the bony dorsum. Conclusions: By standardizing and measuring existing nasal landmarks and understanding the different anatomic configurations of the nasal bones, rhinoplasty surgeons can better plan their operations within the radix and bony and osseocartilaginous vaults

The Removal of Ni2+ and Cd2+ -ions onto Synthetic Mineral Based Composite Functionalized by Polyethylenimine

This study presents the synthesis of porous cordierite- based ceramics and its surface activation by polyethylenimine/nano-CeO2 for the heavy metal removal. The synthesis was carried out by the addition of following powders: MgO, Al2O3, and SiO2 in 2:2:5 molar ratios, respectively. The oxide(s) mixture was further processed in two sequential stages: i) ball milled in the ethanol for 40 minutes and palletized under the pressure of 3 t/cm2, as a pre-sintering process, and ii) the pallets were further sintered for 2h in the air atmosphere at 1350 oC, under a heating rate of 20 oC/min. The sintered mineral composite was crashed and sieved, and mixed with 20 wt % of nanocellulose, as a pore forming agent. Nanocellulose mixture was pressed into pallets under 5 t/cm2 and sintered at 700 oC, under a heating rate of 5 oC/ min. The obtained synthetic cordierite was further tested as the adsorbent activated by polyethylenimine/ nano-CeO2 for the removal of Ni2+ and Cd2+ -ions. The adsorption isotherms, kinetics models, and thermodynamic parameters were also analyzed, manifesting that the adsorption is a spontaneous and endothermic process. The phase composition of the pristine and activated cordierite was analyzed by the X-ray diffraction method (XRD), Fourier transformation infrared (FTIR) spectroscopy and scanning electron microscopy (SEM). This work has shed light on the mechanism of heavy metals removal from the aquatic medium using the novel hybrid (nano)synthesized material

Structure and enhanced antimicrobial activity of mechanically activated nano TiO2

Titanium dioxide is a photocatalyst, known not only for its ability to oxidize organic contaminants, but also for its antimicrobial properties. In this article, significant enhancement of the antimicrobial activity of TiO2 (up to 32 times) was demonstrated after its activation by ball milling. The antimicrobial activity was analyzed for one fungal and 13 bacterial ATCC strains using the microdilution method and recording the minimum inhibitory concentration (MIC) values. In order to further investigate the correlation between the mechanical activation of TiO2 and its antimicrobial activity, the structure, morphology and phase composition of the material were studied by means of Electron Microscopy, X-ray diffraction and nitrogen adsorption-desorption measurements. UV-Vis diffuse reflectance spectra were recorded and the Kubelka-Munk function was applied to convert reflectance into the equivalent band gap energy (E-g) and, consequently, to investigate changes in the E-g value. X-ray photoelectron spectroscopy was used to analyze the influence of mechanical activation on the Ti 2p and O 1s spectra. The presented results are expected to enable the development of more sustainable and effective advanced TiO2-based materials with antimicrobial properties that could be used in numerous green technology applications

High-fidelity 3D microstructural characterization of ZrB2 during hot-pressing (Invited)

Standard ultra-high temperature ceramic (UHTC) manufacturing results in components with large differences in properties due to variability in microstructural “critical flaw” distributions. Critical flaws can be any irregularity in a component, such as a secondary phase, cracks, pores, etc. This is problematic when designing reproducible UHTC components. The goal of this project is to understand how these critical flaws evolve during hot pressing of ZrB2 (a UHTC) by examining them in 3D. This study incorporates 3D imaging such as (i) preliminary in-situ high-temperature pressureless sintering X-ray µ-CT, (ii) ex-situ X-ray µ-CT, and (iii) 3D electron imaging and backscattered diffraction data collected at different stages of densification. 3D microstructure statistics along with unique observations of individual pore and secondary phase evolution will be presented. This data is brought together to give a holistic view of the densification of ZrB2 during hot pressing at multiple length scales. This data will be incorporated into a process-structure-property (PSP) database for statistical modeling to reduce uncertainty during ZrB2 processing

Preparation of cordierite-based adsorbents for water purification

In this study, porous cordierite-based ceramics was synthesized. In the first step, MgO, Al2O3, and SiO2 (all Aldrich, p.a.) were used. MgO and Al2O3 powders were calcined at 1000 oC for 2 h, in order to avoid hydroxides. They were mixed in 2:2:5 molar ratio, in order to form cordierite, Mg2Al4Si5O18. Ethanol was added to the mixture, and then milled in a Fritsch Pulverisette planetary mill, with 300 rpm, in air atmosfere. Times of activation were 0, 10, 40, and 80 min, while balls and vessels were made from ZrO2, and powder to balls mass ratio was 40:1. After milling, powders were dried, and then pressed under 3 t/cm2. Pallets with 8 mm radius were sintered in air at 1350 oC, for 2 h, heating rate was 20 oC/min. Sintered samples were crashed and sieved. In the secons step, the as-prepared cordierite was mixed with 20 wt.% yeast (0.1 g yeast + 0.4 g cordierite per sample). The other mixture was with 20 wt.% nanocellulose (0.1 g NC + 0.4 g cordierite per sample). Both mixtures were pressed into pallets under 5 t/cm2 and sintered at 700 oC, with 5 oC/min heating rate, in air atmosfere. During the second sintering regime, porous cordierite-based ceramics was obtained. The phase composition of the sintered samples as well as microstructures was analyzed by the means of X-ray diffraction method and SEM. Cordierite was the most abundant phase in all sintered samples. It was observed that addition of different pore-forming agent resulted in significantly different microstructures