Title: Experiments from geometrical optics for teaching at primary and secondary school Author: Ing. Filip Hložek Department: Department of Physics Education Supervisor: RNDr. Jitka Houfková, Ph.D., Department of Physics Education Abstract: This work is focused on experiments in geometric optics. There is a research of textbooks for primary and secondary schools, that deals with this topic of physics. Most of the work is dedicated to the proposed manuals for experiments for the excercise of geometric optics in Practical Course in School Experiments I. The manuals were tested with several groups of students at Practical Course. The test results are briefly summarized here, including several adjustments of the manuals that has risen from it. The work also deals with mirror telescopes, aberrations, and the production of models of two telescopes - Newtonian and Cassegrain printed on a 3D printer. The models are then used in two experiments for Practical Course. Keywords: experiments, geometrical optics, optical instruments

In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction. In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view. <b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering / NR 20140805

In this thesis, we present a sensor model comprised of a geometrically nonlinear beam coupled with a nonlinear viscoelastic Pasternak foundation via a distributed system of compliant elements. The governing equations of the system are obtained. By posing an inverse problem, the model is used to simulate the estimation of coupled substrates' material (constitutive) parameters. In the inverse problem, beam deformations are considered as measured parameters, and therefore an eventual hardware implementation would require measurements of these quantities. Different case studies are simulated to assess the robustness and applicability of this sensor model.

<p> Various areas of studies on the natural and the prosthetic aortic valves are reviewed. </p> <p> A microtensile technique devised to investigate the inhomogeneous and anisotropic material properties of a porcine aortic valve's leaflets is described. Also, the theory and apparatus of a new stereophotogrammetric technique to define points in space by their Cartesian coordinates is introduced. The technique is used to investigate the local surface strains and curvatures of a porcine aortic valve's leaflets from 0 to 120 mm. Hg. in-vitro. </p> <p> It is found that the valve leaflets display marked inhomogeneity and anisotropy (orthotropy is assumed) in the elastic moduli and transition strains. For the non-coronary leaflet, the radial post-transition moduli vary from 42 to 215 gm/mm² with a mean of 111 gm/mm² (s.d. = 43 gm/mm²); and the radial transition strains vary from 30% to 70% with a mean of 58% (s.d. = 7%). Areas nearer the leaflet's coaptation edge tend to exhibit lower radial transition strains than the annulus edge. The central region of the leaflet is found to be the stiffest. For the same non-coronary leaflet, the circumferential post-transition moduli vary from 220 to 590 gm/mm² with a mean of 342 gm/mm² (s.d. = 118 gm/mm²); and the circumferential transition strains vary from 22% to 47% with a mean of 33% (s.d. = 3%). </p> <p> Inhomogeneity between leaflets is also observed; preliminary results seem to suggest that the non-coronary leaflet is the stiffest in the radial direction and the least stiff in the circumferential direction. In comparison, the right coronary leaflet exhibits the largest radial transition strains (~80% ) and the smallest circumferential transition strains (~25%). </p> <p> For the diastolic valve in-vitro, the circumferential strains are less than 10% at all pressures; therefore , this suggests pre-transition behaviour during diastole which is contrary to the general belief. Radial strains at diastole vary from 10% to well over 100% and show a definite tendency to increase from the sinus-annulus edge to the coaptation edge. The non-coronary leaflet is the least strained of the leaflets (10% to 60% at diastole). </p> <p> The determination of pre-or post-transition state at diastole is discussed and the implications of the results on stress analyses and trileaflet valve designs are noted. </p> / Thesis / Master of Engineering (ME)

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To better understand the ground motion and associated seismic hazard of earthquakes in the central and eastern United States (CEUS), this dissertation focuses on the source parameters and wave propagation characteristics of both tectonic earthquakes and induced earthquakes in the CEUS. The infrequent occurrence of significant earthquakes in the CEUS limits the necessary observations needed to understand earthquake processes and to reduce uncertainty in seismic-hazard maps. The well-recored aftershock sequence of the 2011 Mineral, Virginia, earthquake offers a rare opportunity to improve our understanding of earthquake processes and earthquake hazard in this populous region of the United States. Moreover, the rapid increase of seismicity in the CEUS since 2009 that has been linked to wastewater injection has raised concern regarding the potential hazard. In this dissertation, I first present a detailed study of the aftershock sequence of the 2011 Mw 5.7 Mineral, Virginia earthquake. It involves the hypocenter locations of ~3000 earthquakes, ~400 focal mechanism solutions, statistics of the aftershock sequence, and the Coulomb stress modeling that explains the triggering mechnanism of those aftershocks. Second, I examine the S-wave attenuation at critical short hypocentral distances (< 60 km) using the aftershock data. The observed S-wave amplitudes decay as a function of hypocenter distance R according to R^-1.3 - R^-1.5, which is substantially steeper than R^-1 for a homogeneous whole space. Finally, I propose and apply a stable multi-window coda spectral ratio method to estimate corner frequencies and Brune-type stress drops for the 2011 Mineral, Virginia mainshock and aftershocks, as well as induced earthquakes in Oklahoma. The goal of this comparative study is to find out whether or not there are systematical differences in source parameters between tectonic earthquakes and induced earthquakes in the CEUS. I found generally much higher stress drops for the Mineral, Virginia sequence. However, the stress drops for those induced earthquakes in Oklahoma exhibit large varation among individual earthquake sequences, with the large mainshocks having high stress drops (20-30 MPa, Brune-type) except for the 2011 Mw 5.6 Prague, Oklahoma earthquake. And spatially varying stress drops indicates strong fault heterogeneity, which in the case of induced earthquakes may be influenced by the injection of fluids into the subsurface. / Ph. D.

Computer aided design (CAD) software delivered by vendors is seldom complete. Customizing and/or developing new software is inevitable. A recent survey indicates that most companies purchase or write custom computer aided design software tailored to their specific needs. Design of such software requires the development of modeling tools for the creation of CAD geometry. This research investigates the capabilities of the proposed graphics standard, PHIGS plus, as a geometric modeling interface in CAD that off-loads many basic modeling functions to PHIGS. Specifically, how the B-spline modeling capabilities of PHIGS plus can be enhanced through the use of a new modeling interface prototype is examined. This prototype consists of a proposed graPHIGS modeling toolbox based entirely on PHIGS plus concepts. The prototype provides functionality to easily create B-spline curves and surface geometric entities based on data points and continuity constraints. Functionality is also included to easily perform modeling operations on B-spline surfaces such as intersection and trimming. / Master of Science

B-Spline curves and surfaces are being used throughout the aircraft industry for geometric modeling. Geometric models having accurate surface representations in the non-uniform B-Spline surface format can contain very large quantities of data. The computing power required by a CAD system for visualization and analysis is directly influenced by these large amounts of data. Accordingly, a method for reducing the amount of data in a geometric model while maintaining accuracy is needed to reduce the computing power necessary to visualize and analyze a design. This thesis describes the refinement and implementation of a data reduction algorithm for non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces. The topic of determining the significance of knots in non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is addressed. Also, a method for determining the order in which knots should be removed from non-uniform cubic B-Spline curves or non-uniform bi-cubic B-Spline surfaces during data reduction is presented. Finally, an algorithm for performing data reduction by removing knots from non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is presented. / Master of Science

This research studies the topic of geometric surface trimming. Most of the work that has been done on surface trimming refers to visual trimming, in which, unwanted portions of a surface patch are not removed but simply hidden. Geometric trimming actually removes the unwanted portion of a surface patch, and in the process, produces a new mathematical surface or set of surface patches. The new surface or surface patches produced should closely resemble the original surface which is being trimmed. However, since the entire procedure involves the creation of a new geometry, the resulting surface will not, in general, be identical with the remaining portion of the original one. For this reason, a means to measure the error in approximating the original surface is implemented and this error is minimized. Trimming criteria is provided by mapping the trimming curves from the two-dimensional parametric space on to the three-dimensional B-spline surface. Since visualization for this kind of procedure is vital a tool kit has been developed, using PHIGS, to model B-spline surfaces along with their approximate trimmed surfaces as well as the approximation error involved. / Master of Science

Novel methods of object recognition that form a bridge between today&rsquo / s local feature frameworks and previous decade&rsquo / s strong but deserted geometric invariance field are presented in this dissertation. The rationale behind this effort is to complement the lowered discriminative capacity of local features, by the invariant geometric descriptions. Similar to our predecessors, we first start with constrained cases and then extend the applicability of our methods to more general scenarios. Local features approach, on which our methods are established, is reviewed in three parts / namely, detectors, descriptors and the methods of object recognition that employ them. Next, a novel planar object recognition framework that lifts the requirement for exact appearance-based local feature matching is presented. This method enables matching of groups of features by utilizing both appearance information and group geometric descriptions. An under investigated area, scene logo recognition, is selected for real life application of this method. Finally, we present a novel method for three-dimensional (3D) object recognition, which utilizes well-known local features in a more efficient way without any reliance on partial or global planarity. Geometrically consistent local features, which form the crucial basis for object recognition, are identified using affine 3D geometric invariants. The utilization of 3D geometric invariants replaces the classical 2D affine transform estimation /verification step, and provides the ability to directly verify 3D geometric consistency. The accuracy and robustness of the proposed method in highly cluttered scenes with no prior segmentation or post 3D reconstruction requirements, are presented during the experiments.