The art and architecture of mathematics education: a study in metaphors

This chapter presents the summary of a talk given at the Eighth European Summer University, held in Oslo in 2018. It attempts to show how art, literature, and history, can paint images of mathematics that are not only useful but relevant to learners as they can support their personal development as well as their appreciation of mathematics as a discipline. To achieve this goal, several metaphors about and of mathematics are explored

Guest Lecture – Foundation Engineering for Gravity Structures in the Northern North Sea

During the past 10 years, 15 gravity structures have been installed in the northern North Sea. As new gravity structures are being designed for installation on softer soils and at greater depths, they still pose a great challenge to soil mechanics and foundation engineering. Great improvements have been made during the 10-year period. This applies to soil investigations, in-situ measurements, undisturbed sampling, laboratory testing and design analyses. Compared to structures on land, offshore gravity structures are characterised by large foundation areas, the installation method, and the cyclic wave loading state. The paper reviews investigation methods, site and soil conditions, construction principles, instrumentation and installation. The main emphasis, however, is given to current foundation design practice and experiences from full scale measurements

Assuming Data Integrity and Empirical Evidence to The Contrary

Background: Not all respondents to surveys apply their minds or understand the posed questions, and as such provide answers which lack coherence, and this threatens the integrity of the research. Casual inspection and limited research of the 10-item Big Five Inventory (BFI-10), included in the dataset of the World Values Survey (WVS), suggested that random responses may be common. Objective: To specify the percentage of cases in the BRI-10 which include incoherent or contradictory responses and to test the extent to which the removal of these cases will improve the quality of the dataset. Method: The WVS data on the BFI-10, measuring the Big Five Personality (B5P), in South Africa (N=3 531), was used. Incoherent or contradictory responses were removed. Then the cases from the cleaned-up dataset were analysed for their theoretical validity. Results: Only 1 612 (45.7%) cases were identified as not including incoherent or contradictory responses. The cleaned-up data did not mirror the B5P- structure, as was envisaged. The test for common method bias was negative. Conclusion: In most cases the responses were incoherent. Cleaning up the data did not improve the psychometric properties of the BFI-10. This raises concerns about the quality of the WVS data, the BFI-10, and the universality of B5P-theory. Given these results, it would be unwise to use the BFI-10 in South Africa. Researchers are alerted to do a proper assessment of the psychometric properties of instruments before they use it, particularly in a cross-cultural setting

Stability Analysis of Plates and Shells

This special publication contains the papers presented at the special sessions honoring Dr. Manuel Stein during the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference held in Kissimmee, Florida, Apdl 7-10, 1997. This volume, and the SDM special sessions, are dedicated to the memory of Dr. Manuel Stein, a major pioneer in structural mechanics, plate and shell buckling, and composite structures. Many of the papers presented are the work of Manny's colleagues and co-workers and are a result, directly or indirectly, of his influence. Dr. Stein earned his Ph.D. in Engineering Mechanics from Virginia Polytechnic Institute and State University in 1958. He worked in the Structural Mechanics Branch at the NASA Langley Research Center from 1943 until 1989. Following his retirement, Dr. Stein continued his involvement with NASA as a Distinguished Research Associate

Technology 2004, Vol. 2

Proceedings from symposia of the Technology 2004 Conference, November 8-10, 1994, Washington, DC. Volume 2 features papers on computers and software, virtual reality simulation, environmental technology, video and imaging, medical technology and life sciences, robotics and artificial intelligence, and electronics

Effcient numerical methods for strongly anisotropic elliptic equations

In this paper, we study an effcient numerical scheme for a strongly anisotropic elliptic problem which arises in the modeling of ionospheric plasma dynamics. A small parameter \varepsilon induces the anisotropy of the problem, which leads to severe numerical diffculties for 0 < \varepsilo

Numerical and experimental modelling of microwave applicators

This thesis presents a time domain finite element method for the solution of microwave heating problems. This is the first time that this particular technique has been applied to microwave heating. It is found that the standard frequency domain finite element method is unsuitable for analysing multimode applicators containing food-like materials due to a severe ill-conditioning of the matrix equations. The field distribution in multimode applicators loaded with low loss materials is found to be very sensitive to small frequency changes. Several solutions at different frequencies are therefore required to characterise the behaviour of the loaded applicator. The time domain finite element method is capable of producing multiple solutions at different frequencies when used with Gaussian pulse excitation; it is therefore ideally suited to the analysis of multimode applicators. A brief survey of the methods available for the solution of the linear equations is provided. The performance of these techniques with both the frequency domain and time domain finite element methods is then studied. Single mode applicators are also analysed and it is found that the frequency domain method is superior in these cases. Comparisons are given between the calculated results and experimental data for both single mode and multimode systems. The importance of experimental verification being stressed. The choice of element type is an important consideration for the finite element method. Three basic types of element are considered; nodal, Whitney edge elements and linear edge elements. Comparisons of the errors with these elements show that Whitney elements produce a consistently lower error when post-processing is used to smooth the solution. The coupled thermal-electromagnetic problem is investigated with many difficulties being identified for the application to multimode cavity problems

Beauty Physics in Lattice Gauge Theory

We summarize the present status of lattice gauge theory computations of the leptonic decay constants $f_D$ and $f_B$. The various sources of systematic errors are explained in a manner easily understood by the non--expert. The results obtained by the different groups are then systematically compared. As a result, we derive estimates for $f_D$ and $f_B$ in the quenched approximation through an appropriate combination of the data available from the different groups. Since we account for a possible lattice spacing dependence, the final errors are quite large. However, it is now well known how these uncertainties can be reduced. For the decay constant of heavy--light pseudoscalar mesons with masses of 1-2~GeV, an interesting comparison of a full QCD result with the corresponding simulation in the quenched approximation can be done. Effects of sea quarks of mass $m_s$ are below the statistical accuracy of these simulations. Related quantities, like $B$--parameters, the spectrum of beauty--hadrons and the breaking of the QCD string are discussed briefly.Comment: 68 pages (all figures included), DESY 93-011 (WUB 94-04

Entwicklung und Anwendung von Hochleistungs-Software für Mantelkonvektionssimulationen

The Earth mantle convects on a global scale, coupling the stress field at every point to every other location at an instant. This way, any change in the buoyancy field has an immediate impact on the convection patterns worldwide. At the same time, mantle convection couples to processes at scales of a few kilometers or even a few hundred meters. Dynamic topography and the geoid are examples of such small-scale expressions of mantle convection. Also, the depth of phase transitions varies locally, with strong influences on the buoyancy, and thus the global stress field. In order to understand these processes dynamically it is essential to resolve the whole mantle at very high numerical resolutions. At the same time, geodynamicists are trying to answer new questions with their models, for example about the rheology of the mantle, which is most likely highly nonlinear. Also, due to the extremely long timescales we cannot observe past mantle states, which calls for simulations backwards in time. All these issues lead to an extreme demand in computing power. To cater to those needs, the physical models of the mantle have to be matched with efficient solvers and fast algorithms, such that we can efficiently exploit the enormous computing power of current and future high performance systems. Here, we first give an extensive overview over the physical models and introduce some numerical concepts to solve the equations. We present a new two-dimensional software as a testbed and elaborate on the implications of realistic mineralogic models for efficient mantle convection simulations. We find that phase transitions present a major challenge and suggest some procedures to incorporate them into mantle convection modeling. Then we give an introduction to the high-performance mantle convection prototype HHG, a multigrid-based software framework that scales to some of the fastest computers currently available. We adapt this framework to a spherical geometry and present first application examples to answer geodynamic questions. In particular, we show that a very thin and very weak asthenosphere is dynamically plausible and consistent with direct and indirect geological observations.Englische Übersetzung des Titels: Development and application of high performance software for mantle convection modelin