Lecture notes on probability, statistics, and experimental errors; an elementary summary for students of experimental science.

Mode of access: Internet.

Ausgleichungsrechnung nach der methode der kleinsten quadrate

Mode of access: Internet.

Die Theorie der Beobachtungsfehler und die Methode der kleinsten Quadrate, mit ihrer Anwendung auf die Geodäsie und die Wassermessungen.

Mode of access: Internet.

Ueber die Genauigkeit logarithmischer Berechnungen / von dr. Hans Stadthagen.

Mode of access: Internet.

The theory of errors and method of least squares,

Mode of access: Internet.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Analysis of torque and speed ripple producing non-idealities of frequency converters in electric drives

Electric motors driven by adjustable-frequency converters may produce periodic excitation forces that can cause torque and speed ripple. Interaction with the driven mechanical system may cause undesirable vibrations that affect the system performance and lifetime. Direct drives in sensitive applications, such as elevators or paper machines, emphasize the importance of smooth torque production. This thesis analyses the non-idealities of frequencyconverters that produce speed and torque ripple in electric drives. The origin of low order harmonics in speed and torque is examined. It is shown how different current measurement error types affect the torque. As the application environment, direct torque control (DTC) method is applied to permanent magnet synchronous machines (PMSM). A simulation model to analyse the effect of the frequency converter non-idealities on the performance of the electric drives is created. Themodel enables to identify potential problems causing torque vibrations and possibly damaging oscillations in electrically driven machine systems. The model is capable of coupling with separate simulation software of complex mechanical loads. Furthermore, the simulation model of the frequency converter's control algorithm can be applied to control a real frequency converter. A commercial frequencyconverter with standard software, a permanent magnet axial flux synchronous motor and a DC motor as the load are used to detect the effect of current measurement errors on load torque. A method to reduce the speed and torque ripple by compensating the current measurement errors is introduced. The method is based on analysing the amplitude of a selected harmonic component of speed as a function oftime and selecting a suitable compensation alternative for the current error. The speed can be either measured or estimated, so the compensation method is applicable also for speed sensorless drives. The proposed compensation method is tested with a laboratory drive, which consists of commercial frequency converter hardware with self-made software and a prototype PMSM. The speed and torque rippleof the test drive are reduced by applying the compensation method. In addition to the direct torque controlled PMSM drives, the compensation method can also beapplied to other motor types and control methods.

Modèles de flammelette en combustion turbulente avec extinction et réallumage : étude asymptotique et numérique, estimation d’erreur a posteriori et modélisation adaptative

On s’intéresse ici aux erreurs de modélisation liées à l’usage de modèles de flammelette sous-maille en combustion turbulente non prémélangée. Le but de cette thèse est de développer une stratégie d’estimation d’erreur a posteriori pour déterminer le meilleur modèle parmi une hiérarchie, à un coût numérique similaire à l’utilisation de ces mêmes modèles. Dans un premier temps, une stratégie faisant appel à un estimateur basé sur les résidus pondérés est développée et testée sur un système d’équations d’advection-diffusion-réaction. Dans un deuxième temps, on teste la méthodologie d’estimation d’erreur sur un autre système d’équations, où des effets d’extinction et de réallumage sont ajoutés. Lorsqu’il n’y a pas d’advection, une analyse asymptotique rigoureuse montre l’existence de plusieurs régimes de combustion déjà observés dans les simulations numériques. Nous obtenons une approximation des paramètres de réallumage et d’extinction avec la courbe en «S», un graphe de la température maximale de la flamme en fonction du nombre de Damköhler, composée de trois branches et d’une double courbure. En ajoutant des effets advectifs, on obtient également une courbe en «S» correspondant aux régimes de combustion déjà identifiés. Nous comparons les erreurs de modélisation liées aux approximations asymptotiques dans les deux régimes stables et établissons une nouvelle hiérarchie des modèles en fonction du régime de combustion. Ces erreurs sont comparées aux estimations données par la stratégie d’estimation d’erreur. Si un seul régime stable de combustion existe, l’estimateur d’erreur l’identifie correctement ; si plus d’un régime est possible, on obtient une fac˛on systématique de choisir un régime. Pour les régimes où plus d’un modèle est approprié, la hiérarchie prédite par l’estimateur est correcte.

Efficient evaluation of highly oscillatory acoustic scattering surface integrals

We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Numerical and experimental analysis of natural convection in a cavity with flush mounted heat sources on a side wall

This work considers a problem of interest in several technological applications such as the thermal control of electronic equipment. It is also important to study the heat transfer performance of these components under off-normal conditions, such as during failure of cooling fans. The effect of natural convection on the flow and heat transfer in a cavity with two flush mounted heat sources on the left vertical wall, simulating electronic components, is studied numerically and experimentally. The influence of the power distribution, spacing between the heat sources and cavity aspect ratio have been investigated. An analysis of the average Nusselt number of the two heat sources was performed to investigate the behavior of the heat transfer coefficients. The results obtained numerically and experimentally, after an error analysis, showed a good agreement.

Analysis of diametrical wear of grinding wheel and roundness errors in the machining of steel VC 131

Due to the high industrial competitiveness, the rigorous laws of environmental protection, the necessary reduction of costs, the mechanical industry sees itself forced to worry more and more with the refinement of your processes and products. In this context, can be mentioned the need to eliminate the roundness errors that appear after the grinding process. This work has the objective of verifying if optimized nozzles for the application of cutting fluid in the grinding process can minimize the formation of the roundness errors and the diametrical wear of grinding wheel in the machining of the steel VC 131 with 60 HRc, when compared to the conventional nozzles. These nozzles were analyzed using two types of grinding wheels and two different cutting fluids. Was verified that the nozzle of 3mm of diameter, integral oil and the CBN grinding wheel, were the best options to obtain smaller roundness errors and the lowest diametrical wears of grinding wheels.

O ensino do conceito de função e conceitos relacionados a partir da resolução de problemas

Pós-graduação em Educação Matemática - IGCE

Análise de resoluções de problemas de cálculo diferencial em um ambiente de interação escrita

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)