At the European Institute for Nuclear Research, CERN, a new electron cooler is being commissioned for the Antiproton Decelerator experiment. In this experiment protons are shot into a block of metal, which creates anti protons. These anti protons will thereafter be focused into a particle beam, a process done in several steps. One of these steps is with an electron cooler. This cooler shoots electrons into the ion-beam path. These electrons then collide with the beam particles, and momentum is transferred from the beam particles to the electrons. The electrons are then steered away from the beam path, into an electron collector. In the beam path drift of the cooler, where the anti protons and electrons meet, a normal conducting solenoid magnet is used to orient the electron path. This magnet comes with strict requirements on field quality, such that the transversal magnetic field must be less than 10 ppm of the lateral field. In this thesis a metrological characterization of a prototype measurement system for solenoidal magnets is presented. Instead of winding measurement coils with wire, they are instead printed on a circuit board over ten layers. Of particular interest was the magnet alignment with respect to the beam aperture, so that the magnetic solenoid axis is in line with the aperture central axis. For this purpose, a mathematical model for solenoidal magnetic fields has been constructed. This model can be used to quantify the sensitivity of the measurement system for an unaligned magnet. Furthermore, some test measurements are presented, along with some simulation campaigns to further characterize the problem. A specific method where the magnetic field peaks are used to measure the alignment is evaluated. / På den Europeiska organisationen för Kärnforskning pågår just nu ett uppgraderingsarbete för AD-experimentet, (fullständigt namn på engelska: Antiproton Decelerator). I detta experiment skjuts protoner in i ett block med metall, vilket skapar antiprotoner. Dessa antiprotoner ska sedan fokuseras till en partikelstråle, vilket görs i en rad olika steg, däribland med vad som kallas för en elektronkylare. Elektronkylaren skjuter in elektroner i partikelstrålens väg, vilka kolliderar med antiprotonerna och på detta sätt reducerar temperaturen i partikelstrålen genom att överföra momentum till elektronerna. Elektronerna leds sedan bort ur strålens väg, in i en elektronsamlare.I strålaperturen, där elektronerna och antiprotonerna möts, används en normalledande solenoidmagnet för att styra elektronerna. Dennasolenoidmagnet kommer med strikta krav på den magnetiska fältprofilen,varför känslig mätutrustning krävs. Det magnetiska fältet måste vara av solenoid karaktär, så att det transversella fältet är mindre än 10 ppm av det longitudinella. I denna rapport presenteras en metrologisk karaktärisering av en ny prototyp på mätsystem för solenoidmagneter. Istället för att linda spolar som en mäter fältkvalitén med, så har dessa istället tryckts på ett kretskort över tio lager. Av speciellt intresse var att mäta magnetens justering, så att solenoidaxeln ligger i linje med strålaperturen. För detta ändamål så har en matematisk modell för solenoida magnetfält konstruerats. Denna modell kan användas för att kvantifiera känsligheten hos mätsystemet för en ojusterad solenoidmagnet. Vidare så presenteras testmätningar med systemet, samt en rad simulationer för att vidare karaktärisera problemet. En specifik mätmetodik där magnetfältstopparna används för att undersöka magnetens justering utvärderas.

Biofilms are communities of microorganisms that can form in the human microbiome and on medical implants among other locations. These communities provide greater protection for their member cells resulting in an increase in resistance to antibiotic treatment and persistent infections. There are several factors that may contribute to antibiotic resistance of biofilms. These studies were done concurrently with biological experiments to test the hypothesis that dense, rigid structures within the biofilm may be an additional mechanism for protection from antibiotics. A computational tool and workflow was developed to analyze bead movement for the characterization of biofilm biomaterial properties including rigidity. With this tool, the analysis revealed that the amyloid, curli, confers rigidity in biofilms, thereby restricting bead movement. Greater movement of the beads is seen in biofilms lacking curli and biofilms that produced complex heterogeneous rigid structures. A new model was also developed that uses microscopy imaging data to simulate diffusion-reaction of antibiotics within heterogeneous biofilms. This model was used to investigate the effect of the dense, rigid structures on antibiotic treatment through test simulations and simulations using biological imaging data. These studies reveal various properties about the dense, rigid structures that confer protection. / Mathematics

Yes / This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitrary set of boundary conditions. Both the boundary conditions which are defined as curves in 3-space and the spine of the corresponding PDE are utilized as interactive design tools for creating and manipulating geometry intuitively. In order to facilitate interactive design in real time, a compact analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme even in the case of general boundary conditions satisfies exactly the boundary conditions where the resulting surface has an closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples.

Yes / This paper extends the PDE method of surface generation. The governing partial differential equation is generalised to sixth order to increase its flexibility. The PDE is solved analytically, even in the case of general boundary conditions, making the method fast. The boundary conditions, which control the surface shape, are specified interactively, allowing intuitive manipulation of generic shapes. A compact user interface is presented which makes use of direct manipulation and other techniques for 3D interaction.

As a perturbation method, averaging is a mathematical tool for dynamic analysis of time-periodic and space-periodic dynamical systems, including those governed by partial differential equations. The control design procedure presented in this work uses averaging techniques, the well-developed linear control strategies, and finite element methods. The controller is designed based on the linear averaged dynamics of a time- or space-periodic system. The controller is then used for trajectory tracking or stabilization of the periodic system. The applicability and performance of the suggested method depend on different physical parameters of the periodic system and the control parameters of the controller. The effects of these parameters are discussed in this work. Numerical simulations show acceptable performance of the proposed control design strategy for two linear and nonlinear time- and space-periodic systems, namely, the one-dimensional heat equation and the Chafee-Infante equation with periodic coefficients. / M.S. / Dynamic analysis and control of dynamical systems with varying parameters is a challenging task. It is always of great help if one can perform the analyses for an approximate system with constant parameters and use the results to study and control the original system with varying parameters. Averaging is a mathematical tool that is used to approximate a system with periodic parameters with a ``simpler'' system with constant parameters. In this research averaging is used for design of controllers for systems with periodic parameters. First, an approximate system with constant parameters, called the averaged system, is determined. The averaged system is used for design of a controller which can be then be used for the original system with periodic parameters.

<p>The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.</p>

The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.

Orientador: Djairo Guedes de Figueiredo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T23:11:17Z (GMT). No. of bitstreams: 1 Monteiro_Evandro_D.pdf: 681089 bytes, checksum: 5ec4729a2d7b386329193adf424f6b42 (MD5) Previous issue date: 2011 / Resumo: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: The complete abstract is available with the full electronic digital thesis or dissertations / Doutorado / Matematica / Doutor em Matemática

Orientador: Francisco Odair Vieira de Paiva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T21:33:51Z (GMT). No. of bitstreams: 1 Cardoso_JoseAndersonValenca_D.pdf: 1655484 bytes, checksum: 6e4f6872240f3317db759e94789f5d34 (MD5) Previous issue date: 2012 / Resumo: Neste trabalho consideramos uma classe de Sistemas Elípticos Hamiltonianos. Esta classe de sistemas surge como modelo natural em áreas como Física e Biologia. Estudamos casos que envolvem crescimento crítico, arbitrário e crítico perturbado e analisamos questões relacionadas a existência, multiplicidade e propriedades de soluções. Os resultados são obtidos com o uso de métodos variacionais, a exemplo dos teoremas de min-max, aliados as propriedades das funções com simetria radial e ao princípio de concentração de compacidade / Abstract: In this work, we consider a class of Hamiltonian Elliptic Systems. This class of systems arise as a natural model in many areas such as Physics and Biology. We studied cases involving critical growth, arbitrary growth and perturbed critical growth and we also investigated questions related to the existence, multiplicity and properties of solutions. The results are obtained by using a variational approach, for instance, min-max theorems, combined with properties of radially symmetric functions and the concentration-compactness principle / Doutorado / Matematica / Doutor em Matemática

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