Photodynamic therapy (PDT) is a multimodality cancer treatment available for the palliation or eradication of systemic and cutaneous malignancies. In this thesis, the application of PDT is for the treatment of non-melanoma skin cancer (NMSC). While PDT has a well-documented track record, there are, at this time no significant indicators to suggest the superiority of one treatment regime over the next. The motivation for this work is to provide additional evidence pertaining to PDT treatment variables, and to assist in optimising PDT treatment regimes. One such variable is the treatment light dose. Determining the light dose more accurately would assist in optimising treatment schedules. Furthermore, choice of photosensitiser pro-drug type and application times still lack an evidence base. To address issues concerning treatment parameters, fluorescence spectroscopy – a valuable optical diagnostic technique – was used. Monitoring the in vivo PpIX fluorescence and photobleaching during PDT was employed to provide information pertaining to the progression of treatment. This was demonstrated by performing a clinical study at the Photobiology Unit, Ninewells Hospital and Medical School, Dundee. Two different photosensitiser pro-drugs – either 5-aminolaevulinic acid (ALA) or its methyl ester (MAL) – were investigated and based on the fluorescence and pain data recorded both may be equally suitable for topical PDT. During PDT, surface fluorescence is observed to diminish with time – due to photobleaching – although cancerous cells may continue to be destroyed deep down in the tissue. Therefore, it is difficult to ascertain what is happening at depth in the tumour. This raised the questions; How long after surface PpIX fluorescence has diminished is the PDT treatment still effective and to what depths below the surface is effective treatment provided? In order to address these important questions, a three-dimensional (3D) Monte Carlo radiation transfer (MCRT) model was used to compute the light dose and the ¹O₂ production within a tumour, and the PpIX fluorescence emission from the tumour. An implicit dosimetry approach based on a single parameter – fluorescence photobleaching – was used in order to determine the ¹O₂ generation, which is assumed to be related to tissue damage. Findings from our model recommended administering a larger treatment light dose, advocating an increase in the treatment time after surface PpIX fluorescence has diminished. This increase may ultimately assist in optimising PDT treatment regimes, particularly at depth within tumours.

Ces travaux de thèse sont consacrés à l'élaboration de revêtement réfléchissant et diffusant par projection plasma d'arc soufflé. Par la sélection des paramètres opératoires et le contrôle de la microstructure des revêtements élaborés, la première partie de cette étude présente la mise en forme d'un revêtement bicouche (micro/nano-structuré) d'alumine possédant une réflectance supérieure à 90% sur la gamme UV-Visible. Le transfert nécessaire à la démonstration pour démontrer la faisabilité d'élaboration de pièces de plus grandes dimensions (0.25 m2) a été entrepris. Dans une seconde partie et à partir de l'exploration de la microstructure des revêtements et de leur physicochimie, l'amélioration de la réflectance dans le proche UV par la couche nanostructurée est explicitée d'une part par la nature de la phase cristallographique moins absorbante et d'autre part par la présence en nombre de pores de faibles dimensions. De plus, la caractérisation des propriétés radiatives des revêtements par inversion de l'Equation du Transfert Radiatif a permis d'obtenir des éléments de compréhension des phénomènes d'interaction rayonnement/matière. Enfin, une dernière partie a pour objectif de mettre en place les différents éléments nécessaires à la prédiction des propriétés optiques de revêtements mis en forme par projection plasma. Un modèle tridimensionnel a été proposé pour représenter numériquement la structure de chacune des couches micro- et nanostructurée à partir des analyses microstructurales. Le code de résolution des équations de Maxwell par méthode FDTD (Finite Difference Time Domain) a été validé et de premières simulations ont été réalisées / This study deals with the manufacturing of reflecting and scattering coatings by plasma spraying process. By the selection of operating parameters and the control of the coatings microstructure, the first part of this work presents the elaboration of a micro/nanostructured bilayer material in alumina with a reflectance up to 90 % in the near UV-Visible range of wavelength. The feasibility of larger pieces (0.25m2) is demonstrated and the different characterizations for inserting the material in the Laser MegaJoule are performed. In a second part, from characterizations of the microstructure (by SEM, Hg Porosimetry, USAXS) and the chemical composition (DRX, X fluorescence), the improvement of the reflectance in the near-UV thanks to the nanostructured layer is explained, on the one hand, by the less absorbing crystallographic phase and, on the other hand, by the smaller and numerous pores. Moreover, the characterization of the radiation properties by the Radiation Transfer Equation inversion brings new elements for understanding the phenomena during radiation/porous media interaction and to determine the spatial repartition of the scattering radiation. The aim of the last part is to set up the different tools which are necessary to compute simulations of plasma-sprayed coatings optical behavior. From the microstructure analysis, a tridimensional numerical representation of each layer is suggested. The resolution of Maxwell equations is performed by FDTD (Finite Difference Time Domain) method. The model is validated and some first simulations are realized

The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too. In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigated. / Die Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert. Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren.

Microalgae cultivation has received much research attention in recent decades due to its high photosynthetic productivity and ability to produce biofuel feedstocks as well as high value compounds for the health food, cosmetics, and agriculture markets. Microalgae are conventionally grown in open pond raceways or closed photobioreactors. Due to the high water contents of these cultivation systems, they require large energy inputs for pumping and mixing the dilute culture, as well as concentrating and dewatering the resultant biomass. The energy required to operate these systems is generally greater than the energy contained in the resultant biomass, which precludes their use in sustainable biofuel production. To address this challenge, we designed a novel photobioreactor inspired by higher plants. In this synthetic leaf system, a modified transpiration mechanism is used which delivers water and nutrients to photosynthetic cells that grow as a biofilm on a porous, wicking substrate. Nutrient medium flow through the reactor is driven by evaporation, thereby eliminating the need for a pump. This dissertation outlines the design, construction, operation, and modeling of such a synthetic leaf system for energy positive biofuel production. First, a scaled down synthetic leaf reactor was operated alongside a conventional stirred tank photobioreactor. It was demonstrated that the synthetic leaf system required only 4% the working water volume as the conventional reactor, and showed growth rates as high as four times that of the conventional reactor. However, inefficiencies in the synthetic leaf system were identified and attributed to light and nutrient limitation of growth in the biofilm. To address these issues, a modeling study was performed with the aim of balancing the fluxes of photons and nutrients in the synthetic leaf environment. The vascular nutrient medium transport system was also modeled, enabling calculation of nutrient delivery rates as a function of environmental parameters and material properties of the porous membrane. These models were validated using an experimental setup in which the nutrient delivery rate, growth rate, and photosynthetic yield were measured for single synthetic leaves. The synthetic leaf system was shown to be competitive with existing technologies in terms of biomass productivity, while requiring zero energy for nutrient and gas delivery to the microorganisms. Future studies should focus on utilizing the synthetic leaf system for passive harvesting of secreted products in addition to passive nutrient delivery. / text

The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too. In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigated. / Die Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert. Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren.

No description available.

Hlavním cílem práce je studium radiačního přenosu energie v termálním plazmatu pomocí aproximační metody sférických harmonických funkcí (PN-aproximace). Práce má teoretický charakter. Pozornost je věnována především P1-aproximaci. Spektrální závislost absorpčních koeficientů byla zpracována pomocí multigroup aproximace. Byl vytvořen výpočetní program pro výpočet radiačních charakteristik v izotermickém válcovém plazmatu a ve válcovém plazmatu s daným teplotním profilem, a vypočteny radiační charakteristiky pro plazma vzduchu a směsí SF6 a PTFE. Získané výsledky umožňují zahrnout radiační ztráty energie do celkové energetické bilance plazmatu elektrického oblouku. Jsou využívány v matematických modelech elektrického oblouku, které vytváří naši spolupracovníci z Ústavu fyziky plazmatu AV ČR v Praze a také ze zahraničních pracovišť (ABB Corporate Research ve Švýcarsku a Siemens AG Corporate Technology v Německu).

This thesis is devoted to improve our knowledge on the theory of polarized line formation in a magneto-turbulent medium, and in a scattering dominated magnetized medium, where partial redistribution (PRD) effects become important. Thus the thesis consists of two parts. In the first part we carry out a detailed investigation on the effect of random magnetic fields on Zeeman line radiative transfer. In the second part we develop the theory of polarized line formation in the presence of arbitrary magnetic fields and with PRD. We present numerical methods of solution of the relevant transfer equation in both part-I and II. In Chapter I we give a general introduction, that describes the basic physical concepts required in both parts of the thesis. Chapters 2-6 deal with the part-I, namely stochastic polarized Zeeman line formation. Chapters 7-10 deal with part –II, namely the theory and numerics of polarized line formation in scattering media. Chapter II is devoted to the future outlook on the problems described in part-I and II of the thesis. Appendices are devoted to additional mathematical details. Part-I of the Thesis: Stochastic polarized line formation in magneto-turbulent media Magneto-convection on the Sun has a size spectrum that spans several orders of magnitudes and hence develops turbulent elements or eddies the sizes of which are much smaller than the spatial resolution of current spectro-polarimeters (about 0.2 arcsec or 150km at the photospheric level). We were thus strongly motivated to consider the Zeeman effect in a medium where the magnetic field is random with characteristic scales of variation comparable to the radiative transfer characteristic scales. In Chapter 2, we consider the micro-turbulent limit and study the mean zeeman absorption matrix in detail. The micro-turbulent limit refers to the case when the scales of fluctuations of the random field are much smaller than the photon mean free paths associated to the line formation. The ‘mean’ absorption and anomalous dispersion coefficients are calculated for random fields with a non-Zero mean value - isotropic or anisotropic Gaussian distributions that are azimuthally invariant about the direction of the mean field. The averaging method is described in detail, and fairly explicit expressions for the mean coefficients are established. A detailed numerical investigation of the mean coefficients illustrates two simple effects of the magnetic field fluctuations: (i) broadening of the components by fluctuations of the field strength, leaving the π-components unchanged, and (ii) averaging over the angular dependence of the π and components. Angular averaging can modify the frequency profiles of the mean coefficients quite drastically, namely, the appearance of an unpolarized central component in the diagonal absorption coefficient, even when the mean field is in the direction of the line-of-sight. For isotropic fluctuations, the mean coefficients can be expressed in terms of generalized Voigt and Faraday-Voigt functions, which are related to the derivatives of the Voigt and Faraday-Voigt functions. In chapter 3, we study these functions in detail. Simple recurrence relations are established and used for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are also derived. In Chapter 4, we consider the Zeeman effect from a magnetic field which has a finite correlation length(meso-turbulence) that can be varied from zero to infinity and thus made comparable to the photon mean free-path. The random vector magnetic field B is modeled by a Kubo-Anderson process – a piecewise constant Markov process characterized by a correlation length and a probability distribution function(PDF) for the random values of the magnetic field. The micro- and macro-turbulent limits are recovered when the correlation length goes to zero or infinity respectively. Mean values and rms fluctuations around the mean values are calculated numerically for a random magnetic field with isotropic Gaussian fluctuations. The effects of a finite correlation length are discussed in detail. The rms fluctuations of the Stokes parameters are shown to be very sensitive to the correlation length of the magnetic field. It is suggested to use them as a diagnostic tools to determine the scale of unresolved features in the solar atmosphere. In Chapter 5, using statistical approach, we analyze the effects of random magnetic fields on Stokes line profiles. We consider the micro and macro-turbulent regimes, which provide bounds for more general random fields with finite scales of variations. The mean Stokes parameters are obtained in the micro-turbulent regime, by first averaging the Zeeman absorption matrix Φ over the PDF P(B) of the magnetic field and then solving the concerned radiative transfer equation. In the macro-turbulent regime, the mean solution is obtained by averaging the emergent solution over P(B). In this chapter, we consider the same Gaussian PDFs that are used to construct (Φ) in chapter 2. Numerical simulations of magneto-convection and analysis of solar magnetograms provide the empirical PDF for the magnetic field line-of-sight component on the solar atmosphere. In Chapter 6, we explore the effects of different kinds of PDFs on Zeeman line formation. We again consider the limits of micro and macro-turbulence. The types of PDFs considered are: (a) Voigt function and stretched exponential type PDFs for fields with fixed direction but fluctuating strength. (b) Cylindrically symmetrical power law for the angular distribution of magnetic fields with given field strength. (c) Composite PDFs accounting for randomness in both strength and direction obtained by combining a Voigt function or a stretched exponential with an angular power law. The composite PDF proposed has an angular distribution peaked about the vertical direction for strong fields and is nearly isotropically distributed for weak fields, which could mimic solar surface random fields. We also describe how the averaging technique for a normal Zeeman triplet may be generalized to the more common case of anomalous Zeeman splitting patterns. Part-II of the Thesis: Polarized line formation in scattering media-Theory and numerical methods Many of the strongest and most conspicuous lines in the Second Solar Spectrum are strong lines that are formed rather high, often in the chromosphere above the temperature minimum. From the standard, unpolarized and non-magnetic line-formation theory such lines are known to be formed under the conditions that are very far from local thermodynamic equilibrium. They are characterized by broad damping wings surrounding the line core. Doppler shifts in combination with collisions cause photons that are absorbed at a given frequency to be redistributed in frequency across the line profile in a complex way during the scattering process. Two idealized, limiting cases to describe this redistribution are “frequency coherence” and “complete redistribution” (CRD), but the general theory that properly combines these two limiting cases goes under the name “partial frequency redistribution” (PRD). Resonance lines which are usually strong can be properly modeled only when PRD is taken into account. To use these strong lines for magnetic field diagnostics we need a line scattering theory of PRD in the presence of magnetic fields of arbitrary strength. In the second part of the thesis we develop such a theory and derive the polarized PRD matrices. These matrices are then used in the polarized line transfer equation to compute the emergent Stokes parameters. Polarized scattering in spectral lines is governed by a 4 x 4 matrix that describes how the Stokes vector is scattered in all directions and redistributed in frequency within the line. In Chapter 7, using a classical approach we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction, and for a J = 0 → 1 → 0 transition. This case of arbitrary magnetic fields is called the Hanle-Zeeman regime, since it covers both the partially overlapping weak and strong-field regimes, in which the Hanle and Zeeman effects respectively dominate the scattering polarization. In this general regime the angle-frequency correlations that describe the so-called PRD are intimately coupled to the polarization properties. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of J quantum numbers. In chapter 8 , we show explicitly that for a J = 0 → 1 → 0 scattering transition there exists an equivalence between the Hanle-Zeeman redistribution matrix that is derived through quantum electrodynamics(Bommier 1997b) and the one derived in Chapter 7 starting from the classical, time-dependent oscillator theory of Bommier & Stenflo (1999). This equivalence holds for all strengths and directions of the magnetic field. Several aspects of the Hanle-Zeeman redistribution matrix are illustrated, and explicit algebraic expressions are given, which are of practical use for the polarized line transfer computations. In chapter 9, we solve the polarized radiative transfer equation numerically, taking into account both the Zeeman absorption matrix and the Hanle-Zeeman redistribution matrix. We compute the line profiles for arbitrary field strengths, and scattering dominated line transitions. We use a perturbation method (see eg. Nagendra et al. 2002) to solve the Hanle-Zeeman line transfer problem. The limiting cases of weak field Hanle scattering and strong field Zeeman true absorption are retrieved. The ilntermediate regime, where both Zeeman absorption and scattering effects are important, is studied in some detail. Numerical method used to solve the Hanle-Zeeman line transfer problem in Chapter 9 is computationally expensive. Hence it is necessary to develop fast iterative methods like PALI (Polarized Approximate Lambda Iteration). As a first step in this direction we develop such a method in Chapter 10 to solve the transfer problem with weak field Hanle scattering. We use a ‘redistribution matrix’ with coupling between frequency redistribution and polarization and no domain decomposition. Such a matrix is constructed by angle-averaging the frequency dependent terms in the exact weak field Hanle redistribution matrix for a two-level atom with unpolarized ground level (that can be obtained by taking the weak field limit of the Hanle-Zeeman redistribution matrix). In the past, the PALI technique has been applied to redistribution matrices in which frequency redistribution is ‘decoupled’ from scattering polarization, the decoupling being achieved by an adequate decomposition of the frequency space into several domains. In this chapter, we examine the consequences of frequency space decomposition, and the resulting decoupling between the frequency redistribution and polarization, on the solution of the polarized transfer equation for the Stokes parameters.