Koagulation ist physikalisch bedeutsam für eine Vielzahl von technischen und naturwissenschaftlichen Anwendungen und bezeichnet die paarweise Verschmelzung von Clustern unterschiedlicher Masse. Der zeitliche Verlauf der Clusterkonzentration läßt sich durch Smoluchowskis Koagulationsgleichung beschreiben, einem unendliches System nichtlinearer Differentialgleichungen. Ausgangspunkt dieser Arbeit ist eine nichtlineare maßwertige Gleichung, die die Koagulations- und andere kinetische Gleichungen beinhaltet und verschiedene physikalische und chemische Mechanismen integriert. Sie ermöglicht einen allgemeinen Zugang zu Fragen bezüglich der Existenz von Lösungen und ihrer Approximation durch stochastische Partikelsysteme. Die Teilchensysteme werden dabei als reguläre Sprungprozesse modelliert, welche eine Menge diskreter Maße auf einem lokal-kompakten Raum als Zustandsraum besitzen. Die Arbeit untergliedert sich in drei Teile: Unter geeigneten Voraussetzungen an die Sprungraten werden zunächst für wachsende Teilchenzahlen Approximations- und Konvergenzaussagen unter Verwendung von Kompaktheitsargumenten, Martingaltheoremen und Lokalisierungstechniken bewiesen. Ihre Anwendung auf die Koagulationsgleichung mit Fragmentation, Quellen und Senken erlaubt anschließend die Herleitung neuer Existenzresultate und stochastischer Algorithmen. Der letzte Abschnitt illustriert die numerischen Eigenschaften und die Effizienz der neuen Algorithmen im Vergleich zu bisherigen Monte Carlo Methoden und ihre besondere Eignung zur Analyse des Gelationsphänomens, einem Phasenübergang, welcher zum Masseverlust im Clustersystem führt. / Coagulation is an important physical process for a wide range of technical and scientific applications and denotes the pairwise merging of clusters with different mass. The dynamic behaviour of the cluster concentration can be described by Smoluchowski's coagulation equation which is an infinite system of nonlinear differential equations. In this thesis we start with a nonlinear measure-valued equation generalizing the coagulation and other kinetic equations and integrating various physical and chemical processes. This equation allows a unified treatment of questions concerning existence of solutions and their approximation by means of stochastic particle systems. Here, the particle systems are defined as regular jump processes living on a set of point measures on a locally compact space. The thesis consists of three parts: First of all, approximation and convergence results for suitable jump rates and increasing particle numbers are proved by means of compactness theorems, martingale techniques and localizing procedures. Then, an application to the coagulation equation with fragmentation, source and efflux terms leads to new existence results and stochastic algorithms. Finally, their numerical features and efficiency are compared to known Monte Carlo methods and their specific convergence properties are presented with respect to a phase transition which is called gelation and leads to a loss of total cluster mass.

I characterize optimal strategies and equilibria in two bandit-type games of strategic information acquisition. The latter game admits a missing data problem, which I develop an estimator to address. I consider a third environment with an additional missing data problem, characterize estimation bias both statistically and empirically, and develop a pair of easily implementable unbiased estimators. In the first chapter, I analyze a two-player, two-armed exponential bandit model in continuous time across several monitoring and disclosure environments, in which breakthroughs are fully informative of the state of the world. In particular, I consider an environment where player actions are observed but the results of experimentation are unobserved, and an environment where both actions and experimentation outcomes are unobserved. In the former environment, I construct a Perfect Bayesian Equilibrium that induces the efficient (cooperative) experimentation path. This equilibrium relies on strategies that deter free-riding by moving to an undesirable, asymmetric experimentation path when the safe arm is played. In the latter environment, I provide conditions on starting beliefs for which it is possible to construct a Perfect Bayesian Equilibrium that induces the efficient experimentation path. This equilibrium requires that players privately, separately experiment and share the results of experimentation at a single point in time. I show how this hybrid Markov approach can be adapted to a general discrete-time setting and provide conditions for which strategies measurable with respect to both the Markov partition and a finite automaton are consistent. In the second chapter, I consider the problem of a rideshare company which makes sequences of take it or leave it offers to drivers for individual trips. When drivers are privately and commonly informed of trip quality, rejected offers are informative about trip quality to the rideshare company. As such, the rideshare company faces a strategic information acquisition problem: offers influence both the current-period payoff and the expectation of future payoffs via posterior beliefs. When unobserved quality is Bernoulli, the value function increases in beliefs over quality, and I characterize the value function and optimal offer sequence using dynamic programming. Moreover, I show that a heuristic 𝑛-offer look-ahead sequence converges uniformly to the optimal revenue, and characterize bounds on the revenue gap. For a general bounded distribution of unobserved trip quality, I show that the value function is decreasing after rejections, and define analogous convergent bounds. Among heterogeneous drivers, driver and platform value can be collapsed into a single-dimensional match value parameter that governs the optimal order of offers. I also illustrate a source of potential bias when estimating driver preferences using a data set with repeated offers, and construct a consistent, easily-implementable estimator to address the issue. In the third chapter, I consider a choice environment where an econometrician only observes certain covariates for goods that are chosen. This missing data may reflect literal omissions from a dataset or inherently counterfactual outcomes, such as in the Roy (1951) model. When partially observed covariates vary stochastically across consumers there is selection bias in the distribution of observed covariates: consumers are more likely to pick goods with preferential characteristic draws. I show that imputation methods that use the observed distribution of covariates to replace missing data bias discrete choice parameter estimates toward zero, regardless of whether missing data or all data are imputed. Moreover, this bias rapidly increases with the variance of the covariate distribution. Instead, I propose two full-information maximum likelihood estimation procedures that jointly estimate preferences and the underlying distribution of covariates. While these estimators necessarily involve Monte Carlo simulation when covariates are distributed continuously, I show that it is possible to avoid simulation when covariates take a discrete set of values.

Ce travail présente un développement et une analyse des approches numériques déterministes et probabilistes efficaces pour les équations aux dérivées partielles avec des coefficients et données aléatoires. On s'intéresse au problème d'écoulement stationnaire avec des données aléatoires. Une méthode de projection dans le cas unidimensionnel est présentée, permettant de calculer efficacement la moyenne de la solution. Nous utilisons la méthode de collocation anisotrope des grilles clairsemées. D'abord, un indicateur de l'erreur satisfaisant une borne supérieure de l'erreur est introduit, il permet de calculer les poids d'anisotropie de la méthode. Ensuite, nous démontrons une amélioration de l'erreur a priori de la méthode. Elle confirme l'efficacité de la méthode en comparaison avec Monte-Carlo et elle sera utilisée pour accélérer la méthode par l'extrapolation de Richardson. Nous présentons aussi une analyse numérique d'une méthode probabiliste pour quantifier la migration d'un contaminant dans un milieu aléatoire. Nous considérons le problème d'écoulement couplé avec l'équation d'advection-diffusion, où on s'intéresse à la moyenne de l'extension et de la dispersion du soluté. Le modèle d'écoulement est discrétisée par une méthode des éléments finis mixtes, la concentration du soluté est une densité d'une solution d'une équation différentielle stochastique, qui sera discrétisée par un schéma d'Euler. Enfin, on présente une formule explicite de la dispersion et des estimations de l'erreur a priori optimales. / This work presents a development and an analysis of an effective deterministic and probabilistic approaches for partial differential equation with random coefficients and data. We are interesting in the steady flow equation with stochastic input data. A projection method in the one-dimensional case is presented to compute efficiently the average of the solution. An anisotropic sparse grid collocation method is also used to solve the flow problem. First, we introduce an indicator of the error satisfying an upper bound of the error, it allows us to compute the anisotropy weights of the method. We demonstrate an improvement of the error estimation of the method which confirms the efficiency of the method compared with Monte Carlo and will be used to accelerate the method using the Richardson extrapolation technique. We also present a numerical analysis of one probabilistic method to quantify the migration of a contaminant in random media. We consider the previous flow problem coupled with the advection-diffusion equation, where we are interested in the computation of the mean extension and the mean dispersion of the solute. The flow model is discretized by a mixed finite elements method and the concentration of the solute is a density of a solution of the stochastic differential equation, this latter will be discretized by an Euler scheme. We also present an explicit formula of the dispersion and an optimal a priori error estimates.

Ce travail présente quelques résultats concernant des méthodes numériques déterministes et probabilistes pour des équations aux dérivées partielles à coefficients aléatoires, avec des applications à l'hydrogéologie. On s'intéresse tout d'abord à l'équation d'écoulement dans un milieu poreux en régime stationnaire avec un coefficient de perméabilité lognormal homogène, incluant le cas d'une fonction de covariance peu régulière. On établit des estimations aux sens fort et faible de l'erreur commise sur la solution en tronquant le développement de Karhunen-Loève du coefficient. Puis on établit des estimations d'erreurs éléments finis dont on déduit une extension de l'estimation d'erreur existante pour la méthode de collocation stochastique, ainsi qu'une estimation d'erreur pour une méthode de Monte-Carlo multi-niveaux. On s'intéresse enfin au couplage de l'équation d'écoulement considérée précédemment avec une équation d'advection-diffusion, dans le cas d'incertitudes importantes et d'une faible longueur de corrélation. On propose l'analyse numérique d'une méthode numérique pour calculer la vitesse moyenne à laquelle la zone contaminée par un polluant s'étend. Il s'agit d'une méthode de Monte-Carlo combinant une méthode d'élements finis pour l'équation d'écoulement et un schéma d'Euler pour l'équation différentielle stochastique associée à l'équation d'advection-diffusion, vue comme une équation de Fokker-Planck. / This work presents some results about probabilistic and deterministic numerical methods for partial differential equations with stochastic coefficients, with applications to hydrogeology. We first consider the steady flow equation in porous media with a homogeneous lognormal permeability coefficient, including the case of a low regularity covariance function. We establish error estimates, both in strong and weak senses, of the error in the solution resulting from the truncature of the Karhunen-Loève expansion of the coefficient. Then we establish finite element error estimates, from which we deduce an extension of the existing error estimate for the stochastic collocation method along with an error estimate for a multilevel Monte-Carlo method. We finally consider the coupling of the previous flow equation with an advection-diffusion equation, in the case when the uncertainty is important and the correlation length is small. We propose the numerical analysis of a numerical method, which aims at computing the mean velocity of the expansion of a pollutant. The method consists in a Monte-Carlo method, combining a finite element method for the flow equation and an Euler scheme for the stochastic differential equation associated to the advection-diffusion equation, seen as a Fokker-Planck equation.

Under current investigation is the re-implementation of the Distorted-Wave Impulse Approximation (DWIA), originally formulated in FORTRAN by N.S. Chant and P.G. Roos, with the intention of developing it in a portable Python environment. This will be complimented by developing a GEANT4 detector simulation application. These two techniques will be used to model the (p,2p) proton knock-out reaction 40Ca(p; 2p)39K (2.52 MeV)1 2 + first excited state, at intermediate incident energies of 150 MeV. This study is a test-bed that lays the foundation and platform from which one may develop an interactive workbench and toolkit in GEANT4 which: (i.) accurately models an accelerator-detector experimental set-up, such as those found at iThemba Labs, and (ii.) incorporates the DWIA formalism as a built-in physics process within the framework of GEANT4. Furthermore the Python modules developed for the specific proton knock-out reaction studied here, can be generalized for an arbitrary set of nuclear scattering reactions and packaged as a suite of scientific Python codes. / Theoretical and Computational Nuclear Physics / M. Sc. (Theoretical and Computational Nuclear Physics)

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: When estimating the covariance matrices of two or more populations, the covariance matrices are often assumed to be either equal or completely unrelated. The common principal components (CPC) model provides an alternative which is situated between these two extreme assumptions: The assumption is made that the population covariance matrices share the same set of eigenvectors, but have di erent sets of eigenvalues. An important question in the application of the CPC model is to determine whether it is appropriate for the data under consideration. Flury (1988) proposed two methods, based on likelihood estimation, to address this question. However, the assumption of multivariate normality is untenable for many real data sets, making the application of these parametric methods questionable. A number of non-parametric methods, based on bootstrap replications of eigenvectors, is proposed to select an appropriate common eigenvector model for two population covariance matrices. Using simulation experiments, it is shown that the proposed selection methods outperform the existing parametric selection methods. If appropriate, the CPC model can provide covariance matrix estimators that are less biased than when assuming equality of the covariance matrices, and of which the elements have smaller standard errors than the elements of the ordinary unbiased covariance matrix estimators. A regularised covariance matrix estimator under the CPC model is proposed, and Monte Carlo simulation results show that it provides more accurate estimates of the population covariance matrices than the competing covariance matrix estimators. Covariance matrix estimation forms an integral part of many multivariate statistical methods. Applications of the CPC model in discriminant analysis, biplots and regression analysis are investigated. It is shown that, in cases where the CPC model is appropriate, CPC discriminant analysis provides signi cantly smaller misclassi cation error rates than both ordinary quadratic discriminant analysis and linear discriminant analysis. A framework for the comparison of di erent types of biplots for data with distinct groups is developed, and CPC biplots constructed from common eigenvectors are compared to other types of principal component biplots using this framework. A subset of data from the Vermont Oxford Network (VON), of infants admitted to participating neonatal intensive care units in South Africa and Namibia during 2009, is analysed using the CPC model. It is shown that the proposed non-parametric methodology o ers an improvement over the known parametric methods in the analysis of this data set which originated from a non-normally distributed multivariate population. CPC regression is compared to principal component regression and partial least squares regression in the tting of models to predict neonatal mortality and length of stay for infants in the VON data set. The tted regression models, using readily available day-of-admission data, can be used by medical sta and hospital administrators to counsel parents and improve the allocation of medical care resources. Predicted values from these models can also be used in benchmarking exercises to assess the performance of neonatal intensive care units in the Southern African context, as part of larger quality improvement programmes. / AFRIKAANSE OPSOMMING: Wanneer die kovariansiematrikse van twee of meer populasies beraam word, word dikwels aanvaar dat die kovariansiematrikse of gelyk, of heeltemal onverwant is. Die gemeenskaplike hoofkomponente (GHK) model verskaf 'n alternatief wat tussen hierdie twee ekstreme aannames gele e is: Die aanname word gemaak dat die populasie kovariansiematrikse dieselfde versameling eievektore deel, maar verskillende versamelings eiewaardes het. 'n Belangrike vraag in die toepassing van die GHK model is om te bepaal of dit geskik is vir die data wat beskou word. Flury (1988) het twee metodes, gebaseer op aanneemlikheidsberaming, voorgestel om hierdie vraag aan te spreek. Die aanname van meerveranderlike normaliteit is egter ongeldig vir baie werklike datastelle, wat die toepassing van hierdie metodes bevraagteken. 'n Aantal nie-parametriese metodes, gebaseer op skoenlus-herhalings van eievektore, word voorgestel om 'n geskikte gemeenskaplike eievektor model te kies vir twee populasie kovariansiematrikse. Met die gebruik van simulasie eksperimente word aangetoon dat die voorgestelde seleksiemetodes beter vaar as die bestaande parametriese seleksiemetodes. Indien toepaslik, kan die GHK model kovariansiematriks beramers verskaf wat minder sydig is as wanneer aanvaar word dat die kovariansiematrikse gelyk is, en waarvan die elemente kleiner standaardfoute het as die elemente van die gewone onsydige kovariansiematriks beramers. 'n Geregulariseerde kovariansiematriks beramer onder die GHK model word voorgestel, en Monte Carlo simulasie resultate toon dat dit meer akkurate beramings van die populasie kovariansiematrikse verskaf as ander mededingende kovariansiematriks beramers. Kovariansiematriks beraming vorm 'n integrale deel van baie meerveranderlike statistiese metodes. Toepassings van die GHK model in diskriminantanalise, bi-stippings en regressie-analise word ondersoek. Daar word aangetoon dat, in gevalle waar die GHK model toepaslik is, GHK diskriminantanalise betekenisvol kleiner misklassi kasie foutkoerse lewer as beide gewone kwadratiese diskriminantanalise en line^ere diskriminantanalise. 'n Raamwerk vir die vergelyking van verskillende tipes bi-stippings vir data met verskeie groepe word ontwikkel, en word gebruik om GHK bi-stippings gekonstrueer vanaf gemeenskaplike eievektore met ander tipe hoofkomponent bi-stippings te vergelyk. 'n Deelversameling van data vanaf die Vermont Oxford Network (VON), van babas opgeneem in deelnemende neonatale intensiewe sorg eenhede in Suid-Afrika en Namibi e gedurende 2009, word met behulp van die GHK model ontleed. Daar word getoon dat die voorgestelde nie-parametriese metodiek 'n verbetering op die bekende parametriese metodes bied in die ontleding van hierdie datastel wat afkomstig is uit 'n nie-normaal verdeelde meerveranderlike populasie. GHK regressie word vergelyk met hoofkomponent regressie en parsi ele kleinste kwadrate regressie in die passing van modelle om neonatale mortaliteit en lengte van verblyf te voorspel vir babas in die VON datastel. Die gepasde regressiemodelle, wat maklik bekombare dag-van-toelating data gebruik, kan deur mediese personeel en hospitaaladministrateurs gebruik word om ouers te adviseer en die toewysing van mediese sorg hulpbronne te verbeter. Voorspelde waardes vanaf hierdie modelle kan ook gebruik word in normwaarde oefeninge om die prestasie van neonatale intensiewe sorg eenhede in die Suider-Afrikaanse konteks, as deel van groter gehalteverbeteringprogramme, te evalueer.

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函數型資料分析為近年發展的統計方法。函數型資料是在一段特定時間上，我們只在離散的時間點上收集觀測值。例如:氣象觀測站所收集到的每月氣溫、雨量資料，即是一種常見的函數型資料。函數型資料主要有三種特色，共同趨勢性、觀測個體反應強度不同，觀測個體時間特色上的差異。本文研究主要是使用，Brumback與Lindstrom在2004所提出的自模型迴歸族(self-modeling)當作模型架構來處理函數型資料的趨勢性與個體反應強度。而為了處理函數型資料的時間差異性，我們在模型中加入時間轉換函數(time transformation function)，處理函數型資料的時間差異性步驟，這個過程稱為同步化。經過同步化的處理後，能幫助研究者更清楚資料的特性。模型中除了時間轉換函數的部份，其餘模型中的參數我們是利用馬可夫鏈蒙地卡羅法中的Gibbs Sampling來進行參數的抽樣，並以取出的抽樣值來估計參數。時間轉換函數的部份，我們使用概似懲罰函數(penalized likelihood function)來估計時間轉換函數的參數部份。由於函數型資料擁有趨勢性，我們預期不同類別的資料，會呈現不同的趨勢性，我們將利用此一特色當做分類上的標準。 關鍵詞:函數型資料分析、曲線同步化、曲線區別分析、馬可夫鏈蒙地卡羅法。 / Functional data are random curves observed in a period of time at discrete time points.They often exhibit a common shape, but with variations in amplitude and phase across curves.To estimate the common shape,some adjustment for synchronization is often made,which is also known as time warping or curve registration.In this thesis,splines are used to model the warping functions and the common shape. Certain parameters are allowed to be random.For the estimation of the random parameters,priors are proposed so that samples from the posteriors can be obtained using Markov chain Monte Carlo methods.For the estimation of non-random parameters, a penalized likelihood approach is used. It is found via simulation studies that for a set of random curves with a common shape,the estimated common shape function looks like the true function up to a location-scale transform,and the curve alignment based on estimated time warping functions looks reasonable.For two groups of random curves which differ in the group common shape functions,synchronization also improves the discrimination between groups in some cases. Key words: functional data analysis,curve registration,curve discrimination,markov chain monte carlo method.

The future fusion power plants that are based on magnetic confinement will deal with plasmas that inevitably contain energetic (non-thermal) particles. These particles come, for instance, from fusion reactions or from external heating of the plasma. Ensembles of energetic ions can excite eigenmodes in the Alfvén frequency range to such an extent that the resulting wave fields redistribute the energetic ions, and potentially eject them from the plasma. The redistribution of ions may cause a substantial reduction of heating efficiency. Understanding the dynamics of such instabilities is necessary to optimise the operation of fusion experiments and of future fusion power plants. Two models have been developed to simulate the interaction between energetic ions and Alfvén eigenmodes. One is a bump-on-tail model, of which two versions have been developed: one fully nonlinear and one quasilinear. The quasilinear version has a lower dimensionality of particle phase space than the nonlinear one. Unlike previous similar studies, the bump-on-tail model contains a decorrelation of the wave-particle phase in order to model stochasticity of the system. When the characteristic time scale for macroscopic phase decorrelation is similar to or shorter than the time scale of nonlinear wave-particle dynamics, the nonlinear and the quasilinear descriptions quantitatively agree. A finite phase decorrelation changes the growth rate and the saturation amplitude of the wave mode in systems with an inverted energy distribution around the wave-particle resonance. Analytical expressions for the correction of the growth rate and the saturation amplitude have been derived, which agree well with numerical simulations. A relatively weak phase decorrelation also diminishes frequency chirping events of the eigenmode. The second model is called FOXTAIL, and it has a wider regime of validity than the bump-on-tail model. FOXTAIL is able to simulate systems with multiple eigenmodes, and it includes effects of different individual particle orbits relative to the wave fields. Simulations with FOXTAIL and the nonlinear bump-on-tail model have been compared in order to determine the regimes of validity of the bump-on-tail model quantitatively. Studies of two-mode scenarios confirmed the expected consequences of a fulfillment of the Chirikov criterion for resonance overlap. The influence of ICRH on the eigenmode-energetic ion system has also been studied, showing qualitatively similar effects as seen by the presence of phase decorrelation. Another model, describing the efficiency of fast wave current drive, has been developed in order to study the influence of passive components close to the antenna, in which currents can be induced by the antenna generated wave field. It was found that the directivity of the launched wave, averaged over model parameters, was lowered by the presence of passive components in general, except for low values of the single pass damping of the wave, where the directivity was slightly increased, but reversed in the toroidal direction. / De framtida fusionskraftverken baserade på magnetisk inneslutning kommer att hantera plasmor som oundvikligen innehåller energetiska (icke-termiska) partiklar. Dessa partiklar kommer exempelvis från fusionsreaktioner eller från externa uppvärmningsmekanismer av plasmat. Ensembler av energetiska joner kan excitera egenmoder i Alfvén-frekvensområdet i en sådan utsträckning att de resulterande vågfälten omfördelar de energetiska jonerna i rummet, och potentiellt slungar ut jonerna ur plasmat. Omfördelningen av joner kan orsaka en väsentligen minskad uppvärmningseffekt. Det är nödvändigt att förstå dynamiken hos denna typ av instabilitet för att kunna optimera verkningsgraden hos experiment och hos framtida fusionskraftverk. Två modeller har utvecklats för att simulera interaktionen mellan energetiska joner och Alfvén-egenmoder. Den första är en bump-on-tail-modell, av vilken två versioner har utvecklats: en fullt icke-linjär och en kvasi-linjär. I den kvasi-linjära versionen har partiklarnas fasrum en lägre dimensionalitet än i den icke-linjära versionen. Till skillnad från tidigare liknande studier innehåller denna bump-on-tail-modell en dekorrelation av våg-partikelfasen för att modellera stokasticitet hos systemet. När den karakteristiska tidsskalan för makroskopisk fasdekorrelation är ungefär samma som eller kortare än tidsskalan för icke-linjär våg-partikeldynamik så stämmer den icke-linjära och den kvasi-linjära beskrivningen överens kvantitativt. En ändlig fasdekorrelation förändrar vågmodens tillväxthastighet och satureringsamplitud i system med en inverterad energifördelning omkring våg-partikelresonansen. Analytiska uttryck för korrektionen av tillväxthastigheten och satureringsamplituden har härletts, vilka stämmer väl överens med numeriska simuleringar. En relativt svag fasdekorrelation försvagar även "frequency chirping events" (snabba frekvensskiftningar i korttids-Fourier-transformen av egenmodens amplitudutveckling) hos egenmoden. Den andra modellen, kallad FOXTAIL, har ett mycket bredare giltighetsområde än bump-on-tail-modellen. FOXTAIL kan simulera system med flera egenmoder, och den inkluderar effekter av olika enskilda partikelbanor relativt vågfälten. Simuleringar med FOXTAIL och med bump-on-tail-modellen har jämförts för att kvantitativt bestämma bump-on-tail-modellens giltighetsområde. Studier av scenarier med två egenmoder bekräftar de förväntade effekterna av när Chirikov-kriteriet för resonansöverlapp uppfylls. Även inflytandet av ICRH på dynamiken mellan egenmoder och energetiska joner har studerats, vilket har visat kvalitativt liknande effekter som har observerats i närvaron av fasdekorrelation. En annan modell, vilken beskriver effektiviteten hos "fast wave current drive" (strömdrivning med snabba magnetosoniska vågor), har utvecklats för att studera inflytandet av passiva komponenter nära antennen, i vilka strömmar kan induceras av vågfälten som genereras av antennen. Det visades att den utskickade vågens direktivitet, medelvärdesbildat över modellparametrar, generellt sett minskade vid närvaron av passiva komponenter, förutom vid låg "sinlge pass damping" (dämpning av vågen vid propagering genom hela plasmat), då direktiviteten istället ökade något, men bytte tecken i toroidal riktning. / <p>QC 20160927</p>