Stromrichtertransformatoren der Hochspannungsgleichstromübertragung bilden das Bindeglied zwischen Gleichspannungs- und Drehstromsystem. Um den ausfallsicheren Betrieb über die gesamte Lebensdauer zu gewährleisten, muss deren Öl-Papier-Isoliersystem entsprechend dimensioniert werden. Eine optimale Dimensionierung setzt ein detailliertes Verständnis über die Beanspruchung des Isoliersystems sowie deren zuverlässige Modellierung sowohl unter Betriebsspannung als auch bei den überlagerten, transienten Überspannungen voraus. Im Rahmen dieser Arbeit wird daher das dielektrische Verhalten des Öl-Papier-Isoliersystems in Anlehnung an dielektrische Prüfungen sowohl unter Gleichspannungsbelastung als auch einer zusammengesetzten Spannungsbelastung aus einer Gleich- und einer Blitzstoßspannung (einer sog. Mischspannungsbelastung) untersucht. Der Vergleich von numerischen Berechnungen auf Grundlage eines ladungsträgerbasierten Ansatzes nach Poisson-Nernst-Planck (PNP) mit Durchschlagexperimenten gibt dabei Aufschluss über die Beanspruchung des Öl-Papier-Isoliersystems. Weiterhin wird gezeigt, dass der in den etablierten, resistiv-kapazitiven Berechnungsmodellen vernachlässigte Ladungsträgereinfluss in Bezug auf die Beanspruchung des Isoliersystems unzureichende Ergebnisse zur Folge hat und demnach zwingend zu berücksichtigen ist. Die an realitätsnahen, Öl-Papier-isolierten Anordnungen erzielten Ergebnisse zeigen nicht nur den Einfluss der an Grenzflächen oder im Papier akkumulierten Ladungsträger auf die Beanspruchung des Isoliersystems. Ebenso werden die Annahmen des ladungsträgerbasierten Ansatzes und die Berechnungsergebnisse des PNP-Modells qualitativ bestätigt. Infolge der Ladungsakkumulation im Papier tritt die höchste Beanspruchung im Ölspalt und nicht im Papier auf. Öl-Papier-isolierte Anordnungen werden somit geringer beansprucht, als eine Strömungsfeldberechnung vermuten lässt. Dies widerspricht den Annahmen der etablierten Berechnungsmodelle und wird im Weiteren durch Polaritätseffekte an homogenen, aber unsymmetrischen, papierisolierten Elektrodenanordnungen oder durch den nachweisbaren Einfluss des Ölvolumens im Prüfgefäß auf die Beanspruchung einer Anordnung verdeutlicht. Unter Mischspannungsbelastung wird weiterhin gezeigt, dass eine Überlagerung der Gleichspannung und damit auch der Polaritätswechsel keine höhere Beanspruchung des Isoliersystems im Vergleich zur reinen Gleichspannungsbelastung zur Folge hat. Die etablierten, resistiv-kapazitiven Modelle ließen jedoch den Polaritätswechsel als kritischste Beanspruchung vermuten. Somit wird nicht nur die Anwendbarkeit der ladungsträgerbasierten PNP-Modellierung an Öl-Papier-Isolieranordnungen qualitativ verifiziert. Ebenso wird demonstriert, dass die stark vereinfachten Annahmen der etablierten Berechnungsmodelle die Beanspruchungen unter Gleich- und der untersuchten Mischspannungsbelastung nicht abbilden können. Der Einsatz klassischer Strömungsfeldberechnungen zur Nachbildung der Beanspruchung des Öl-Papier-Isoliersystems unter Gleichspannungsbelastung entspricht damit nicht mehr dem Stand der Forschung. / Converter transformers of HVDC transmission systems connect HVDC and HVAC systems. To ensure a reliable operation during the entire lifetime, their oil-paper-insulation system must be designed appropriately. An optimized dielectric design demands a fundamental understanding of the dielectric stresses as well as a reliable modeling of the insulation system both under operating voltages and under superimposed, transient overvoltages. Hence, in this work the dielectric behavior of the oil-paper-insulation system is investigated. Based on dielectric tests the investigations are performed under DC voltage stress and a composite voltage stress of a DC voltage in stationary conditions superimposed by a lightning impulse voltage. The comparison of numerical calculations using a charge-carrier-based approach according to Poisson-Nernst-Planck (PNP) with breakdown experiments clarifies the dielectric stress of the oil-paper-insulation system. Furthermore, the comparison with results determined by the established, resistive-capacitive calculation models shows that it is mandatory to take the influence of the charge carrier accumulation into account. The presented results, which were obtained at oil-paper-insulated arrangements which represent the dielectic stress of real arrangements, show the influence of the charge carriers accumulating at interfaces or in the paper insulationon on the dielectric stress. The results confirm the calculations and the assumptions according to the charge-carrier-based model as well. Due to the charge carrier accumulation, the highest dielectric stress occurs in the mineral oil and not in the paper insulation. In contrast, the findings obtained assuming an ohmic conductivity would results in a higher dielectric stress of the oil-paperinsulated arrangements. Furthermore, polarity effects in homogeneous but asymmetrical, paper-insulated electrode arrangements or the influence of the surrounding oil in the test vessel demonstrate the effects of the charge carriers. Under composite voltage stresses it is also shown, that the applied superimposed voltage as well as the fast polarity reversal does not lead to a higher dielectric stress of the arrangements compared to the pure DC voltage stress. Commonly used calculation models would determine higher stresses due to the fast polarity reversal instead. Consequently, the applicability of the charge-carrier-based PNP calculation model is verified qualitatively in the presented investigations. Furthermore, it is demonstrated that the simplified assumptions of the commonly used calculation models cannot simulate the dielectric stresses under DC voltage stress and under the investigated superimposed voltage stresses. Hence, the determination of the dielectric stresses of oil-paper-insulation systems under DC voltage stress according to the commonly used calculation models assuming an ohmic conductivity does not correspond to the current state of research.

Les systèmes en interaction à longue portée sont connus pour avoir des propriétés statistiques et dynamiques particulières. Pour décrire leur évolution dynamique, on utilise des équations cinétiques décrivant leur densité dans l'espace des phases. Ce manuscrit est divisé en deux parties indépendantes. La première traite de notre collaboration avec une équipe expérimentale sur un Piège Magnéto-Optique. Ce dispositif à grand nombre d'atomes présente des interactions coulombiennes effectives provenant de la rediffusion des photons. Nous avons proposé des tests expérimentaux pour mettre en évidence l'analogue d'une longueur de Debye, et son influence sur la réponse du système. Les expériences réalisées ne permettent pour l'instant pas de conclure de façon définitive. Dans la deuxième partie, nous avons analysé les modèles cinétiques de Vlasov et de Kuramoto. Pour étudier leur dynamique de dimension infinie, nous avons examiné les bifurcations autour des états stationnaires instables, l'objectif étant d'obtenir des équations réduites décrivant la dynamique de ces états. Nous avons réalisé des développements en variété instable sur cinq systèmes différents. Ces réductions sont parsemées de singularités, mais prédisent correctement la nature de la bifurcation, que nous avons testée numériquement. Nous avons conjecturé une réduction exacte (obtenue via la forme normale Triple Zero) autour des états inhomogènes de l'équation de Vlasov. Ces résultats génériques pourraient être pertinents dans un contexte astrophysique. Les autres résultats s'appliquent aux phénomènes de synchronisation du modèle de Kuramoto pour les oscillateurs avec inertie et/ou interactions retardées. / Long-range interacting systems are known to display particular statistical and dynamical properties.To describe their dynamical evolution, we can use kinetic equations describing their density in the phase space. This PhD thesis is divided into two distinct parts. The first part concerns our collaboration with an experimental team on a Magneto-Optical Trap. The physics of this widely-used device, operating with a large number of atoms, is supposed to display effective Coulomb interactions coming from photon rescattering. We have proposed experimental tests to highlight the analog of a Debye length, and its influence on the system response. The experimental realizations do not allow yet a definitive conclusion. In the second part, we analyzed the Vlasov and Kuramoto kinetic models. To study their infinite dimensional dynamics, we looked at bifurcations around unstable steady states. The goal was to obtain reduced equations describing the dynamical evolution. We performed unstable manifold expansions on five different kinetic systems. These reductions are in general not exact and plagued by singularities, yet they predict correctly the nature and scaling of the bifurcation, which we tested numerically. We conjectured an exact dimensional reduction (obtained using the Triple Zero normal form) around the inhomogeneous states of the Vlasov equation. These results are expected to be very generic and could be relevant in an astrophysical context. Other results apply to synchronization phenomena through the Kuramoto model for oscillators with inertia and/or delayed interactions.

Quantification of stochastic or quantum systems by a joint probability density or wave function is a notoriously difficult computational problem, since the solution depends on all possible states (or realizations) of the system. Due to this combinatorial flavor, even a system containing as few as ten particles may yield as many as $10^{10}$ discretized states. None of even modern supercomputers are capable to cope with this curse of dimensionality straightforwardly, when the amount of quantum particles, for example, grows up to more or less interesting order of hundreds. A traditional approach for a long time was to avoid models formulated in terms of probabilistic functions, and simulate particular system realizations in a randomized process. Since different times in different communities, data-sparse methods came into play. Generally, they aim to define all data points indirectly, by a map from a low amount of representers, and recast all operations (e.g. linear system solution) from the initial data to the effective parameters. The most advanced techniques can be applied (at least, tried) to any given array, and do not rely explicitly on its origin. The current work contributes further progress to this area in the particular direction: tensor product methods for separation of variables. The separation of variables has a long history, and is based on the following elementary concept: a function of many variables may be expanded as a product of univariate functions. On the discrete level, a function is encoded by an array of its values, or a tensor. Therefore, instead of a huge initial array, the separation of variables allows to work with univariate factors with much less efforts. The dissertation contains a short overview of existing tensor representations: canonical PARAFAC, Hierarchical Tucker, Tensor Train (TT) formats, as well as the artificial tensorisation, resulting in the Quantized Tensor Train (QTT) approximation method. The contribution of the dissertation consists in both theoretical constructions and practical numerical algorithms for high-dimensional models, illustrated on the examples of the Fokker-Planck and the chemical master equations. Both arise from stochastic dynamical processes in multiconfigurational systems, and govern the evolution of the probability function in time. A special focus is put on time propagation schemes and their properties related to tensor product methods. We show that these applications yield large-scale systems of linear equations, and prove analytical separable representations of the involved functions and operators. We propose a new combined tensor format (QTT-Tucker), which descends from the TT format (hence TT algorithms may be generalized smoothly), but provides complexity reduction by an order of magnitude. We develop a robust iterative solution algorithm, constituting most advantageous properties of the classical iterative methods from numerical analysis and alternating density matrix renormalization group (DMRG) techniques from quantum physics. Numerical experiments confirm that the new method is preferable to DMRG algorithms. It is as fast as the simplest alternating schemes, but as reliable and accurate as the Krylov methods in linear algebra.

My thesis addresses a systematic approach to stochastic models in population genetics; in particular, the Wright-Fisher models affected only by the random genetic drift. I used various mathematical methods such as Probability, PDE, and Geometry to answer an important question: \"How do genetic change factors (random genetic drift, selection, mutation, migration, random environment, etc.) affect the behavior of gene frequencies or genotype frequencies in generations?”. In a Hardy-Weinberg model, the Mendelian population model of a very large number of individuals without genetic change factors, the answer is simple by the Hardy-Weinberg principle: gene frequencies remain unchanged from generation to generation, and genotype frequencies from the second generation onward remain also unchanged from generation to generation. With directional genetic change factors (selection, mutation, migration), we will have a deterministic dynamics of gene frequencies, which has been studied rather in detail. With non-directional genetic change factors (random genetic drift, random environment), we will have a stochastic dynamics of gene frequencies, which has been studied with much more interests. A combination of these factors has also been considered. We consider a monoecious diploid population of fixed size N with n + 1 possible alleles at a given locus A, and assume that the evolution of population was only affected by the random genetic drift. The question is that what the behavior of the distribution of relative frequencies of alleles in time and its stochastic quantities are. When N is large enough, we can approximate this discrete Markov chain to a continuous Markov with the same characteristics. In 1931, Kolmogorov first introduced a nice relation between a continuous Markov process and diffusion equations. These equations called the (backward/forward) Kolmogorov equations which have been first applied in population genetics in 1945 by Wright. Note that these equations are singular parabolic equations (diffusion coefficients vanish on boundary). To solve them, we use generalized hypergeometric functions. To know more about what will happen after the first exit time, or more general, the behavior of whole process, in joint work with J. Hofrichter, we define the global solution by moment conditions; calculate the component solutions by boundary flux method and combinatorics method. One interesting property is that some statistical quantities of interest are solutions of a singular elliptic second order linear equation with discontinuous (or incomplete) boundary values. A lot of papers, textbooks have used this property to find those quantities. However, the uniqueness of these problems has not been proved. Littler, in his PhD thesis in 1975, took up the uniqueness problem but his proof, in my view, is not rigorous. In joint work with J. Hofrichter, we showed two different ways to prove the uniqueness rigorously. The first way is the approximation method. The second way is the blow-up method which is conducted by J. Hofrichter. By applying the Information Geometry, which was first introduced by Amari in 1985, we see that the local state space is an Einstein space, and also a dually flat manifold with the Fisher metric; the differential operator of the Kolmogorov equation is the affine Laplacian which can be represented in various coordinates and on various spaces. Dynamics on the whole state space explains some biological phenomena.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.

Cette thèse s'inscrit dans le domaine des probabilités et des statistiques, et plus précisément des matrices aléatoires. Dans la première partie, on étudie les grandes déviations de la mesure spectrale de matrices de covariance $XX^*$, où $X$ est une matrice aléatoire rectangulaire à coefficients i.i.d. ayant une queue de probabilité en $exp(-at^{alpha})$, $alpha in ]0,2[$. On établit un principe de grandes déviations analogue à celui de Bordenave et Caputo, de vitesse $n^{1+alpha/2}$ et de fonction de taux explicite faisant intervenir la convolution libre rectangulaire. La démonstration repose sur un résultat de quantification de la liberté asymptotique dans le modèle information-plus-bruit. La seconde partie de cette thèse est consacrée à l'étude du comportement en temps long de la solution de l'équation de Fokker-Planck libre en présence du potentiel quartique $V(x) = frac14 x^4 + frac{c}{2} x^2$ avec $c ge -2$. On montre que quand $t to +infty$, la solution $mu_t$ de cette équation aux dérivées partielles converge en distance de Wasserstein vers la mesure d'équilibre associée au potentiel $V$. Ce résultat fournit un premier exemple de convergence en temps long de la solution de l'équation des milieux granulaires en présence d'un potentiel non convexe et d'une interaction logarithmique. Sa démonstration utilise notamment des techniques de probabilités libres. / This thesis lies within the field of probability and statistics, and more precisely of random matrix theory. In the first part, we study the large deviations of the spectral measure of covariance matrices XX*, where X is a rectangular random matrix with i.i.d. coefficients having a probability tail like $exp(-at^{alpha})$, $alpha in (0,2)$. We establish a large deviation principle similar to Bordenave and Caputo's one, with speed $n^{1+alpha/2}$ and explicit rate function involving rectangular free convolution. The proof relies on a quantification result of asymptotic freeness in the information-plus-noise model. The second part of this thesis is devoted to the study of the long-time behaviour of the solution to free Fokker-Planck equation in the setting of the quartic potential $V(x) = frac14 x^4 + frac{c}{2} x^2$ with $c ge -2$. We prove that when $t to +infty$, the solution $mu_t$ to this partial differential equation converge in Wasserstein distance towards the equilibrium measure associated to the potential $V$. This result provides a first example of long-time convergence for the solution of granular media equation with a non-convex potential and a logarithmic interaction. Its proof involves in particular free probability techniques.

Ce mémoire de thèse est consacré à l’équation de Fokker-Planckpartial_ f=∆f+div(Ef).Il est subdivisé en deux parties :une partie linéaire et une partie non linéaire. Dans la partie linéaire on considère un champ de vecteur E(x) dépendant seulement de x. Cette partie est constituée des chapitres 3, 4 et 5. Dans le chapitre 3 on montre que l’opérateur linéaire Lf :=∆ f + div(E f ) est le générateur d’un semi-groupe fortement continu (SL(t))_{t≥0} dans tous les espaces L^p. On y établit également que le semi-groupe (SL(t))_{t≥0} est positif et ultracontractif. Dans le chapitre 4 nous montrons comment est qu’une décomposition adéquate de l’opérateur L permet d’établir certaines propriétés du semi-groupe (SL(t))_{t≥0} notamment sa bornitude. Le chapitre 5 est consacré à l’existence d’un état d’équilibre. De plus on y montre que cet état d’équi- libre est asymptotiquement stable. Dans la partie non linéaire on considère un champ de vecteur de la forme E(x,f) := x+nabla (a*f) ou a et f sont des fonctions assez régulières et * est l’opérateur de convolution. Cette parties est contituée des chapitre 6 et 7. Dans le chapitre 6 nous établissons que poura appartenant à W^{2,infini}_locl’équation de Fokker-Planck non linéaire admet une unique solution locale dans l’espace L^2_{K_alpha} (R^d). Dans le dernier chapitre nous montrons que le problème non linéaire admet une solution globale. De plus cette solution dépend continument des données. / This thesis is devoted to the Fokker-Planck équation partial_t f =∆f + div(E f).It is divided into two parts. The rst part deals with the linear problem. In this part we consider a vector E(x) depending only on x. It is composed of chapters 3, 4 and 5. In chapter 3 we prove that the linear operator Lf :=∆f + div(Ef ) is an in nitesimal generator of a strong continuous semigroup (SL(t))_{t≥0}. We establish also that (SL(t))_{t≥0} is positive and ultracontractive. In chapter 4 we show how an adequate decomposition of the linear operator L allows us to deduce interesting properties for the semigroup (SL(t))_{t≥0}. Indeed using this decomposition we prove that (SL(t))_{t≥0} is a bounded semigroup. In the last chapter of this part we establish that the linear Fokker-Planck admits a unique steady state. Moreover this stationary solution is asymptotically stable.In the nonlinear part we consider a vector eld of the form E(x, f ) := x +nabla (a *f ), where a and f are regular functions. It is composed of two chapters. In chapter 6 we establish that fora in W^{2,infini}_locthe nonlinear problem has a unique local solution in L^2_{K_alpha}(R^d); . To end this part we prove in chapter 7 that the nonlinear problem has a unique global solution in L^2_k(R^d). This solution depends continuously on the data.

Ziel dieser Arbeit ist die Untersuchung des Einflusses der stochastischen Interpretation der Langevin Gleichung mit zustandsabhängigen Diffusionskoeffizienten auf den Propagator des zugehörigen stochastischen Prozesses bzw. dessen Mittelwerte. Dies dient dem besseren Verständnis und der Interpretation von Messdaten von Diffusion in inhomogenen Systemen und geht einher mit der Frage der Form der Diffusionsgleichung in solchen Systemen. Zur Vereinfachung der Fragestellung werden in dieser Arbeit nur Systeme untersucht die vollständig durch einen ortsabhängigen Diffusionskoeffizienten und Angabe der stochastischen Interpretation beschrieben werden können. Dazu wird zunächst für mehrere experimentell relevante eindimensionale Systeme der jeweilige allgemeine Propagator bestimmt, der für jede denkbare stochastische Interpretation gültig ist. Der analytisch bestimmte Propagator wird dann für zwei exemplarisch ausgewählte stochastische Interpretationen, hier für die Itô und Klimontovich-Hänggi Interpretation, gegenübergestellt und die Unterschiede identifiziert. Für Mittelwert und Varianz der Prozesse werden die drei wesentlichen stochastischen Interpretationen verglichen, also Itô, Stratonovich und Klimontovich-Hänggi Interpretation. Diese systematische Untersuchung von inhomogenen Diffusionsprozessen kann zukünftig helfen diese Art von, in genau einer stochastischen Interpretation, driftfreien Systemen einfacher zu identifizieren. Ein weiterer wesentlicher Teil der Arbeit erweitert die Frage auf mehrdimensionale inhomogene anisotrope Systeme. Dies wird z.B. bei der Untersuchung von Diffusion in Flüssigkristallen mit inhomogenem Direktorfeld relevant. Obwohl hier, im Gegensatz zu eindimensionalen Systemen, der Propagator nicht allgemein berechnet werden kann, wird dennoch der Einfluss der Inhomogenität auf Messgrößen, wie die mittlere quadratische Verschiebung oder die Verteilung der Diffusivitäten, bestimmt. Anhand eines Beispiels wird auch der Einfluss der stochastischen Interpretation auf diese Messgrößen demonstriert. / The aim of this thesis is to investigate the influence of the stochastic interpretation of the Langevin equation with state-dependent diffusion coefficient on the propagator of the related stochastic process, or its averages, respectively. This helps to obtain a deeper understanding and to interpret measurement data of diffusion in inhomogeneous systems and is accompanied with the question of the proper form of the diffusion equation in such systems. To simplify the question, in this thesis only systems are considered which can be fully described by a spatially dependent diffusion coefficient and a given stochastic interpretation. Therefore, for several experimentally relevant one-dimensional systems, the respective general propagator is determined, which is valid for any possible stochastic interpretation. Then, the propagator for two exemplary stochastic interpretations, here the Itô and Klimontovich-Hänggi interpretation, are compared and the differences are identified. For mean and variance of the processes three major interpretations are compared, namely the Itô, the Stratonovich and the Klimontovich-Hänggi interpretation. This systematic research on inhomogeneous diffusion process may help in future to identify these kind of, in exactly one stochastic interpretation, drift-free systems more easily. Another important part of this thesis extends this question to multidimensional inhomogeneous anisotropic systems. This is of high relevance, for instance, for the research of diffusion in liquid crystalline systems with an inhomogeneous director field. Although, in contrast to one-dimensional systems, the propagator may not be calculated generally, the influence of the inhomogeneity on measurement data like the mean squared displacement or the distribution of diffusivities is determined. Based on one example, also the influence of the stochastic interpretation on these quantities is demonstrated.

Bereits vor zehn Jahren gab es den ersten großen E-Book-Boom. Während damals noch digitale Buchinhalte für spezielle Lesegeräte im Mittelpunkt der Diskussion standen, dominieren inzwischen webbasierte Angebote den stetig wachsenden Markt. Für Bibliotheken eröffnen sich durch diese E-Books der nächsten Generation völlig neue Möglichkeiten in der Informationsversorgung ihrer Benutzer. Sowohl der globale Wissensaustausch, als auch der Zugriff auf Fachinformationen können mit ihrer Hilfe beschleunigt werden. Dies spielt insbesondere für Spezialbibliotheken, wie die der Max-Planck-Gesellschaft, eine große Rolle. Denn gerade von ihnen wird erwartet, dass sie die Mitarbeiter ihrer Institute stets mit den aktuellsten Fachinformationen versorgen. Aufgrund der Vielzahl an Lizenzierungs- und Angebotsformen auf dem E-Book-Markt ist hier ein Anbietervergleich unerlässlich. Dieser erfolgt im Rahmen dieser Diplomarbeit für die Bibliotheken der Max-Planck- Gesellschaft. Hierfür werden zunächst die aktuelle E-Book-Marktsituation und die Strukturen der Max-Planck-Gesellschaft beschrieben. Anschließend untersucht die Verfasserin die bisherigen Entwicklungen in der zentralen und lokalen E-Book-Erwerbung der Max-Planck-Gesellschaft. Zu diesem Zweck werden u.a. eine Befragung unter den Institutsbibliothekaren und mehrere Experteninterviews durchgeführt. Auf diese Weise können geeignete E-Book-Anbieter für die Max-Planck-Gesellschaft ermittelt und Kriterien gefunden werden, um diese schließlich miteinander vergleichen zu können. Im Ergebnis des Vergleichs gibt die Verfasserin Empfehlungen für die weitere E-Book-Erwerbung in der Max-Planck-Gesellschaft ab.

Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.