The Dynamics of a Small Model Glass Former as Viewed from Its Potential Energy Landscape

Despite intensive research during the last decades, thetheoreticalunderstanding of supercooled liquids and the glasstransition is stillfar from being complete. Besides analytical investigations,theso-called energy-landscape approach has turned out to beveryfruitful. In the literature, many numerical studies havedemonstratedthat, at sufficiently low temperatures, all thermodynamicquantities can be predicted with the help of the propertiesof localminima in the potential-energy-landscape (PEL). The main purpose of this thesis is to strive for anunderstanding ofdynamics in terms of the potential energy landscape. Incontrast to the study of static quantities, this requirestheknowledge of barriers separating the minima.Up to now, it has been the general viewpoint that thermallyactivatedprocesses ('hopping') determine the dynamics only belowTc(the critical temperature of mode-coupling theory), in thesense that relaxation rates follow from local energybarriers.As we show here, this viewpoint should be revisedsince the temperature dependence of dynamics is governed byhoppingprocesses already below 1.5Tc.At the example of a binary mixture of Lennard-Jonesparticles (BMLJ),we establish a quantitative link from the diffusioncoefficient,D(T), to the PEL topology. This is achieved in three steps:First, we show that it is essential to consider wholesuperstructuresof many PEL minima, called metabasins, rather than singleminima. Thisis a consequence of strong correlations within groups of PELminima.Second, we show that D(T) is inversely proportional to theaverageresidence time in these metabasins. Third, the temperaturedependenceof the residence times is related to the depths of themetabasins, asgiven by the surrounding energy barriers. We further discuss that the study of small (but not toosmall) systemsis essential, in that one deals with a less complex energylandscapethan in large systems. In a detailed analysis of differentsystemsizes, we show that the small BMLJ system consideredthroughout thethesis is free of major finite-size-related artifacts.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

In vitro generation and characterization of acute myeloid leukemia-reactive CD8 + cytotoxic T-lymphocyte clones from healthy donors

Donor-derived CD8+ cytotoxic T lymphocytes (CTLs) eliminating host leukemic cells mediate curative graft-versus-leukemia (GVL) reactions after allogeneic hematopoietic stem cell transplantation (HSCT). The leukemia-reactive CTLs recognize hematopoiesis-restricted or broadly expressed minor histocompatibility and leukemia-associated peptide antigens that are presented by human leukocyte antigen (HLA) class I molecules on recipient cells. The development of allogeneic CTL therapy in acute myeloid leukemia (AML) is hampered by the poor efficiency of current techniques for generating leukemia-reactive CTLs from unprimed healthy donors in vitro. In this work, a novel allogeneic mini-mixed lymphocyte/leukemia culture (mini-MLLC) approach was established by stimulating CD8+ T cells isolated from peripheral blood of healthy donors at comparably low numbers (i.e. 10e4/well) with HLA class I-matched primary AML blasts in 96-well microtiter plates. Before culture, CD8+ T cells were immunomagnetically separated into CD62L(high)+ and CD62L(low)+/neg subsets enriched for naive/central memory and effector memory cells, respectively. The application of 96-well microtiter plates aimed at creating multiple different responder-stimulator cell compositions in order to provide for the growth of leukemia-reactive CTLs optimized culture conditions by chance. The culture medium was supplemented with interleukin (IL)-7, IL-12, and IL-15. On day 14, IL-12 was replaced by IL-2. In eight different related and unrelated donor/AML pairs with complete HLA class I match, numerous CTL populations were isolated that specifically lysed myeloid leukemias in association with various HLA-A, -B, or -C alleles. These CTLs recognized neither lymphoblastoid B cell lines of donor and patient origin nor primary B cell leukemias expressing the corresponding HLA restriction element. CTLs expressed T cell receptors of single V-beta chain families, indicating their clonality. The vast majority of CTL clones were obtained from mini-MLLCs initiated with CD8+ CD62L(high)+ cells. Using antigen-specific stimulation, multiple CTL populations were amplified to 10e8-10e10 cells within six to eight weeks. The capability of mini-MLLC derived AML-reactive CTL clones to inhibit the engraftment of human primary AML blasts was investigated in the immunodeficient nonobese diabetic/severe combined immune deficient IL-2 receptor common γ-chain deficient (NOD/SCID IL2Rγnull) mouse model. The leukemic engraftment in NOD/SCID IL2Rγnull was specifically prevented if inoculated AML blasts had been pre-incubated in vitro with AML-reactive CTLs, but not with anti-melanoma control CTLs. These results demonstrate that myeloid leukemia-specific CTL clones capable of preventing AML engraftment in mice can be rapidly isolated from CD8+ CD62L(high)+ T cells of healthy donors in vitro. The efficient generation and expansion of these CTLs by the newly established mini-MLLC approach opens the door for several potential applications. First, CTLs can be used within T cell-driven antigen identification strategies to extend the panel of molecularly defined AML antigens that are recognizable by T cells of healthy donors. Second, because these CTLs can be isolated from the stem cell donor by mini-MLLC prior to transplantation, they could be infused into AML patients as a part of the stem cell allograft, or early after transplantation when the leukemia burden is low. The capability of these T cells to expand and function in vivo might require the simultaneous administration of AML-reactive CD4+ T cells generated by a similar in vitro strategy or, less complex, the co-transfer of CD8-depleted donor lymphocytes. To prepare clinical testing, the mini-MLLC approach should now be translated into a protocol that is compatible with good manufacturing practice guidelines.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Charge generation, transport and recombination in organic solar cells

This thesis presents a study of the charge generation, transport, and recombination processes in organic solar cells performed with time-resolved experimental techniques. Organic solar cells based on polymers can be solution-processed on large areas and thus promise to become an inexpensive source of renewable energy. Despite significant improvements of the power conversion efficiency over the last decade, the fundamental working principles of organic solar cells are still not fully understood. It is the aim of this thesis to clarify the role of different performance limiting processes in organic solar cells and to correlate them with the molecular structure of the studied materials, i.e. poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61 butyric acid methyl ester (PCBM). By combining time-of-flight charge transport measurements, transient absorption spectroscopy, a newly developed experimental technique called time delayed double pulse experiment and drift-diffusion simulations a comprehensive analysis of the working principles of P3HT:PCBM solar cells could be performed. It was found that the molecular structure of P3HT (i.e. the regioregularity) has a pronounced influence on the morphology of thin films of pristine P3HT and of blends of P3HT with PCBM. This morphology in turn affected the charge transport properties as well as the charge generation and recombination kinetics. Well-ordered regioregular P3HT was found to be characterized by a high charge carrier mobility, efficient charge generation and low but field-dependent (non-geminate) recombination. Importantly, the charge generation yield was found to be independent of temperature and applied electric field as opposed to the expectations of the Onsager-Braun model that is commonly applied to describe the temperature and field dependence of charge generation in organic solar cells. These properties resulted in a reasonably good power conversion efficiency. In contrast to this, amorphous regiorandom P3HT was found to show poor charge generation, transport and recombination properties that combine to a much lower power conversion efficiency.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Analysis and numerical solution of the Peterlin viscoelastic model

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