Der Austausch von Carbonylsulfid (COS) zwischen Vegetation und Atmosphäre unter erhöhter CO 2-Umgebungskonzentration

The responses of photosynthetic plant gas exchange, COS uptake and carbonic anhydrase (CA) activity were studied on Quercus ilex (Holm oak), and beech Fagus sylvatica L

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Gleichmäßig dünne Basen zweiter Ordnung

Eine Menge B nicht negativer ganzer Zahlen heißt Basis h-ter Ordnung, wenn jede nicht negative ganze Zahl Summe von höchstens h Elementen von B ist. Eine der großen Fragen der additiven Zahlentheorie ist die nach der effektivsten Basis h-ter Ordnung für ein gegebenes h>=2. Im Fokus des Interesses steht dabei der immer noch offene Fall h=2. Bezeichnet B(x) die Anzahl der Elemente b aus B mit 0= af(x), wobei f die Wurzelfunktion bezeichne. Andererseits gibt es Basen B zweiter Ordnung mit B(x) <= cf(x). Daher kann man den Limes superior S(B), den Limes inferior s(B) sowie im Falle der Existenz den Limes d(B) des Quotienten B(x) / f(x) als Dichtefunktionen von Basen zweiter Ordnung betrachten. J. W. S. Cassels konstruierte 1957 eine Basis C zweiter Ordnung mit d(C)=5,196…. G. Hofmeister gab 2001 eine Basis H zweiter Ordnung mit asymptotischer Wurzeldichte d(H)=4,638… an. In der vorliegenden Arbeit wird eine Basis S zweiter Ordnung mit asymptotischer Wurzeldichte d(S)=3,464… konstruiert. Darüber hinaus wird für die von J. W. S. Cassels, für die von G. Hofmeister und für die in dieser Arbeit verwendete Klasse von Basen zweiter Ordnung gezeigt, dass die asymptotische Wurzeldichte innerhalb der jeweiligen Klasse nicht mehr zu verbessern ist. Bisher war die Frage nach möglichen Verbesserungen innerhalb der jeweiligen Konstruktionsprinzipien offen geblieben.

Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Vibrational spectroscopic and electrochemical investigations of multi-centered heme proteins in biomimetic membrane architectures

Membrane proteins play a major role in every living cell. They are the key factors in the cell’s metabolism and in other functions, for example in cell-cell interaction, signal transduction, and transport of ions and nutrients. Cytochrome c oxidase (CcO), as one of the membrane proteins of the respiratory chain, plays a significant role in the energy transformation of higher organisms. CcO is a multi centered heme protein, utilizing redox energy to actively transport protons across the mitochondrial membrane. One aim of this dissertation is to investigate single steps in the mechanism of the ion transfer process coupled to electron transfer, which are not fully understood. The protein-tethered bilayer lipid membrane is a general approach to immobilize membrane proteins in an oriented fashion on a planar electrode embedded in a biomimetic membrane. This system enables the combination of electrochemical techniques with surface enhanced resonance Raman (SERRS), surface enhanced reflection absorption infrared (SEIRAS), and surface plasmon spectroscopy to study protein mediated electron and ion transport processes. The orientation of the enzymes within the surface confined architecture can be controlled by specific site-mutations, i.e. the insertion of a poly-histidine tag to different subunits of the enzyme. CcO can, thus, be oriented uniformly with its natural electron pathway entry pointing either towards or away from the electrode surface. The first orientation allows an ultra-fast direct electron transfer(ET) into the protein, not provided by conventional systems, which can be leveraged to study intrinsic charge transfer processes. The second orientation permits to study the interaction with its natural electron donor cytochrome c. Electrochemical and SERR measurements show conclusively that the redox site structure and the activity of the surface confined enzyme are preserved. Therefore, this biomimetic system offers a unique platform to study the kinetics of the ET processes in order to clarify mechanistic properties of the enzyme. Highly sensitive and ultra fast electrochemical techniques allow the separation of ET steps between all four redox centres including the determination of ET rates. Furthermore, proton transfer coupled to ET could be directly measured and discriminated from other ion transfer processes, revealing novel mechanistic information of the proton transfer mechanism of cytochrome c oxidase. In order to study the kinetics of the ET inside the protein, including the catalytic center, time resolved SEIRAS and SERRS measurements were performed to gain more insight into the structural and coordination changes of the heme environment. The electrical behaviour of tethered membrane systems and membrane intrinsic proteins as well as related charge transfer processes were simulated by solving the respective sets of differential equations, utilizing a software package called SPICE. This helps to understand charge transfer processes across membranes and to develop models that can help to elucidate mechanisms of complex enzymatic processes.

Template-assisted patterning of functional polymers

In this thesis, anodic aluminum oxide (AAO) membranes, which provide well-aligned uniform mesoscopic pores with adjustable pore parameters, were fabricated and successfully utilized as templates for the fabrication of functional organic nanowires, nanorods and the respective well-ordered arrays. The template-assisted patterning technique was successfully applied for the realization of different objectives:rnHigh-density and well-ordered arrays of hole-conducting nanorods composed of cross-linked triphenylamine (TPA) and tetraphenylbenzidine (TPD) derivatives on conductive substrates like ITO/glass have been successfully fabricated. By applying a freeze-drying technique to remove the aqueous medium after the wet-chemical etching of the template, aggregation and collapsing of the rods was prevented and macroscopic areas of perfectly freestanding nanorods were feasible. Based on the hole-conducting nanorod arrays and their subsequent embedding into an electron-conducting polymer matrix via spin-coating, a novel routine concept for the fabrication of well-ordered all-organic bulk heterojunction for organic photovoltaic applications was successfully demonstrated. The increased donor/acceptor interface of the fabricated devices resulted in a remarkable increase of the photoluminescence quenching compared to a planar bilayer morphology. Further, the fundamental working principle of the templating approach for the solution-based all-organic photovoltaic device was demonstrated for the first time.rnFurthermore, in order to broaden the applicability of patterned surfaces, which are feasible via the template-based patterning of functional materials, AAO with hierarchically branched pores were fabricated and utilized as templates. By pursuing the common templating process hierarchically polymeric replicas, which show remarkable similarities with interesting biostructures, like the surface of the lotus leaf and the feet of a gecko, were successfully prepared.rnIn contrast to the direct infiltration of organic functional materials, a novel route for the fabrication of functional nanowires via post-modification of reactive nanowires was established. Therefore, reactive nanowires based on cross-linked pentafluorophenylesters were fabricated by utilizing AAO templates. The post-modification with fluorescent dyes was demonstrated. Furthermore, reactive wires were converted into well-dispersed poly(N-isopropylacrylamide) (PNIPAM) hydrogels, which exhibit a thermal-responsive reversible phase transition. The reversible thermal-responsible swelling of the PNIPAM nanowires exhibited a more than 50 % extended length than in the collapsed PNIPAM state. rnLast but not least, the shape-anisotropic pores of AAO were utilized to uniformly align the mesogens of a nematic liquid crystalline elastomer. Liquid crystalline nanowires with a narrow size distribution and uniform orientation of the liquid crystalline material were fabricated. It was shown that during the transition from the nematic to the isotropic phase the rod’s length shortened by roughly 40 percent. As such these liquid crystalline elastomeric nanowires may find application, as wire-shaped nanoactuators in various fields of research, like lab-on-chip systems, micro fluidics and biomimetics.rn

Convergence results for stochastic particle systems with social interaction

We consider stochastic individual-based models for social behaviour of groups of animals. In these models the trajectory of each animal is given by a stochastic differential equation with interaction. The social interaction is contained in the drift term of the SDE. We consider a global aggregation force and a short-range repulsion force. The repulsion range and strength gets rescaled with the number of animals N. We show that for N tending to infinity stochastic fluctuations disappear and a smoothed version of the empirical process converges uniformly towards the solution of a nonlinear, nonlocal partial differential equation of advection-reaction-diffusion type. The rescaling of the repulsion in the individual-based model implies that the corresponding term in the limit equation is local while the aggregation term is non-local. Moreover, we discuss the effect of a predator on the system and derive an analogous convergence result. The predator acts as an repulsive force. Different laws of motion for the predator are considered.