Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Neuronal differentiation and epithelial integrity: the role of Drosophila Short stop

The nervous system is the most complex organ in animals and the ordered interconnection of neurons is an essential prerequisite for normal behaviour. Neuronal connectivity requires controlled neuronal growth and differentiation. Neuronal growth essentially depends on the actin and microtubule cytoskeleton, and it has become increasingly clear, that crosslinking of these cytoskeletal fractions is a crucial regulatory process. The Drosophila Spectraplakin family member Short stop (Shot) is such a crosslinker and is crucial for several aspects of neuronal growth. Shot comprises various domains: An actin binding domain, a plakin-like domain, a rod domain, calcium responsive EF-hand motifs, a microtubule binding Gas2 domain, a GSR motif and a C-terminal EB1aff domain. Amongst other phenotypes, shot mutant animals exhibit severely reduced dendrites and neuromuscular junctions, the subcellular compartmentalisation of the transmembrane protein Fasciclin2 is affected, but it is also crucially required in other tissues, for example for the integrity of tendon cells, specialised epidermal cells which anchor muscles to the body wall. Despite these striking phenotypes, Shot function is little understood, and especially we do not understand how it can carry out functions as diverse as those described above. To bridge this gap, I capitalised on the genetic possibilities of the model system Drosophila melanogaster and carried out a structure-function analysis in different neurodevelopmental contexts and in tendon cells. To this end, I used targeted gene expression of existing and newly generated Shot deletion constructs in Drosophila embryos and larvae, analyses of different shot mutant alleles, and transfection of Shot constructs into S2 cells or cultured fibroblasts. My analyses reveal that a part of the Shot C-terminus is not essential in the nervous system but in tendon cells where it stabilises microtubules. The precise molecular mechanism underlying this activity is not yet elucidated but, based on the findings presented here, I have developed three alternative testable hypothesis. Thus, either binding of the microtubule plus-end tracking molecule EB1 through an EB1aff domain, microtubulebundling through a GSR rich motif or a combination of both may explain a context-specific requirement of the Shot C-terminus for tendon cell integrity. Furthermore, I find that the calcium binding EF-hand motif in Shot is exclusively required for a subset of neuronal functions of Shot but not in the epidermal tendon cells. These findings pave the way for complementary studies studying the impact of [Ca2+] on Shot function. Besides these differential requirements of Shot domains I find, that most Shot domains are required in the nervous system and tendon cells alike. Thus the microtubule Gas2 domain shows no context specific requirements and is equally essential in all analysed cellular contexts. Furthermore, I could demonstrate a partial requirement of the large spectrin-repeat rod domain of Shot in neuronal and epidermal contexts. I demonstrate that this domain is partially required in processes involving growth and/or tissue stability but dispensable for cellular processes where no mechanical stress resistance is required. In addition, I demonstrate that the CH1 domain a part of the N-terminal actin binding domain of Shot is only partially required for all analysed contexts. Thus, I conclude that Shot domains are functioning different in various cellular environments. In addition my study lays the base for future projects, such as the elucidation of Shot function in growth cones. Given the high degree of conservation between Shot and its mammalian orthologues MACF1/ACF7 and BPAG1, I believe that the findings presented in this study will contribute to the general understanding of spectraplakins across species borders.

Early steps in ventral nerve cord development in chelicerates and myriapods and formation of brain compartments in spiders

The central point of this work is the investigation of neurogenesis in chelicerates and myriapods. By comparing decisive mechanisms in neurogenesis in the four arthropod groups (Chelicerata, Crustacea, Insecta, Myriapoda) I was able to show which of these mechanisms are conserved and which developmental modules have diverged. Thereby two processes of embryonic development of the central nervous system were brought into focus. On the one hand I studied early neurogenesis in the ventral nerve cord of the spiders Cupiennius salei and Achaearanea tepidariorum and the millipede Glomeris marginata and on the other hand the development of the brain in Cupiennius salei.rnWhile the nervous system of insects and crustaceans is formed by the progeny of single neural stem cells (neuroblasts), in chelicerates and myriapods whole groups of cells adopt the neural cell fate and give rise to the ventral nerve cord after their invagination. The detailed comparison of the positions and the number of the neural precursor groups within the neuromeres in chelicerates and myriapods showed that the pattern is almost identical which suggests that the neural precursors groups in these arthropod groups are homologous. This pattern is also very similar to the neuroblast pattern in insects. This raises the question if the mechanisms that confer regional identity to the neural precursors is conserved in arthropods although the mode of neural precursor formation is different. The analysis of the functions and expression patterns of genes which are known to be involved in this mechanism in Drosophila melanogaster showed that neural patterning is highly conserved in arthropods. But I also discovered differences in early neurogenesis which reflect modifications and adaptations in the development of the nervous systems in the different arthropod groups.rnThe embryonic development of the brain in chelicerates which was investigated for the first time in this work shows similarities but also some modifications to insects. In vertebrates and arthropods the adult brain is composed of distinct centres with different functions. Investigating how these centres, which are organised in smaller compartments, develop during embryogenesis was part of this work. By tracing the morphogenetic movements and analysing marker gene expressions I could show the formation of the visual brain centres from the single-layered precheliceral neuroectoderm. The optic ganglia, the mushroom bodies and the arcuate body (central body) are formed by large invaginations in the peripheral precheliceral neuroectoderm. This epithelium itself contains neural precursor groups which are assigned to the respective centres and thereby build the three-dimensional optical centres. The single neural precursor groups are distinguishable during this process leading to the assumption that they carry positional information which might subdivide the individual brain centres into smaller functional compartments.rn

Conceptual and normative issues of memory enhancement

Our growing understanding of human mind and cognition and the development of neurotechnology has triggered debate around cognitive enhancement in neuroethics. The dissertation examines the normative issues of memory enhancement, and focuses on two issues: (1) the distinction between memory treatment and enhancement; and (2) how the issue of authenticity concerns memory interventions, including memory treatments and enhancements. rnThe first part consists of a conceptual analysis of the concepts required for normative considerations. First, the representational nature and the function of memory are discussed. Memory is regarded as a special form of self-representation resulting from a constructive processes. Next, the concepts of selfhood, personhood, and identity are examined and a conceptual tool—the autobiographical self-model (ASM)—is introduced. An ASM is a collection of mental representations of the system’s relations with its past and potential future states. Third, the debate between objectivist and constructivist views of health are considered. I argue for a phenomenological account of health, which is based on the primacy of illness and negative utilitarianism.rnThe second part presents a synthesis of the relevant normative issues based on the conceptual tools developed. I argue that memory enhancement can be distinguished from memory treatment using a demarcation regarding the existence of memory-related suffering. That is, memory enhancements are, under standard circumstances and without any unwilling suffering or potential suffering resulting from the alteration of memory functions, interventions that aim to manipulate memory function based on the self-interests of the individual. I then consider the issue of authenticity, namely whether memory intervention or enhancement endangers “one’s true self”. By analyzing two conceptions of authenticity—authenticity as self-discovery and authenticity as self-creation, I propose that authenticity should be understood in terms of the satisfaction of the functional constraints of an ASM—synchronic coherence, diachronic coherence, and global veridicality. This framework provides clearer criteria for considering the relevant concerns and allows us to examine the moral values of authenticity. rn