Correlated transport and non-Fermi liquid behavior in single-wall carbon nanotubes

We derive the effective low-energy theory for single-wall carbon nanotubes including the Coulomb interactions among electrons. The generic model found here consists of two spin-1/2 fermion chains which are coupled by the interaction. We analyze the theory using bosonization, renormalization-group techniques, and Majorana refermionization. Several experimentally relevant consequences of the breakdown of Fermi liquid theory observed here are discussed in detail, e.g., magnetic instabilities, anomalous conductance laws, and impurity screening profiles.Comment: 23 pages REVTeX, incl 5 figs, to appear in Europ.Phys.Journal

LEP Constraints on 5-Dimensional Extensions of the Standard Model

We study minimal 5-dimensional extensions of the Standard Model, in which all or only some of the SU(2)$_L$ and U(1)$_Y$ gauge fields and Higgs bosons propagate in the fifth compact dimension. In all the 5-dimensional settings, the fermions are assumed to be localized on a 3-brane. In addition, we present the consistent procedure for quantizing 5-dimensional models in the generalized $R_\xi$ gauge. Bounds on the compactification scale between 4 and 6 TeV, depending on the model, are established by analyzing electroweak precision measurements and LEP2 cross sections.Comment: 6 pages, talk given at the 10th international conference on ``Supersymmetry and Unification of Fundamental Interactions,'' Hamburg, Germany, 17--23 June 200

Exact solution of the three-boson problem at vanishing energy

A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.Comment: 12 page

A Space-Time Variational Method for Optimal Control Problems

We consider a space-time variational formulation of a PDE-constrained optimal control problem with box constraints on the control and a parabolic PDE with Robin boundary conditions. In this setting, the optimal control problem reduces to an optimization problem for which we derive necessary and sufficient optimality conditions. Next, we introduce a space-time (tensorproduct) discretization using finite elements in space and piecewise linear functions in time. This setting is known to be equivalent to a Crank-Nicolson time stepping scheme for parabolic problems. The optimization problem is solved by a projected gradient method. We show numerical comparisons for problems in 1d, 2d and 3d in space. It is shown that the classical semi-discrete primal-dual setting is more efficient for small problem sizes and moderate accuracy. However, the space-time discretization shows good stability properties and even outperforms the classical approach as the dimension in space and/or the desired accuracy increases.Comment: 20 page

Geospatial Innovation in the Digital Humanities:Implementation and Evaluation of Deep Mapping in the Lake District

This thesis explores the concept of Deep Mapping and how it can be implemented and evaluated using historic texts from the Lake District region. Deep Mapping is a new way to approach, understand and analyze the relationship between geography, history and literature through a variety of media. Deep Mapping has been discussed in the literature, but few practical implementations of the concept have been created. This thesis works to bridge the gap between the theoretical concept of Deep Mapping and its real-world application and use. The primary data used for this thesis is the Corpus of Lake District Writing, a collection of texts collected by researchers. This corpus contains 80 manually digitized texts about the Lake District region from 1622 to 1900. The corpus is made up of several different genres, including travel journals, essays, novels, and poetry. These texts, along with other multimedia, were brought together with interdisciplinary methods drawn from the fields of history, literature, corpus linguistics, spatial and digital humanities and computer science to create Deep Mapping prototypes. A series of case studies, discussed in chapters 3-7, were undertaken to explore Deep Mapping. Each case study focuses on developing a different Deep Map prototype addressing a new problem and set of objectives. Each prototype was then evaluated based on three sets of criteria: addressing the problem and objectives (design), this thesis’s research questions (research), and classifications of digital and spatial humanities and Deep Mapping (data). The last case study, chapter 7, focuses on processing data not related to the Lake District in order to explore if the methods used to develop the prototypes in chapters 3-6 are repeatable with other data sources. The final chapters discuss the implementation and evaluation of Deep Mapping. This thesis produced four Deep Mapping prototypes that can be used as exemplars for future research. The evaluation of these prototypes led to the development of the Evaluation Rubric, that can be used in the evaluation of applications to help determine their fit as a Deep Map and to assist in the comparison in Deep Mapping applications developed in contrasting forms and based on differing content

K-Funktionen als Instrument zur Analyse räumlicher (De-)Konzentrationsprozesse

Zur Messung räumlicher Konzentration ökonomischer Aktivitäten stehen verschiedene Verfahren zur Verfügung. Nachstehend wird mit den distanzbasierten uni- und bivariaten KFunktionen eine neue Methode vorgestellt, die Vorteile gegenüber den herkömmlichen, auf regionaler Abgrenzung basierenden Verfahren aufweist. Mit Hilfe der univariaten KFunktionen wird die Clusterung innerhalb der Sektoren im Verarbeitenden Gewerbe in Deutschland untersucht. Mit bivariaten K-Funktionen werden gegenseitige Abhängigkeiten bei der Clusterung dieser Sektoren untersucht.