Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number

We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over Calabi-Yau hypersurfaces in toric varieties, with the number of Kahler moduli equal to one, two, and three and extract physically interesting models. We select models which can lead to three families of matter after dividing by a freely-acting discrete symmetry and including Wilson lines. About 2000 such models on two manifolds are found.Comment: 26 pages, 1 figur

Heterotic Particle Models from various Perspectives

We consider the compactification of heterotic string theory on toroidal orbifolds and their resolutions. In the framework of gauged linear sigma models we develop realizations of such spaces, allowing to continously vary the moduli and thus smoothly interpolate between differrent corners of the theory. This way all factorizable orbifold resolutions as well as some non-factorizable ones can be obtained. We find that for a given geometry there are many model which realize it as a target space, differing in their complexity. We explore regions of moduli space which otherwise would not be accessible. In particular we are interested in the orbifold regime, where exact string calculations are possible, and the large volume regime, where techniques of supergravity compactification can be applied. By comparing these two theories and matching the spectra we find evidence for non-perturbative effects which interpolate between these regimes

D-branes on Calabi-Yau Spaces

In this thesis the properties of D-branes on Calabi–Yau spaces are investigated. Compactifications of type II string theories on these spaces to which D-branes are added lead to N = 1 supersymmetric gauge theories on the world-volume of these D-branes. Both the Calabi–Yau spaces and the D-branes have in general a moduli space. We examine the dependence of the gauge theory on the choice of the moduli, in particular those of the K¨ahler structure of the Calabi–Yau manifold. For this purpose we choose two points in this moduli space which are distinguished by the fact that there exists an explicit description of the spectrum of the D-branes. One of these points corresponds to a manifold in the large volume limit on which the D-branes are described by classical geometry of vector bundles. At the other points the size of the manifold is smaller than its quantum fluctuations such that the classical geometry looses its meaning and has to be replaced by a conformal field theory. The Witten index in the open string sector is independent of the variation of these moduli and serves, together with mirror symmetry, as a tool to compare the two descriptions. We give an extensive and general presentation of these two descriptions for the class of Fermat hypersurfaces in weighted projective spaces. We explicitly carry out the comparison in many representative examples. Among them are manifolds admitting elliptic and K3-fibrations and manifolds whose moduli space can be embedded into the moduli space of another manifold. One main focus is on D4-branes, in particular on the dimension of their moduli space. Using the methods developed we are able to further confirm with our results the modified geometric hypothesis by Douglas. It essentially states that the properties of these D-branes or of these gauge theories can be determined partly by classical geometry, partly by mirror symmetry. A peculiarity of these gauge theories is the appearance of lines of marginal stability at which BPS states can decay. We show the existence of such lines in the framework of this class of Calabi–Yau spaces in two di®erent ways and discuss the connection to the formation of bound states. Of particular interest is the D0-brane whose appearance in this framework is explained

Numerical modeling of F-.Actin bundles interacting with cell membranes

Actin is one of the most aboundant proteins in eukaryotic cells, where it forms a dendridic network (cytoskeleton) beneath the cell membrane providing mechanical stability and performing fundamental tasks in several functions, including cellular motility. The first step in cell locomotion is the protrusion of a leading edge, for which a significant deformation of the membrane is required: this step relies essentially on the forces generated by actin polymerization pushing the plasma membrane outward. Different types of structures can emerge from the plasma membrane, like lamellipodia (quasi-2d actin mesh) and filopodia (parallel actin bundles). The main topic of the research project is the dynamics of bundles of parallel actin filaments growing against barriers, either rigid (a wall) or flexible (a membrane). In the first part of the thesis, the dynamic behavior of bundles of actin filaments growing against a loaded wall is investigated through a generalized version of the standard multi filaments Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semi-flexible discrete wormlike chains with a realistic value of the persistence length. A Statistical Mechanics framework is built for bundles of actin filaments growing in optical trap apparatus (harmonic external load) and several equilibrium properties are derived from it, like the maximum force that the filaments can exert (stalling force) or the number of filaments in contact with the wall. Besides, Stochastic Dynamic simulations are employed to study the non-equilibrium relaxation of the bundle of filaments growing in the same optical trap apparatus, interpreting the system evolution by a suitable Markovian approach. Thanks to the observed time scale separation between the wall motion and the filament size relaxation, the optical trap set-up allows to extract the full velocity-load curve V(F) -- the velocity at which the obstacle moves when subject to the combined action of the polymerizing filaments and the external load F -- from a single experiment. The main finding is the observation of a systematic evolution of steady non-equilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L Λ), where the velocity V(F,L) is an increasing function of the bundle length L at fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore to the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to Perfect Load Sharing. In the second part of the thesis, filaments growing against a flexible, deformable membrane are studied by means of Langevin dynamics simulations; the membrane is discretized into a dynamically triangulated network of tethered beads, while the filaments are described as chains of bonded monomers. Both the monomers in the filaments and the membrane beads, which interact with each other via a purely repulsive potential, are followed in space and time integrating its equations of motion with a second order accurate scheme. The elastic properties of the membrane are studied in detail via several methods, showing an unprecedentent level of agreement among them. The onset of filopodial protrusions is observed for N>1 filaments growing from beneath the membrane and pushing it upwards, with a velocity which is systematically larger for flexible filaments than for rigid ones. Since filaments are wrapped by the membrane in the protrusion, escaping filaments are not predicted nor observed in this case

Planar Nef polyhedra and generic higher-dimensional geometry

We present two generic software projects that are part of the software library CGAL. The first part described the design of a geometry kernel for higher-dimensional Euclidian geometry and the interaction with application programs. We describe software structures, interface concepts, and their models that are based on cooordinate representation, number types, and memory layout. In the higher-dimensional software kernel the interaction between linear algebra and geometric objects and primitves is one important facet. In the actual design our users can replace number types, representation types, and the traits classes that inflate kernel functionality into our current application programs: higher-dimensional convex hulls and Delaunay tedrahedralisations. In the second part we present the realization of planar Nef polyhedra. The concept of Nef polyhedra subsumes all kinds of rectilinear polyhedral subdivisions and is therefore of general applicability within a geometric software library. The software is based on the theory of extended points and segments that allows us to reuse classical algorithmic solutions like plane sweep to realize binary operations of Nef polyhedra.Wir präsentieren zwei Softwareprojekte, die Teil der Softwarebibliothek CGAL sind. Der erste Teil beschreibt den Entwurf eines Geometriekerns für höherdimensionale euklidische Geometrie und dessen Interaktion mit Anwendungsprogrammen. Wir beschreiben die Softwarestruktur, die auf der Herausarbeitung von Schnittstellenkonzepten und ihren Modellen hinsichtlich Koordinatenrepräsentation, Zahlentypen und Speicherablage beruht. Dabei spielt im Höherdimensionalen die Interaktion zwischen linearer Algebra und den entsprechenden geometrischen Objekten und primitiven Operationen eine wesentliche Rolle. Unser Entwurf erlaubt das Auswechseln von Zahlentypen, Repräsentations- und Traitsklassen bei der Berechnung von d-dimensionalen konvexen Hüllen und Delaunay-Simplexzerlegungen. Im zweiten Teil stellen wir die Realisierung von planaren Nef-Polyedern vor. Das Konzept der Nef-Polyeder umfasst alle linear-polyedrisch begrenzten Unterteilungen. Wir beschreiben ein Softwaremodul das umfassende Funktionalität zur Verfügung stellt. Als theoretische Grundlage des Entwurfs dient die Theorie erweiterter Punkte und Segmente, die es uns erlaubt, vorhandene Algorithmen wie z.B. Plane-Sweep zur Realisierung binärer Operationen von Nef-Polyedern zu nutzen