Moduli spaces of colored graphs

We introduce moduli spaces of colored graphs, defined as spaces of non-degenerate metrics on certain families of edge-colored graphs. Apart from fixing the rank and number of legs these families are determined by various conditions on the coloring of their graphs. The motivation for this is to study Feynman integrals in quantum field theory using the combinatorial structure of these moduli spaces. Here a family of graphs is specified by the allowed Feynman diagrams in a particular quantum field theory such as (massive) scalar fields or quantum electrodynamics. The resulting spaces are cell complexes with a rich and interesting combinatorial structure. We treat some examples in detail and discuss their topological properties, connectivity and homology groups

Phase Diagram of the Dzyaloshinskii-Moriya Helimagnet Ba2CuGe2O7 in Canted Magnetic Fields

The evolution of different magnetic structures of non-centrosymmetric Ba2CuGe2O7 is systematically studied as function of the orientation of the magnetic field H. Neutron diffraction in combination with measurements of magnetization and specific heat show a virtually identical behaviour of the phase diagram of Ba2CuGe2O7 for H confined in both the (1,0,0) and (1,1,0) plane. The existence of a recently proposed incommensurate double-k AF-cone phase is confirmed in a narrow range for H close to the tetragonal c-axis. For large angles enclosed by H and the c-axis a complexely distorted non-sinusoidal magnetic structure has recently been observed. We show that its critical field Hc systematically increases for larger canting. Measurements of magnetic susceptibility and specific heat finally indicate the existence of an incommensurate/commensurate transition for H /sim 9 T applied in the basal (a,b)-plane and agree with a non-planar, distorted cycloidal magnetic structure.Comment: 14 pages, 13 figure

Commensurate Nb2Zr5O15: Accessible Within the Field Nb2ZrxO2x+5 After All

Doped niobium zirconium oxides are applied in field-effect transistors and as special-purpose coatings. Whereas their material properties are sufficiently known, their crystal structures remain widely uncharacterized. Herein, we report on the comparably mild sol–gel synthesis of Nb2Zr5O15 and the elucidation of its commensurately modulated structure via neutron diffraction. We describe the structure using the most appropriate superspace as well as the convenient supercell approach. It is part of an α-PbO2-homeotypic field with the formula Nb2ZrxO2x+5, which has previously been reported only for x ≥ 5.1, and is closely related to the structure of Hf3Ta2O11. The results, supported by X-ray diffraction and additional synthesis experiments, are contextualized within the existing literature. Via the sol–gel route, metastable Nb–Zr–O compounds and their heavier congeners are accessible that shed light on possible structures of these commercially utilized materials.DFG, 198634447, SPP 1613: Regenerativ erzeugte Brennstoffe durch lichtgetriebene Wasserspaltung: Aufklärung der Elementarprozesse und Umsetzungsperspektiven auf technologische KonzepteTU Berlin, Open-Access-Mittel - 201

Cutkosky’s theorem for massive one-loop Feynman integrals: part 1

We formulate and prove Cutkosky’s Theorem regarding the discontinuity of Feynman integrals in the massive one-loop case up to the involved intersection index. This is done by applying the techniques to treat singular integrals developed in Fotiadi et al. (Topology 4(2):159–191, 1965) . We write one-loop integrals as an integral of a holomorphic family of holomorphic forms over a compact cycle. Then, we determine at which points simple pinches occur and explicitly compute a representative of the corresponding vanishing sphere. This also yields an algorithm to compute the Landau surface of a one-loop graph without explicitly solving the Landau equations. We also discuss the bubble, triangle and box graph in detail.Peer Reviewe

Multiskalenmodellierung heterogener Katalyse in porösen Metallschäumen mithilfe partikelbasierter Simulationsmethoden

In this work, we investigate and optimize heterogeneous catalysis in porous metal foams. First, we consider the gas dynamics together with the reaction and diffusion processes in individual foam pores on the mesoscale. Second, we condense the detailed simulation results on the mesoscale to relations between few, dimensionless numbers. Based on these relations, we follow a multiscale approach to derive an efficient, one-dimensional, macroscale model for metal foam filled catalytic converters. Due to its industrial relevance, we focus on the mass transfer limited regime. Finally, we develop a simple recipe to determine optimum pore size configurations.For realistic heat release values, the heat transfer out of the catalytic converter is critical. We show hat, in order to keep temperature fluctuations small, the optimum configuration consists of several, stacked foam segments with decreasing pore size along the main flow direction. For typical parameters, we observe that, compared to foam with constant pore size, the trade-off between chemical conversion and flow resistance can be increased significantly, while the required reactive surface area, i.e., the needed amount of catalytic material, is reduced substantially.Diese Arbeit befasst sich mit der Untersuchung und Optimierung heterogener Katalyse in porösen Metallschaumstrukturen. Zunächst betrachten wir die Strömungsverhältnisse sowie die Reaktions- und Diffusionsprozesse innerhalb einer einzelnen Schaumpore auf Mesoskala. Im Anschluss daran, kondensieren wir die detaillierten Simulationsergebnisse auf Mesoskala zu Zusammenhängen zwischen wenigen, dimensionslosen Kennzahlen. Darauf aufbauend wenden wir einen Multiskalenansatz an, um ein effizientes, eindimensionales, makroskopisches Modell zur Beschreibung heterogener Katalyse in offenporigen, porösen, Metallschäumen abzuleiten. Aufgrund seiner industriellen Bedeutung konzentrieren wir uns auf das Regime, in dem der Stofftransport den limitierenden Faktor darstellt. Abschließend erstellen wir eine einfache Anleitung, um die optimale Konfiguration für mit Metallschaum gefüllte Katalysatoren zu bestimmen. Für realistische Werte der Reaktionswärme ist die Wärmeableitung aus dem Katalysator entscheidend. Um Temperaturschwankungen gering zu halten, besteht die optimale Konfiguration in diesem Fall aus mehreren, aneinandergereihten Schaumsegmenten mit abnehmender Porengröße entlang der Hauptströmungsrichtung. Für typische Parameter zeigt sich, dass im Vergleich zur Konfiguration mit konstanter Porengröße der Trade-off zwischen chemischer Umwandlung und Strömungswiderstand deutlich verbessert werden kann, wobei gleichzeitig die erforderliche reaktive Oberfläche, d.h. die benötigte Menge an katalytischem Material, erheblich reduziert wird