Feynman integrals for a class of exponentially growing potentials

We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schroedinger equation. The Morse potential is considered as a special case

Correlations between high-p(T) and flavour physics

Squark and gluino decays are governed by the same mixing matrices as the contributions to flavour violating loop transitions of B-mesons. This allows for possible direct correlations between flavour non-diagonal observables in B and high-p_T physics. The present bounds on squark mixing, induced by the low-energy data on b to s transitions, still allow for large contributions to flavour violating squark decays at tree level. Due to the restrictions in flavour tagging at the LHC, additional information from future flavour experiments will be necessary to interpret those LHC data properly. Also the measurement of correlations between various squark decay modes at a future ILC would provide information about the flavour violating parameters

A hydrodynamical perspective on the turbulent transport of bacteria in rivers

The transport of bacteria in turbulent river-like environments is addressed, where bacterial populations are frequently encountered attached to solids. This transport mode is investigated by studying the transient settling of heavy particles in turbulent channel flows featuring sediment beds. A numerical method is used to fully resolve turbulence and finite-size particles, which enables the assessment of the complex interplay between flow structures, suspended solids and river sediment

A hydrodynamical perspective on the turbulent transport of bacteria in rivers

The transport of bacteria in river systems is a phenomenon which occurs on a multitude of length scales ranging from the size of individual microbes up to the size of an entire estuary. At the same time the understanding of the spreading of microbial populations after a localised contamination event such as a combined sewer overflow is crucial for the prediction of the water quality downstream of the source, which is in turn essential to managing public health. It is well-established that microbial populations in fluvial systems may preferably be found on the surface of small particles rather than solely freely suspended in the water body. The attachment to particles provides an environment beneficial to the survival of bacteria due to the improved access to nutrients and the shielding from environmental stressors, but also alters their dispersion characteristics as the transport of bacteria is then coupled to the trajectories of heavy particles. The importance in the distinction between the particle-attached and the freely-suspended mode of transport has been recognised in the mechanistic modelling of bacteria fate and transport. However, due to the multiscale nature of the problem, the mechanisms which govern the transport of particles in river-like flows are never resolved explicitly, and hence, the models profoundly rely upon the availability of accurate descriptions thereof. The associated problem of particles settling in a turbulent carrier flow is an active topic of research by itself, and is rich in emerging phenomena such as the emergence of spatial inhomogeneities or non-trivial modifications of the settling characteristics compared to quiescent environments. In particular, the transient settling of particles in horizontal open channels, which serves as an abstraction of particle-attached bacteria transport in rivers, has hitherto received only little attention in the literature. As a consequence, the knowledge on the impact of its defining features such as boundedness, anisotropy and vertical inhomogeneity on the settling characteristics is limited and needs to be addressed to enable the formulation of reliable models thereof. The aim of this thesis is to fill the knowledge gap on the transport characteristics of heavy particles in turbulent horizontal open channel flows, and to identify phenomena which may be of importance in the context of bacteria transport modelling. For this purpose, the incompressible Navier--Stokes equations and the momentum balance equations for dispersed particles are solved using direct numerical simulations and the immersed boundary method. This approach resolves all relevant scales of turbulence and the microscopic flow around each particle explicitly, and thus, describes the particle-fluid interaction from fundamental principles of physics without the need of additional modelling. Apart from the contaminated particles, which are introduced near the free surface of the flow, the simulation domain includes approximately 100,000 fully resolved particles at the bottom of the domain, which form a realistic sediment bed, and enable the examination of the interaction between contaminated particles and mobile sediments. Concerning the parameter space, the value of the friction Reynolds number is varied within the range $Re_{\tau} \in [241,838]$, while the contaminant parameter space is chosen such that the resulting relative turbulence intensities---defined as the ratio between the friction velocity and the undisturbed terminal velocity---lie within the range $I_{\tau} \in [0.47,2.88]$. Moreover, two types of sediment bedforms are investigated in order to assess their effect on contaminant transport, namely a macroscopically flat bed and a bed featuring ripples. The analysis of the simulation data shows that the settling velocity of the contaminant particles is enhanced in the ensemble-averaged sense, yet, the time from beginning of the settling until the initial deposition is prolonged when compared to the ratio between the channel height and the terminal velocity. The enhancement is demonstrated to be a result of the preferential sampling of turbulent sweep events, which also implies that the streamwise component of the particle velocity is increased compared to the mean fluid velocity at the same position. A closer examination of the spatial organisation of contaminated particles reveals that they tend to accumulate in large-scale high-speed velocity streaks in the outer region of turbulence. Due to this focusing mechanism, the mean-squared lateral displacement of the settling particles stagnates in the lower half of the channel such that contaminants are not further dispersed in cross-stream direction until shortly before deposition. The same behaviour could be reproduced using a time-invariant exact coherent flow state resembling a hairpin vortex as a proxy for turbulence, and an extended parameter sweep in this setup suggests that this transport barrier effect persists even at high relative turbulence intensities. It is speculated that this phenomenon might confine contaminated particles to a region close to the river bank over a considerable downstream distance in the aftermath of a combined sewer overflow event, which might seriously impact decisions regarding public health measures. Near the sediment bed, the barrier effect of the large-scale motions is inactive and contaminants are found to disperse laterally at a rate which presumably depends on the Shields parameter. The interaction between the sediment and the contaminants is distinct for the two bed topologies under investigation. In the case of macroscopically flat beds, the contaminated particles are transported towards sediment ridges which are in turn known to be a result of the action of large-scale fluid motions, and the mixing of contaminants and sediment particles is restricted to the thin layer of sediment near the interface. In contrast, the presence of ripples leads to a capturing effect where contaminated particles are preferentially deposited in the trough of the ripple, and subsequently buried by a thick layer of sediment due to the propagation of the bed feature. This mechanism temporarily immobilises a large share of all contaminated particles until the displacement of the ripple has sufficiently progressed for them to be eroded on the windward side. During the immobilisation, the associated bacteria are shielded from solar radiation to a substantial degree, which likely has a significant impact on their inactivation, especially in shallow waters. Moreover, the cyclic nature of this phenomenon may provide one of many explanations for bacteria storages which are known to exist in river sediments and may cause bursts in fecal bacteria indicator levels even in absence of immediate contamination events. It is concluded that direct numerical simulation can be a valuable tool for the analysis of bacteria transport, and recommendations are made on how the conjectures compiled in this thesis can be targeted in laboratory experiments to examine their relevance

Dark matter scenarios in a constrained model with Dirac gauginos

We perform the first analysis of Dark Matter scenarios in a constrained model with Dirac Gauginos. The model under investigation is the Constrained Minimal Dirac Gaugino Supersymmetric Standard model (CMDGSSM) where the Majorana mass terms of gauginos vanish. However, $R$-symmetry is broken in the Higgs sector by an explicit and/or effective $B_\mu$-term. This causes a mass splitting between Dirac states in the fermion sector and the neutralinos, which provide the dark matter candidate, become pseudo-Dirac states. We discuss two scenarios: the universal case with all scalar masses unified at the GUT scale, and the case with non-universal Higgs soft-terms. We identify different regions in the parameter space which fullfil all constraints from the dark matter abundance, the limits from SUSY and direct dark matter searches and the Higgs mass. Most of these points can be tested with the next generation of direct dark matter detection experiments.Comment: 28 pages, 11 figures; v2: minor changes, title modified; matches published versio

Controlling hole spin dynamics in two‐dimensional hole systems at low temperatures

With the recent discovery of very long hole spin decoherence times in GaAs/AlGaAs heterostructures of more than 70 ns in two-dimensional hole systems, using the hole spin as a viable alternative to electron spins in spintronic applications seems possible. Furthermore, as the hyperfine interaction with the nuclear spins is likely to be the limiting factor for electron spin lifetimes in zero dimensions, holes with their suppressed Fermi contact hyperfine interaction due to their p-like nature should be able to show even longer lifetimes than electrons. For spintronic applications, electric-field control of hole spin dynamics is desirable. Here, we report on time-resolved Kerr rotation and resonant spin amplification measurements on a two-dimensional hole system in a p-doped GaAs/AlGaAs heterostructure. Via a semitransparent gate, we tune the charge density within the sample. We are able to observe a change in the hole g factor, as well as in the hole spin dephasing time at high magnetic fields