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Recently, Aumüller and Dietzfelbinger proposed a version of a dual-pivot Quicksort, called "Count", which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this master's thesis we provide further probabilistic analysis of "Count". We derive an exact formula for the average number of swaps needed by "Count" as well as an asymptotic formula for the variance of the number of swaps and a limit law. Also for the number of key comparisons the asymptotic variance and a limit law are identified. We also consider both complexity measures jointly and find their asymptotic correlation.
In thesis I investigate the possibility that at the smallest length scale (Planck scale) the very notion of "dimension" needs to be revisited. Due to "quantum effects" spacetime might become very turbulent at these scales and properties like those of "fractals" emerge, including a "scale dependent dimension". It seems that this "spontaneous dimensional reduction" and the appearance of a minimal physical length are very general effects that most approaches to quantum gravity share. Main emphasis is given to the"spectral dimension" and its calculation for strings and p-branes.
The aim of this thesis is finding a geometric configuration that allows electron insertion into a Gabor plasma lens in order to increase the density of the confined electrons and provide ignition conditions at parameters where ignition is not possible. First, simulations using CST and bender were conducted to investigate several geometric configurations in terms of their performance of inserting electrons manually. One particular design has been chosen as a basis for an experiment. In order to prepare the experiment, further simulations using the code bender have been conducted to investigate the density distribution that is formed inside the Gabor lens when inserting electrons transversally in compliance with the chosen design. Additionally, bender was used to investigate the impact of the initial electron energy on the distribution inside the lens. Simulations with and without space charge effects have shown a significant impact of the space charge effects on the resulting density dstribution. Therefore, space charge effects have proven to be the major electron redistribution process. A given electron source was characterised in order to find the performance under the conditions inside a Gabor lens. In particular, a transversal magnetic field that will be present in the experiment has to be compensated by shielding the inner regions of the source by a μ-metal layer. Using a μ-metal shield, transversal magnetic fields are sufficiently tolerable to perform measurements in a Gabor lens. Additionally, operating close to 100 eV electron energy yields a maximum in the emitted current. Adding a Wehnelt cylinder to the electron source furthermore improves the extracted current to roughly 1 mA. A test stand consisting of a newly designed anode for the Gabor lens, as well as a terminal for the electron source, was constructed. The electron source was thoroughly characterised in the environment of the Gabor lens and the ignition properties of the new system were evaluated. In further experiments, electron beam assisted ignition by increasing the residual gas pressure was observed and the impact of the position of the electron source on the ignition properties was investigated. In addition, ignition of a sub-critical state, that is a state consisting of potential, magnetic field and pressure that did not yet perform ignition by itself, was performed by increasing the extracted current from the electron source. Finally, the electron source was used to influence a pre-ignited plasma. The density was measured, which was increased by the use of the electron source in most cases. This project is part of the EDEN collaboration (Electron DENsity boosting) of the NNP Group at IAP Frankfurt with INFN institutes in Bologna and Catania.
Cleaning an ion beam from unwanted fractions is crucial for intense ion beams. This thesis will explore separation methods using a collimation channel, electric and magnetic dipoles and a velocity selector for low intensity beams on an experimental basis. In addition, statistical data of degassing events during the commissioning of a pentode extraction system for beam energies from 20 - 120keV will be presented.
Gabor lenses were invented for focusing hadron beams by the electric field of a confined electron column. A homogenous magnetic field created by a solenoid confines electrons in transverse direction while a potential well created by a cylindrical electrode system confines them longitudinally.
In this thesis the investigation and characterization of a nonneutral electron plasma (NNP) in a Gabor lens with a toroidal magnetic confinement and a 30 degree-bent anode is presented. Motivated by fundamental research on NNPs in this special environment, diagnostic methods were investigated to characterize the plasma. As a non-invasive method a PCO camera is placed in front of the experimental setup. A ring of 31 photodiodes is used inside the plasma for light intensity and distribution measurements. The experimental data is evaluated and the following results will be presented.
Electron identification with a likelihood method and measurements of di-electrons for the CBM-TRD
(2017)
In this work a likelihood method has been implemented and investigated as particle identification algorithm for the CBM-TRD.
The creation of the probability distributions for the likelihood method via V0-topologies seems to be feasible and the purity of the obtained samples is sufficient for the usage in the likelihood method.
The comparison between the ANN and the likelihood method shows no differences in the identification performance. The pion suppression factor reaches the same values for the same electron identification efficiencies and the yields of the resulting di-lepton signals are comparable. The signal-to-background ratios for both methods have the same values and show a value of about 10−2 in the invariant mass range of minv = 1.5 - 2.5 GeV/c2, which is expected to be sufficient to provide access to the thermal in-medium and QGP radiation.
The investigation of a detector system without a TRD shows no pion suppression for a momentum above p = 6 GeV/c. Therefore, the background contributions increase drastically and the signal-to-background ratio decreases at all invariant masses, but especially in the invariant mass range of minv = 1.5 - 2.5 GeV/c2.
The background contributions in the invariant mass range of minv = 1.5 - 2.5 GeV/c 2 are also influenced by the selected electron identification efficiency of the TRD, which significantly shifts the fraction of the eπ contributions relative to the total number of pairs.
Der digitale Wandel wirkt sich auf das alltägliche Leben in der modernen Lebenswelt im 21. Jahrhundert aus. Ob im Berufs- oder Privatleben, digitale Medien sind nicht mehr aus dem alltäglichen Leben wegzudenken und sie erleichtern das Leben maßgeblich.
E-Learning wird insbesondere in der Erwachsenenbildung benutzt und diese Branche "boomt". Umstritten ist dennoch, ob digitale Medien und E-Learning in Schulen eingesetzt werden sollten und ob ein Lernen und Lehren mit neuen Medien sinnvoll ist. Derzeitig ist keine bundesweite einheitliche Lehrerausbildung bezüglich des Umgangs mit digitalen Medien im Kontext Lehren und Lernen und den damit verbundenen Herausforderungen vorhanden.
Es stellt sich die Frage, wie neue Medien im Unterricht verwendet werden und welche Aspekte beim Lehren zu beachten sind.
Der digitale Wandel wirkt sich auf das alltägliche Leben in der modernen Lebenswelt im 21. Jahrhundert aus. Ob im Berufs- oder Privatleben, digitale Medien sind nicht mehr aus dem alltäglichen Leben wegzudenken und sie erleichtern das Leben maßgeblich.
E-Learning wird insbesondere in der Erwachsenenbildung benutzt und diese Branche "boomt". Umstritten ist dennoch, ob digitale Medien und E-Learning in Schulen eingesetzt werden sollten und ob ein Lernen und Lehren mit neuen Medien sinnvoll ist. Derzeitig ist keine bundesweite einheitliche Lehrerausbildung bezüglich des Umgangs mit digitalen Medien im Kontext Lehren und Lernen und den damit verbundenen Herausforderungen vorhanden.
Es stellt sich die Frage, wie neue Medien im Unterricht verwendet werden und welche Aspekte beim Lehren zu beachten sind.
In April and May 2012 data on Au+Au collisions at beam energies of Ekin = 1.23A GeV were collected with the High Acceptance Di-Electron Spectrometer (HADES) at the GSI Helmholtzzentrum für Schwerionenforschung facility in Darmstadt, Germany. In this thesis, the production of deuterons in this collision system is investigated.
A total number of 2.1 × 109 Au+Au events is selected, containing the most central 0-40% of events. After particle identification, based on a mass determination via time-of-flight and momentum and on a measurement of the energy loss, the transverse mass spectra of the deuteron candidates are extracted for various rapidities and subsequently corrected for acceptance and efficiency.
The inverse slope parameter of a Boltzmann fit applied to the transverse mass spectra at midrapidity, which is referred to as the effective temperature, is extracted. For a static thermal source, this parameter corresponds to the kinetic freeze-out temperature Tkin and is therefore expected to be smaller or equal to the chemical freeze-out temperature Tchem. The extracted effective temperature of Tef f = (190 ± 10) MeV however exceeds the chemical freeze-out temperature that was obtained by a statistical model fit to different particle yields. The effective temperatures of various particle species, obtained in previous analyses, suggest a systematic rise with increasing particle mass, which is confirmed by the deuteron results.
An explanation can be the influence of a collective expansion with a radial expansion velocity βr. By fitting a Siemens-Rasmussen function to the transverse mass spectra, the global temperature of T = (100 ± 8) MeV and radial expansion velocity βr = 0.37 ± 0.01 are obtained. This temperature is still very high and only takes into account the production of deuteron nuclei.
The simultaneous fit of a blast-wave function to the transverse mass spectra of deuterons and other particles, as obtained by previous analyses, considers a velocity profile for the radial expansion velocity and takes into account the production of various particle species. The resulting global temperature Tkin = (68 ± 1) MeV and average transverse expansion velocity hβri = 0.341 ± 0.003 are within the expected range for the collision energy.
The Siemens-Rasmussen fits are also used to extrapolate the transverse mass spectra into unmeasured regions, to integrate them and obtain a rapidity-dependent count rate. This count rate exhibits a thermal shape for central events and shows increasing spectator contributions for more peripheral events.
The invariant yield spectra of the deuterons are compared to those of protons, as obtained by a previous analysis, in the context of a nucleon coalescence model. The hereby extracted nucleon coalescence factor B2 = (4.6 ± 0.1) × 10−3 agrees with the expected result for the beam energy that was studied.