Analytische Ableitungen der Energie für den "Equation-of-Motion-Coupled-Cluster"-Ansatz zur Berechnung von Ionisationspotentialen

In der vorliegenden Arbeit wird die Theorie der analytischen zweiten Ableitungen für die EOMIP-CCSD-Methode formuliert sowie die durchgeführte Implementierung im Quantenchemieprogramm CFOUR beschrieben. Diese Ableitungen sind von Bedeutung bei der Bestimmung statischer Polarisierbarkeiten und harmonischer Schwingungsfrequenzen und in dieser Arbeit wird die Genauigkeit des EOMIP-CCSD-Ansatzes bei der Berechnung dieser Eigenschaften für verschiedene radikalische Systeme untersucht. Des Weiteren können mit Hilfe der ersten und zweiten Ableitungen vibronische Kopplungsparameter berechnet werden, welche zur Simulation von Molekülspektren in Kombination mit dem Köppel-Domcke-Cederbaum (KDC)-Modell - in der Arbeit am Beispiel des Formyloxyl (HCO2)-Radikals demonstriert - benötigt werden.rnrnDer konzeptionell einfache EOMIP-CC-Ansatz wurde gewählt, da hier die Wellenfunktion eines Radikalsystems ausgehend von einem stabilen geschlossenschaligen Zustand durch die Entfernung eines Elektrons gebildet wird und somit die Problematik der Symmetriebrechung umgangen werden kann. Im Rahmen der Implementierung wurden neue Programmteile zur Lösung der erforderlichen Gleichungen für die gestörten EOMIP-CC-Amplituden und die gestörten Lagrange-Multiplikatoren zeta zum Quantenchemieprogramm CFOUR hinzugefügt. Die unter Verwendung des Programms bestimmten Eigenschaften werden hinsichtlich ihrer Leistungsfähigkeit im Vergleich zu etablierten Methoden wie z.B. CCSD(T) untersucht. Bei der Berechnung von Polarisierbarkeiten und harmonischen Schwingungsfrequenzen liefert die EOMIP-CCSD-Theorie meist gute Resultate, welche nur wenig von den CCSD(T)-Ergebnissen abweichen. Einzig bei der Betrachtung von Radikalen, für die die entsprechenden Anionen nicht stabil sind (z.B. NH2⁻ und CH3⁻), liefert der EOMIP-CCSD-Ansatz aufgrund methodischer Nachteile keine aussagekräftige Beschreibung. rnrnDie Ableitungen der EOMIP-CCSD-Energie lassen sich auch zur Simulation vibronischer Kopplungen innerhalb des KDC-Modells einsetzen.rnZur Kopplung verschiedener radikalischer Zustände in einem solchen Modellpotential spielen vor allem die Ableitungen von Übergangsmatrixelementen eine wichtige Rolle. Diese sogenannten Kopplungskonstanten können in der EOMIP-CC-Theorie besonders leicht definiert und berechnet werden. Bei der Betrachtung des Photoelektronenspektrums von HCO2⁻ werden zwei Alternativen untersucht: Die vertikale Bestimmung an der Gleichgewichtsgeometrie des HCO2⁻-Anions und die Ermittlung adiabatischer Kraftkonstanten an den Gleichgewichtsgeometrien des Radikals. Lediglich das adiabatische Modell liefert bei Beschränkung auf harmonische Kraftkonstanten eine qualitativ sinnvolle Beschreibung des Spektrums. Erweitert man beide Modelle um kubische und quartische Kraftkonstanten, so nähern sich diese einander an und ermöglichen eine vollständige Zuordnung des gemessenen Spektrums innerhalb der ersten 1500 cm⁻¹. Die adiabatische Darstellung erreicht dabei nahezu quantitative Genauigkeit.

Geological evolution of the Monte Rosa

Eine detaillierte geochemische und geochronologische Studie an Gesteinen der Monte Rosa Decke (MR; Westalpen) wurde durchgeführt. Die MR wurde während der alpinen Orogenese zunächst eklogitfaziell und nachfolgend grünschieferfaziell überprägt.Eine detaillierte U-Pb geochronologische Studie an Zirkonen und Monaziten des MR Granits ergab ein Permisches Intrusionsalter (270 ± 4 Ma). Der MR Granit gehört zu den post-variszischen magmatischen Einheiten, welche die Instabilität der variszischen kontinentalen Kruste andeuten. Für die MR kann eine paläogeographische Position als Teil der 'Briançonnais-Schwelle' angenommen werden.Innerhalb des MR Granits treten Talk-Kyanit-Chloritoid-Gesteine ('Weißschiefer') auf. Diese stellen wesentliche Indikatoren für eine alpine Hochdruckmetamorphose in der MR dar. Massenbilanzberechnungen wurden durchgeführt, um den Massentransfer zu quantifizieren, welcher für die Bildung eines Weißschiefers aus einem granitischen Protolith notwendig ist. Ein Modell für die Entwicklung der Weißschiefer wurde entwickelt.Es wurde eine in-situ 40Ar/39Ar UV-Laser-Ablationsstudie an Hellglimmern der alpinen Mineralparagenese durchgeführt. Sie ergab eine heterogene Altersverteilung. Diese Alter können durch Glimmerrekristallisation unter relativ 'trockenen' hochdruckmetamorphen Bedingungen begleitet von partiellem Verlust von radiogenem Argon während der alpinen Metamorphose erklärt werden. Eine ähnlich komplexe Entwicklung mit partieller Homogenisierung des Isotopensystems kann in der Strontium-Isotopie beobachtet werden. Diese Isotopenstudien liefern Hinweise auf das Schließverhalten von Isotopensystemen unter hochdruckmetamorphen Bedingungen.

Monte Carlo simulations of Potts glasses

A complete understanding of the glass transition isstill a challenging problem. Some researchers attributeit to the (hypothetical) occurrence of a static phasetransition, others emphasize the dynamical transitionof mode coupling-theory from an ergodic to a non ergodicstate. A class of disordered spin models has been foundwhich unifies both scenarios. One of these models isthe p-state infinite range Potts glass with p>4, whichexhibits in the thermodynamic limit both a dynamicalphase transition at a temperature T_D, and a static oneat T_0 < T_D. In this model every spins interacts withall the others, irrespective of distance. Interactionsare taken from a Gaussian distribution.In order to understand better its behavior forfinite number N of spins and the approach to thethermodynamic limit, we have performed extensive MonteCarlo simulations of the p=10 Potts glass up to N=2560.The time-dependent spin-autocorrelation function C(t)shows strong finite size effects and it does not showa plateau even for temperatures around the dynamicalcritical temperature T_D. We show that the N-andT-dependence of the relaxation time for T > T_D can beunderstood by means of a dynamical finite size scalingAnsatz.The behavior in the spin glass phase down to atemperature T=0.7 (about 60% of the transitiontemperature) is studied. Well equilibratedconfigurations are obtained with the paralleltempering method, which is also useful for properlyestablishing static properties, such as the orderparameter distribution function P(q). Evidence is givenfor the compatibility with a one step replica symmetrybreaking scenario. The study of the cumulants of theorder parameter does not permit a reliable estimation ofthe static transition temperature. The autocorrelationfunction at low T exhibits a two-step decay, and ascaling behavior typical of supercooled liquids, thetime-temperature superposition principle, is observed. Inthis region the dynamics is governed by Arrheniusrelaxations, with barriers growing like N^{1/2}.We analyzed the single spin dynamics down to temperaturesmuch lower than the dynamical transition temperature. We found strong dynamical heterogeneities, which explainthe non-exponential character of the spin autocorrelationfunction. The spins seem to relax according to dynamicalclusters. The model in three dimensions tends to acquireferromagnetic order for equal concentration of ferro-and antiferromagnetic bonds. The ordering has differentcharacteristics from the pure ferromagnet. The spinglass susceptibility behaves like chi_{SG} proportionalto 1/T in the region where a spin glass is predicted toexist in mean-field. Also the analysis of the cumulantsis consistent with the absence of spin glass orderingat finite temperature. The dynamics shows multi-scalerelaxations if a bimodal distribution of bonds isused. We propose to understand it with a model based onthe local spin configuration. This is consistent with theabsence of plateaus if Gaussian interactions are used.

Supramolecular order and dynamics of discotic materials studied by solid-state NMR recoupling methods

The topic of this thesis is the investigation of structure,order and dynamics in discotic mesogens by advancedsolid-state NMR spectroscopy. Most of the discotic mesogensunder investigation are hexa-peri-hexabenzocoronene (HBC)derivatives which are of particular interest for potentialdevice applications due to their high one-dimensional chargecarrier mobilities. The supramolecular stacking arrangement of the discoticcores was investigated by 2D 1H-1H double-quantum (DQ)methods, which were modified by incorporating the WATERGATEsuppression technique into the experiments in order toovercome severe phase problems arising from the strongsignal of the long alkyl sidechains. Molecular dynamics and sample orientation was probed throughthe generation of sideband patterns by reconversion rotorencoding in 2D recoupling experiments. These experimentswere extended by new recoupling schemes to enable thedistinction of motion and orientation effects. The solid-state NMR studies presented in this work aim tothe understanding of structure-property relationships in theinvestigated discotic materials, while the experimentsapplied to these materials include new recoupling schemeswhich make the desired information on molecular orientationand dynamics accessible without isotope labelling.

The swelling behaviour of polyelectrolyte networks

Being basic ingredients of numerous daily-life products with significant industrial importance as well as basic building blocks for biomaterials, charged hydrogels continue to pose a series of unanswered challenges for scientists even after decades of practical applications and intensive research efforts. Despite a rather simple internal structure it is mainly the unique combination of short- and long-range forces which render scientific investigations of their characteristic properties to be quite difficult. Hence early on computer simulations were used to link analytical theory and empirical experiments, bridging the gap between the simplifying assumptions of the models and the complexity of real world measurements. Due to the immense numerical effort, even for high performance supercomputers, system sizes and time scales were rather restricted until recently, whereas it only now has become possible to also simulate a network of charged macromolecules. This is the topic of the presented thesis which investigates one of the fundamental and at the same time highly fascinating phenomenon of polymer research: The swelling behaviour of polyelectrolyte networks. For this an extensible simulation package for the research on soft matter systems, ESPResSo for short, was created which puts a particular emphasis on mesoscopic bead-spring-models of complex systems. Highly efficient algorithms and a consistent parallelization reduced the necessary computation time for solving equations of motion even in case of long-ranged electrostatics and large number of particles, allowing to tackle even expensive calculations and applications. Nevertheless, the program has a modular and simple structure, enabling a continuous process of adding new potentials, interactions, degrees of freedom, ensembles, and integrators, while staying easily accessible for newcomers due to a Tcl-script steering level controlling the C-implemented simulation core. Numerous analysis routines provide means to investigate system properties and observables on-the-fly. Even though analytical theories agreed on the modeling of networks in the past years, our numerical MD-simulations show that even in case of simple model systems fundamental theoretical assumptions no longer apply except for a small parameter regime, prohibiting correct predictions of observables. Applying a "microscopic" analysis of the isolated contributions of individual system components, one of the particular strengths of computer simulations, it was then possible to describe the behaviour of charged polymer networks at swelling equilibrium in good solvent and close to the Theta-point by introducing appropriate model modifications. This became possible by enhancing known simple scaling arguments with components deemed crucial in our detailed study, through which a generalized model could be constructed. Herewith an agreement of the final system volume of swollen polyelectrolyte gels with results of computer simulations could be shown successfully over the entire investigated range of parameters, for different network sizes, charge fractions, and interaction strengths. In addition, the "cell under tension" was presented as a self-regulating approach for predicting the amount of swelling based on the used system parameters only. Without the need for measured observables as input, minimizing the free energy alone already allows to determine the the equilibrium behaviour. In poor solvent the shape of the network chains changes considerably, as now their hydrophobicity counteracts the repulsion of like-wise charged monomers and pursues collapsing the polyelectrolytes. Depending on the chosen parameters a fragile balance emerges, giving rise to fascinating geometrical structures such as the so-called pear-necklaces. This behaviour, known from single chain polyelectrolytes under similar environmental conditions and also theoretically predicted, could be detected for the first time for networks as well. An analysis of the total structure factors confirmed first evidences for the existence of such structures found in experimental results.

Computation of direction selectivity in retinal starburst amacrine cell dendrites – studied using electrophysiological recordings and two-photon imaging

Neuronal circuits in the retina analyze images according to qualitative aspects such as color or motion, before the information is transmitted to higher visual areas of the brain. One example, studied for over the last four decades, is the detection of motion direction in ‘direction selective’ neurons. Recently, the starburst amacrine cell, one type of retinal interneuron, has emerged as an essential player in the computation of direction selectivity. In this study the mechanisms underlying the computation of direction selective calcium signals in starburst cell dendrites were investigated using whole-cell electrical recordings and two-photon calcium imaging. Analysis of the somatic electrical responses to visual stimulation and pharmacological agents indicated that the directional signal (i) is not computed presynaptically to starburst cells or by inhibitory network interactions. It is thus computed via a cell-intrinsic mechanism, which (ii) depends upon the differential, i.e. direction selective, activation of voltage-gated channels. Optically measuring dendritic calcium signals as a function of somatic voltage suggests (iii) a difference in resting membrane potential between the starburst cell’s soma and its distal dendrites. In conclusion, it is proposed that the mechanism underlying direction selectivity in starburst cell dendrites relies on intrinsic properties of the cell, particularly on the interaction of spatio-temporally structured synaptic inputs with voltage-gated channels, and their differential activation due to a somato-dendritic difference in membrane potential.

Synthesis and surface modification of semiconductor nanocrystals

The last decade has witnessed an exponential growth of activities in the field of nanoscience and nanotechnology worldwide, driven both by the excitement of understanding new science and by the potential hope for applications and economic impacts. The largest activity in this field up to date has been in the synthesis and characterization of new materials consisting of particles with dimensions in the order of a few nanometers, so-called nanocrystalline materials. [1-8] Semiconductor nanomaterials such as III/V or II/VI compound semiconductors exhibit strong quantum confinement behavior in the size range from 1 to 10 nm. Therefore, preparation of high quality semiconductor nanocrystals has been a challenge for synthetic chemists, leading to the recent rapid progress in delivering a wide variety of semiconducting nanomaterials. Semiconductor nanocrystals, also called quantum dots, possess physical properties distinctly different from those of the bulk material. Typically, in the size range from 1 to 10 nm, when the particle size is changed, the band gap between the valence and the conduction band will change, too. In a simple approximation a particle in a box model has been used to describe the phenomenon[9]: at nanoscale dimensions the degenerate energy states of a semiconductor separate into discrete states and the system behaves like one big molecule. The size-dependent transformation of the energy levels of the particles is called “quantum size-effect”. Quantum confinement of both the electron and hole in all three dimensions leads to an increase in the effective bandgap of the material with decreasing crystallite size. Consequently, both the optical absorption and emission of semiconductor nanaocrystals shift to the blue (higher energies) as the size of the particles gets smaller. This color tuning is well documented for CdSe nanocrystals whose absorption and emission covers almost the whole visible spectral range. As particle sizes become smaller the ratio of surface atoms to those in the interior increases, which has a strong impact on particle properties, too. Prominent examples are the low melting point [8] and size/shape dependent pressure resistance [10] of semiconductor nanocrystals. Given the size dependence of particle properties, chemists and material scientists now have the unique opportunity to change the electronic and chemical properties of a material by simply controlling the particle size. In particular, CdSe nanocrystals have been widely investigated. Mainly due to their size-dependent optoelectronic properties [11, 12] and flexible chemical processibility [13], they have played a distinguished role for a number of seminal studies [11, 12, 14, 15]. Potential technical applications have been discussed, too. [8, 16-27] Improvement of the optoelectronic properties of semiconductor nanocrystals is still a prominent research topic. One of the most important approaches is fabricating composite type-I core-shell structures which exhibit improved properties, making them attractive from both a fundamental and a practical point of view. Overcoating of nanocrystallites with higher band gap inorganic materials has been shown to increase the photoluminescence quantum yields by eliminating surface nonradiative recombination sites. [28] Particles passivated with inorganic shells are more robust than nanocrystals covered by organic ligands only and have greater tolerance to processing conditions necessary for incorporation into solid state structures or for other applications. Some examples of core-shell nanocrystals reported earlier include CdS on CdSe [29], CdSe on CdS, [30], ZnS on CdS, [31] ZnS on CdSe[28, 32], ZnSe on CdSe [33] and CdS/HgS/CdS [34]. The characterization and preparation of a new core-shell structure, CdSe nanocrystals overcoated by different shells (CdS, ZnS), is presented in chapter 4. Type-I core-shell structures as mentioned above greatly improve the photoluminescence quantum yield and chemical and photochemical stability of nanocrystals. The emission wavelengths of type-I core/shell nanocrystals typically only shows a small red-shift when compared to the plain core nanocrystals. [30, 31, 35] In contrast to type-I core-shell nanocrystals, only few studies have been conducted on colloidal type-II core/shell structures [36-38] which are characterized by a staggered alignment of conduction and valence bands giving rise to a broad tunability of absorption and emission wavelengths, as was shown for CdTe/CdSe core-shell nanocrystals. [36] The emission of type-II core/shell nanocrystals mainly originates from the radiative recombination of electron-hole pairs across the core-shell interface leading to a long photoluminescence lifetime. Type-II core/shell nanocrystals are promising with respect to photoconduction or photovoltaic applications as has been discussed in the literature.[39] Novel type-II core-shell structures with ZnTe cores are reported in chapter 5. The recent progress in the shape control of semiconductor nanocrystals opens new fields of applications. For instance, rod shaped CdSe nanocrystals can enhance the photo-electro conversion efficiency of photovoltaic cells, [40, 41] and also allow for polarized emission in light emitting diodes. [42, 43] Shape control of anisotropic nanocrystals can be achieved by the use of surfactants, [44, 45] regular or inverse micelles as regulating agents, [46, 47] electrochemical processes, [48] template-assisted [49, 50] and solution-liquid-solution (SLS) growth mechnism. [51-53] Recently, formation of various CdSe nanocrystal shapes has been reported by the groups of Alivisatos [54] and Peng, [55] respectively. Furthermore, it has been reported by the group of Prasad [56] that noble metal nanoparticles can induce anisotropic growth of CdSe nanocrystals at lower temperatures than typically used in other methods for preparing anisotropic CdSe structures. Although several approaches for anisotropic crystal growth have been reported by now, developing new synthetic methods for the shape control of colloidal semiconductor nanocrystals remains an important goal. Accordingly, we have attempted to utilize a crystal phase control approach for the controllable synthesis of colloidal ZnE/CdSe (E = S, Se, Te) heterostructures in a variety of morphologies. The complex heterostructures obtained are presented in chapter 6. The unique optical properties of nanocrystals make them appealing as in vivo and in vitro fluorophores in a variety of biological and chemical investigations, in which traditional fluorescence labels based on organic molecules fall short of providing long-term stability and simultaneous detection of multiple emission colours [References]. The ability to prepare water soluble nanocrystals with high stability and quantum yield has led to promising applications in cellular labeling, [57, 58] deep-tissue imaging, [59, 60] and assay labeling [61, 62]. Furthermore, appropriately solubilized nanocrystals have been used as donors in fluorescence resonance energy transfer (FRET) couples. [63-65] Despite recent progress, much work still needs to be done to achieve reproducible and robust surface functionalization and develop flexible (bio-) conjugation techniques. Based on multi-shell CdSe nanocrystals, several new solubilization and ligand exchange protocols have been developed which are presented in chapter 7. The organization of this thesis is as follows: A short overview describing synthesis and properties of CdSe nanocrystals is given in chapter 2. Chapter 3 is the experimental part providing some background information about the optical and analytical methods used in this thesis. The following chapters report the results of this work: synthesis and characterization of type-I multi-shell and type-II core/shell nanocrystals are described in chapter 4 and chapter 5, respectively. In chapter 6, a high–yield synthesis of various CdSe architectures by crystal phase control is reported. Experiments about surface modification of nanocrystals are described in chapter 7. At last, a short summary of the results is given in chapter 8.

Influence of spatial constraints in non-crystalline regions on the polymer dynamics in semi-crystalline polyethylene: a solid state NMR study

A broad variety of solid state NMR techniques were used to investigate the chain dynamics in several polyethylene (PE) samples, including ultrahigh molecular weight PEs (UHMW-PEs) and low molecular weight PEs (LMW-PEs). Via changing the processing history, i.e. melt/solution crystallization and drawing processes, these samples gain different morphologies, leading to different molecular dynamics. Due to the long chain nature, the molecular dynamics of polyethylene can be distinguished in local fluctuation and long range motion. With the help of NMR these different kinds of molecular dynamics can be monitored separately. In this work the local chain dynamics in non-crystalline regions of polyethylene samples was investigated via measuring 1H-13C heteronuclear dipolar coupling and 13C chemical shift anisotropy (CSA). By analyzing the motionally averaged 1H-13C heteronuclear dipolar coupling and 13C CSA, the information about the local anisotropy and geometry of motion was obtained. Taking advantage of the big difference of the 13C T1 relaxation time in crystalline and non-crystalline regions of PEs, the 1D 13C MAS exchange experiment was used to investigate the cooperative chain motion between these regions. The different chain organizations in non-crystalline regions were used to explain the relationship between the local fluctuation and the long range motion of the samples. In a simple manner the cooperative chain motion between crystalline and non-crystalline regions of PE results in the experimentally observed diffusive behavior of PE chain. The morphological influences on the diffusion motion have been discussed. The morphological factors include lamellar thickness, chain organization in non-crystalline regions and chain entanglements. Thermodynamics of the diffusion motion in melt and solution crystallized UHMW-PEs is discussed, revealing entropy-controlled features of the chain diffusion in PE. This thermodynamic consideration explains the counterintuitive relationship between the local fluctuation and the long range motion of the samples. Using the chain diffusion coefficient, the rates of jump motion in crystals of the melt crystallized PE have been calculated. A concept of "effective" jump motion has been proposed to explain the difference between the values derived from the chain diffusion coefficients and those in literatures. The observations of this thesis give a clear demonstration of the strong relationship between the sample morphology and chain dynamics. The sample morphologies governed by the processing history lead to different spatial constraints for the molecular chains, leading to different features of the local and long range chain dynamics. The knowledge of the morphological influence on the microscopic chain motion has many implications in our understanding of the alpha-relaxation process in PE and the related phenomena such as crystal thickening, drawability of PE, the easy creep of PE fiber, etc.

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

Topological mass of magnetic Skyrmions probed by ultrafast dynamic imaging

In dieser Arbeit untersuchen wir mittels zeitaufgelöster Abbildungen die Gigahertz-Dynamik von magnetischen Skyrmionen, um die Bewegungsgleichungen für diese Quasiteilchen zu bestimmen. Um dieses Ziel zu erreichen haben wir zunächst ein CoB/Pt Schichtsystem entwickelt, das starke senkrechte magnetische Anisotropie mit einer besonders geringen Rauigkeit der Energielandschaft verbindet. Diese Eigenschaften sind für das repetitive dynamische Abbildungsverfahren unerlässlich. In einem zweiten Schritt haben wir das Probendesign optimiert und so weiterentwickelt, dass eine Beobachtung der Skyrmionenbewegung mit einer Auflösung von besser als 3 nm möglich wurde. Aufgrund dieser Verbesserungen ist es uns gelungen, die Trajektorie eines Skyrmionen aufzuzeichnen. Diese Bewegung ist eine Superposition von zwei Drehbewegungen, einer im Uhrzeigersinn und einer gegen läufigen. Aus der Existenz dieser zwei Moden lässt sich schließen, dass Skyrmionen träge Quasiteilchen sind, und aus den Frequenzen können wir einen Wert für die träge Masse ableiten. Es stellt sich heraus, dass die Masse von Skyrmion fünfmal größer ist als von existierenden Theorien vorhergesagt. Die Masse wird folglich durch einen neuartigen Mechanismus bestimmt, der sich aus der räumlichen Beschränkung der Skyrmionen ergibt, welche sich direkt aus der Topologie bleitenrnlässt.

Dynamic distance analysis : new geometric data structures and algorithms for the real-time calculation of tolerance violating regions in the digital mockup process

In vielen Industriezweigen, zum Beispiel in der Automobilindustrie, werden Digitale Versuchsmodelle (Digital MockUps) eingesetzt, um die Konstruktion und die Funktion eines Produkts am virtuellen Prototypen zu überprüfen. Ein Anwendungsfall ist dabei die Überprüfung von Sicherheitsabständen einzelner Bauteile, die sogenannte Abstandsanalyse. Ingenieure ermitteln dabei für bestimmte Bauteile, ob diese in ihrer Ruhelage sowie während einer Bewegung einen vorgegeben Sicherheitsabstand zu den umgebenden Bauteilen einhalten. Unterschreiten Bauteile den Sicherheitsabstand, so muss deren Form oder Lage verändert werden. Dazu ist es wichtig, die Bereiche der Bauteile, welche den Sicherhabstand verletzen, genau zu kennen. rnrnIn dieser Arbeit präsentieren wir eine Lösung zur Echtzeitberechnung aller den Sicherheitsabstand unterschreitenden Bereiche zwischen zwei geometrischen Objekten. Die Objekte sind dabei jeweils als Menge von Primitiven (z.B. Dreiecken) gegeben. Für jeden Zeitpunkt, in dem eine Transformation auf eines der Objekte angewendet wird, berechnen wir die Menge aller den Sicherheitsabstand unterschreitenden Primitive und bezeichnen diese als die Menge aller toleranzverletzenden Primitive. Wir präsentieren in dieser Arbeit eine ganzheitliche Lösung, welche sich in die folgenden drei großen Themengebiete unterteilen lässt.rnrnIm ersten Teil dieser Arbeit untersuchen wir Algorithmen, die für zwei Dreiecke überprüfen, ob diese toleranzverletzend sind. Hierfür präsentieren wir verschiedene Ansätze für Dreiecks-Dreiecks Toleranztests und zeigen, dass spezielle Toleranztests deutlich performanter sind als bisher verwendete Abstandsberechnungen. Im Fokus unserer Arbeit steht dabei die Entwicklung eines neuartigen Toleranztests, welcher im Dualraum arbeitet. In all unseren Benchmarks zur Berechnung aller toleranzverletzenden Primitive beweist sich unser Ansatz im dualen Raum immer als der Performanteste.rnrnDer zweite Teil dieser Arbeit befasst sich mit Datenstrukturen und Algorithmen zur Echtzeitberechnung aller toleranzverletzenden Primitive zwischen zwei geometrischen Objekten. Wir entwickeln eine kombinierte Datenstruktur, die sich aus einer flachen hierarchischen Datenstruktur und mehreren Uniform Grids zusammensetzt. Um effiziente Laufzeiten zu gewährleisten ist es vor allem wichtig, den geforderten Sicherheitsabstand sinnvoll im Design der Datenstrukturen und der Anfragealgorithmen zu beachten. Wir präsentieren hierzu Lösungen, die die Menge der zu testenden Paare von Primitiven schnell bestimmen. Darüber hinaus entwickeln wir Strategien, wie Primitive als toleranzverletzend erkannt werden können, ohne einen aufwändigen Primitiv-Primitiv Toleranztest zu berechnen. In unseren Benchmarks zeigen wir, dass wir mit unseren Lösungen in der Lage sind, in Echtzeit alle toleranzverletzenden Primitive zwischen zwei komplexen geometrischen Objekten, bestehend aus jeweils vielen hunderttausend Primitiven, zu berechnen. rnrnIm dritten Teil präsentieren wir eine neuartige, speicheroptimierte Datenstruktur zur Verwaltung der Zellinhalte der zuvor verwendeten Uniform Grids. Wir bezeichnen diese Datenstruktur als Shrubs. Bisherige Ansätze zur Speicheroptimierung von Uniform Grids beziehen sich vor allem auf Hashing Methoden. Diese reduzieren aber nicht den Speicherverbrauch der Zellinhalte. In unserem Anwendungsfall haben benachbarte Zellen oft ähnliche Inhalte. Unser Ansatz ist in der Lage, den Speicherbedarf der Zellinhalte eines Uniform Grids, basierend auf den redundanten Zellinhalten, verlustlos auf ein fünftel der bisherigen Größe zu komprimieren und zur Laufzeit zu dekomprimieren.rnrnAbschießend zeigen wir, wie unsere Lösung zur Berechnung aller toleranzverletzenden Primitive Anwendung in der Praxis finden kann. Neben der reinen Abstandsanalyse zeigen wir Anwendungen für verschiedene Problemstellungen der Pfadplanung.