Informationsstrukturen der protokollbasierten Medizin

Die protokollbasierte Medizin stellt einen interdisziplinären Brennpunkt der Informatik dar. Als besonderer Ausschnitt der medizinischen Teilgebiete erlaubt sie die relativ formale Spezifikation von Prozessen in den drei Bereichen der Prävention, Diagnose und Therapie.Letzterer wurde immer besonders fokussiert und gilt seit jeher im Rahmen klinischer Studien als Projektionsfläche für informationstechnologische Konzepte. Die Euphorie der frühen Jahre ernüchtert sich jedoch bei jeder Bilanz. Nur sehr wenige der unzählbaren Projekte haben ihre Routine in der alltäglichen Praxis gefunden. Die meisten Vorhaben sind an der Illusion der vollständigen Berechenbarkeit medizinischer Arbeitsabläufe gescheitert. Die traditionelle Sichtweise der klinischen Praxis beruht auf einer blockorientierten Vorstellung des Therapieausführungsprozesses. Sie entsteht durch seine Zerlegung in einzelne Therapiezweige, welche aus vordefinierten Blöcken zusammengesetzt sind. Diese können sequentiell oder parallel ausgeführt werden und sind selbst zusammengesetzt aus jeweils einer Menge von Elementen,welche die Aktivitäten der untersten Ebene darstellen. Das blockorientierte Aufbaumodell wird ergänzt durch ein regelorientiertes Ablaufmodell. Ein komplexes Regelwerk bestimmt Bedingungen für die zeitlichen und logischen Abhängigkeiten der Blöcke, deren Anordnung durch den Ausführungsprozeß gebildet wird. Die Modellierung der Therapieausführung steht zunächst vor der grundsätzlichen Frage, inwieweit die traditionelle Sichtweise für eine interne Repräsentation geeignet ist. Das übergeordnete Ziel besteht in der Integration der unterschiedlichen Ebenen der Therapiespezifikation. Dazu gehört nicht nur die strukturelle Komponente, sondern vorallem die Ablaufkomponente. Ein geeignetes Regelmodell ist erforderlich, welches den spezifischen Bedürfnissen der Therapieüberwachung gerecht wird. Die zentrale Aufgabe besteht darin, diese unterschiedlichen Ebenen zusammenzuführen. Eine sinnvolle Alternative zur traditionellen Sichtweise liefert das zustandsorientierte Modell des Therapieausführungsprozesses. Das zustandsorientierte Modell beruht auf der Sichtweise, daß der gesamte Therapieausführungsprozeß letztendlich eine lineare Folge von Zuständen beschreibt, wobei jeder Zustandsübergang durch ein Ereignis eingeleitet wird, an bestimmte Bedingungen geknüpft ist und bestimmte Aktionen auslösen kann. Die Parallelität des blockorientierten Modells tritt in den Hintergrund, denn die Menge der durchzuführenden Maßnahmen sind lediglich Eigenschaften der Zustände und keine strukturellen Elemente der Ablaufspezifikation. Zu jedem Zeitpunkt ist genau ein Zustand aktiv, und er repräsentiert eine von endlich vielen klinischen Situationen, mit all ihren spezifischen Aktivitäten und Ausführungsregeln. Die Vorteile des zustandsorientierten Modells liegen in der Integration. Die Grundstruktur verbindet die statische Darstellung der möglichen Phasenanordnungen mit der dynamischen Ausführung aktiver Regeln. Die ursprünglichen Inhalte des blockorientierten Modells werden als gewöhnliche Eigenschaften der Zustände reproduziert und stellen damit nur einen Spezialfall der zustandsbezogenen Sicht dar.Weitere Möglichkeiten für die Anreicherung der Zustände mit zusätzlichen Details sind denkbar wie sinnvoll. Die Grundstruktur bleibt bei jeder Erweiterung jedoch die gleiche. Es ergibt sich ein wiederverwendbares Grundgerüst,ein gemeinsamer Nenner für die Erfüllung der Überwachungsaufgabe.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Structural and elastic properties of DNA and chromatin

We investigate a chain consisting of two coupled worm-like chains withconstant distance between the strands. The effects due todouble-strandedness of the chain are studied. In a previous analyticalstudy of this system an intrinsic twist-stretch coupling and atendency of kinking is predicted. Even though a local twist structureis observed the predicted features are not recovered. A new model for DNA at the base-pair level is presented. Thebase-pairs are treated as flat rigid ellipsoids and thesugar-phosphate backbones are represented as stiff harmonic springs.The base-pair stacking interaction is modeled by a variant of theGay-Berne potential. It is shown by systematic coarse-graininghow the elastic constants of a worm-like chain are related to thelocal fluctuations of the base-pair step parameters. Even though a lotof microscopic details of the base-pair geometry is neglected themodel can be optimized to obtain a B-DNA conformation as ground stateand reasonable elastic properties. Moreover the model allows tosimulate much larger length scales than it is possible with atomisticsimulations due to the simplification of the force-field and inparticular due to the possibility of non-local Monte-Carlo moves. Asa first application the behavior under stretching is investigated. Inagreement with micromanipulation experiments on single DNA moleculesone observes a force-plateau in the force-extension curvescorresponding to an overstretching transition from B-DNA to aso-called S-DNA state. The model suggests a structure for S-DNA withhighly inclined base-pairs in order to enable at least partialbase-pair stacking. Finally a simple model for chromatin is introduced to study itsstructural and elastic properties. The underlying geometry of themodeled fiber is based on a crossed-linker model. The chromatosomesare treated as disk-like objects. Excluded volume and short rangenucleosomal interaction are taken into account by a variant of theGay-Berne potential. It is found that the bending rigidity and thestretching modulus of the fiber increase with more compact fibers. Fora reasonable parameterization of the fiber for physiologicalconditions and sufficiently high attraction between the nucleosomes aforce-extension curve is found similar to stretching experiments onsingle chromatin fibers. For very small stretching forces a kinkedfiber forming a loop is observed. If larger forces are applied theloop formation is stretched out and a decondensation of the fibertakes place.

A sampling method for detecting buried objects using electromagnetic scattering

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular set-up.

Untersuchung der Struktur und Assemblierung des Lichtsammelkomplexes II höherer Pflanzen mittels elektronenparamagnetischer Resonanz (EPR)

Der Haupt-Lichtsammelkomplex (LHCII) des Photosyntheseapparates höherer Pflanzen gehört zu den häufigsten Membranproteinen der Erde. Seine Kristallstruktur ist bekannt. Das Apoprotein kann rekombinant in Escherichia coli überexprimiert und somit molekularbiologisch vielfältig verändert werden. In Detergenzlösung besitzt das denaturierte Protein die erstaunliche Fähigkeit, sich spontan zu funktionalen Protein-Pigment-Komplexen zu organisieren, welche strukturell nahezu identisch sind mit nativem LHCII. Der Faltungsprozess findet in vitro im Zeitbereich von Sekunden bis Minuten statt und ist abhängig von der Bindung der Cofaktoren Chlorophyll a und b sowie verschiedenen Carotinoiden.rn Diese Eigenschaften machen LHCII besonders geeignet für Strukturuntersuchungen mittels der elektronenparamagnetischen Resonanz (EPR)-Spektrokopie. Diese setzt eine punktspezifische Spinmarkierung des LHCII voraus, die in dieser Arbeit zunächst optimiert wurde. Einschließlich der Beiträge Anderer stand eine breite Auswahl von über 40 spinmarkierten Mutanten des LHCII bereit, einen N-terminalen „Cys walk“ eingeschlossen. Weder der hierfür notwendige Austausch einzelner Aminosäuren noch die Anknüpfung des Spinmarkers beeinträchtigten die Funktion des LHCII. Zudem konnte ein Protokoll zur Präparation heterogen spinmarkierter LHCII-Trimere entwickelt werden, also von Trimeren, die jeweils nur ein Monomer mit einer Spinmarkierung enthalten.rn Spinmarkierte Proben des Detergenz-solubilisierten LHCII wurden unter Verwendung verschiedener EPR-Techniken strukturell analysiert. Als besonders aussagekräftig erwies sich die Messung der Wasserzugänglichkeit einzelner Aminosäurepositionen anhand der Electron Spin Echo Envelope Modulation (ESEEM). In Kombination mit der etablierten Double Electron-Electron Resonance (DEER)-Technik zur Detektion von Abständen zwischen zwei Spinmarkern wurde der membranständige Kernbereich des LHCII in Lösung eingehend untersucht und strukturell der Kristallstruktur für sehr ähnlich befunden. Die Vermessung kristallographisch nicht erfasster Bereiche nahe dem N-Terminus offenbarte die schon früher detektierte Strukturdynamik der Domäne in Abhängigkeit des Oligomerisierungsgrades. Der neue, noch zu vervollständigende Datensatz aus Abstandsverteilungen und ESEEM-Wasserzugänglichkeiten monomerer wie trimerer Proben sollte in naher Zukunft die sehr genaue Modellierung der N-terminalen Domäne des LHCII ermöglichen.rn In einem weiteren Abschnitt der Arbeit wurde die Faltung des LHCII-Apoproteins bei der LHCII-Assemblierung in vitro untersucht. Vorausgegangene fluoreszenzspektroskopi-sche Arbeiten hatten gezeigt, dass die Bindung von Chlorophyll a und b in aufeinanderfolgenden Schritten im Zeitbereich von weniger als einer Minute bzw. mehreren Minuten erfolgten. Sowohl die Wasserzugänglichkeit einzelner Aminosäurepositionen als auch Spin-Spin-Abstände änderten sich in ähnlichen Zeitbereichen. Die Daten deuten darauf hin, dass die Ausbildung der mittleren Transmembran-Helix mit der schnelleren Chlorophyll-a-Bindung einhergeht, während sich die Superhelix aus den beiden anderen Transmembranhelices erst im langsameren Schritt, zusammen mit der Chlorophyll-b-Bindung, ausbildet.rn

Oxidation photochemistry in the remote marine boundary layer

Die bedeutendste Folge der Luftverschmutzung ist eine erhöhte Konzentration an Ozon (O3) in der Troposphäre innerhalb der letzten 150 Jahre. Ozon ist ein photochemisches Oxidationsmittel und ein Treibhausgas, das als wichtigste Vorstufe des Hydroxyradikals OH die Oxidationskraft der Atmosphäre stark beeinflusst. Um die Oxidationskraft der Atmosphäre und ihren Einfluss auf das Klima verstehen zu können, ist es von großer Bedeutung ein detailliertes Wissen über die Photochemie des Ozons und seiner Vorläufer, den Stickoxiden (NOx), in der Troposphäre zu besitzen. Dies erfordert das Verstehen der Bildungs- und Abbaumechanismen von Ozon und seiner Vorläufer. Als eine für den chemischen Ozonabbau wichtige Region kann die vom Menschen weitgehend unberührte marine Grenzschicht (Marine boundary layer (MBL)) angesehen werden. Bisher wurden für diese Region jedoch kaum Spurengasmessungen durchgeführt, und so sind die dort ablaufenden photochemischen Prozesse wenig untersucht. Da etwa 70 % der Erdoberfläche mit Ozeanen bedeckt sind, können die in der marinen Granzschicht ablaufenden Prozesse als signifikant für die gesamte Atmosphäre angesehen werden. Dies macht eine genaue Untersuchung dieser Region interessant. Um die photochemische Produktion und den Abbau von Ozon abschätzen zu können und den Einfluss antrophogener Emissionen auf troposphärisches Ozon zu quantifizieren, sind aktuelle Messergebnisse von NOx im pptv-Bereich für diese Region erforderlich. Die notwendigen Messungen von NO, NO2, O3, JNO2, J(O1D), HO2, OH, ROx sowie einiger meteorologischer Parameter wurden während der Fahrt des französischen Forschungsschiffes Marion-Dufresne auf dem südlichen Atlantik (28°S-57°S, 46°W-34°E) im März 2007 durchgeführt. Dabei sind für NO und NO2 die bisher niedrigsten gemessenen Werte zu verzeichnen. Die während der Messcampagne gewonnen Daten wurden hinsichtlich Ihrer Übereinstimmung mit den Bedingungen des photochemischen stationären Gleichgewichts (photochemical steady state (PSS)) überprüft. Dabei konnte eine Abweichung vom PSS festgestellt werden, welche unter Bedingungen niedriger NOx-Konzentrationen (5 bis 25pptv) einen unerwarteten Trend im Leighton-Verhältnis bewirkt, der abhängig vom NOx Mischungsverhältnis und der JNO2 Intensität ist. Signifikante Abweichungen vom Verhältnis liegen bei einer Zunahme der JNO2 Intensität vor. Diese Ergebnisse zeigen, dass die Abweichung vom PSS nicht beim Minimum der NOx-Konzentrationen und der JNO2 Werte liegt, so wie es in bisherigen theoretischen Studien dargelegt wurde und können als Hinweis auf weitere photochemische Prozesse bei höheren JNO2-Werten in einem System mit niedrigem NOx verstanden werden. Das wichtigste Ergebnis dieser Untersuchung, ist die Verifizierung des Leighton-Verhältnisses, das zur Charakterisierung des PSS dient, bei sehr geringen NOx-Konzentrationen in der MBL. Die bei dieser Doktorarbeit gewonnenen Erkenntnisse beweisen, dass unter den Bedingungen der marinen Granzschicht rein photochemischer Abbau von Ozon stattfindet und als Hauptursache hierfür während des Tages die Photolyse gilt. Mit Hilfe der gemessenen Parameter wurde der kritische NO-Level auf Werte zwischen 5 und 9 pptv abgeschätzt, wobei diese Werte im Vergleich zu bisherigen Studien vergleichsweise niedrig sind. Möglicherweise bedeutet dies, dass das Ozon Produktion/ Abbau-Potential des südlichen Atlantiks deutlich stärker auf die Verfügbarkeit von NO reagiert, als es in anderen Regionen der Fall ist. Im Rahmen der Doktorarbeit wurde desweiteren ein direkter Vergleich der gemessenen Spezies mit dem Modelergebnis eines 3-dimensionalen Zirkulationsmodel zur Simulation atmosphären chemischer Prozesse (EMAC) entlang der exakten Schiffsstrecke durchgeführt. Um die Übereinstimmung der Messergebnisse mit dem bisherigen Verständnis der atmosphärischen Radikalchemie zu überprüfen, wurde ein Gleichgewichtspunktmodel entwickelt, das die während der Überfahrt erhaltenen Daten für Berechungen verwendet. Ein Vergleich zwischen der gemessenen und der modellierten ROx Konzentrationen in einer Umgebung mit niedrigem NOx zeigt, dass die herkömmliche Theorie zur Reproduktion der Beobachtungen unzureichend ist. Die möglichen Gründe hierfür und die Folgen werden in dieser Doktorarbeit diskutiert.

Coarse-graining and quantum-classical adaptive coupling in soft matter

Die vorliegende Arbeit untersucht den Zusammenhang zwischen Skalen in Systemen weicher Materie, der für Multiskalen-Simulationen eine wichtige Rolle spielt. Zu diesem Zweck wurde eine Methode entwickelt, die die Approximation der Separierbarkeit von Variablen für die Molekulardynamik und ähnliche Anwendungen bewertet. Der zweite und größere Teil dieser Arbeit beschäftigt sich mit der konzeptionellen und technischen Erweiterung des Adaptive Resolution Scheme'' (AdResS), einer Methode zur gleichzeitigen Simulation von Systemen mit mehreren Auflösungsebenen. Diese Methode wurde auf Systeme erweitert, in denen klassische und quantenmechanische Effekte eine Rolle spielen.rnrnDie oben genannte erste Methode benötigt nur die analytische Form der Potentiale, wie sie die meisten Molekulardynamik-Programme zur Verfügung stellen. Die Anwendung der Methode auf ein spezielles Problem gibt bei erfolgreichem Ausgang einen numerischen Hinweis auf die Gültigkeit der Variablenseparation. Bei nicht erfolgreichem Ausgang garantiert sie, dass keine Separation der Variablen möglich ist. Die Methode wird exemplarisch auf ein zweiatomiges Molekül auf einer Oberfläche und für die zweidimensionale Version des Rotational Isomer State (RIS) Modells einer Polymerkette angewandt.rnrnDer zweite Teil der Arbeit behandelt die Entwicklung eines Algorithmus zur adaptiven Simulation von Systemen, in denen Quanteneffekte berücksichtigt werden. Die Quantennatur von Atomen wird dabei in der Pfadintegral-Methode durch einen klassischen Polymerring repräsentiert. Die adaptive Pfadintegral-Methode wird zunächst für einatomige Flüssigkeiten und tetraedrische Moleküle unter normalen thermodynamischen Bedingungen getestet. Schließlich wird die Stabilität der Methode durch ihre Anwendung auf flüssigen para-Wasserstoff bei niedrigen Temperaturen geprüft.

High-mass Drell-Yan cross-section and search for new phenomena in multi-electron/positron final states with the ATLAS detector

The Standard Model of particle physics is a very successful theory which describes nearly all known processes of particle physics very precisely. Nevertheless, there are several observations which cannot be explained within the existing theory. In this thesis, two analyses with high energy electrons and positrons using data of the ATLAS detector are presented. One, probing the Standard Model of particle physics and another searching for phenomena beyond the Standard Model.rnThe production of an electron-positron pair via the Drell-Yan process leads to a very clean signature in the detector with low background contributions. This allows for a very precise measurement of the cross-section and can be used as a precision test of perturbative quantum chromodynamics (pQCD) where this process has been calculated at next-to-next-to-leading order (NNLO). The invariant mass spectrum mee is sensitive to parton distribution functions (PFDs), in particular to the poorly known distribution of antiquarks at large momentum fraction (Bjoerken x). The measurementrnof the high-mass Drell-Yan cross-section in proton-proton collisions at a center-of-mass energy of sqrt(s) = 7 TeV is performed on a dataset collected with the ATLAS detector, corresponding to an integrated luminosity of 4.7 fb-1. The differential cross-section of pp -> Z/gamma + X -> e+e- + X is measured as a function of the invariant mass in the range 116 GeV < mee < 1500 GeV. The background is estimated using a data driven method and Monte Carlo simulations. The final cross-section is corrected for detector effects and different levels of final state radiation corrections. A comparison isrnmade to various event generators and to predictions of pQCD calculations at NNLO. A good agreement within the uncertainties between measured cross-sections and Standard Model predictions is observed.rnExamples of observed phenomena which can not be explained by the Standard Model are the amount of dark matter in the universe and neutrino oscillations. To explain these phenomena several extensions of the Standard Model are proposed, some of them leading to new processes with a high multiplicity of electrons and/or positrons in the final state. A model independent search in multi-object final states, with objects defined as electrons and positrons, is performed to search for these phenomenas. Therndataset collected at a center-of-mass energy of sqrt(s) = 8 TeV, corresponding to an integrated luminosity of 20.3 fb-1 is used. The events are separated in different categories using the object multiplicity. The data-driven background method, already used for the cross-section measurement was developed further for up to five objects to get an estimation of the number of events including fake contributions. Within the uncertainties the comparison between data and Standard Model predictions shows no significant deviations.

Stochastic foundations of dynamic trade and labor market models

This dissertation consists of three self-contained papers that are related to two main topics. In particular, the first and third studies focus on labor market modeling, whereas the second essay presents a dynamic international trade setup.rnrnIn Chapter "Expenses on Labor Market Reforms during Transitional Dynamics", we investigate the arising costs of a potential labor market reform from a government point of view. To analyze various effects of unemployment benefits system changes, this chapter develops a dynamic model with heterogeneous employed and unemployed workers.rn rnIn Chapter "Endogenous Markup Distributions", we study how markup distributions adjust when a closed economy opens up. In order to perform this analysis, we first present a closed-economy general-equilibrium industry dynamics model, where firms enter and exit markets, and then extend our analysis to the open-economy case.rn rnIn Chapter "Unemployment in the OECD - Pure Chance or Institutions?", we examine effects of aggregate shocks on the distribution of the unemployment rates in OECD member countries.rn rnIn all three chapters we model systems that behave randomly and operate on stochastic processes. We therefore exploit stochastic calculus that establishes clear methodological links between the chapters.

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.

Ground state properties of neutron-rich Mg isotopes

Studies in regions of the nuclear chart in which the model predictions of properties of nuclei fail can bring a better understanding of the strong interaction in the nuclear medium. To such regions belongs the so called "island of inversion" centered around Ne, Na and Mg isotopes with 20 neutrons in which unexpected ground-state spins, large deformations and dense low-energy spectra appear. This is a strong argument that the magic N = 20 is not a closed shell in this area. In this thesis investigations of isotope shifts of stable 24,25,26Mg, as well as spins and magnetic moments of short-lived 29,31Mg are presented. The successful studies were performed at the ISOLDE facility at CERN using collinear laser and beta-NMR spectroscopy techniques. The isotopes were investigated as single-charged ions in the 280-nm transition from the atomic ground state 2S1/2 to one of the two lowest excited states 2P1/2,3/2 using continuous wave laser beams. The isotope-shift measurements with fluorescence detection for the three stable isotopes show that it is feasible to perform the same studies on radioactive Mg isotopes up to the "island of inversion". This will allow to determine differences in the mean charge square radii and interpret them in terms of deformation. The high detection efficiency for beta particles and optical pumping close to saturation allowed to obtain very good beta-asymmetry signals for 29Mg and 31Mg with half-lives around 1 s and production yields about 10^5 ions/s. For this purpose the ions were implanted into a host crystal lattice. Such detection of the atomic resonances revealed their hyperfine structure, which gives the sign and a first estimate of the value of the magnetic moment. The nuclear magnetic resonance gave also their g-factors with the relative uncertainty smaller than 0.2 %. By combining the two techniques also the nuclear spin of both isotopes could be unambiguously determined. The measured spins and g-factors show that 29Mg with 17 neutrons lies outside the "island of inversion". On the other hand, 31Mg with 19 neutrons has an unexpected ground-state spin which can be explained only by promoting at least two neutrons across the N = 20 shell gap. This places the above nucleus inside the "island". However, modern shell-model approaches cannot predict this level as the ground state but only as one of the low-lying states, even though they reproduce very well the experimental g-factor. This indicates that modifications to the available interactions are required. Future measurements include isotope shift measurements on radioactive Mg isotopes and beta-NMR studies on 33Mg.

Solid-state NMR on columnar supramolecular structures

The present work deals with the characterisation of three columnar self-assembled systems, that is, benzene-1,3,5-tricarboxamides, a peripherally thioalkyl-substituted phthalocyanine, and several oligo-(p-phenylenevinylene)s. In order to probe the supramolecular organisation solid-state NMR has been used as the main technique, supported by X-ray measurements, theoretical methods, and thermal analysis. rnrnBenzene-1,3,5-tricarboxamides (BTAs) turned out to be well suited model compounds to study various fundamental supramolecular interactions, such as π-π-interactions, hydrogen bonding, as well as dynamic and steric effects of attached side chains. Six BTAs have been investigated in total, five with a CO-centred amide group bearing different side chains and one with an inverted N-centred amide group. The physical properties of these BTAs have been investigated as a function of temperature. The results indicated that in case of the CO-centred BTAs the stability of the columnar mesophase depends strongly on the nature of the side chains. Further experiments revealed a coplanar orientation of adjacent BTA molecules in the columnar assembly of CO-centred BTAs, whereas the N-centred BTA, showed a deviating not fully coplanar arrangement. These differences were ascribed to distinct hydrogen bonding schemes, involving a parallel alignment of hydrogen bonds in case of CO-centred BTAs and an antiparallel alignment in case of the N-centred counterpart.rnrn The fundamental insights of the supramolecular organisation of BTAs could be partially adapted to an octa-substituted phthalocyanine with thiododecyl moieties. Solid-state NMR in combination with chemical shift calculations determined a tilted herringbone arrangement of phthalocyanine rings in the crystalline phase as well as in the mesophase. Moreover, 1H NMR measurements in the mesophase of this compound suggested an axial rotation of molecules, which is inhibited in the crystalline phase.rnrnAs a third task, the supramolecular assembly of oligo-(p-phenylenevinylene)s of varying length and with different polar head groups have been investigated by a combined X-ray and solid-state NMR study. The results revealed a columnar structure formation of these compounds, being promoted by phase separation of alkyl side chains and aromatic rigid rods. In this system solid-state NMR yielded meaningful insight into the isotropisation process of butoxy and 2-S-methylbutoxy substituted oligo-(p-phenylenevinylene) rods.rn

Investigation of the lithium ion mobility in cyclic model compounds and their ion conducting properties

Efficient energy storage and conversion is playing a key role in overcoming the present and future challenges in energy supply. Batteries provide portable, electrochemical storage of green energy sources and potentially allow for a reduction of the dependence on fossil fuels, which is of great importance with respect to the issue of global warming. In view of both, energy density and energy drain, rechargeable lithium ion batteries outperform other present accumulator systems. However, despite great efforts over the last decades, the ideal electrolyte in terms of key characteristics such as capacity, cycle life, and most important reliable safety, has not yet been identified. rnrnSteps ahead in lithium ion battery technology require a fundamental understanding of lithium ion transport, salt association, and ion solvation within the electrolyte. Indeed, well-defined model compounds allow for systematic studies of molecular ion transport. Thus, in the present work, based on the concept of ‘immobilizing’ ion solvents, three main series with a cyclotriphosphazene (CTP), hexaphenylbenzene (HBP), and tetramethylcyclotetrasiloxane (TMS) scaffold were prepared. Lithium ion solvents, among others ethylene carbonate (EC), which has proven to fulfill together with pro-pylene carbonate safety and market concerns in commercial lithium ion batteries, were attached to the different cores via alkyl spacers of variable length.rnrnAll model compounds were fully characterized, pure and thermally stable up to at least 235 °C, covering the requested broad range of glass transition temperatures from -78.1 °C up to +6.2 °C. While the CTP models tend to rearrange at elevated temperatures over time, which questions the general stability of alkoxide related (poly)phosphazenes, both, the HPB and CTP based models show no evidence of core stacking. In particular the CTP derivatives represent good solvents for various lithium salts, exhibiting no significant differences in the ionic conductivity σ_dc and thus indicating comparable salt dissociation and rather independent motion of cations and ions.rnrnIn general, temperature-dependent bulk ionic conductivities investigated via impedance spectroscopy follow a William-Landel-Ferry (WLF) type behavior. Modifications of the alkyl spacer length were shown to influence ionic conductivities only in combination to changes in glass transition temperatures. Though the glass transition temperatures of the blends are low, their conductivities are only in the range of typical polymer electrolytes. The highest σ_dc obtained at ambient temperatures was 6.0 x 10-6 S•cm-1, strongly suggesting a rather tight coordination of the lithium ions to the solvating 2-oxo-1,3-dioxolane moieties, supported by the increased σ_dc values for the oligo(ethylene oxide) based analogues.rnrnFurther insights into the mechanism of lithium ion dynamics were derived from 7Li and 13C Solid- State NMR investigations. While localized ion motion was probed by i.e. 7Li spin-lattice relaxation measurements with apparent activation energies E_a of 20 to 40 kJ/mol, long-range macroscopic transport was monitored by Pulsed-Field Gradient (PFG) NMR, providing an E_a of 61 kJ/mol. The latter is in good agreement with the values determined from bulk conductivity data, indicating the major contribution of ion transport was only detected by PFG NMR. However, the μm-diffusion is rather slow, emphasizing the strong lithium coordination to the carbonyl oxygens, which hampers sufficient ion conductivities and suggests exploring ‘softer’ solvating moieties in future electrolytes.rn

Interacting bosons and fermions in three-dimensional optical lattice potentials

This thesis reports on the realization, characterization and analysis of ultracold bosonic and fermionic atoms in three-dimensional optical lattice potentials. Ultracold quantum gases in optical lattices can be regarded as ideal model systems to investigate quantum many-body physics. In this work interacting ensembles of bosonic 87Rb and fermionic 40K atoms are employed to study equilibrium phases and nonequilibrium dynamics. The investigations are enabled by a versatile experimental setup, whose core feature is a blue-detuned optical lattice that is combined with Feshbach resonances and a red-detuned dipole trap to allow for independent control of tunneling, interactions and external confinement. The Fermi-Hubbard model, which plays a central role in the theoretical description of strongly correlated electrons, is experimentally realized by loading interacting fermionic spin mixtures into the optical lattice. Using phase-contrast imaging the in-situ size of the atomic density distribution is measured, which allows to extract the global compressibility of the many-body state as a function of interaction and external confinement. Thereby, metallic and insulating phases are clearly identified. At strongly repulsive interaction, a vanishing compressibility and suppression of doubly occupied lattice sites signal the emergence of a fermionic Mott insulator. In a second series of experiments interaction effects in bosonic lattice quantum gases are analyzed. Typically, interactions between microscopic particles are described as two-body interactions. As such they are also contained in the single-band Bose-Hubbard model. However, our measurements demonstrate the presence of multi-body interactions that effectively emerge via virtual transitions of atoms to higher lattice bands. These findings are enabled by the development of a novel atom optical measurement technique: In quantum phase revival spectroscopy periodic collapse and revival dynamics of the bosonic matter wave field are induced. The frequencies of the dynamics are directly related to the on-site interaction energies of atomic Fock states and can be read out with high precision. The third part of this work deals with mixtures of bosons and fermions in optical lattices, in which the interspecies interactions are accurately controlled by means of a Feshbach resonance. Studies of the equilibrium phases show that the bosonic superfluid to Mott insulator transition is shifted towards lower lattice depths when bosons and fermions interact attractively. This observation is further analyzed by applying quantum phase revival spectroscopy to few-body systems consisting of a single fermion and a coherent bosonic field on individual lattice sites. In addition to the direct measurement of Bose-Fermi interaction energies, Bose-Bose interactions are proven to be modified by the presence of a fermion. This renormalization of bosonic interaction energies can explain the shift of the Mott insulator transition. The experiments of this thesis lay important foundations for future studies of quantum magnetism with fermionic spin mixtures as well as for the realization of complex quantum phases with Bose-Fermi mixtures. They furthermore point towards physics that reaches beyond the single-band Hubbard model.

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.