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In den Neurowissenschaften führt die Erforschung des vegetativen Nervensystem (VNS) immer noch ein Schattendasein. Einer der wichtigsten Teile des VNS, der Hirnstamm, ist dabei besonders schlecht erforscht, obwohl er die Steuerzentren für Herzschlag, Blutdruckregulation, Atmung, Verdauung, und viele weitere lebenswichtige Funktionen beherbergt. Ein wichtiger Grund für diesen Umstand ist, dass die funktionelle Kernspintomographie (fMRT) sich in ihrer bisherigen Form nur bedingt für Messungen im Hirnstamm eignet. Ziel dieser Arbeit war es daher, neue Ansätze zur fMRT-Messung vegetativer Zentren im menschlichen Hirnstamm zu entwickeln. Nach einer Einführung in die Neuroanatomie sowie die physikalischen und physiologischen Grundlagen der strukturellen und funktionellen MRT werden im mittleren Teil der Arbeit die Entwicklung sowie der Test neuer Ansätze zur Hirnstamm-fMRT beschrieben. Dabei untersucht der Autor zunächst, welche grundlegenden Probleme einer konventionellen fMRT-Messung im Hirnstamm entgegenstehen. Es stellt sich heraus, dass alle hirnstamm-spezifischen Störquellen direkt oder indirekt auf den Herzschlag zurückzuführen sind. Aus den vorhandenen Ansätzen zur Korrektur solcher Störungen wird die Herzschlag-Taktung ausgewählt. Bei diesem Verfahren erfolgt die Aufnahme der fMRT-Bilder zeitlich gekoppelt an dem Herzschlag des Probanden, um sämtliche kardiogenen Rauschquellen zu unterdrücken. Anstelle des häufig verwendeten, aber statistisch problematischen Guimaraes-Verfahrens zur Korrektur der durch die Herzfrequenzvariabilität bedingten Schwankungen des MR-Signals wird in der vorliegenden Arbeit der die sog. Dual-Echo-Bildgebung verwendet. Dabei wird die konventionelle EPI-Sequenz (echo-planar imaging) dahingehend erweitert, dass pro Bild anstelle eines Echos zwei aufgenommen werden. Durch Quotientenbildung der beiden Bilder kann so der fluktuierende Teil des Signals entfernt werden. Beim Vergleich verschiedener Varianten der Quotientenbildung stellt sich ein neu entwickelter, exponentieller Ansatz als überlegen heraus. Danach werden die Auswirkungen verschiedener Methoden der Bewegungskorrektur und Schichtorientierung verglichen, um das Optimum für Messungen im Hirnstamm zu ermitteln. Nach Tests des neuen Verfahrens an verschiedenen fMRT-Datensätzen werden Empfehlungen für die Kombination der verschiedenen Parameter gegeben. Es zeigt sich, dass die Standardabweichung der fMRT-Bilder mit der neuen Methode im unteren Hirnstamm um 13% - 33% reduziert werden kann. Ein Sensitivitätstest an motorischen Hirnstammkernen, welche durch ein motorisches Paradigma aktiviert werden, zeigt, dass die jeweiligen Kerne in 85% - 95% der Fälle eindeutig identifiziert werden können. Im dritten Teil der Arbeit erfolgt die Anwendung der neuen Methode auf die Messung von Aktivierungen vegetativer Zentren. Hier wird als unkonventionellen Stimulus des vegetativen Nervensystems die Akupunktur verwendet. Dies geschieht u.a. mit der Zielsetzung, zur Aufdeckung des noch immer unbekannten Wirkmechanismus dieser Therapieform beizutragen. Als Akupunkturpunkt wird Pc6 am Handgelenk gewählt, da die Studienlage eindeutig dessen Effektivität bei der Behandlung von Übelkeit und Erbrechen sowie eine Beeinflussung der Magen-Peristaltik zeigt und die neuralen Zentren hierfür größtenteils im Hirnstamm lokalisiert sind. Der Autor stellt daher die Hypothese auf, dass die Akupunkturwirkung in diesem Fall über den Vagusnerv und dessen Hirnstammkern, den Nucleus dorsalis nervi vagi, vermittelt wird. Vor der Überprüfung dieser Hypothese erfolgt zunächst eine Methodenkritik der bisherigen Akupunktur-fMRT-Forschung. Anhand einer Gruppe von Studien, welche über Aktivierungen der Sehrinde bei Akupunktur visuell relevanter Punkte berichten, weist der Autor eine Reihe methodischer Probleme nach. Anhand einer eigenen Studie kann er mittels Independent Component Analysis (ICA) zeigen, dass die von den bisherigen Studien berichteten, visuellen Aktivierungen höchstwahrscheinlich nicht auf die Wirkung der Akupunktur zurückzuführen sind. Um einige der Probleme dieser Studien zu umgehen, entwickelt der Autor ein neues psychophysikalisches Verfahren, bei dem die Probanden während der Akupunktur kontinuierlich die Stärke der Nadelempfindung („DeQi“) auf einer visuellen Analogskala bewerten. Mit Hilfe dieses Verfahrens gelingt schließlich der Nachweis einer Hirnstamm-Aktivierung unter Akupunktur-Stimulation, deren Lokalisation mit der des Nucleus dorsalis nervi vagi vereinbar ist. Dies bestätigt die ursprüngliche Hypothese und zeigt gleichzeitig die Eignung des neuen Verfahrens für die Bildgebung vegetativer Hirnstammzentren.
Den Geheimnissen der Materie auf der Spur : neue Denkfabrik für physikalische Grundlagenforschung
(2009)
Bei Darmstadt entsteht FAIR, eines der größten internationalen Forschungszentren für Physik. Durch das von der Landesregierung geförderte Exzellenzzentrum »HIC for FAIR« erhält die Forschung in Hessen die einmalige Chance, sich direkt an globaler Spitzenforschung zu beteiligen: auf der Suche nach den letzten Geheimnissen der Materie.
In this thesis, we studied the single impurity Anderson model and developed a new and fast impurity solver for the dynamical mean field theory (DMFT). Using this new impurity solver, we studied the Hubbard model and periodic Anderson model for various parameters. This work is motivated by the fact that the dynamical mean field theory is widely used for the studies of strongly correlated systems, and the most frequently used methods, e.g. the quantum Monte-Carlo method (QMC), and the exact digonalization method are much CPU time consuming and usually limited by the available computers. Therefore, a fast and reliable impurity solver is needed. This new impurity solver was explored based on the equation-of-motion method (also called Green's function and decoupling method in some literature). Using the retarded Green's function, we first derived the equations of motion of Green's functions. Then, we employed a decoupling scheme to close the equations. By solving self-consistently the obtained closed set of integral equations, we obtained the single particle Green's function for the single impurity Anderson model. After that, the single impurity Anderson model was solved along with self-consistency conditions within the framework of DMFT. In this work, we studied and compared two decoupling schemes. Moreover, we also derived possible higher order approximations which will be tested in future work. Besides the theoretical work, we tested the method in numerical calculations. The integral equations are first solved by iterative methods with linear mixing and Broyden mixing, respectively. However, these two methods are not sufficient for finding the self-consistent solutions of the DMFT equations because converged results are difficult to obtain. Moreover, the computing speed of the two methods is also not satisfactory. Especially the iterative method with linear mixing costs always a lot of CPU time due to the required small mixing. Hence, we developed a new method, which is a combination of genetic algorithm and iterative method. This new method converges very fast and removes artifacts appearing in the results from the iterative method with linear and Broyden mixing. It can directly operate on the real axis, where no numerical error from the high frequency tail corrections and the analytical continuation is introduced. In addition, our new technique strongly improves the precision of the numerical results by removing the broadening. With this newly developed impurity solver and numerical technique, we studied the single impurity Anderson model, the single band Hubbard model and the periodic Anderson model with arbitrary spin and orbital degeneracy N on the real axis. For the single impurity Anderson model, the spectral functions are calculated for the infinite and finite Coulomb interaction strength. We also studied the spectral functions in dependence of the parameters of impurity position and hybridization. For the Hubbard model, we studied the bandwidth control and filling control Mott metal-insulator transition for spin and orbital degeneracy N = 2. It gives qualitatively the critical value of Coulomb interaction strength for the Mott metal-insulator transition, and the spectral functions which are comparable to those obtained in QMC and numerical renormalization group methods. We also studied the quasiparticle weight and the self-energy in metallic states. The latter shows almost Fermi liquid behavior. At last we calculated the densities of states for the Hubbard model with arbitrary spin and orbital degeneracy N. The periodic Anderson model (PAM) is also studied as another important lattice model. It was solved for various combinations of parameters: the Coulomb interaction strength, the impurity position, the center position of the conduction band, the hybridization, the spin and orbital degeneracy. The PAM results represents the physics of impurities in a metal. In short, our method works for the Hubbard model and the periodic Anderson model in a large range of parameters, and gives good results. Therefore, our impurity solver could be very useful in calculations within LDA+DMFT. Finally, we also made a preliminary investigation of the multi-band system based on the success in single band case. We first studied the two-band system in a simplified treatment by neglecting the interaction between the two bands through the bath. This has given promising numerical results for the two-band Hubbard model. Moreover, we have studied theoretically the two-band system with mean field approximation and Hubbard-I approximation in dealing with the higher order cross Green's functions which are related to both the two bands. In the mean field approximation, we even generalized the two-band system to arbitrary M=N/2 band system. Potential improvement can be carried out on the basis of this work.
The current thesis is devoted to a systematic study of fluctuations and correlations in heavy-ion collisions, which might be considered as probes for the phase transition and the critical point in the phase diagram, within the Hadron-String- Dynamics (HSD) microscopic transport approach. This is a powerful tool to study nucleus-nucleus collisions and allows to completely simulate experimental collisions on an event-by-event basis. Thus, the transport model has been used to study fluctuations and correlations including the influence of experimental acceptance as well as centrality, system size and collision energy. The comparison to experimental data can separate the effects induced by a phase transition since there is no phase transition in the HSD version used here. Firstly the centrality dependence of multiplicity fluctuations has been studied. Different centrality selections have been performed in the analysis in correspondence to the experimental situation. For the fixed target experiment NA49 events with fixed numbers of the projectile participants have been studied while in the collider experiment PHENIX centrality classes of events have been defined by the multiplicity in certain phase space region. A decrease of participant number fluctuations (and thus volume fluctuations) in more central collisions for both experiments has been obtained. Another area of this work addresses to transport model calculations of multiplicity fluctuations in nucleus-nucleus collisions as a function of colliding energy and system size. This study is in full correspondence to the experimental program of the NA61 Collaboration at the SPS. Central C+C, S+S, In+In, and Pb+Pb nuclear collisions at Elab = 10, 20, 30, 40, 80, 158 AGeV have been investigated. The expected enhanced fluctuations - attributed to the critical point and phase transition - can be observed experimentally on top of a monotonic and smooth ‘hadronic background’. These findings should be helpful for the optimal choice of collision systems and collision energies for the experimental search of the QCD critical point. Other observables are fluctuations of ratios of hadrons (e.g. pions, kaons, protons, etc.) which are not so much affected by volume fluctuations. In particular HSD results for the kaon-to-pion ratio fluctuations, which has been regarded as promising observable for a long time, are presented from low SPS energies up to high energies at RHIC. In addition to the HSD calculations statistical model is also used in terms of microcanonical, canonical and grand canonical ensembles. Further a study of the system size event-by-event fluctuations causing rapidity forward-backward correlations in relativistic heavy-ion collisions is presented. The HSD simulations reveal strong forward-backward correlations and reproduce the main qualitative features of the STAR data in A+A collisions at RHIC energies. It has been shown that strong forward-backward correlations arise due to an averaging over many different events that belong to one centrality bin. An optimization of the experimental selection of centrality classes is presented, which is relevant for the program of the NA61 collaboration at CERN, the low-energy program at RHIC, as well as future experiments at FAIR.
Kaon and pion production in centrality selected minimum bias Pb+Pb collisions at 40 and 158A GeV
(2009)
Results on charged kaon and negatively charged pion production and spectra for centrality selected Pb+Pb mininimum bias events at 40 and 158A GeV have been presented in this thesis. All analysis are based on data taken by the NA49 experiment at the accelerator Super Proton Synchrotron (SPS) at the European Organization for Nuclear Research (CERN) in Geneva, Switzerland. The kaon results are based on an analysis of the mean energy loss <dE/dx> of the charged particles traversing the detector gas of the time projection chambers (TPCs). The pion results are from an analysis of all negatively charged particles h- corrected for contributions from particle decays and secondary interactions. For the dE/dx analysis of charged kaons, main TPC tracks with a total momentum between 4 and 50 GeV have been analyzed in logarithmic momentum log(p) and transverse momentum pt bins. The resulting dE/dx spectra have been fitted by the sum of 5 Gaussians, one for each main particle type (electrons, pions, kaons, protons, deuterons). The amplitude of the Gaussian used for the kaon part of the spectra has been corrected for efficiency and acceptance and the binning has been transformed to rapidity y and transverse momentum pt bins. The multiplicity dN/dy of the single rapidity bins has been derived by summing the measured range of the transverse momentum spectra and an extrapolation to full coverage with a single exponential function fitted to the measured range. The results have been combined with the mid-rapidity measurements from the time-of-flight detectors and a double Gaussian fit to the dN/dy spectra has been used for extrapolation to rapidity outside of the acceptance of the dE/dx analysis. For the h- analysis of negatively charged pions, all negatively charged tracks have been analyzed. The background from secondary reactions, particle decays, and gamma-conversions has been corrected with the VENUS event generator. The results were also corrected for efficiency and acceptance and the pt spectra were analyzed and extrapolated where necessary to derive the mean yield per rapidity bin dN/dy. The mean multiplicity <pi-> has been derived by summing up the measured dN/dy and extrapolating the rapidity spectrum with a double Gaussian fit to 4pi coverage. The results have been discussed in detail and compared to various model calculations. Microscopical models like URQMD and HSD do not describe the full complexity of Pb+Pb collisions. Especially the production of the positively charged kaons, which carry the major part of strange quarks, cannot be consistently reproduced by the model calculations. Centrality selected minimum bias Pb+Pb collisions can be described as a mixture of a high-density region of multiply colliding nucleons (core) and practically independent nucleon-nucleon collisions (corona). This leads to a smooth evolution from peripheral to central collisions. A more detailed approach derives the ensemble volume from a percolation of elementary clusters. In the percolation model all clusters are formed from coalescing strings that are assumed to decay statistically with the volume dependence of canonical strangeness suppression. The percolation model describes the measured data for top SPS and RHIC energies. At 40A GeV, the system size dependence of the relative strangeness production starts to evolve from the saturation seen at higher energies from peripheral events onwards towards a linear dependence at SIS and AGS. This change of the dependence on system size occurs in the energy region of the observed maximum of the K+ to pi ratio for central Pb+Pb collisions. Future measurements with heavy ion beam energies around this maximum at RHIC and FAIR as well as the upgraded NA49 successor experiment NA61 will further improve our understanding of quark matter and its reflection in modern heavy ion physics and theories.
In dieser Arbeit wurden zwei Systeme der biologischen Energiewandlung mit verschiedenen spektroskopischen Methoden untersucht und es wurden neue Erkenntnisse über die Funktion und Aktivierung der Proteine Proteorhodopsin und RuBisCO gewonnen. Zusätzlich konnte eine neue methodische Herangehensweise zur Untersuchung von Carboxylierungsreaktionen etabliert werden. Dieser Ansatz bietet in Zukunft breite Anwendungsmöglichkeiten zur Studie dieser biologisch so bedeutenden Reaktionsklasse. Mit Hilfe der Infrarotspektroskopie und vor allem durch den Einsatz von Tieftemperaturmessungen konnte der bisher kontrovers diskutierte Photozyklus von Proteorhodopsin (PR) eingehend charakterisiert werden. Jenseits des gut verstandenen aktiven Transports bei pH 9,0 wurde vor allem der pH 5,1 Photozyklus untersucht. Erstmals konnte auch in Infrarotspektren das M-Intermediat bei pH 5,1 nachgewiesen werden. Dieses Intermediat ist von entscheidender Bedeutung für den aktiven Transport über die Zellmembran und seine Existenz wurde bisher vielfach angezweifelt. Zudem konnte Glu-108 als ein möglicher Protonenakzeptor des Photozyklus bei pH 5,1 identifiziert werden. Durch einen pH-Indikator ließ sich der Nachweis erbringen, dass auch im sauren pH-Bereich Protonen freigesetzt werden. Damit steht fest, dass ein aktiver Protonentransport bei pH 5,1 möglich ist. Zusammen mit Informationen zu protonierbaren Aminosäureseitenketten (vornehmlich Asp und Glu) lässt sich zudem mit Einschränkungen die These unterstützen, dass PR ober- und unterhalb des pKa-Werts von Asp-97 in verschiedene Richtungen Protonen pumpt. Damit ergibt sich ein differenziertes Bild für den pH-abhängigen Photozyklus von PR mit drei pH-Bereichen (pH 9,0, 8,5 bis 5,5 und 5,1) in denen PR unterschiedliche Protonentransportwege zeigt. Als weiteres biologischen System wurde RuBisCO genauer untersucht. Im Fokus der Arbeit war dabei die Aktivierung durch die Bildung eines Lysin-Carbamats im aktiven Zentrum. Obwohl RuBisCO das am häufigsten vorkommende Enzym unseres Planeten ist, in der Kohlenstofffixierung eine bedeutende Rolle spielt und obwohl mehrere Dutzend Kristallstrukturen existieren, gibt es noch immer genügend offene Fragen zur Aktivierung. Mit Hilfe eines Käfig-CO2 konnte die Carbamatbildung im Enzym direkt verfolgt und der Einfluss von Magnesiumionen auf die Aktivierung beobachtet werden. Damit ließ sich ganz klar ausschließen, dass Magnesium bereits für die Carbamatbildung erforderlich ist. Die Koordination von Mg2+ ist erst für die Endiol-Bildung im weiteren Reaktionszyklus essentiell. Zusätzlich wurde gezeigt, dass Azid eine Inhibierung des Enzyms durch die Konkurrenz mit CO2 um die Bindungsstelle auslöst, allerdings verdrängt CO2 das Azidion im Laufe der Zeit. Mit den Ergebnissen für RuBisCO konnte klar gezeigt werden, dass die Kombination aus Käfig-CO2 und Rapid-Scan IR-Spektroskopie ein völlig neues Feld für die Untersuchung von Carboxylierungsreaktionen eröffnet. Gerade die offenen Fragen zu Biotin bindenden Carboxylasen bieten ein breites Anwendungsgebiet für diese Methodik.
Inhaltsverzeichnis 1. Einleitung …………………………………………………………………...3 1.1 Erklärungsversuche und Forschungsergebnisse der Gegenwart ……8 1.2 Zielrichtung und Abgrenzung der aktuellen Arbeit ………………..21 1.3 Intention und Erläuterung der Versuchsreihen ………………….....25 2. Grundlagen und Methodiken bezüglich des subjektiven visuellen Wahrnehmungsraums …………………………………………………........27 2.1 Die nativistische und die empiristische Anschauung ………………27 2.2 Räumliche Anordnungen der wahrgenommenen Objekte …………31 2.3 Über die visuell vermittelte Richtungs- und Lagebestimmung …....33 2.4 Visuelle Auswertungen der korrespondierenden Netzhautstellen …42 2.5 Visuelle Auswertungen der disparaten Netzhautstellen …………...44 2.6 Die Größenkonstanzleistung ………………………………………47 2.7 Psychophysikalische Grundlagen und Schwellenwerte …………...50 2.8 Physiologische Grundlagen ………………………………………..54 3. Experimentelle Untersuchung ……………………………………………..60 3.1 Versuchsaufbau und Ablauf zur Durchführung der Experimente …60 3.1.1 Zusammensetzungen der Versuchsteilnehmer ……………66 3.1.2 Erläuterungen und Ablauf der 2 Versuchsreihen …………66 3.2 Graphische Darstellungen der Messergebnisse ……………………71 3.2.1 I.Versuchsreihe ……………………………………………71 3.2.2 II.Versuchsreihe …………………………………………...93 3.3 Auswertung und Aufbereitung der Messdaten …………………..102 3.3.1 Auswertungen der I.Versuchsreihe ……………………..102 3.3.2 Auswertungen der II.Versuchsreihe …………………….120 3.3.3 Fehlerbetrachtungen der Versuchsreihen I und II ………122 3.4 Diskussion der Messdaten ……………………………………….124 4. Zusammenfassung und Ausblick ………………………………………...135 Begriffsverzeichnis mit kurzer Erklärung.…………………………………...137 Literaturverzeichnis …………………………………………………….........141 Bildquellenverzeichnis ………………………………………………….......143 Als Fazit kann man folgendes zusammenfassend sagen: Die aufgestellte Arbeitshypothese wurde durch die beiden Versuchsreihen verifiziert, denn die Ergebnisse ergaben folgendes: - In den Messreihen der Versuchsreihe I ist jeweils ein Anstieg der eingestellten Größe, je mehr Abstandsinformationen zugelassen wurden, zu verzeichnen. Das bedeutet, der Anstieg wurde umso größer, desto größer die AID wurde. Auch waren in allen Messreihen die monokularen Größeneinstellungen, bei sonst konstanter AID, gegenüber der binokularen Größeneinstellung geringer. Bei Verringerung der Einstellentfernung wurden die Abweichungen zwischen den subjektiven und den objektiven Größen ebenfalls größer. Das heißt also, die subjektive visuelle Wahrnehmungsgröße ist von der AID wie folgt abhängig: Das visuelle System bewertet subjektiv die Wahrnehmungsgröße bei maximaler AID nach oben und relativ dazu, bei minimaler AID nach unten. - Dass die aufgestellten Parameter die AID bedingen, konnte durch die 1. Messreihe gezeigt werden, da der jeweilige Anstieg der eingestellten Größe, nur durch die Variation eines Parameters erfolgte. Die Querdisparation konnte aber hier nicht als Parameter der die AID bedingt isoliert untersucht werden. Bei den meisten Probanden ergaben sich sehr schnell Doppelbilder und erzeugten bei ihnen ein Unbehagen. Aber dennoch floss dieser Parameter als einflussnehmende Größe in den Konvergenzgrad mit ein. Das Netzhautbild konnte nur kombiniert mit dem psychologischen Gefühl der Nähe isoliert betrachtet werden. Damit die Voraussetzungen in beiden Versuchen gleich waren, wurde in der Versuchsreihe II unter gleichen Versuchsbedingungen wie in der Versuchsreihe I gemessen. Auch hier wurden die Abstandsinformationen von minimal bis maximal sukzessive zugelassen. Durch die Messdaten der Versuchsreihe II konnte eindeutig gezeigt werden, dass die Abstandsunterschiedsschwelle umso geringer ausfällt, desto mehr Abstandskriterien hinzukamen, also die AID erhöht wurde. Analog kehren sich die Verhältnisse um, wenn die AID erniedrigt wird. Durch diesen kausalen Zusammenhang zwischen der Abstandsunterschiedsschwelle des visuellen Systems und der Güte der AID bestätigt sich zusätzlich die Annahme, dass die eingeführten Parameter des Abstandes tatsächlich als solche zu betrachten sind und die AID konstituieren. Denn wären sie keine Konstituenten der AID, so müssten die Unterschiedsschwellen der Versuchsreihe II in etwa gleich sein. Da aber die Änderung der Randbedingungen sich auf die verwertbaren Abstandsinformationen bezogen und somit die AID jeweils geändert wurde, ist die aufgestellte Annahme über die Parameter, welche die AID bedingen, berechtigt. - Dass im orthostereoskopischen Bereich die subjektiven Größeneinstellungen gegenüber der Zentralprojektion am weitesten auseinander liegen, bestätigte sich durch alle Messreihen der Versuchsreihe I. In diesem Bereich existiert die maximale Unabhängigkeit der visuellen Wahrnehmungsgröße vom Gesichtswinkel. In diesem Bereich liegt eine sehr hohe Güte in der Größenkonstanzleistung des visuellen Systems vor. Dass die Größenkonstanz qualitativ dem aufgestellten Formalismus aus Annahme 2 genügt und die aufgestellte qualitative Relation sie beschreibt, konnte nicht gezeigt werden. Das begründet sich durch das Zustandekommen der Größenkonstanz. Sie resultiert bekanntlich aus einer Entfernungsänderung. Je nach dem, ob sich ein Objekt dem Beobachter nähert oder entfernt, setzt diese Bildgrößenkompensation ein. Von daher unterliegt sie einem dynamischen Prozess und kann dadurch mit Relation (2´) nicht beschreiben werden. - Mit der Relation 2´ kann man qualitativ die Unbestimmtheit in der visuellen Wahrnehmungsentfernung beschreiben und qualitativ erklären. Der Aspekt der Abstandsunterschiedsschwelle ist etwas verwirrend. Auf der einen Seite handelt es sich um eine Vermögensleistung des visuellen Systems, welches abhängig ist von den vorliegenden Abstandsinformationen, die ihrerseits die AID bedingen. Auf der anderen Seite bedingt die Abstandsunterschiedsschwelle die AID durch ihre Güte und Qualität, beeinflusst also umgekehrt auch die AID. In der Versuchsreihe 2 wurde auf die Vermögensleistung des visuellen Systems und deren Abhängigkeit von den Parametern eingegangen, die auch die AID bedingen. Dies diente dazu, zusätzlich zu zeigen, dass es sich bei diesen Parametern um Parameter handelt, welche die AID bedingen. Die Argumentationskette lautete wie folgt: Die Abstandsunterschiedsschwelle beeinflusst die AID. Die betrachteten Parameter beeinflussten die Abstandsunterschiedsschwelle, dass experimentell verifiziert wurde. Daraus folgte dann, dass eben diese Parameter auch die AID bedingen. Diese Argumentation diente nur als zusätzliches Hilfsmittel. Bei Punkt 4 sollte die Abstandsunterschiedsschwelle und ihr Einfluss auf die Unbestimmtheit hin betrachtet werden. Dies hat aber nur sekundäre Relevanz, da hier die Anwendung der Relation 2´ im Vordergrund stand. - Ob die Fitting-Funktion, welche die Messdaten der Versuchsreihe I approximierte, sich als Algorithmus für die Darstellung einer Bewegungssimulation eignet, kann noch nicht gesagt werden. Es müssen noch Untersuchungen umgesetzt werden, welche die Diagonalbewegung beschreiben. In der stirnfrontalen Vor- und Zurückbewegung ist der simulierte Bewegungsablauf mit der Fitting-Funktion gegenüber der linearen Darstellung realistischer. Dies ist in der ersten 100cm Raumtiefe besonders merklich, da die Fitting-Funktion die Größenkonstanzleistung des visuellen Systems berücksichtigt. Die auf dem konventionellen Computerspielmarkt eingesetzten Algorithmen für die Darstellung von Vor- und Zurückbewegungen sind dagegen nahezu linear, welches dem Beobachter einen etwas unnatürlichen Seheindruck vermittelt. Die Fitting-Funktion könnte auch für die Simulation von Zeichentrickfilmen verwendet werden. Auch dort wird die Größenkonstanzleistung des visuellen Systems nicht berücksichtigt. Aber gerade diese Konstanzleistung gestaltet die Größenvariation der wahrgenommenen Objekte bei Entfernungsänderungen. Dies ist besonders im orthostereoskopischen Bereich merklich.
Starting from the first observation of the halo phenomenon 20 years ago, more and more neutron-rich light nuclei were observed. The study of unstable nuclear systems beyond the dripline is a relatively new branch of nuclear physics. In the present work, the results of an experiment at GSI (Darmstadt) with relativistic beams of the halo nuclei 8He, 11Li and 14Be with energies of 240, 280 and 305 MeV/nucleon, respectively, impinging on a liquid hydrogen target are discussed. Neutron/proton knockout reactions lead to the formation of unbound systems, followed by their immediate decay. The experimental setup, consisting of the neutron detector LAND, the dipole spectrometer ALADIN and different types of tracking detectors, allows the reconstruction of the momentum vectors of all reaction products measured in coincidence. The properties of unbound nuclei are investigated by reconstructing the relative-energy spectra as well as by studying the angular correlations between the reaction products. The observed systems are 9He, 10He, 10Li, 12Li and 13Li. The isotopes 12Li and 13Li are observed for the first time. They are produced in the 1H(14Be, 2pn)12Li and 1H(14Be, 2p)13Li knockout reactions. The obtained relative-energy spectrum of 12Li is described as a single virtual s-state with a scattering length of as = -22;13.7(1.6) fm. The spectrum of 13Li is interpreted as a resonance at an energy of Er = 1.47(13) MeV and a width of Gamma ~ 2 MeV superimposed on a broad correlated background distribution. The isotope 10Li is observed after one-neutron knockout from the halo nucleus 11Li. The obtained relative-energy spectrum is described by a low-lying virtual s-state with a scattering length as = -22.4(4.8) fm and a p-wave resonance with Er = 0.566(14) MeV and Gamma = 0.548(30) MeV, in agreement with previous experiments. The observation of the nucleus 8He in coincidence with one or two neutrons, as a result of proton knockout from 11Li, allows to reconstruct the relative-energy spectra for the heavy helium isotopes, 9He and 10He. The low-energy part of the 9He spectrum is described by a virtual s-state with a scattering length as = -3.16(78) fm. In addition, two resonance states with l 6= 0 at energies of 1.33(8) and 2.4 MeV are observed. For the 10He spectrum, two interpretations are possible. It can be interpreted as a superposition of a narrow resonance at 1.42(10) MeV and a broad correlated background distribution. Alternatively, the spectrum is being well described by two resonances at energies of 1.54(11) and 3.99(26) MeV. Additionally, three-body energy and angular correlations in 10He and 13Li nuclei at the region of the ground state (0 < ECnn < 3 MeV) are studied, providing information about structure of these unbound nuclear systems.
This thesis is devoted to the developement of a classical model for the study of the energetics and stability of carbon nanotubes. The motivation behind such a model stems from the fact that production of nanotubes in a well-controlled manner requires a detailed understanding of their energetics. In order to study this different theoretical approaches are possible, ranging from the computationally expensive quantum mechanical first principle methods to the relatively simple classical models. A wisely developed classical model has the advantage that it could be used for systems of any possible size while still producing reasonable results. The model developed in this thesis is based on the well-known liquid drop model without the volume term and hence we call it liquid surface model. Based on the assumption that the energy of a nanotube can be expressed in terms of its geometrical parameters like surface area, curvature and shape of the edge, liquid surface model is able to predict the binding energy of nanotubes of any chirality once the total energy and the chiral indices of it are known. The model is suggested for open end and capped nanotubes and it is shown that the energy of capped nanotubes is determined by five physical parameters, while for the open end nanotubes three parameters are sufficient. The parameters of the liquid surface model are determined from the calculations performed with the use of empirical Tersoff and Brenner potentials and the accuracy of the model is analysed. It is shown that the liquid surface model can predict the binding energy per atom for capped nanotubes with relative error below 0.3% from that calculated using Brenner potential, corresponding to the absolute energy difference being less than 0.01 eV. The influence of the catalytic nanoparticle on top of which a nanotube grows, on the nanotube energetics is also discussed. It is demonstrated that the presence of catalytic nanoparticle changes the binding energy per atom in such a way that if the interaction of a nanotube with the catalytic nanoparticle is weak then attachment of an additional atom to a nanotube is an energetically favourable process, while if the catalytic nanoparticle nanotube interaction is strong , it becomes energetically more favourable for the nanotube to collapse. The suggested model gives important insights in the energetics and stability of nanotubes of different chiralities and is an important step towards the understanding of nanotube growth process. Young modulus and curvature constant are calculated for single-wall carbon nanotubes from the paremeters of the liquid surface model and demonstrated that the obtained values are in agreement with the values reported earlier both theoretically and experimentally. The calculated Young modulus and the curvature constant were used to conclude about the accuracy of the Tersoff and Brenner potentials. Since the parameters of the liquid surface model are obtained from the Tersoff and Brenner potential calculations, the agreement of elastic properties derived from these parameters corresponds to the fact that both potentials are capable of describing the elastic properties of nanotubes. Finally, the thesis discuss the possible extension of the model to various systems of interest.
This thesis investigates the jet-medium interactions in a Quark-Gluon Plasma using a hydrodynamical model. Such a Quark-Gluon Plasma represents a very early stage of our universe and is assumed to be created in heavy-ion collisions. Its properties are subject of current research. Since the comparison of measured data to model calculations suggests that the Quark-Gluon Plasma behaves like a nearly perfect liquid, the medium created in a heavy-ion collision can be described applying hydrodynamical simulations. One of the crucial questions in this context is if highly energetic particles (so-called jets), which are produced at the beginning of the collision and traverse the formed medium, may lead to the creation of a Mach cone. Such a Mach cone is always expected to develop if a jet moves with a velocity larger than the speed of sound relative to the medium. In that case, the measured angular particle distributions are supposed to exhibit a characteristic structure allowing for direct conclusions about the Equation of State and in particular about the speed of sound of the medium. Several different scenarios of jet energy loss are examined (the exact form of which is not known from first principles) and different mechanisms of energy and momentum loss are analyzed, ranging from weak interactions (based on calculations from perturbative Quantum Chromodynamics, pQCD) to strong interactions (formulated using the Anti-de-Sitter/Conformal Field Theory Correspondence, AdS/CFT). Though they result in different angular particle correlations which could in principle allow to distinguish the underlying processes (if it becomes possible to analyze single-jet events), it is shown that the characteristic structure observed in experimental data can be obtained due to the different contributions of several possible jet trajectories through an expanding medium. Such a structure cannot directly be connected to the Equation of State. In this context, the impact of a strong flow created behind the jet is examined which is common to almost all jet deposition scenarios. Besides that, the transport equations for dissipative hydrodynamics are discussed which are fundamental for any numerical computation of viscous effects in a Quark-Gluon Plasma.
Für ein System ('ideales Gas') von N miteinander nicht wechselwirkenden Teilchen oder Zuständen, deren Wellenfunktionen φ(x) der Randbedingung φ(x)=0 für x aus Ŵ. gehorchen sollen, (W sei dabei die Oberfläche eines geschlossenen Hohlraumes Ŵ beliebiger Gestalt), ist von verschiedenen Autoren eine halbklassische Eigenwertdichteformel angegeben worden. Diese hängt nur linear über die Integrale V ,W und L über Ŵ (Volumen, Oberflächeninhalt und totale Krümmung von Ŵ) von der Gestalt. des Hohlraumes ab. Während von H. Weyl mathematisch bewiesen, werden konnte, daß der führende Volumterm im Gebiet großer Eigenwerte alle folgenden Terme überwiegt, konnte für den Oberflächenterm eine gleichartige Vermutung bisher nur numerisch begründet werden. Von dieser halbklassischen Eigenwertdichteformel ausgehend, werden die thermodynamischen Relationen des idealen Gases aufgebaut und einige Größen wie innere Energie, spezifische Wärme sowie die Oberflächen- und Krümmungs-Spannung für die Grenzfälle starker, ein Gebiet mittlerer und schwacher Entartung explizit berechnet, und zwar sowohl für die Fermi-Dirac als auch die Bose-Einstein-Statistik, als auch für deren klassischen Grenzfall, die Boltzmann-Maxwell-Statistik (s.Diagramm). Ausgenommen wird nur der Spezialfall der Einsteinkondensation, weil hier die (nur im Gebiet großer Eigenwerte gültige) halbklassische Eigenwertdichteformel nicht angewendet werden darf. Die in dieser Arbeit untersuchten quantenmechanisch bedingten Oberflächeneffekte idealer Quantengase sind experimentell bisher wenig untersucht worden; für Molekülgase sind sie verschwindend klein. Die experimentell beobachtete Oberflächenspannung stabiler Atomkerne wird von dem Modell, das den Kern als ideales, entartetes Fermigas der Temperatur T beschreibt, im wesentlichen richtig wiedergegeben. Mit dem in Kap. 3b) abgeleiteten Ausdruck für die Oberflächenspannung stark entarteter idealer Fermigase endlicher Temperatur kann eine Voraussage über die Oberflächenspannung angeregter Atomkerne gemacht werden.
The surface tension sigma and the surface density thickness t of nuclear matter have been calculated in the Fermi-gas model, the nucleons moving in a self-made shell model potential with a realistic slope and velocity dependence ( parameters alpha and beta ). One gets the experimental values for sigma and t with alpha and beta agreeing with earlier data.
Theoretical studies in the shell model have led to the conclusion that the shape dependence of the liquid-drop part of the semi-empirical mass formula of the Weizsaecker-Bethe type should contain terms proportional to the volume, the surface, and the mean-total curvature of the surface of the drop, respectively. Now the surface tension beta_e and the curvature tension gamma_e are fitted to the experimentally known fission barriers of 35 nuclei. Furthermore, the parameters of the liquid-drop part of the mass formula are roughly fitted to the ground-state masses of about 600 beta-stable nuclei. For the elementary radius r_e, the value 1.123 fm ( determined by Elton ) is used. As a result, gamma_e should be in the range 6-8 MeV, with the value 6.8 MeV being the most probable, thus beta_e=17.85 MeV. For sufficiently large values of the curvature tension ( e.g. gamma_e=13.4 MeV ), a small double-hump fission barrier occurs in the region of Ra.
Die Reform der Lehrerausbildung spielt in der aktuellen bildungspolitischen Diskussion eine wichtige Rolle. In der Auseinandersetzung um fachdidaktische Ausbildungsstandards und Kerncurricula werden von den Studierenden, neben fachlichen Fähigkeiten, Reflexions-, Kommunikations- und unterrichtsbezogene Handlungskompetenzen gefordert. In der Physik-lehrerausbildung der universitären Phase müssen Lernumgebungen zur Schulung dieser Kom-petenzen häufig erst noch geschaffen werden. Aus diesem Grund wird seit dem Wintersemester 2002/03 der Universität Frankfurt/M. eine Seminarreihe mit dem Charakter einer Lernwerkstatt angeboten, in der die Studierenden selbstorganisiert Unterrichtsmaterialien entwickeln. Von den Zielen, der Durchführung und den Ergebnissen dieses Projekts wird berichtet und ein Seminarkonzept in Kombination mit den schulpraktischen Studien vorgestellt.
We compare away-side hadron correlations with respect to tagged heavy quark jets computed within a weakly coupled pQCD and a strongly coupled AdS/CFT model. While both models feature similar far zone Mach and diffusion wakes, the far zone stress features are shown to be too weak to survive thermal broadening at hadron freeze-out. Observable away-side conical correlations are dominated by the jet-induced transverse flow in near zone “Neck” region, which differs significantly for both models. Unlike in AdS/CFT, the induced transverse flow in the Neck zone is too weak in pQCD to produce conical correlations after Cooper-Frye freeze-out. The observation of conical correlations violating Mach’s law would favor the strongly-coupled AdS/CFT string drag dynamics, while their absence would favor weakly-coupled pQCD-based hydrodynamics.
Malignant neoplasms are one of the top causes of death in all developed countries around the world and account for almost one quarter of all deaths. An individual cell based computational model with strong connections to the experimental data through lattice free, newtonian interaction could be used to validate experimental results and eventually make predictions guiding further experiments. This model was build as a part of the thesis and shall be extended to the modelling of the effects of ionic radition on the vascularised tumour as a possible treatment for inoperable tumours.
A novel experimental approach for studying exotic transitions in few-electron high-Z ions was developed. In this approach, few-electron ions with selectively produced single K-shell holes are used for the investigation of the transition modes that follow the decay of the excited ions. The feasibility of the developed approach was confirmed by an experimental study of the production of low-lying excited states in He-like uranium, produced by K-shell ionization of initially Li-like species. It was found that K-shell ionization is a very selective process that leads to the production of only two excited states, namely the 1s2s 21S0 and 1s2s 23S1. This high level of selectivity stays undisturbed by the rearrangement processes. These experimental findings can be explained using perturbation theory and an independent-particle model, and are a result of the very different impact parameter dependencies of K-shell ionization and L- intrashell excitation. The L-shell electron can be assumed to stay passive in the collision, whereas the K-shell electron is ionized. It was stressed that the current result might directly be applied to accurate studies of the two-photon decay in He-like ions. Up to now, the experimental challenge in conventional 2E1 experiments has been the photon-photon coincidence technique, which is required to separate the true 2E1 events from the x-ray background associated with single photon transitions. In contrast, by exploiting K-shell ionization, the spectral distribution of the two-photon decay could be obtained simply by a measurement of the photon emission, using only a single x-ray detector in coincidence with projectile ionization. One further particular advantage arises from the fact that the 1s2p 3P0 state is not populated, and does not contribute to the continuum distribution of the two-photon emission. At high Z, this state also undergoes a two-photon E1M1 decay, which would be indistinguishable from the 2E1 decay of the 1s2s 1S0. The first measurement of the two-photon energy distribution from the decay of 1s2s 1S0 level in He-like tin was performed by adopting the technique developed in this thesis. In this technique, excited He-like heavy ions were formed by K-shell ionization of initially Li-like species in collisions with a low-Z gas target, and x-ray spectra following the decay of the He-like ions were measured in coincidence with the up-charged tin ions. The observed intense production of the 2E1 transitions, and a very high level of selectivity, make this process particularly suited for the study of the two-photon continuum, and thus for a detailed investigation of the structure of high-Z He-like systems. The method allowed for a background-free measurement of the distribution of the two-photon decay (21S0 -> 11S0) in He-like tin. The measured distribution could also be discriminated from that of other He-like ions, and confirmed, for the first time, the fully relativistic calculations. In addition, the feasibility of the method was confirmed by studying another exotic transition, namely the two-electron one-photon transition (TEOP) in Li-like high-Z ions. An experimental investigation of the radiative decay modes of the 1s2s2 state in Li-like heavy ions has been started. In the first dedicated beam time at the ESR, selective population of this state via K-shell ionization of initially Be-like species was achieved. The x-rays produced in this process were measured by a multitude of x-ray detectors, each placed under different observation angles with respect to the ion beam direction. The spectra associated with projectile electron loss consist (in all cases) of one single x-ray transition, which was attributed to the TEOP decay to the 1s2 2p1/2 level, possibly contaminated by the M1 decay to the 1s22s. Thus it was proven that, by adopting the developed approach, one can indeed produce the desired initial state. This makes this method perfectly suited for studies of TEOP transitions in high-Z systems. An extension of this study, by the inclusion of an electron spectrometer, would also allow for measurements of the autoionization channel, which would provide complete information on the various decay modes of the 1s2s2 state.
The study of the electromagnetic structure of hadrons plays an important role in understanding the nature of matter. In particular the emission of lepton pairs out of the hot and dense collision zone in heavy-ion reactions is a promising probe to investigate in-medium properties of hadrons and in general the properties of matter under such extreme conditions. The first experimental observation of an enhanced di-electron yield in the invariant-mass region 0:3 - 0:7 GeV/c2 in p+Be collisions at 4:9 GeV/u beam energy [2] was announced by the DLS collaboration [1]. Recent results of the HADES collaboration show a moderate enhancement above n Dalitz decay contributions for 12C+12C at 1 and 2 GeV/u [3, 4] confirming the DLS results. There are several theoretical explanations of this observation, most of them focusing on possible in-medium modifications of the properties of vector mesons. At low beam energies the question whether the observed excess is related to any in-medium effects remains open because of uncertainties in the description of elementary di-electron sources. In this work the di-electron production in p+p and d+p reactions at a kinetic beam energy of 1:25 GeV/u measured by the HADES spectrometer is discussed. At Ekin = 1:25 GeV/u, i.e. below the n meson production threshold in proton-proton reactions, the delta Dalitz decay is expected to be the most abundant source above the pi 0 Dalitz decay region. The observed large difference in di-electron production in p+p and d+p collisions suggests that di-electron production in the d+p system is dominated by the n+p interaction. In order to separate delta Dalitz decays and np bremsstrahlung the di-electron yield observed in p+p and n+p reactions, both measured at the same beam energy, has been compared. The main interest here is the investigation of iso-spin effects in baryonic resonance excitations and the off-shell production of vector mesons [5]. We indeed observe a large difference in di-electron production in p+p and n+p reactions. Results of these studies will be compared to recent calculations. We will also present our experimentally defined cocktail for heavy-ion data. At much higher beam energies experimental results of the CERES [6] and NA60 [7] collaborations also show an enhancement in the invariant mass region 0:3 - 0:7 GeV/c2, in principle similar to the situation in DLS. A strong excess of lepton pairs observed by recent high energy heavy-ion dilepton experiments hint to a strong influence of baryons, however no data exist at highly compressed baryonic matter, achievable in heavy-ion collisions from 8 - 45 GeV/u beam energy. These conditions would allow to study the expected restoration of chiral symmetry by measuring in-medium modifications of hadronic properties, an experimental program which is foreseen by the future CBM experiment at FAIR. The experimental challenge is to suppress the large physical background on the one hand and to provide a clean identification of electrons on the other hand. In this work, strategies to reduce the combinatorial background in electron pair measurements with the CBM detector are discussed. The main goal is to study the feasibility of effectively reducing combinatorial background with the currently foreseen experimental setup, which does not provide electron identification in front of the magnetic field.
In der vorliegenden Arbeit wird ein schnelles Choppersystem für einen hochintensiven niederenergetischen Protonenstrahl untersucht. Das Choppersystem wird in der Niedrigenergiesektion (LEBT) der Frankfurter Neutronenquelle FRANZ eingesetzt. Der Treiberstrahl hat dort eine Energie von 120 keV und eine Intensität von bis zu 200 mA Protonen. Gefordert ist die Erzeugung eines gepulsten Strahls mit einem 50 bis 100 ns langen Pulsplateau und einer Wiederholrate von 250 kHz. Nach der Diskussion verschiedener Chopperkonzepte wird der Einsatz eines Kickersystems vorgeschlagen. Magnetische und elektrische Kicker werden im Hinblick auf Geometrie, Ablenkfelder, Strahldynamik, Emittanzwachstum, Leistungsbedarf sowie Betrieb im Schwingungs- oder im Pulsmodus untersucht. Die Realisierung des Choppersystems wird mit Hilfe von numerischen Simulationen und Vorexperimenten geprüft. Ein eigens dazu entwickelter Particle-in-cell (PIC)-Code wird vorgestellt. Er erlaubt die Simulation von Vielteilchen-Prozessen in zeitabhängigen Kickerfeldern unter Berücksichtigung der Effekte der Sekundärelektronen. Die Vorexperimente für die Ansteuerung des Kickers werden präsentiert. Für den magnetischen Kicker wurde eine niederinduktive Testspule und für den elektrischen Kicker ein Transformator bestehend aus einem nanokristallinen Ringbandkern aufgebaut. Abschließend werden die beiden Systeme miteinander verglichen. Ein magnetischer Kicker ist auch bei hohen Strahlintensitäten weniger anfällig für Strahlverluste und kann ohne die Gefahr von Spannungsdurchschlägen betrieben werden. Bei den geforderten hohen Wiederholraten ist jedoch der Leistungsbedarf nicht annehmbar, so dass im Ausblick die Weiterentwicklung eines elektrischen Kickersystems vorgeschlagen wird.
Background: In this interdisciplinary project, the biological effects of heavy ions are compared to those of X-rays using tissue slice culture preparations from rodents and humans. Advantages of this biological model are the conservation of an organotypic environment and the independency from genetic immortalization strategies used to generate cell lines. Its open access allows easy treatment and observation via live-imaging microscopy. Materials and methods: Rat brains and human brain tumor tissue are cut into 300 micro m thick tissue slices. These slices are cultivated using a membrane-based culture system and kept in an incubator at 37°C until treatment. The slices are treated with X-rays at the radiation facility of the University Hospital in Frankfurt at doses of up to 40 Gy. The heavy ion irradiations were performed at the UNILAC facility at GSI with different ions of 11.4 A MeV and fluences ranging from 0.5–10 x 106 particles/cm². Using 3D-confocal microscopy, cell-death and immune cell activation of the irradiated slices are analyzed. Planning of the irradiation experiments is done with simulation programs developed at GSI and FIAS. Results: After receiving a single application of either X-rays or heavy ions, slices were kept in culture for up to 9d post irradiation. DNA damage was visualized using gamma H2AXstaining. Here, a dose-dependent increase and time-dependent decrease could clearly be observed for the X-ray irradiation. Slices irradiated with heavy ions showed less gamma H2AX-positive cells distributed evenly throughout the slice, even though particles were calculated to penetrate only 90–100 micro m into the slice. Conclusions: Single irradiations of brain tissue, even at high doses of 40 Gy, will result neither in tissue damage visible on a macroscopic level nor necrosis. This is in line with the view that the brain is highly radio-resistant. However, DNA damage can be detected very well in tissue slices using gamma H2AX-immuno staining. Thus, slice cultures are an excellent tool to study radiation-induced damage and repair mechanisms in living tissues.
Recent results of the NA49 collaboration are presented. Transverse mass spectra as well as total multiplicities of identified particles are discussed. The study of their evolution from AGS over SPS to the highest RHIC energy reveals a couple of interesting features. These include a sudden change in the energy dependence of the mt-spectra and of the yields of strange hadrons around 30A GeV. Additionally, new results on particle production at high-pt for Pb+Pb collsions at 158A GeV, as well as on the v2 of L, are discussed.
We study the line shapes of radiative φ-decays with a direct coupling of the φ meson to the f0(980) and a0(980) scalar mesons. The latter couple via derivative interactions to π0π0 and π0η, respectively. Although the kaon-loop mechanism is usually regarded as the dominant mechanism in radiative φ decays, here we test a different possibility: we set the kaon-loop to zero and we fit the theoretical curves to the data by retaining only the direct coupling. Remarkably, satisfactory fits can be achieved, mainly due to the effects of derivative interactions of scalar with pseudoscalar mesons.
There is little doubt that Quantumchromodynamics (QCD) is the theory which describes strong interaction physics. Lattice gauge simulations of QCD predict that in the m,T plane there is a line where a transition from confined hadronic matter to deconfined quarks takes place. The transition is either a cross over (at low m) or of first order (at high m). It is the goal of the present and future heavy ion experiment at RHIC and FAIR to study this phase transition at different locations in the m,T plane and to explore the properties of the deconfined phase. It is the purpose of this contribution to discuss some of the observables which are considered as useful for this purpose.
The mechanism by which the enzyme pyruvate decarboxylase from yeast is activated allosterically has been elucidated. A total of seven three-dimensional structures of the enzyme, of enzyme variants or of enzyme complexes from two yeast species (three of them reported here for the first time) provide detailed atomic resolution snapshots along the activation coordinate. The prime event is the covalent binding of the substrate pyruvate to the side chain of cysteine 221, thus forming a thiohemiketal. This reaction causes the shift of a neighbouring amino acid, which eventually leads to the rigidification of two otherwise flexible loops, where one of the loops provides two histidine residues necessary to complete the enzymatically competent active site architecture. The structural data are complemented and supported by kinetic investigations and binding studies and provide a consistent picture of the structural changes, which occur upon enzyme activation.
In this work we study the properties of quarkonium states in a quark-gluon plasma which, due to expansion and non-zero viscosity, exhibits a local anisotropy in momentum space. We determine the hard-loop resummed gluon propagator in an anisotropic QCD plasma in general linear gauges and define a potential between heavy quarks from the Fourier transform of its static limit. This potential which arises due to one-gluon exchange describes the force between a quark and anti-quark at short distances. It is closer to the vacuum potential as compared to the isotropic Debye screened potential which indicates the reduced screening in an anisotropic QCD plasma. In addition, angular dependence appears in the potential; we find that there is stronger attraction on distance scales on the order of the inverse Debye mass for quark pairs aligned along the direction of anisotropy than for transverse alignment. The potential at long distances, however, is non-perturbative and modeled as a QCD string which is screened at the same scale as the Coulomb field. At asymptotic separation the potential energy is non-zero and inversely proportional to the temperature. With a phenomenological potential model which incorporates the different behaviors at short and long distances, we solve the three-dimensional Schrödinger equation. Our numerical results show that quarkonium binding is stronger at non-vanishing viscosity and expansion rate, and that the anisotropy leads to polarization of the P-wave states. Furthermore, we determine viscosity corrections to the imaginary part of the heavyquark potential in the weak-coupling hard-loop approximation. The imaginary part is found to be smaller (in magnitude) than at vanishing viscosity. This implies a smaller decay width of quarkonium bound states in an anisotropic plasma.
Poster presentation: The brain is autonomously active and this self-sustained neural activity is in general modulated, but not driven, by the sensory input data stream [1,2]. Traditionally one has regarded this eigendynamics as resulting from inter-modular recurrent neural activity [3]. Understanding the basic modules for cognitive computation is, in this view, the primary focus of research and the overall neural dynamics would be determined by the the topology of the intermodular pathways. Here we examine an alternative point of view, asking whether certain aspects of the neural eigendynamics have a central functional role for overall cognitive computation [4,5]. Transiently stable neural activity is regularly observed on the cognitive time-scale of 80–100 ms, with indications that neural competition [6] plays an important role in the selection of the transiently stable neural ensembles [7], also denoted winning coalitions [8]. We report on a theory approach which implements these two principles, transient-state dynamics and neural competition, in terms of an associative neural network with clique encoding [9]. A cognitive system [10] with a non-trivial internal eigendynamics has two seemingly contrasting tasks to fulfill. The internal processes need to be regular and not chaotic on one side, but sensitive to the afferent sensory stimuli on the other side. We show, that these two contrasting demands can be reconciled within our approach based on competitive transient-state dynamics, when allowing the sensory stimuli to modulate the competition for the next winning coalition. By testing the system with the bars problem, we find an emerging cognitive capability. Only based on the two basic architectural principles, neural competition and transient-state dynamics, with no explicit algorithmic encoding, the system performs on its own a non-linear independent component analysis of input data stream. The system has rudimentary biological features. All learning is local Hebbian-style, unsupervised and online. It exhibits an ever-ongoing eigendynamics and at no time is the state or the value of synaptic strengths reset or the system restarted; there is no separation between training and performance. We believe that this kind of approach – cognitive computation with autonomously active neural networks – to be an emerging field, relevant both for system neuroscience and synthetic cognitive systems.
In this thesis we report on the high pressure synthesis, crystal growth, structural characterisation and magnetic properties of the cubic vanadate pyrochlores A2V2O7 (with A = Y, Er and Dy). We have found that high pressure is requisite for the stabilization of the selected compounds. For this purpose, a multianvil high pressure apparatus was built in our laboratory and a new multianvil inset (i.e., a ceramic pressure medium and the interior parts) was developed. The multianvil press is based on a hydraulic press with a maximum force of 7.73 MN (corresponds to 788 tons), a Walker type module and a specially designed hydraulic and electric control. Pressure calibration of the multianvil setup was performed by high pressure fixed points (i.e. solid-solid transformation of Bi I-II (2.55 GPa) and Bi II-III (3.15 GPa)). A maximum pressure of 6 GPa was attained using hardened metal anvils (tungsten carbide) with truncation edge length (TEL) of 14 mm and a sample volume of ~ 70 mm3. Heating of the sample in our current multianvil setup (TEL = 14 mm) was achieved by resistive heating of a graphite furnace. Temperatures up to 1500 °C could be obtained at pressures up to 6 GPa. By systematic variation of the synthesis conditions (for instance the operation temperature or the choice of the crucible material) under high pressure and taking into account the well known ternary compounds, when accessing the phase diagram, the cubic vanadate pyrochlores A2V2O7 (with A = Y, Er and Dy) were synthesized successfully. It was found that the oxygen partial pressure is crucial for the formation of the desired pyrochlore phase. Gas-tight platinum crucibles were used as container material for the synthesis of the vanadate pyrochlores. We have investigated, that pressures of the order of 5.0 GPa and temperatures of approximately 1200 °C are necessary for the stabilization of the monophasic samples of the vanadate pyrochlores. Lu2V2O7 could be synthesized under ambient pressure conditions and is used in our studies for comparison purposes. A special graphite furnace was developed for the high pressure crystal growth of the vanadate pyrochlores. For the first time, A2V2O7 (with A = Y, Er and Dy) single crystals with a maximum size of 0.4 mm were grown by using the grain growth method at high pressure and high temperature conditions. The samples (i.e., powders and single crystals) were characterised by single crystal Xray diffraction, X-ray powder diffraction method, Laue method and scanning electron microscopy (SEM). Complementary to the X-ray diffraction methods, infrared absorsoption spectroscopy was used to distinguish between the fluorite and pyrochlore structure. It has been shown that all samples crystallize in a well-ordered cubic structure with the space group F d 3m. The vanadium (+4) content in the samples was determined by oxidative weight gain in air using a thermogravimetric (TG) balance. A structural phase transformation of cubic to tetragonal was observed by differential thermal analysis (DTA) in conjunction with high temperature diffractometry. The magnetic characterisation of the vanadate pyrochlores A2V2O7 (Y, Lu, Er and Dy) was performed by Katarina Removic-Langer in the laboratory of Prof. Dr. M. Lang. All materials studied are ferromagnetic. The ferromagnetic critical temperatures are between 70 and 73 K. In case of Er2V2O7 and Dy2V2O7 an additional increase in the magnetization was observed below 20 K. The increase in the magnetization below 20 K exhibited by Er2V2O7 and Dy2V2O7 originates from the interactions between the two magnetic sublattices (i.e., the rare earth- and the vanadium sublattice).
The paper will focus on the early texts of Galileo Galilei (1613~1623) and Daniel Bernoulli (1738) as examples of pure combinatorical analysis and perspectively considerations within the mathematical discipline of probability theory. It is argued that Bernoulli's approach needed to be developed further in order to achieve a successful and satisfactory theory of risk. In modern economy the need for a proper definition of a notion of risk is seen and currently discussed within the frame of ISO standards. But as already mentioned this interest is mainly owed to the governmental demands of the Basel II and Solvency standards and therefore an external demand. On the other hand an intrinsic understanding of the meaning of risk, as could be provided by a conclusive theory, could lead to a better success in modelling various risks and help to achieve better prognosis.
In the framework of this thesis the intense low energy ion beam transport was investigated. Especially, the beam transport in toroidal magnetic field configurations was discussed, as it may allow the accumulation of high intensive beams in the future. One of the specific tasks is to design an injection system that can be used for the proposed low energy accumulator ring. This thesis regarding beam transport investigations is related to the larger research fields, storage rings used in accelerator physics and non-neutral plasmas. The proposal of building a storage ring with longitudinal guiding magnetic fields was made. Due to natural transversal focussing in magnetic fields it is possible to accumulate very intense charged particle beams, a subject of interest within the physics community. A simulation code (TBT) was written to describe the particle motion in curved segments. Particle in Cell techniques were utilized to simulate a multi particle dynamics. This code allows the user to generate different particle distributions as input parameter. A possibility of reading an external data file was made available so that a measured distribution can be used to compare simulation results with measured ones. A second order cloud in cell method was used to calculate charge density and in turn to solve Poisson’s equation. The circular toroidal coordinate system was used. The drift motion and gyrating motion was proved to be consistent with analytical values. Further simulations were performed to study the self field effects on beam transport. The experiments with single toroidal segments find niche in the work. The experiments were performed to compare the simulation results and gain practical experience. The toroidal segment has similar dimensions (major axis R = 1:3 m, minor axis r = 0:1 m, arc angle 30°) as for a full scale ring design. The main difference lies in the magnetic field strength. The available segments can be operated at room temperature producing 0:6T on axis maximum magnetic field, while for the storage ring design this value is in the range of 5T. The preparatory experiments consisted of building and characterization of the ion source in a first step. Along with the momentum spectrometer and emittance scanner the beam properties were studied. Low mass ion beams He+ and mixed p, H2+, H3+ beams were analyzed. The proton beam consisting of a 48% H+ fraction was extracted regularly and used for further experiments. A moderate beam energy of 10 keV was chosen as operational energy for which 3.08 mA proton beam current was measured. In the second stage, beams were transported through a solenoid and the phase space distribution was measured as a function of the magnetic field for different beam energies. The phase-space as distributions measured in a first stage were simulated backward and then again forward transported through the solenoid. The simulated results were then compared with the measured distribution. The LINTRA transport program was used. The phase-space distribution was further simulated for transport experiments in a toroidal magnetic field. The experiments with a single toroidal segment give basic results necessary to compare the results between transport code (TBT) and measurements. The optical diagnostic provides measurements which can be well compared with the simulated results. A digital camera with a magnetic shield was used to record images in jpeg file format. A subroutine was written to analyze an image file to give the intensity distribution of a given image file. The integrated profile in vertical and horizontal direction was used to calculate the vertical drift and the beam size. The simulated values were in good agreement with the measured ones. The injection system needs most care. The transport program that was used to simulate the beam in the toroid was also used to design the injection system. The injection system with its special field configurations was designed to perform experiments with room temperature segments. The main point to tackle was to smoothly bring the charged particles generated outside the trap into the acceptance of the ring. The designed system consists of two sources, one representing a ring beam and the other one the injection beam. While simulations showed a clear way, how to inject the particle beam via a well positioned solenoid and in combination with a transverse electric field element causing an ExB drift into the main ring acceptance. After construction of these injection elements it will be very important to measure the robustness of such a system with respect to the beam stability- especially of the injection channel.
The bulk viscosity of several quark matter phases is calculated. It is found that the effect of color superconductivity is not trivial, it may suppress, or enhance the bulk viscosity depending on the critical temperature and the temperature at which the bulk viscosity is calculated. Also, is it found that the effect of neutrino-emitting Urca processes cannot be neglected in the consideration of the bulk viscosity of strange quark matter. The results for the bulk viscosity of strange quark matter are used to calculate the r-mode instability window of quark stars with several possible phases. It is shown that each possible phase has a different structure for the r-mode instability window.
Ein wesentliches Ziel der Physik mit schweren Ionen ist die Untersuchung der Zustände von Kernmaterie bei hohen Dichten bzw. Temperaturen. Solche Zustände lassen sich durch Kollisionen von hochenergetischen schweren Ionen in Teilchenbeschleunigern wie dem Super Proton Synchrotron SPS am Europäischen Kernforschungszentrum CERN in Genf erzeugen und untersuchen. Die vorliegende Arbeit beschäftigt sich mit der Analyse des Einflusses des in einer solchen Kollision erzeugten Mediums auf hochenergetische Teilchen, welche dieses Medium durchqueren. Hierzu werden Korrelationen zwischen Teilchen mit hohem Transversalimpuls pt als Funktion der Zentralität der Kollisionen und der Ladung der beteiligten Teilchen untersucht. Ziel ist es, hierdurch eine experimentelle Grundlage für die theoretische Beschreibung der Eigenschaften des Mediums in solchen Kollisionen bereitzustellen. ...
The production of quarkonia, the bound state of an heavy quark with its anti-particle, has for a long time been seen as a key process to understand the properties of nuclear matter in a relativistic heavy-ion collision. This thesis presents studies on the production of quarkonia in heavy-ion collisions at the new Large Hadron collider (LHC). The focus is set on the decay of J/Psi and Upsilon-states into their di-electronic decay channel, measured within the central detectors of the ALICE detector.
The physics of interacting bosons in the phase with broken symmetry is determined by the presence of the condensate and is very different from the physics in the symmetric phase. The Functional Renormalization Group (FRG) represents a powerful investigation method which allows the description of symmetry breaking with high efficiency. In the present thesis we apply FRG for studying the physics of two different models in the broken symmetry phase. In the first part of this thesis we consider the classical O(1)-model close to the critical point of the second order phase transition. Employing a truncation scheme based on the relevance of coupling parameters we study the behavior of the RG-flow which is shown to be influenced by competition between two characteristic lengths of the system. We also calculate the momentum dependent self-energy and study its dependence on both length scales. In the second part we apply the FRG-formalism to systems of interacting bosons in the phase with spontaneously broken U(1)-symmetry in arbitrary spatial dimensions at zero temperature. We use a truncation scheme based on a new non-local potential approximation which satisfy both exact relations postulated by Hugenholtz and Pines, and Nepomnyashchy and Nepomnyashchy. We study the RG-flow of the model, discuss different scaling regimes, calculate the single-particle spectral density function of interacting bosons and extract both damping of quasi-particles and spectrum of elementary excitations from the latter.
In der vorliegenden Arbeit wurde die 1s Photoionisation von Neondimeren mit einer Photonenenergie von 10 eV über der 1s Schwelle von Neon durchgeführt. Das Ziel dieser Messung war die Beantwortung der seit vielen Jahren diskutierten Frage nach der Lokalisierung oder Delokalisierung von Vakanzen in homonuklearen diatomaren Systemen am Beispiel des Neondimers. Können die Vakanzen also einem Atom des Dimers zugeordnet werden oder sind sie über beide Atome verteilt? Bezüglich dieser Frage wurden sowohl die in der Photoionisation direkt entstandenen 1s Vakanzen als auch die aus der Relaxation durch einen interatomic Coulombic decay (ICD) resultierenden Vakanzen in der Valenzschale des Neondimers untersucht. Als Observable dienten dabei die Elektronen-Winkelverteilungen im dimerfesten Koordinatensystem, wobei eine bezüglich der ‘rechten’ und der ‘linken’ Seite des homonuklearen diatomaren Moleküls auftretende Asymmetrie in der Winkelverteilung eindeutig eine Lokalisierung der Vakanz indiziert. Dies lässt sich damit begründen, dass die Elektronenwellen im Fall einer delokalisierten Vakanz durch die symmetrisierten Wellenfunktionen beschrieben werden, welche sich aus der kohärenten Überlagerung der lokalisierten Wellenfunktionen ergeben. Die resultierende Winkelverteilung der Elektronen um die Dimerachse ist somit symmetrisch. Im Fall einer lokalisierten Vakanz wird die Elektronenwelle dagegen durch die ‘rechts’ oder ‘links’ lokalisierten Wellenfunktionen, welche aus der kohärenten Überlagerung der symmetrisierten Wellenfunktionen gebildet werden, beschrieben, so dass abhängig von der Elektronenwellenlänge Asymmetrien in der Elektronen-Winkelverteilung auftreten können. Die Möglichkeit, eine eventuelle Asymmetrie in der Winkelverteilung um die Dimerachse zu beobachten ist allerdings nur dann gegeben, wenn die beiden Seiten des Dimers im Anschluss an die Reaktion unterscheidbar sind, d.h. der Ursprung des emittierten Elektrons feststellbar ist, da sich sonst der Fall einer ‘links’ lokalisierten Vakanz mit dem Fall einer ‘rechts’ lokalisierten Vakanz kohärent überlagert. Die Unterscheidung konnte in der vorliegenden Messung anhand der aus einigen Relaxationen hervorgehenden unterschiedlichen Ladungen der ionischen Fragmente des Neondimers durchgeführt werden. Insgesamt wurden im Anschluss an die 1s Photoionisation von Ne2 mit einer Rate von 3:1 der symmetrische Ladungsaufbruch Ne1+ + Ne1+ und der für die Untersuchung der Winkelverteilungen relevante asymmetrische Ladungsaufbruch Ne2+ + Ne1+ des Neondimers beobachtet. Alle in diesen beiden Ladungsaufbrüchen resultierenden intra- und interatomaren Relaxationsprozesse sowie ihre Raten wurden im Rahmen dieser Arbeit identifiziert und analysiert. Der dominante Zerfallskanal des symmetrischen Ladungsaufbruchs resultierte dabei aus dem im Anschluss an einen KL2,3L2,3 stattfindenden Radiative Charge Transfer, bei welchem unter Aussendung eines Photons ein Ladungsaustausch zwischen den Neonionen des Dimers stattfindet. Der dominante Zerfallskanal des asymmetrischen Ladungsaufbruchs wurde durch den im Anschluss an einen KL1L2,3 stattfindenden ICD bestimmt. Bei diesem in Clustern auftretenden Relaxationsprozess wird die Innerschalenvakanz aus Atom 1 durch ein Valenzelektron aus Atom 1 aufgefüllt. Sobald die Relaxationsenergie dabei nicht ausreicht, um, wie beim Augerzerfall, ein weiteres Valenzelektron aus Atom 1 zu ionisieren, wird die Energie mittels eines virtuellen Photons zum neutralen Nachbaratom des Dimers transferiert, und aus diesem wird ein Elektron, das ICD-Elektron, emittiert. Zur experimentellen Untersuchung der verschiedenen Zerfälle wurde die COLTRIMS (COLd Target Recoil Ion Momentum Spectroscopy)-Technik verwendet. Bei dieser Impulsspektroskopie werden die Fragmente mit einer Raumwinkelakzeptanz von 4pi mit Hilfe eines elektrischen und eines magnetischen Feldes auf die ortsauflösenden Detektoren geführt, und ihre Flugzeiten und Auftrefforte werden gemessen. Die COLTRIMS-Technik zeichnet sich dabei dadurch aus, dass eine koinzidente Messung der Elektronen und Ionen möglich ist, wodurch die Fragmente eines Reaktionsereignisses einander zugeordnet werden können. Innerhalb der Reaktionsereignisse fragmentierte das Neondimer im Anschluss an die Relaxation in beiden Ladungsaufbrüchen Ne1+ + Ne1+ und Ne2+ + Ne1+ unter 180° in einer Coulombexplosion. Somit spiegelten die Richtungen der Relativimpulse der Ionen im Rahmen der ‘Axial-Recoil-Approximation’ die Position der Dimerachse zum Zeitpunkt der Reaktion wider, und aus den Impulsen der Elektronen konnten die Emissionsrichtungen der Elektronen bezüglich der Dimerachse abgeleitet werden. In dieser Arbeit wurde mit der beschriebenen Messtechnik eine deutliche Asymmetrie in der Winkelverteilung der 1s Photoelektronen sowie der 2p ICD-Elektronen um die Dimerachse beobachtet. Die gemessene Winkelverteilung der 1s Photoelektronen wies dabei eine qualitativ sehr gute Übereinstimmung mit einer innerhalb einer Hartree-Fock-Rechnung erhaltenen Winkelverteilung für eine vollständig lokalisierte 1s Vakanz im Neondimer auf. Für die Winkelverteilungen der ICD-Elektronen existieren bis heute noch keine theoretischen Vorhersagen. Mit den Ergebnissen der vorliegenden Arbeit konnte somit gezeigt werden, dass entgegen den heute gängigen Theorien zur Beschreibung des Neondimers sowohl die Vakanzen der innersten Schale als auch die Vakanzen der Valenzschale des Neondimers als lokalisiert beschrieben werden müssen.
Es wurde eine neue Routine zur Berechnung der Raumladungskräfte basierend auf einer schnellen Fourier-Transformation entwickelt und in das Teilchensimulationsprogramm LORASR integriert. Dadurch werden einzelne oder bis zu mehreren 100 Simulationen im Batch-Modus mit je 1 Million Makroteilchen und akzeptablen Rechenzeiten ermöglicht. Die neue Raumladungsroutine wurde im Rahmen der Europäischen „High Intensity Pulsed Proton Injectors” (HIPPI) Kollaboration erfolgreich validiert. Dabei wurden verschiedene statische Vergleichstests der Poisson-Solver und schließlich Vergleichsrechnungen entlang des Alvarez-Beschleunigerabschnittes des GSI UNILAC durchgeführt. Darüber hinaus wurden Werkzeuge zum Aufprägen und zur Analyse von Maschinenfehlern entwickelt. Diese wurden erstmals für Fehlertoleranzstudien an der IH-Kavität des Heidelberger Therapiebeschleunigers, am Protonen-Linearbeschleuniger für das FAIR Projekt in Darmstadt sowie am Vorschlag eines supraleitenden CH-Beschleunigers für die “International Fusion Materials Irradiation Facility” (IFMIF) eingesetzt.
In this work the preparation of organic donor-acceptor thin films was studied. A chamber for organic molecular beam deposition was designed and integrated into an existing deposition system for metallic thin films. Furthermore, the deposition system was extended by a load-lock with integrated bake-out function, a chamber for the deposition of metallic contacts via stencil mask technique and a sputtering chamber. For the sublimation of the organic compounds several effusion cells were designed. The evaporation characteristic and the temperature profile within the cells was studied. Additionally, a simulation program was developed, which calculates the evaporation characteristics of different cell types. The following processes were integrated: evaporation of particles, migration on the cell walls and collisions in the gas phase. It is also possible to consider a temperature gradient within the cell. All processes can be studied separately and their relative strength can be varied. To verify the simulation results several evaporation experiments with different cell types were employed. The thickness profile of the prepared thin films was measured position-dependently. The results are in good agreement with the simulation. Furthermore, the simulation program was extended to the field of electron beam induced deposition (EBID). The second part of this work deals with the preparation and characterization of organic thin films. The focus hereby lies on the charge transfer salt (BEDT-TTF)(TCNQ), which has three known structure variants. Thin films were prepared by different methods of co-evaporation and were studied with optical microscopy, X-ray diffraction and energy dispersive X-ray spectroscopy (EDX).The formation of the monoclinic phase of (BEDT-TTF)(TCNQ) could be shown. As a last part tunnel structures were prepared as first thin film devices and measured in a He4 cryostat.
This work presents the study on the suitability of single-crystal CVD diamond for particle-detection systems in present and future hadron physics experiments. Different characterization methods of the electrical and the structural properties were applied to gain a deeper understanding of the crystal quality and the charge transport properties of this novel semiconductor material. First measurements regarding the radiation tolerance of diamond were performed with sensors heavily irradiated with protons and neutrons. Finally, detector prototypes were fabricated and successfully tested in various experiments as time detectors for minimum ionizing particles as well as for spectroscopy of heavy ions at the energy ranges available at the SIS and the UNILAC facilities of GSI. ...
Induced charge computation
(2009)
One of the main aspects of statistical mechanics is that the properties of a thermodynamics state point do not depend on the choice of the statistical ensemble. It breaks down for small systems e.g. single molecules. Hence, the choice of the statistical ensemble is crucial for the interpretation of single molecule experiments, where the outcome of measurements depends on which variables or control parameters, are held fixed and which ones are allowed to fluctuate. Following this principle, this thesis investigates the thermodynamics of a single polymer pulling experiments within two different statistical ensembles. The scaling of the conjugate chain ensembles, the fixed end-to-end vector (Helmholtz) and the fixed applied force (Gibbs), are studied in depth. This thesis further investigates the ensemble equivalence for different force regimes and polymer-chain contour lengths. Using coarse-grained molecular dynamic simulations, i.e. Langevin dynamics, the simulations were found to complement the theoretical predictions for the scaling of ensemble difference of Gaussian chains in different force-regimes, giving special attention to the zero force regime. After constructing Helmholtz and Gibbs conjugate ensembles for a Gaussian chain, two different data sets of thermodynamic states on the force-extension plane, i.e. force-extension curves, were generated. The ensemble difference is computed for different polymer-chain lengths by using force-extension curves. The scaling of the ensemble difference versus relative polymer-chain length under different force regimes has been derived from the simulation data and compared to theoretical predictions. The results demonstrate that the Gaussian chain in the zero force limit generates nonequivalent ensembles, regardless of its equilibrium bond length and polymer-chain contour length. Moreover, if polymers are charged in confinement, coarse-graining is problematic, owing to dielectric interfaces. Hence, the effect of dielectric interfaces must be taken into account when describing physical systems such as ionic channels or biopolymers inside nanopores. It is shown that the effect of dielectrics is crucial for the dynamics of a biopolymer or an ion inside a nanopore. In the simulations, the feasibility of an efficient and accurate computation of electrostatic interactions in the presence of an arbitrarily shaped dielectric domain is challenging. Several solutions for this problem have been previously proposed in the literature such as a density functional approach, or transforming problem at hand into an algebraic problem ( Induced Charge Computation (ICC) ) and boundary element methods. Even though the essential concept is the same, which is to replace the dielectric interface with a polarization charge density, these approaches have been analyzed and the ICC algorithm has been implemented. A new superior boundary element method has been devised utilizing the force computation via the Particle-Particle Particle-Mesh (P3M) method for periodic geometries (ICCP3M). This method has been compared to the ICC algorithm, the algebraic solutions, and to density functional approaches. Extensive numerical tests against analytically tractable geometries have confirmed the correctness and applicability of developed and implemented algorithms, demonstrating that the ICCP3M is the fastest and the most versatile algorithm. Further optimization issues are also discussed in obtaining accurate induced charge densities. The potential of mean force (PMF) of DNA modelled on a coarsed-grain level inside a nanopore is investigated with and without the inclusion of dielectric effects. Despite the simplicity of the model, the dramatic effect of dielectric inclusions is clearly seen in the observed force profile.
Neutron stars are very dense objects. One teaspoon of their material would have a mass of five billion tons. Their gravitational force is so strong that if an object were to fall from just one meter high it would hit the surface of the respective neutron star at two thousand kilometers per second. In such dense bodies, different particles from the ones present in atomic nuclei, the nucleons, can exist. These particles can be hyperons, that contain non-zero strangeness, or broader resonances. There can also be different states of matter inside neutron stars, such as meson condensates and if the density is height enough to deconfine the nucleons, quark matter. As new degrees of freedom appear in the system, different aspects of matter have to be taken into account. The most important of them being the restoration of the chiral symmetry. This symmetry is spontaneously broken, which is a fact related to the presence of a condensate of scalar quark-antiquark pairs, that for this reason is called chiral condensate. This condensate is present at low densities and even in vacuum. It is important to remember at this point that the modern concept of vacuum is far away from emptiness. It is full of virtual particles that are constantly created and annihilated, being their existence allowed by the uncertainty principle. At very high temperature/density, when the composite particles are dissolved into constituents, the chiral consensate vanishes and the chiral symmetry is restored. To explain how and when chiral symmetry is restored in neutron stars we use a model called non-linear sigma model. This is an effective quantum relativistic model that was developed in order to describe systems of hadrons interacting via meson exchange. The model was constructed from symmetry relations, which allow it to be chiral invariant. The first consequence of this invariance is that there are no bare mass terms in the lagrangian density, causing all, or most of the particles masses to come from the interactions with the medium. There are still other interesting features in neutron stars that cannot be found anywhere else in nature. One of them is the high isospin asymmetry. In a normal nucleus, the amount of protons and neutrons is more or less the same. In a neutron star the amount of neutrons is much higher than the protons. The resulting extra energy (called Fermi energy) increases the energy of the system, allowing the star to support more mass against gravitational collapse. As a consequence of that in early stages of the neutron star evolution, when there are still many trapped neutrinos, the proton fraction is higher than in later stages and consequently the maximum mass that the star can support against gravity is smaller. This, between many other features, shows how the microscopic phenomena of the star can reflect into the macroscopic properties. Another important property of neutron stars is charge neutrality. It is a required assumption for stability in neutron stars, but there are others. One example is chemical equilibrium. It means that the number of particles from each kind is not conserved, but they are created and annihilated through specific reactions that happen at the same rate in both directions. Although to calculate microscopic physics of neutron stars the space-time of special relativity, the Minkowski space, can be used, this is not true for the global properties of the star. In this case general relativity has to be used. The solution of Einstein's equations simplified to static, spherical and isotropic stars correspond to the configurations in which the star is in hydrostatic equilibrium. That means that the internal pressure, coming mainly from the Fermi energy of the neutrons, balances the gravity avoiding the collapse. When rotation is included the star becomes more stable, and consequently, can be more massive. The movement also makes it non-spherical, what requires the metric of the star to also be a function of the polar coordinate. Another important feature that has to be taken into account is the dragging of the local inertial frame. It generates centrifugal forces that are not originated in interactions with other bodies, but from the non-rotation of the frame of reference within which observations are made. These modifications are introduced through the Hartle's approximation that solves the problem by applying perturbation theory. In the mean field approximation, the couplings as well as the parameters of the non-linear sigma model are calibrated to reproduce massive neutron stars. The introduction of new degrees of freedom decreases the maximum mass allowed for the neutron star, as they soften the equation of state. In practice, the only baryons present in the star besides the nucleons are the Lambda and Sigma-, in the case in which the baryon octet is included, and Lambda and Delta-,0,+,++, in the case in which the baryon decuplet is included. The leptons are included to ensure charge neutrality. We choose to proceed our calculations including the baryon octet but not the decuplet, in order to avoid uncertainties in the couplings. The couplings of the hyperons were fitted to the depth of their potentials in nuclei. In this case the chiral symmetry restoration can be observed through the behavior of the related order parameter. The symmetry begins to be restored inside neutron stars and the transition is a smooth crossover. Different stages of the neutron star cooling are reproduced taking into account trapped neutrinos, finite temperature and entropy. Finite-temperature calculations include the heat bath of hadronic quasiparticles within the grand canonical potential of the system. Different schemes are considered, with constant temperature, metric dependent temperature and constant entropy. The neutrino chemical potential is introduced by fixing the lepton number in the system, that also controls the amount of electrons and protons (for charge neutrality). The balance between these two features is delicate and influenced mainly by the baryon number conservation. Isolated stars have a fixed number of baryons, which creates a link between different stages of the cooling. The maximum masses allowed in each stage of the cooling process, the one with high entropy and trapped neutrinos, the deleptonized one with high entropy, and the cold one in beta equilibrium. The cooling process is also influenced by constraints related to the rotation of the star. When rotation is included the star becomes more stable, and consequently, can be more massive. The movement also deforms it, requiring the metric of the star to include modifications that are introduced through the use of perturbation theory. The analysis of the first stages of the neutron star, when it is called proto-neutron star, gives certain constraints on the possible rotation frequencies in the colder stages. Instability windows are calculated in which the star can be stable during certain stages but collapses into black holes during the cooling process. In the last part of the work the hadronic SU(3) model is extended to include quark degrees of freedom. A new effective potential to the order parameter for deconfinement, the Polyakov loop, makes the connection between the physics at low chemical potential and hight temperature of the QCD phase diagram with the height chemical potential and low temperature part. This is done through the introduction of a chemical potential dependency on the already temperature dependent potential. Analyzing the effect of both order parameters, the chiral condensate and the Polyakov loop, we can drawn a phase diagram for symmetric as well as for star matter. The diagram contains a crossover region as well as a first order phase transition line. The new couplings and parameters of the model are chosen mainly to fit lattice QCD, including the position of the critical point. Finally, this matter containing different degrees of freedom (depending on which phase of the diagram we are) is used to calculate hybrid star properties.
We explain how fluctuations of ratios can constrain and falsify the statistical model of particle production in heavy ion collisions, using K/p fluctuations as an example. We define an observable capable of determining which statistical model, if any, governs freeze-out in ultrarelativistic heavy ion collisions. We calculate this observable for K/p fluctuations, and show that it should be the same for RHIC and LHC energies, as well as independent of centrality, if the Grand-Canonical statistical model is an appropriate description and chemical equilibrium applies. We describe variations of this scaling for deviations from this scenario, such as light quark chemical non-equilibrium, strange quark over-saturation and local conservation (canonical ensemble) for strange quarks. We also introduce a similar observable capable, together with the published K*/K measurement, of ascertaining if an interacting hadron gas phase governs the system between thermal and chemical freeze-out, and of ascertaining its duration and impact on hadronic chemistry.
In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. To model the dynamical evolution of the collective system assuming local thermal equilibrium ideal hydrodynamics seems to be a good tool. Nowadays, the development of either viscous hydrodynamic codes or hybrid approaches is favoured. For the microscopic description of the hadronic as well as the partonic stage of the evolution transport approaches have beeen successfully applied, since they generate the full phse-space dynamics of all the particles. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. It constitutes an effective solution of the relativistic Boltzmann equation and is restricted to binary collisions of the propagated hadrons. Therefore, the Boltzmann equation and the basic assumptions of this model are introduced. Furthermore, predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies and the new approach leads to reasonable results over the whole energy range. Studies of phase diagram trajectories using hydrodynamics are performed as a first move into the direction of the development of the hybrid approach. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The initial energy and baryon number density distributions are not smooth and not symmetric in any direction and the initial velocity profiles are non-trivial since they are generated by the non-equilibrium transport approach. The fulll (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. For the present work, three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. Either an in the computational frame isochronous freeze-out or an gradual freeze-out that mimics an iso-eigentime criterion. The particle vectors are generated by Monte Carlo methods according to the Cooper-Frye formula and UrQMD takes care of the final decoupling procedure of the particles. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The elliptic flow values at SPS energies are shown to be in line with an ideal hydrodynamic evolution if a proper initial state is used and the final freeze-out proceeds gradually. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent $v_2$ values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from $E_{\rm lab}=2-160A~$GeV. It is observed that the different freeze-out procedures have almost as much influence on the mean transverse mass excitation function as the equation of state. The experimentally observed step-like behaviour of the mean transverse mass excitation function is only reproduced, if a first order phase transition with a large latent heat is applied or the EoS is effectively softened due to non-equilibrium effects in the hadronic transport calculation. The HBT correlation of the negatively charged pion source created in central Pb+Pb collisions at SPS energies are investigated with the hybrid model. It has been found that the latent heat influences the emission of particles visibly and hence the HBT radii of the pion source. The final hadronic interactions after the hydrodynamic freeze-out are very important for the HBT correlation since a large amount of collisions and decays still takes place during this period.