Thermodynamic concepts in adaptive resolution simulations

This thesis work is devoted to the conceptual and technical development of the Adaptive Resolution Scheme (AdResS), a molecular dynamics method that allows the simulation of a system with different levels of resolution simultaneously. The simulation domain is divided into high and low resolution zones and a transition region that links them, through which molecules can freely diffuse.rnThe first issue of this work regards the thermodynamic consistency of the method, which is tested and verified in a model liquid of tetrahedral molecules. The results allow the introduction of the concept of the Thermodynamic Force, an external field able to correct spurious density fluctuations present in the transition region in usual AdResS simulations.rnThe AdResS is also applied to a system where two different representations with the same degree of resolution are confronted. This simple test extends the method from an Adaptive Resolution Scheme to an Adaptive Representation Scheme, providing a way of coupling different force fields based on thermodynamic consistency arguments. The Thermodynamic Force is successfully applied to the example described in this work as well.rnAn alternative approach of deducing the Thermodynamic Force from pressure consistency considerations allows the interpretation of AdResS as a first step towards a molecular dynamics simulation in the Grand Canonical ensemble. Additionally, such a definition leads to a practical way of determining the Thermodynamic Force, tested in the well studied tetrahedral liquid. The effects of AdResS and this correction on the atomistic domain are analyzed by inspecting the local distribution of velocities, radial distribution functions, pressure and particle number fluctuation. Their comparison with analogous results coming from purely atomistic simulations shows good agreement, which is greatly improved under the effect of the external field.rnA further step in the development of AdResS, necessary for several applications in biophysics and material science, consists of its application to multicomponent systems. To this aim, the high-resolution representation of a model binary mixture is confronted with its coarse-grained representation systematically parametrized. The Thermodynamic Force, whose development requires a more delicate treatment, also gives satisfactory results.rnFinally, AdResS is tested in systems including two-body bonded forces, through the simulation of a model polymer allowed to adaptively change its representation. It is shown that the distribution functions that characterize the polymer structure are in practice not affected by the change of resolution.rnThe technical details of the implementation of AdResS in the ESPResSo package conclude this thesis work.

Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

Untersuchung von Mischungs- und Transportprozessen in der oberen Troposphäre - unteren Stratosphäre basierend auf in-situ Spurengasmessungen

Die obere Troposphäre / untere Stratosphäre (UTLS: Upper Troposphere / Lower Stratosphere)ist die Übergangsgregion zwischen den dynamisch, chemisch und mikrophysikalisch sehr verschiedenen untersten Atmosphärenschichten, der Troposphäre und der Stratosphäre. Strahlungsaktive Spurengase, wie zum Beispiel Wasserdampf (H2O), Ozon (O3) oder Kohlenstoffdioxid (CO2), und Wolken in der UTLS beeinflussen das Strahlungsbudget der Atmosphäre und das globale Klima. Mögliche Veränderungen in den Verteilungen und Konzentrationen dieser Spurengase modifizieren den Strahlungsantrieb der Atmosphäre und können zum beobachteten Klimawandel beitragen. Ziel dieser Arbeit ist es, Austausch- und Mischungsprozesse innerhalb der UTLS besser zu verstehen und damit Veränderungen der Spurengaszusammensetzung dieser Region genauer prognostizieren zu können. Grundlage hierfür bilden flugzeuggetragene in-situ Spurengasmessungen in der UTLS, welche während der Flugzeugmesskampagnen TACTS / ESMVal 2012 und AIRTOSS - ICE 2013 durchgeführt wurden. Hierbei wurde bei den Messungen von AIRTOSS - ICE 2013 das im Rahmen dieser Arbeit aufgebaute UMAQS (University of Mainz Airborne QCLbased Spectrometer) - Instrument zur Messung der troposphärischen Spurengase Distickstoffmonoxid (N2O) und Kohlenstoffmonoxid (CO) eingesetzt. Dieses erreicht bei einer zeitlichen Auflösung von 1 s eine Messunsicherheit von 0,39 ppbv und 1,39 ppbv der N2O bzw. CO-Mischungsverhältnisse. Die hohe Zeitauflösung und Messgenauigkeit der N2O- und CO- Daten erlaubt die Untersuchung von kleinskaligen Austauschprozessen zwischen Troposphäre und Stratosphäre im Bereich der Tropopause auf räumlichen Skalen kleiner 200 m. Anhand der N2O-Daten von AIRTOSS - ICE 2013 können in-situ detektierte Zirruspartikel in eisübersättigter Luft oberhalb der N2O-basierten chemischen Tropopause nachgewiesen werden. Mit Hilfe der N2O-CO-Korrelation sowie der Analyse von ECMWF-Modelldaten und der Berechnung von Rückwärtstrajektorien kann deren Existenz auf das irreversible Vermischen von troposphärischen und stratosphärischen Luftmassen zurückgeführt werden. Mit den in-situ Messungen von N2O, CO und CH4 (Methan) von TACTS und ESMVal 2012 werden die großräumigen Spurengasverteilungen bis zu einer potentiellen Temperatur von Theta = 410 K in der extratropischen Stratosphäre untersucht. Hierbei kann eine Verjüngung der Luftmassen in der extratropischen Stratosphäre mit Delta Theta > 30 K (relativ zur dynamischen Tropopause) über den Zeitraum der Messkampagne (28.08.2012 - 27.09.2012) nachgewiesen werden. Die Korrelation von N2O mit O3 zeigt, dass diese Verjüngung aufgrund des verstärkten Eintrages von Luftmassen aus der tropischen unteren Stratosphäre verursacht wird. Diese werden über den flachen Zweig der Brewer-Dobson-Zirkulation auf Zeitskalen von wenigen Wochen in die extratropische Stratosphäre transportiert. Anhandrnder Analyse der CO-O3-Korrelation eines Messfluges vom 30.08.2012 wird das irreversible Einmischen von Luftmassen aus der tropischen Stratosphäre in die Extratropen auf Isentropen mit Theta > 380 K identifiziert. Rückwärtstrajektorien zeigen, dass der Ursprung der eingemischten tropischen Luftmassen im Bereich der sommerlichen Antizyklone des asiatischen Monsuns liegt.