Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.

Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.

Gas-liquid two-phase flows occur in many industrial applications and apparatuses. The design and optimization of such apparatuses and processes requires the numerical simulation of two-phase flows. However, two-phase flow simulations are still a challenging task, especially for industrial scales. Here, the simulation of large flow domains and high Reynolds number flows require a reduction of the resolved time-scales and length-scales by a high level of modeling to decrease the computational effort. Therefore, physics-based models are needed to depict the complex transport processes between the phases. Thus, two-phase flows are the object of ongoing research. Up to now, the majority of closure models for turbulence, interfacial forces or bubble breakup and coalescence were validated against experimental data derived from experiments in simple flow channel geometries like straight pipes. Their application for the simulation of two-phase flows with three-dimensional flow structures like e.g. recirculating areas, flow separation or strong velocity gradients requires constant experimental validation and further development. Hence, improved experimental methods are required for investigations of gas-liquid two-phase flows to provide reliable data for further development and validation of numerical flow simulation models. Therefore, experiments were performed in a constricted pipe under bubbly two-phase flow conditions. Three-dimensional flow structures were created by two types of flow constrictions for a variety of gas and liquid superficial velocities up to jg = 0.1400 m⋅s-1 and jl = 1.6110 m⋅s-1. The flow fields upstream and downstream of the flow constrictions were studied using ultrafast X-ray tomography and hot-film anemometry to obtain cross-sectional phase distribution, bubble characteristics and liquid velocity. The analysis of the ultrafast X-ray tomography image data was significantly improved by development of a histogram-based gas holdup calculation. Furthermore, the spatial dependence of the axial image plane distance was studied to improve the determination of axial bubble velocities and, thus, bubble sizes. The experimental method was advanced by simultaneous application of ultrafast X-ray tomography and hot-film anemometry. Eventually, the experimental data was compared to state-of-the-art Euler/Euler two-fluid simulations. The simulations were performed in the framework of a parallel doctoral thesis in the Experimental Thermal Fluid Dynamics department at the Helmholtz-Zentrum Dresden – Rossendorf by Ms. Sibel Tas-Koehler following the baseline approach. The results were compared in terms of the phase distribution, bubble sizes and gas velocity for two operating conditions using the homogeneous multiple size group model. / Zweiphasenströmungen aus Gasen und Flüssigkeiten treten in vielen industriellen Anwendungen und Apparaten auf. Um einen sicheren, zuverlässigen und optimalen Betrieb einzelner Komponenten und gesamter Anlagen zu gewährleisten, sind die Strömungen Gegenstand zahlreicher Untersuchungen. Numerische Simulationen sind ein unverzichtbares Instrument, um Prozesse unter diesen Aspekten zu bewerten. Die Simulation von Zweiphasenströmungen, insbesondere im industriellen Maßstab, ist jedoch nach wie vor eine anspruchsvolle Aufgabe. Um den Rechenaufwand zu verringern und die Simulation von großen Strömungsgebieten und Strömungen mit hohen Reynoldszahlen zu ermöglichen, ist ein hohes Maß an Modellierung notwendig. Gleichzeitig wurden die meisten Schließungsmodelle zur Beschreibung von Turbulenz, Grenzflächenkräften oder Blasenzerfall und -koaleszenz für einfache Geometrien wie beispielsweise gerade Rohre entwickelt. Die Anwendung dieser Modelle für die Simulation von Zweiphasenströmungen mit dreidimensionalen Strömungsstrukturen, wie z.B. Rezirkulationsgebieten, Strömungsablösungen oder starken Geschwindigkeitsgradienten, erfordert eine ständige experimentelle Validierung und Weiterentwicklung. Dies wiederum erfordert eine immer höhere Auflösung der eingesetzten Messsysteme und steigende Qualität der experimentellen Daten. Um verlässliche Daten für die Weiterentwicklung und Validierung von Modellen für die numerische Strömungssimulation zu erhalten sind daher verbesserte experimentelle Methoden zur Untersuchung von Gas-Flüssig-Strömungen erforderlich. Aus diesem Grund wurden Experimente an einer Blasenströmung in einem Rohr mit einer Strömungsverengung durchgeführt. Zwei Arten von Verengungen wurden genutzt, um dreidimensionale Strömungsstrukturen für eine Vielzahl von Betriebsbedingungen zu erzeugen. Diese sind durch Gas- und Flüssigkeitsleerrohrgeschwindigkeiten bis zu jg = 0.1400 m⋅s-1 und jl = 1.6110 m⋅s-1 definiert. Um die Phasenverteilung im Querschnitt der Strömung, Blaseneigenschaften und die Flüssigphasengeschwindigkeit stromauf- und -abwärts der Verengung zu ermittelt, wurde die Strömung mit Hilfe der ultraschnellen Röntgentomographie und Heißfilm-Anemometrie untersucht. Die Datenanalyse für die Bilddaten der ultraschnellen Röntgentomographie wurde durch die Entwicklung einer Histogramm-basierten Gasgehaltsberechnung erheblich verbessert. Um die Bestimmung der axialen Blasengeschwindigkeiten und damit der Blasengrößen zu verbessern, wurde außerdem die räumliche Abhängigkeit des axialen Bildebenenabstands untersucht. Die experimentellen Methoden wurden durch die gleichzeitige Anwendung von ultraschneller Röntgentomographie und Heißfilm-Anemometrie weiterentwickelt. Die experimentellen Daten wurden mit dem Stand der Technik von Euler/Euler-Zweiphasen-Simulationen verglichen. Die Simulationen wurden im Rahmen eines parallelen Promotionsvorhabens in der Abteilung Experimentelle Thermofluiddynamik am Helmholtz-Zentrum Dresden – Rossendorf von Frau Sibel Tas-Köhler durchgeführt und folgten der Baseline-Modell Strategie. Die Ergebnisse wurden unter Verwendung des homogenen Modells mehrerer Größenklassen bezüglich der Phasenverteilung, der Blasengrößen und der Gasgeschwindigkeit für zwei Betriebsbedingungen verglichen.

Die Arbeit befaßt sich mit der Messung und Analyse der spezifischen Wärme verschiedener stark korrelierter Elektronensysteme bei tiefen Temperaturen und hohen Magnetfeldern. Zunächst wird der im Rahmen dieser Arbeit verwendete, auf der Meßmethode der thermischen Relaxation beruhende Aufbau des Kalorimeters (Einsatzbereich 0.05K<T<4K und 0<B<12T) ausführlich erläutert. Danach werden die Ergebnisse von Messungen an den drei Schwere-Fermionen-Verbindungen CeCu2Si2, CeNi2Ge2 und YbRh2Si2 dargelegt. Wenngleich alle drei Systeme bei tiefen Temperaturen durch den für Schwere-Fermionen-Systeme charakteristischen, stark erhöhten elektronischen Beitrag zur spezifischen Wärme gekennzeichnet sind zeigen sich deutliche Unterschiede im beobachteten Grundzustandsverhalten. An CeCu2Si2 wird die für T<1K auftretende Konkurrenz zwischen einem supraleitenden und einem magnetischen Grundzustand ausführlich studiert. In YbRh2Si2 zeigt sich bei einer für 4f-Systeme bemerkenswert tiefen Temperatur von ca. 70mK ein Übergang in eine magnetische Phase, während der Grundzustand von CeNi2Ge2 wegen stark ausgeprägter Probenabhängigkeiten immer noch kontrovers diskutiert wird. Des weiteren zeigen alle drei Verbindungen deutliche Abweichungen vom Verhalten einer Fermi-Flüssigkeit. Die Theorie der Fermi-Flüssigkeit hat sich für metallische Verbindungen als sehr erfolgreich auch bei der Beschreibung des Verhaltens eines Systems aus stark wechselwirkenden Ladungsträgern erwiesen. Warum diese Theorie auf die untersuchten Verbindungen nicht anwendbar zu sein scheint, wird im Rahmen moderner Modellvorstellungen wie z. B. der Nähe zu einem quantenkritischen Punkt diskutiert. Die an Sr2RuO4, dem ersten Kupfer-freien Perowskit Supraleiter, durchgeführten Messungen der spezifischen Wärme dokumentieren das Auftreten von zwei Zusatzbeiträgen für T<Tc, die eine Interpretation der spezifischen Wärme des supraleitenden Zustands von Sr2RuO4 im Hinblick auf die Topologie des Ordnungsparameters deutlich erschweren.

Die Arbeit befaßt sich mit der Messung und Analyse der spezifischen Wärme verschiedener stark korrelierter Elektronensysteme bei tiefen Temperaturen und hohen Magnetfeldern. Zunächst wird der im Rahmen dieser Arbeit verwendete, auf der Meßmethode der thermischen Relaxation beruhende Aufbau des Kalorimeters (Einsatzbereich 0.05K<T<4K und 0<B<12T) ausführlich erläutert. Danach werden die Ergebnisse von Messungen an den drei Schwere-Fermionen-Verbindungen CeCu2Si2, CeNi2Ge2 und YbRh2Si2 dargelegt. Wenngleich alle drei Systeme bei tiefen Temperaturen durch den für Schwere-Fermionen-Systeme charakteristischen, stark erhöhten elektronischen Beitrag zur spezifischen Wärme gekennzeichnet sind zeigen sich deutliche Unterschiede im beobachteten Grundzustandsverhalten. An CeCu2Si2 wird die für T<1K auftretende Konkurrenz zwischen einem supraleitenden und einem magnetischen Grundzustand ausführlich studiert. In YbRh2Si2 zeigt sich bei einer für 4f-Systeme bemerkenswert tiefen Temperatur von ca. 70mK ein Übergang in eine magnetische Phase, während der Grundzustand von CeNi2Ge2 wegen stark ausgeprägter Probenabhängigkeiten immer noch kontrovers diskutiert wird. Des weiteren zeigen alle drei Verbindungen deutliche Abweichungen vom Verhalten einer Fermi-Flüssigkeit. Die Theorie der Fermi-Flüssigkeit hat sich für metallische Verbindungen als sehr erfolgreich auch bei der Beschreibung des Verhaltens eines Systems aus stark wechselwirkenden Ladungsträgern erwiesen. Warum diese Theorie auf die untersuchten Verbindungen nicht anwendbar zu sein scheint, wird im Rahmen moderner Modellvorstellungen wie z. B. der Nähe zu einem quantenkritischen Punkt diskutiert. Die an Sr2RuO4, dem ersten Kupfer-freien Perowskit Supraleiter, durchgeführten Messungen der spezifischen Wärme dokumentieren das Auftreten von zwei Zusatzbeiträgen für T<Tc, die eine Interpretation der spezifischen Wärme des supraleitenden Zustands von Sr2RuO4 im Hinblick auf die Topologie des Ordnungsparameters deutlich erschweren.

No description available.