Gas-liquid annular two phase flow in pipes is important in the oil and gas, nuclear and the process industries. It has been identified as one of the most frequently encountered flow regimes and many models (empirical and theoretical) for the film flow and droplet behaviour for example have been developed since the 1950s. However, the behaviour in large pipes (those with diameter greater than 100 mm) has not been fully explored. As a result, the two- phase flow characteristics, data, and models specifically for such pipes are scarce or non-existent such that those from smaller pipes are extrapolated for use in design and operation. Many authors have cautioned against this approach since multiphase pipe flow behaviour is different between small and large pipes. For instance the typical slug flows seem not to occur in vertical upwards flows when the pipe diameter exceeds 100 mm. It is therefore imperative that theoretical models and empirical correlations for such large diameter pipes are specifically developed.

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This thesis deals with the adiabatic cooling air. Adiabatic cooling is a possible kind of cooling and air humidification with low energy requirements. Experimentally, evaporative cooler is tested with different types of material in order to find out the most efficient and practically useful filling for adiabatic cooling that could be used as part of the air-conditioning equipment in practice. The results are used in the practical part. The project compares the application of air-conditioning equipment with/without adiabatic cooling in the possible design of the air-conditioning equipment for the shopping center. The use of the air conditioning system with adiabatic cooling, as a more efficient variant, is then applied to the design itself.

One of the major challenges hindering advancement of quantum computing is the sensitive nature of the physical systems used to build a quantum computer. One suggestion for improving reliability is a particular type of logic gates, based on Berry's geometric phase, showing improved robustness to external disturbance of the quantum system over the course of a calculation. Such logic gates have previously been shown for the smallest possible two-level qubits. Using the method of adiabatic shortcut we endevour to discover similarly realistic and robust logic gates for units of quantum information in higher dimensions. The example shown in this paper discusses three-level qutrits, but is expected to apply to theoretically unlimited higher dimensions since new geometric complications are expected to arise primarily when moving from a two-level to a multi-level problem.  We here present a set of primitive single-qutrit gates able to perform universal quantum computations if supplemented by a two-qutrit gate. We also present a set of condensed single-qutrit gates for commonly needed operations. By detailing the underlying mathematical framework, relying on the multi-dimensional generalisation of Berry's phase describing the time evolution of degenerate quantum states, we also suggest an easily scalable geometric interpretation of quantum gates in higher dimensions along with visual representation of logic gates using parameters of the physical system to sequentially unlock and manipulate subspaces of the quantum information unit.

On etudie la contrôlabilité des systèmes quantiques dans deux contextes différents: le cadre standard fermé, dans lequel un système quantique est considéré comme isolé et le problème de contrôle est formulé sur l'équation de Schrödinger; le cadre ouvert qui décrit un système quantique en interaction avec un plus grand, dont seuls les paramètres qualitatifs sont connus, au moyen de l'équation de Lindblad sur les états.Dans le contexte des systèmes fermés on se focalise sur la classe intéressante des systèmes spin-boson, qui décrivent l'interaction entre un système quantique à deux niveaux et un nombre fini de modes distingués d'un champ bosonique. On considère deux exemples prototypiques, le modèle de Rabi et le modèle de Jaynes-Cummings qui sont encore très populaires dans plusieurs domaines de la physique quantique. Notamment, dans le contexte de la Cavity Quantum Electro Dynamics (C-QED), ils fournissent une description précise de la dynamique d'un atome à deux niveaux dans une cavité micro-onde en résonance, comme dans les expériences récentes de S. Haroche. Nous étudions les propriétés de contrôlabilité de ces modèles avec deux types différents d'opérateurs de contrôle agissant sur la partie bosonique, correspondant respectivement – dans l'application à la C-QED – à un champ électrique et magnétique externe. On passe en revue quelques résultats récents et prouvons la contrôlabilité approximative du modèle de Jaynes-Cummings avec ces contrôles. Ce résultat est basé sur une analyse spectrale exploitant les non-résonances du spectre. En ce qui concerne la relation entre l'Hamiltonien de Rabi et Jaynes-Cummings nous traitons dans un cadre rigoureux l'approximation appelée d'onde tournante. On formule le problème comme une limite adiabatique dans lequel la fréquence de detuning et le paramètre de force d'interaction tombent à zero, ce cas est connu sous le nom de régime de weak-coupling. On prouve que, sous certaines hypothèses sur le rapport entre le detuning et le couplage, la dynamique de Jaynes-Cumming et Rabi montrent le même comportement, plus précisément les opérateurs d'évolution qu'ils génèrent sont proches à la norme.Dans le cadre des systèmes quantiques ouverts nous étudions la contrôlabilité de l'équation de Lindblad. Nous considérons un contrôle agissant adiabatiquement sur la partie interne du système, que nous voyons comme un degré de liberté qui peut être utilisé pour contraster l'action de l'environnement. L'action adiabatique du contrôle est choisie pour produire une transition robuste. On prouve, dans le cas prototype d'un système à deux niveaux, que le système approche un ensemble de points d'équilibre déterminés par l'environnement, plus précisément les paramètres qui spécifient l'opérateur de Lindblad. Sur cet ensemble, le système peut être piloté adiabatiquement en choisissant un contrôle approprié. L'analyse est fondée sur l'application de méthodes de perturbation géométrique singulière. / We investigate the controllability of quantum systems in two differentsettings: the standard 'closed' setting, in which a quantum system is seen as isolated, the control problem is formulated on the Schroedinger equation; the open setting that describes a quantum system in interaction with a larger one, of which just qualitative parameters are known, by means of the Lindblad equation on states.In the context of closed systems we focus our attention to an interesting class ofmodels, namely the spin-boson models. The latter describe the interaction between a 2-level quantum system and finitely many distinguished modes of a bosonic field. We discuss two prototypical examples, the Rabi model and the Jaynes-Cummings model, which despite their age are still very popular in several fields of quantum physics. Notably, in the context of cavity Quantum Electro Dynamics (C-QED) they provide an approximate yet accurate description of the dynamics of a 2-level atom in a resonant microwave cavity, as in recent experiments of S. Haroche. We investigate the controllability properties of these models, analyzing two different types of control operators acting on the bosonic part, corresponding -in the application to cavity QED- to an external electric and magnetic field, respectively. We review some recent results and prove the approximate controllability of the Jaynes-Cummings model with these controls. This result is based on a spectral analysis exploiting the non-resonances of the spectrum. As far as the relation between the Rabi andthe Jaynes-Cummings Hamiltonians concerns, we treat the so called rotating waveapproximation in a rigorous framework. We formulate the problem as an adiabaticlimit in which the detuning frequency and the interaction strength parameter goes to zero, known as the weak-coupling regime. We prove that, under certain hypothesis on the ratio between the detuning and the coupling, the Jaynes-Cumming and the Rabi dynamics exhibit the same behaviour, more precisely the evolution operators they generate are close in norm.In the framework of open quantum systems we investigate the controllability ofthe Lindblad equation. We consider a control acting adiabatically on the internal part of the system, which we see as a degree of freedom that can be used to contrast the action of the environment. The adiabatic action of the control is chosen to produce a robust transition. We prove, in the prototype case of a two-level system, that the system approach a set of equilibrium points determined by the environment, i.e. the parameters that specify the Lindblad operator. On that set the system can be adiabatically steered choosing a suitable control. The analysis is based on the application of geometrical singular perturbation methods.

Light or photons can excite electrons in a molecule, leading to creation of electronically excited states. Such processes are ubiquitous in nature, such as, vision, photo-protection of DNA/RNA nucleobases, light harvesting, energy and charger transfer etc. This photoexcitation induces nuclear motion on the excited states, leading the excess energy to dissipate either non-radiatively via internal conversion back down to the ground state, isomerization, and dissociation, or radiatively via fluorescence and phosphorescence. In this dissertation, we investigate the non-radiative processes in organic chromophores that ensue in an ultrafast manner, mediated via conical intersections (CoIn). Description of such excited state processes generally require multi-reference treatment because of quasi-degeneracy near CoIns. Hence, most insight about these processes is typically gained by constructing potential energy surface (PES) using multi-reference electronic structure methods along important reaction coordinates. Nonetheless, the aforementioned static treatment fails to provide any dynamical information, such as, excited state lifetime, state populations, branching ratio, quantum yield etc. In this dissertation, we have gone beyond the static treatment by undertaking computationally expensive non-adiabatic excited state molecular dynamics simulations employing trajectory surface hopping (TSH) methodology on PESs created on-the-fly using multi-reference electronic structure methods. This allows us to compare theoretical results to experimental observables, when possible, strengthening the explanations underlying those processes. Our goal is to examine the effect of structure, and of electronic structure methods on the excited state dynamics. We have examined the non-adiabatic excited state dynamics of cis,cis-1,3-cyclooctadiene (cc-COD), a cyclic diene, in an effort to systematically compare and contrast the dynamics of cc-COD to that of other well studied conjugated molecules. Such exploration is very significant, since the majority of the molecules involved in natural photoexcited processes, include an ethylenic double bond or alternating double bonds creating conjugation. Our calculations have revealed ultrafast sub-ps decay for cc-COD, and have illustrated that the internal conversion dynamics is facilitated by CoIns, dominated by twisting of one of the double bonds and pyramidalization of one of the carbons of that double bond, similar to trans-1,3-butadiene and unlike 1,3-cyclohexadiene (CHD). Our high-level electronic structure calculations have also explained the features in the experimental time-resolved photoelectron spectrum of cc-COD. Another molecule of biological importance, uracil, was also investigated using TSH simulations, by systematically increasing dynamical correlation. We have found that the inclusion of dynamical correlation for uracil leads to an almost barrierless PES on S2, leading to a faster decay and no population trap on this state. Uracil also contains a double bond and the simulations have revealed that the ultrafast relaxation is dominated by an ethylenic twist and pyramidalization of a carbon of that bond, increasing importance of such nuclear motion in photoexcited molecular dynamics. A comparison of the molecules studied have illustrated that the rigid molecules, such as uracil, CHD, have a very local CoIn seam space, whereas cc-COD, which is flexible having many low frequency degrees of freedom, has a non-local or extended CoIn seam space. Overall, the work performed in this dissertation, elucidates the significance of structure and conjugation, in the photoinduced coupled electron-nuclear dynamics in organic molecules. / Chemistry

The study of topological phases in condensed matter physics has seen remarkable advancements, primarily focusing on systems with a well-defined bulk and boundary. However, the emergence of topological phenomena on self-similar systems, characterized by the absence of a clear distinction between bulk and boundary, presents a fascinating challenge. This thesis focuses on the topological phases on self-similar systems, shedding light on their unique properties through the lens of adiabatic charge pumping. We observe that the spectral flow in these systems exhibits striking qualitative distinctions from that of translationally invariant non-interacting systems subjected to a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. Furthermore, we establish a correspondence between the local contributions to the Hall conductivity and the spectral flow of edge-like states. We also find that the edge-like states can be approximated as eigenstates of the discrete angular-momentum operator, with their chiral characteristics stemming from this unique perspective. We also investigate the effect of local structure on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both structures host topologically nontrivial phases and the phase diagrams are different on the two structures, emphasizing the interplay between non-spatial symmetries and the local structure of the self-similar unit in determining topological phases. Furthermore, we demonstrate the presence of topologically ordered chiral spin liquid on fractals by extending the Kitaev model to the Sierpinski Gasket. We show a way to perform the Jordan-Wigner transformation to make this model exactly solvable on the Sierpinski Gasket. This system exhibits a fractal density of states for Majorana modes and showcases a transition from a gapped to a gapless phase. Notably, the gapped phase features symmetry-protected Majorana corner modes, while the gapless phase harbors robust zero-energy and low-energy self-similar Majorana edge-like modes. We also study the vortex excitations, characterized by remarkable localization properties even in small fractal generations. These localized excitations exhibit anyonic behavior, with preliminary calculations hinting at their fundamental differences from Ising anyons observed in the Kitaev model on a honeycomb lattice.

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The work presented in this dissertation is the first numerical investigation conducted to study leading edge film cooling with Large Eddy Simulation (LES). A cylindrical leading edge with a flat after-body represents the leading edge, where coolant is injected with a 30Ë compound angle. Three blowing ratios of 0.4, 0.8, and 1.2 are studied. Free-stream Reynolds number is 100,000 and coolant-to-mainstream density ratio is unity. At blowing ratio of 0.4, the effect of coolant inlet condition is investigated. Results show that the fully-turbulent coolant jet increases mixing with the mainstream in the outer shear layer but does not influence the flow dynamics in the turbulent boundary layer at the surface. As a result, the turbulent jet decreases adiabatic effectiveness but does not have a substantial effect on the heat transfer coefficient. At B.R.=0.4, three types of coherent structures are identified which consist of a primary entrainment vortex at the leeward aft-side of the coolant hole, vortex tubes at the windward side of the coolant hole, and hairpin vortices typical of turbulent boundary layers produced by the turbulent interaction of the coolant and mainstream downstream of injection. At B.R. = 0.8 and 1.2, coherent vortex tubes are no longer discernable, whereas the primary vortex structure gains in strength. In all cases, the bulk of the mixing occurs by entrainment which takes place at the leeward aft-side of the coolant jet. This region is characterized by a low pressure core and the primary entrainment vortex. Turbulent shear interaction between coolant jet and mainstream increases substantially with blowing ratio and contributes to the dilution of the coolant jet. As a result of the increased mixing in the shear layer and primary structure, adiabatic effectiveness decreases and heat transfer coefficient increases with increase in blowing ratio. The dissertation also investigates the deposition and erosion of Syngas ash particles in the film cooled leading edge region. Three ash particle sizes of 1, 5, and 10 microns are investigated at all blowing ratios using Lagrangian dynamics. The 1 micron particles with momentum Stokes number St = 0.03 (based on approach velocity and cylinder diameter), show negligible deposition/erosion. The 10 micron particles, on the other hand with a high momentum Stokes number, St = 3, directly impinge and deposit on the surface, with blowing ratio having a minimal effect. The 5 micron particles with St=0.8, show the largest receptivity to coolant flow and blowing ratio. On a mass basis, 90% of deposited mass is from 10 micron particles, with 5 micron particles contributing the other 10%. Overall there is a slight decrease in deposited mass with increase in blowing ratio. About 0.03% of the total incoming particle energy can potentially be transferred as erosive energy to the surface and coolant hole, with contribution coming from only 5 micron particles at B.R.=0.4 and 0.8, and both 5 and 10 micron particles at B.R.=1.2. / Ph. D.