Enhanced SPH modeling of free-surface flows with large deformations

The subject of the present thesis is the development of a numerical solver to study the violent interaction of marine flows with rigid structures. Among the many numerical models available, the Smoothed Particle Hydrodynamics (SPH) has been chosen as it proved appropriate in dealing with violent free-surface flows. Due to its Lagrangian and meshless character it can naturally handle breaking waves and fragmentation that generally are not easily treated by standard methods. On the other hand, some consolidated features of mesh-based methods, such as the solid boundary treatment, still remain unsolved issues in the SPH context. In the present work a great part of the research activity has been devoted to tackle some of the bottlenecks of the method. Firstly, an enhanced SPH model, called delta-SPH, has been proposed. In this model, a proper numerical diffusive term has been added in the continuity equation in order to remove the spurious numerical noise in the pressure field which typically affects the weakly-compressible SPH models. Then, particular attention has been paid to the development of suitable techniques for the enforcement of the boundary conditions. As for the free-surface, a specific algorithm has been designed to detect free-surface particles and to define a related level-set function with two main targets: to allow the imposition of peculiar conditions on the free-surface and to analyse and visualize more easily the simulation outcome (especially in 3D cases). Concerning the solid boundary treatment, much effort has been spent to devise new techniques for handling generic body geometries with an adequate accuracy in both 2D and 3D problems. Two different techniques have been described: in the first one the standard ghost fluid method has been extended in order to treat complex solid geometries. Both free-slip and no-slip boundary conditions have been implemented, the latter being a quite complex matter in the SPH context. The proposed boundary treatment proved to be robust and accurate in evaluating local and global loads, though it is not easy to extend to generic 3D surfaces. The second technique has been adopted for these cases. Such a technique has been developed in the context of Riemann-SPH methods and in the present work is reformulated in the context of the standard SPH scheme. The method proved to be robust in treating complex 3D solid surfaces though less accurate than the former. Finally, an algorithm to correctly initialize the SPH simulation in the case of generic geometries has been described. It forces a resettlement of the fluid particles to achieve a regular and uniform spacing even in complex configurations. This pre-processing procedure avoids the generation of spurious currents due to local defects in the particle distribution at the beginning of the simulation. The delta-SPH model has been validated against several problems concerning fluid-structure interactions. Firstly, the capability of the solver in dealing with water impacts has been tested by simulating a jet impinging on a flat plate and a dam-break flow against a vertical wall. In this cases, the accuracy in the prediction of local loads and of the pressure field have been the main focus. Then, the viscous flow around a cylinder, in both steady and unsteady conditions, has been simulated comparing the results with reference solutions. Finally, the generation and propagation of 2D gravity waves has been simulated. Several regimes of propagation have been tested and the results compared against a potential flow solver. The developed numerical solver has been applied to several cases of free-surface flows striking rigid structures and to the problem of the generation and evolution of ship generated waves. In the former case, the robustness of the solver has been challenged by simulating 2D and 3D water impacts against complex solid surfaces. The numerical outcome have been compared with analytical solutions, experimental data and other numerical results and the limits of the model have been discussed. As for the ship generated waves, the problem has been firstly studied within the 2D+t approximation, focusing on the occurrence and features of the breaking bow waves. Then, a dedicated 3D SPH parallel solver has been developed to tackle the simulation of the entire ship in constant forward motion. This simulation is quite demanding in terms of complexities of the boundary geometry and computational resources required. The wave pattern obtained has been compared against experimental data and results from other numerical methods, showing in both the cases a fair and promising agreement

Simulation of the Quantum Ising Model in an Ion Trap

In a proof-of-principle experiment, we simulate the dynamics of a quantum spin system in an ion trap. Following a theoretical proposal by D. Porras and I. Cirac, we use a system of ground state cooled trapped ions to simulate and study the dynamics of a quantum-mechanical system, or more precisely, the dynamics of a quantum spin Hamiltonian. We implement the smallest non-trivial quantum spin Hamiltonian, the quantum Ising model for two spins. Each spin is represented by two hyperfine ground levels of trapped 25Mg+ ions. The interaction with an external magnetic field is simulated by coherently coupling these hyperfine levels via laser and radiofrequency radiation. The spin-spin interaction is simulated via optical dipole forces, where the effective interaction is mediated by the phonons of the linear ion chain. We demonstrate the adiabatic evolution from a paramagnetically ordered system to ferromagnetic order. The final state of this adiabatic transition is a superposition state of the two degenerate spin configurations of ferromagnetic order Psi_final = 1/sqrt(2) (|up up> + |down down>) with a quantum magnetisation of 98%. We also show the transition from paramagnetic to antiferromagnetic order with the final state Psi_final = 1/sqrt(2) (|up down> + |down up>). Moreover, we prove that this transition which is to become a quantum phase transition in the thermodynamic limit of infinitely many spins, is driven by quantum fluctuations which dominate the dynamics of such systems at the absolute zero-point of temperature rather than thermal fluctuations which are absent at 0 K. This is verified by the fact that the final state of our adiabatic evolution is entangled, close to a Bell state at a fidelity exceeding 88%. The set of tools presented in this thesis might serve as a basis for larger scale quantum simulations which might help in gaining insight into many-particle effects that are intractable on classical computers such as spin frustration in triangular lattices or high-Tc superconductivity.Mit der vorliegenden Arbeit demonstrieren wir die Realisierbarkeit von Quantensimulationsexperimenten in einer Ionenfalle. Wir setzen hiermit einen experimentellen Vorschlag von D. Porras und I. Cirac um, in dem ein grundzustandsgekühltes System mehrerer Ionen in einer Falle dazu herangezogen wird, quantenmechanische Systeme, genauer gesagt, Quantenspin-Hamilton-Operatoren zu simulieren. Wir simulieren das einfachste nicht-triviale System, das Quanten-Ising-Modell für zwei Spins. Die Spins werden durch Hyperfeinzustände individueller Magnesiumionen kodiert. Durch kohärente Kopplung mit Hilfe von Laser- und Radiofrequenzfeldern lassen sich externe magnetische Felder simulieren. Die Isingwechselwirkung wird durch optische Dipolkräfte realisiert, die mit Hilfe der Phononen der Spinkette in eine zustandsabhängige Kraft übersetzt werden. Wir zeigen den Übergang von einem paramagnetisch geordneten System zweier Spins zu einem Ferromagneten. Der Endzustand dieser adiabatischen Simulation ist durch eine kohärente Überlagerung der beiden entarteten ferromagnetischen Ausrichtungen der Spin Psi_final = 1/sqrt(2) (|up up> + |down down>) gegeben, wobei wir eine Quantenmagnetisierung des Systems von 98% erreichen. Desweiteren zeigen wir den Übergang vom selben Ausgangszustand zur antiferromagnetischen Phase Psi_final = 1/sqrt(2) (|up down> + |down up>)). Durch die Tatsache, daß der Endzustand nach der Simulation in hohem Maße deterministisch verschränkt ist, verifizieren wir, daß dieser Übergang allein durch Quantenfluktuationen und nicht durch thermische Fluktuationen getrieben wird. Im thermodynamischen Limes unendlich vieler Teilchen wird dieser Übergang zu einem Quantenphasenübergang. Man erhofft, durch derartige Experimente, ein tieferes Verständnis für Vielteilchen-Quantensysteme, die mit klassischen Computern nicht lösbar sind, zu gewinnen, und damit Effekte wie Spin-Frustration in Dreiecks-Gittern oder Hochtemperatursupraleitung und deren Dynamik besser zu verstehen

MODELLING SUPERFLUID NEUTRON STARS APPLICATIONS TO PULSAR GLITCHES

In this dissertation I discuss how observations of the maximum glitch occurred in a certain pulsar provides a test for the microscopic physics of neutron star interiors, in particular the pinning forces (a parameter which effectively describes the strength of the vortex-lattice interaction at the mesoscopic scale). Conversely, by fixing the input parameters by taking estimates from recent literature, it is possible to estimate the mass of a glitching pulsar. A proof of concept of this thesis is given by constructing a quantitative model for pulsar rotational dynamics that can consistently encode state of the art models of the pinning force between vortices and ions in the crust, as well as the stratified structure of a neutron star. This point is far from being secondary as most studies on pulsar glitches are based on body-averaged models or differential models that tacitly assume a cylindrical symmetry, not consistent with the spherically layered structure

Holographic quark gluon plasma with flavor

In this work I explore theoretical and phenomenological implications of chemical potentials and charge densities inside a strongly coupled thermal plasma, using the gauge/gravity correspondence. Strong coupling effects discovered in this model theory are interpreted geometrically and may be taken as qualitative predictions for heavy ion collisions at RHIC and LHC. In particular I examine the thermodynamics, spectral functions, transport coefficients and the phase diagram of the strongly coupled plasma. For example stable mesons, which are the analogs of the QCD Rho-mesons, are found to survive beyond the deconfinement transition. This paper is based on partly unpublished work performed in the context of my PhD thesis. New results and ideas extending significantly beyond those published until now are stressed.Comment: 45 figures, 166 page