This thesis deals with design and implementation of the computing system, which would allow interactive simulation of kinematics and dynamics of vehicle mechanical systems or general mechanisms with the help of modern computer technology. In the thesis is described a basic working principle, optimization of numerical simulation parameters, as well as the implementation itself in the form of functional application and its key parts. Described are also possibilities for the use of virtual reality devices in conjunction with visualization of simulation process. Final comparative tests have confirmed the functionality and high performance of the created system.

Analogue quantum simulators have proven to be an extremely versatile tool for the study of strongly-correlated condensed matter systems both near and far from equilibrium. An enticing prospect is the quantum simulation of non- Fermi liquids which lack a quasiparticle description and feature prominently in the study of strange metals, fast scrambling of quantum information, as well as holographic quantum matter. Yet, large-scale laboratory realisations of such systems remain outstanding. In this thesis, we present a proposal for the analogue quantum simulation of one such system, the Sachdev–Ye–Kitaev (SYK) model, using cavity quantum electrodynamics (cQED). We discuss recent experimental advances in this pursuit, and perform analysis of this and related models. Through a combination of analytic calculations and numeric simulations, we show how driving a cloud of fermionic atoms trapped in a multi- mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift, can realise an effective model which retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Working towards the SYK model, we present results from a recent proof-of-principle cQED experiment which implemented the disordered light-shift technique to quantum simulate all- to-all interacting spin models with quenched disorder. In this context, we show analytically how disorder-driven localisation can be extracted from spectroscopic probes employed in cQED experiments, despite their lack of spatially resolved information. Further, we numerically investigate the post-quench dynamics of the SYK model, finding a universal, super-exponential equilibration in the disorder-averaged far-from-equilibrium dynamics. These are reproduced analytically through an effective master equation. Our work demonstrates the increasing capabilities of cQED quantum simulators, highlighting how these may be used to study the fascinating physics of holographic quantum matter and other disorder models in the lab.

This thesis presents the derivation of the dynamic model of an autonomous underwater vehicle that tows a large payload. Our analysis is motivated by the fact that the payload is so large that it cannot be modeled by simply appending its dynamics to the dynamics of the autonomous underwater vehicle. Hence, the coupling between the vehicle and payload must be fully modeled. Furthermore, several approximation techniques based on analytic and empirical formulations are investigated for computing the hydrodynamic coefficients of the vehicle. Efficacy and limitations of the approximation techniques are assessed by comparison with hydrodynamic coefficients that are estimated using high-fidelity computational fluid dynamics simulations. / Master of Science / This thesis presents the model to used to predict the motion of an autonomous underwater vehicle that tows a large object. Our analysis is motivated by the fact that the size of the object is so large that it will have a substantial impact on the motion of the vehicle, and likewise the vehicle will have a substantial impact on the object, requiring that the interaction between the two bodies to be fully modeled. The fluid forces and moments acting on the vehicle are approximated using techniques from hydrodynamic theory and experimental results. The accuracy of the approximation is assessed by comparing of the estimated forces and moments with those seen in high-fidelity simulations.

No description available.

Thesis (MSc (Physics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities. / AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede.

Esta tese apresenta o desenvolvimento de um método de elementos de contorno (BEM) no domínio do tempo baseado em fontes de Rankine para analise linear de comportamento no mar de sistemas oceânicos. O método e formulado por dois problemas de valor inicial de contorno definidos para os potenciais de velocidade e aceleração, sendo este ultimo utilizado para calcular de maneira acurada a derivada temporal do potencial de velocidades. Testes de verificação são realizados para a solução dos problemas de difração, radiação e de corpo livre para flutuar. Uma vez verificada, a ferramenta e aplicada em dois problemas multicorpos considerados no estado-da-arte em termos de modelagem hidrodinâmica utilizando BEM. O primeiro trata do problema envolvendo duas embarcações atracadas a contrabordo. Este é um caso no qual os códigos baseados na teoria de escoamento potencial são conhecidos por apresentarem dificuldades na determinação das soluções, tendendo a superestimar as elevações de onda no vão entre as embarcações e a apresentar problemas de convergência numérica associados a efeitos ressonantes de onda. O problema e tratado por meio do método de damping lid e a convergência das series temporais e investigada avaliando diferentes níveis de amortecimento. Os resultados são comparados com dados experimentais. O segundo problema se refere a analise de sistemas multicorpos com grandes deslocamentos relativos. Neste problema, ferramentas no domínio da frequência nao podem ser utilizadas, por considerarem apenas malhas fixas. Deste modo, o presente método e estendido para considerar um gerador de malhas de paineis e um algoritmo de interpolação de ordem alta no laco de tempo do código, possibilitando a mudança de posições relativas entre os corpos durante a simulação. Os resultados são comparados com dados de experimentos executados especificamente para fins de verificação do código, apresentando uma boa concordância. De acordo com o conhecimento do autor, esta e a primeira vez que certas questões relativas a modelagem numérica destes dois problemas multicorpos são relatadas na literatura especializada em hidrodinâmica computacional. / The development of a time domain boundary elements method (BEM) based on Rankine\'s sources for linear seakeeping analysis of offshore systems is here addressed. The method is formulated by means of two Initial Boundary Value Problems defined for the velocity and acceleration potentials, the latter being used to ensure an accurate calculation of the time derivatives of the velocity potential. Verification tests for solving the difraction, radiation and free floating problems are presented. Once verified, the code is applied for two complex multi-body problems considered to be in the state-of-the-art for hydrodynamic modelling using BEM. The first is the seakeeping problem of two ships arranged in side-by-side, a problem in which all potential flow codes are known to have a poor performance, tending to provide unrealistic high wave elevations in the gap between the vessels and to present numerical convergence problems associated to resonant effects. The problem is here addressed by means of a damping lid method and the convergence of the time series with different damping levels is investigated. Results are compared to data measured in an experimental campaign. The second problem refers to the analysis of multi-body systems composed of bodies undergoing large relative displacements. This is a case that cannot be properly analyzed by frequency domain codes, since they only consider fixed meshes. For this application, the present numerical method is extended to consider a panel mesh generator in the time loop of the code, enabling the change of body relative positions during the computations. Furthermore, a higher order interpolation algorithm designed to recover the solutions of a previous time-step was also implemented, enabling the calculations to progress with reasonable accuracy in time. The numerical results are compared to data of experimental tests designed and executed for verification of the code, and presented a very good agreement. To the author\'s knowledge, this is the first time that certain issues concerning the numerical modelling of these two complex multi-body problems are reported in the literature specialized in hydrodynamic computations.

No description available.

Rigid multibody systems have been studied extensivley due to its direct application in design and analysis of various mechanical systems such as robots and spacecraft structures. The dynamics of multibody system is governed by its equations of motion and various terms associated with it, such as the mass matrix, the generalized force vector, are well known..Forward dynamics algorithms play an important role in the simulation of multibody systems and the recursive forward dynamics algorithm for branched multibody systems is very popular. The recursive forward dynamic algorithm is highly efficient algorithm with O(n) computational complexity and scores over other algorithms when number of rigid bodies n in the system is very large. The algorithm involves finding an important mass matrix, which has been popularly termed as articulated body inertia (AB inertia). To find ijth term of any general mass matrix, we separately give virtual change to ith and jth generalized coordinates. At each point of the multibody system, the dot product of the resulting virtual displacements are taken with each other and eventually integrated over the entire multibody system, weighted by the mass. This quantity divided by the virtual changes in ith and jth coordinates gives the ijth element of the mass matrix. This is one of the fundamental ways of looking at the mass matrix. However, in literature, the AB inertia is obtained as a result of mathematical manipulation and its physical or geometrical significance from the above view point is not clear. In this thesis we present a more geometric and physical explanation for the AB inertia. The main step is to obtain a new set of generalized coordinates which relate directly to the AB inertia. We have also shown the equivalence of our method with existing methods. A comprehensive treatement on change of generalized coordinates and its effect on equations of motion has also been presented as preliminaries. The second part of the thesis deals with closed loop multibody systems.A few years ago an iterative algorithm called the sequential regularization method (SRM) was proposed for simulation of closed loop multibody systems with attractive claims on its efficiency. In literature we find that this algorithm has been implemented and studied only for planar multibody systems. As a part of the thesis work, we have developed a C-programming language code which can simulate 3-dimensional spatial multibody systems using the SRM algorithm. The programme can also perform simulation using a relatively efficient Conventional algorithm having O(n+m3) complexity, where m denotes number of closed loop constraints. Simulation studies have been carried out on a few multibody systems using the two algorithms. Some of the results have been also been validated using the commercial simulation package -ADAMS. As a result of our simulation studies, we have detected certain points, after which the solution from SRM loses it convergence. More study is required to understand this lack of convergence.

Esta tese apresenta o desenvolvimento de um método de elementos de contorno (BEM) no domínio do tempo baseado em fontes de Rankine para analise linear de comportamento no mar de sistemas oceânicos. O método e formulado por dois problemas de valor inicial de contorno definidos para os potenciais de velocidade e aceleração, sendo este ultimo utilizado para calcular de maneira acurada a derivada temporal do potencial de velocidades. Testes de verificação são realizados para a solução dos problemas de difração, radiação e de corpo livre para flutuar. Uma vez verificada, a ferramenta e aplicada em dois problemas multicorpos considerados no estado-da-arte em termos de modelagem hidrodinâmica utilizando BEM. O primeiro trata do problema envolvendo duas embarcações atracadas a contrabordo. Este é um caso no qual os códigos baseados na teoria de escoamento potencial são conhecidos por apresentarem dificuldades na determinação das soluções, tendendo a superestimar as elevações de onda no vão entre as embarcações e a apresentar problemas de convergência numérica associados a efeitos ressonantes de onda. O problema e tratado por meio do método de damping lid e a convergência das series temporais e investigada avaliando diferentes níveis de amortecimento. Os resultados são comparados com dados experimentais. O segundo problema se refere a analise de sistemas multicorpos com grandes deslocamentos relativos. Neste problema, ferramentas no domínio da frequência nao podem ser utilizadas, por considerarem apenas malhas fixas. Deste modo, o presente método e estendido para considerar um gerador de malhas de paineis e um algoritmo de interpolação de ordem alta no laco de tempo do código, possibilitando a mudança de posições relativas entre os corpos durante a simulação. Os resultados são comparados com dados de experimentos executados especificamente para fins de verificação do código, apresentando uma boa concordância. De acordo com o conhecimento do autor, esta e a primeira vez que certas questões relativas a modelagem numérica destes dois problemas multicorpos são relatadas na literatura especializada em hidrodinâmica computacional. / The development of a time domain boundary elements method (BEM) based on Rankine\'s sources for linear seakeeping analysis of offshore systems is here addressed. The method is formulated by means of two Initial Boundary Value Problems defined for the velocity and acceleration potentials, the latter being used to ensure an accurate calculation of the time derivatives of the velocity potential. Verification tests for solving the difraction, radiation and free floating problems are presented. Once verified, the code is applied for two complex multi-body problems considered to be in the state-of-the-art for hydrodynamic modelling using BEM. The first is the seakeeping problem of two ships arranged in side-by-side, a problem in which all potential flow codes are known to have a poor performance, tending to provide unrealistic high wave elevations in the gap between the vessels and to present numerical convergence problems associated to resonant effects. The problem is here addressed by means of a damping lid method and the convergence of the time series with different damping levels is investigated. Results are compared to data measured in an experimental campaign. The second problem refers to the analysis of multi-body systems composed of bodies undergoing large relative displacements. This is a case that cannot be properly analyzed by frequency domain codes, since they only consider fixed meshes. For this application, the present numerical method is extended to consider a panel mesh generator in the time loop of the code, enabling the change of body relative positions during the computations. Furthermore, a higher order interpolation algorithm designed to recover the solutions of a previous time-step was also implemented, enabling the calculations to progress with reasonable accuracy in time. The numerical results are compared to data of experimental tests designed and executed for verification of the code, and presented a very good agreement. To the author\'s knowledge, this is the first time that certain issues concerning the numerical modelling of these two complex multi-body problems are reported in the literature specialized in hydrodynamic computations.

Entanglement is a fundamental property of quantum systems and its characterization is a central problem for physics. Moreover, there is an increasing demand for scalable protocols that can certify the presence of entanglement. This is primarily due to the role of entanglement as a crucial resource for quantum technologies. However, systematic entanglement certification is highly challenging, and this is particularly the case for quantum many-body systems. In this dissertation, we tackle this challenge and introduce some techniques that allow the certification of multipartite entanglement in many-body systems. This is demonstrated with an application to a model of interacting fermions that shows the presence of resilient multipartite entanglement at finite temperatures. Moreover, we also discuss some subtleties concerning the definition entanglement in systems of indistinguishable particles and provide a formal characterization of multipartite mode entanglement. This requires us to work with an abstract formalism that can be used to define entanglement in quantum many-body systems without reference to a specific structure of the states. To further showcase this technique, and also motivated by current quantum simulation efforts, we use it to extend the framework of entanglement witnesses to lattice gauge theories. / L'entanglement è una proprietà fondamentale dei sistemi quantistici e la sua caratterizzazione è un problema centrale per la fisica. Inoltre, vi è una crescente richiesta di protocolli scalabili in grado di certificare la presenza di entanglement. Ciò è dovuto principalmente al ruolo dell'entanglement come risorsa cruciale per le tecnologie quantistiche. Tuttavia, la certificazione sistematica dell'entanglement è molto impegnativa, e questo è particolarmente vero per i sistemi quantistici a molti corpi. In questa dissertazione, affrontiamo questa sfida e introduciamo alcune tecniche che consentono la certificazione dell'entanglement multipartito in sistemi a molti corpi. Ciò è dimostrato con un'applicazione a un modello di fermioni interagenti che mostra la presenza di entanglement multipartito resiliente a temperature finite. Inoltre, discutiamo anche alcune sottigliezze riguardanti la definizione di entanglement in sistemi di particelle indistinguibili e forniamo una caratterizzazione formale dell'entanglement multipartito. Ciò ci richiede di lavorare con un formalismo astratto che può essere utilizzato per definire l'entanglement nei sistemi quantistici a molti corpi senza fare riferimento a una struttura specifica degli stati. Per mostrare ulteriormente questa tecnica, e anche motivata dagli attuali sforzi di simulazione quantistica, la usiamo per estendere la struttura dei testimoni di entanglement alle teorie di gauge del reticolo.