Heating the Early Universe : Numerical Methods and Their Analysis

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Numerical analysis of the modal coupling at low resonances in a Colombian Andean Bandola in C using the finite element method

The work presented in this thesis is concerned with the dynamical behavior of a CBandola's acoustical box at low resonances -- Two models consisting of two and three coupled oscillators are proposed in order to analyse the response at the first two and three resonances, respectively -- These models describe the first resonances in a bandola as a combination of the lowest modes of vibration of enclosed air, top and back plates -- Physically, the coupling between these elements is caused by the fluid-structure interaction that gives rise to coupled modes of vibration for the assembled resonance box -- In this sense, the coupling in the models is expressed in terms of the ratio of effective areas and masses of the elements which is an useful parameter to control the coupling -- Numerical models are developed for the analysis of modal coupling which is performed using the Finite Element Method -- First, it is analysed the modal behavior of separate elements: enclosed air, top plate and back plate -- This step is important to identify participating modes in the coupling -- Then, a numerical model of the resonance box is used to compute the coupled modes -- The computation of normal modes of vibration was executed in the frequency range of 0-800Hz -- Although the introduced models of coupled oscillators only predict maximum the first three resonances, they also allow to study qualitatively the coupling between the rest of the computed modes in the range -- Considering that dynamic response of a structure can be described in terms of the modal parameters, this work represents, in a good approach, the basic behavior of a CBandola, although experimental measurements are suggested as further work to verify the obtained results and get more information about some characteristics of the coupled modes, for instance, the phase of vibration of the air mode and the radiation e ciency

Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Geotechnical Data and Numerical Analysis of Edifice Collapse and Related Hazards at Pacaya Volcano, Guatemala

The continual eruptive activity, occurrence of an ancestral catastrophic collapse, and inherent geologic features of Pacaya volcano (Guatemala) demands an evaluation of potential collapse hazards. This thesis merges techniques in the field and laboratory for a better rock mass characterization of volcanic slopes and slope stability evaluation. New field geological, structural, rock mechanical and geotechnical data on Pacaya is reported and is integrated with laboratory tests to better define the physical-mechanical rock mass properties. Additionally, this data is used in numerical models for the quantitative evaluation of lateral instability of large sector collapses and shallow landslides. Regional tectonics and local structures indicate that the local stress regime is transtensional, with an ENE-WSW sigma 3 stress component. Aligned features trending NNW-SSE can be considered as an expression of this weakness zone that favors magma upwelling to the surface. Numerical modeling suggests that a large-scale collapse could be triggered by reasonable ranges of magma pressure (greater than or equal to 7.7 MPa if constant along a central dyke) and seismic acceleration (greater than or equal to 460 cm/s2), and that a layer of pyroclastic deposits beneath the edifice could have been a factor which controlled the ancestral collapse. Finally, the formation of shear cracks within zones of maximum shear strain could provide conduits for lateral flow, which would account for long lava flows erupted at lower elevations.

Experimental and Numerical Analysis of Gas Flows in Microchannels and Micro Heat Exchanger

Due to increased interest in miniaturization, great attention has been given in the recent decade to the micro heat exchanging systems. Literature survey suggests that there is still a limited understanding of gas flows in micro heat exchanging systems. The aim of the current thesis is to further the understanding of fluid flow and heat transfer phenomenon inside such geometries when a compressible working fluid is utilized. A combined experimental and numerical approach has been utilized in order to overcome the lack of employable sensors for micro dimensional channels. After conducting a detailed comparison between various data reduction methodologies employed in the literature, the best suited methodology for gas microflow experimentalists is proposed. A transitional turbulence model is extensively validated against the experimental results of the microtubes and microchannels under adiabatic wall conditions. Heat transfer analysis of single microtubes showed that when the compressible working fluid is used, Nusselt number results are in partial disagreement with the conventional theory at highly turbulent flow regime for microtubes having a hydraulic diameter less than 250 microns. Experimental and numerical analysis on a prototype double layer microchannel heat exchanger showed that compressibility is detrimental to the thermal performance. It has been found that compressibility effects for micro heat exchangers are significant when the average Mach number at the outlet of the microchannel is greater than 0.1 compared to the adiabatic limit of 0.3. Lastly, to avoid a staggering amount of the computational power needed to simulate the micro heat exchanging systems with hundreds of microchannels, a reduced order model based on the porous medium has been developed that considers the compressibility of the gas inside microchannels. The validation of the proposed model against experimental results of average thermal effectiveness and the pressure loss showed an excellent match between the two.

Microbiological indicators for the assessment of performance in the hazard analysis and critical control points (HACCP) system in meat lasagna production

The HACCP system is being increasingly used to ensure food safety. This study investigated the validation of the control measures technique in order to establish performance indicators of this HACCP system in the manufacturing process of Lasagna Bolognese (meat lasagna). Samples were collected along the manufacturing process as a whole, before and after the CCPs. The following microorganism s indicator (MIs) was assessed: total mesophile and faecal coliform counts. The same MIs were analyzed in the final product, as well as, the microbiological standards required by the current legislation. A significant reduction in the total mesophile count was observed after cooking (p < 0.001). After storage, there was a numerical, however non-significant change in the MI count. Faecal coliform counts were also significantly reduced (p < 0.001) after cooking. We were able to demonstrate that the HACCP system allowed us to meet the standards set by both, the company and the Brazilian regulations, proved by the reduction in the established indicators

Finite Element Analysis and Optimization of a Single-Axis Acoustic Levitator

A finite element analysis and a parametric optimization of single-axis acoustic levitators are presented. The finite element method is used to simulate a levitator consisting of a Langevin ultrasonic transducer with a plane radiating surface and a plane reflector. The transducer electrical impedance, the transducer face displacement, and the acoustic radiation potential that acts on small spheres are determined by the finite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a fiber-optic vibration sensor. The numerical acoustic radiation potential is verified experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reflector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reflector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W.

Failure assessments of corroded pipelines with axial defects using stress-based criteria: Numerical studies and verification analyses

Conventional procedures used to assess the integrity of corroded piping systems with axial defects generally employ simplified failure criteria based upon a plastic collapse failure mechanism incorporating the tensile properties of the pipe material. These methods establish acceptance criteria for defects based on limited experimental data for low strength structural steels which do not necessarily address specific requirements for the high grade steels currently used. For these cases, failure assessments may be overly conservative or provide significant scatter in their predictions, which lead to unnecessary repair or replacement of in-service pipelines. Motivated by these observations, this study examines the applicability of a stress-based criterion based upon plastic instability analysis to predict the failure pressure of corroded pipelines with axial defects. A central focus is to gain additional insight into effects of defect geometry and material properties on the attainment of a local limit load to support the development of stress-based burst strength criteria. The work provides an extensive body of results which lend further support to adopt failure criteria for corroded pipelines based upon ligament instability analyses. A verification study conducted on burst testing of large-diameter pipe specimens with different defect length shows the effectiveness of a stress-based criterion using local ligament instability in burst pressure predictions, even though the adopted burst criterion exhibits a potential dependence on defect geometry and possibly on material`s strain hardening capacity. Overall, the results presented here suggests that use of stress-based criteria based upon plastic instability analysis of the defect ligament is a valid engineering tool for integrity assessments of pipelines with axial corroded defects. (C) 2008 Elsevier Ltd. All rights reserved.

Data grid for the management, reconstruction, analysis and visualisation of archaeological data

In 2007 Associate Professor Jay Hall retires from the University of Queensland after more than 30 years of service to the Australian archaeological community. Celebrated as a gifted teacher and a pioneer of Queensland archaeology, Jay leaves a rich legacy of scholarship and achievement across a wide range of archaeological endeavours. An Archæological Life brings together past and present students, colleagues and friends to celebrate Jay’s contributions, influences and interests.

Analysis and simulation of a-Si Ha-SiC HPINIP structures for color image detection

It is presented in this paper a study on the photo-electronic properties of multi layer a-Si: H/a-SiC: H p-i-n-i-p structures. This study is aimed to give an insight into the internal electrical characteristics of such a structure in thermal equilibrium, under applied Was and under different illumination condition. Taking advantage of this insight it is possible to establish a relation among-the electrical behavior of the structure the structure geometry (i.e. thickness of the light absorbing intrinsic layers and of the internal n-layer) and the composition of the layers (i.e. optical bandgap controlled through percentage of carbon dilution in the a-Si1-xCx: H layers). Showing an optical gain for low incident light power controllable by means of externally applied bias or structure composition, these structures are quite attractive for photo-sensing device applications, like color sensors and large area color image detector. An analysis based on numerical ASCA simulations is presented for describing the behavior of different configurations of the device and compared with experimental measurements (spectral response and current-voltage characteristic). (c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Moisture recycling in the Iberian Peninsula from a regional climate simulation: spatiotemporal analysis and impact on the precipitation regime

The contribution of the evapotranspiration from a certain region to the precipitation over the same area is referred to as water recycling. In this paper, we explore the spatiotemporal links between the recycling mechanism and the Iberian rainfall regime. We use a 9 km resolution Weather Research and Forecasting simulation of 18 years (1990-2007) to compute local and regional recycling ratios over Iberia, at the monthly scale, through both an analytical and a numerical recycling model. In contrast to coastal areas, the interior of Iberia experiences a relative maximum of precipitation in spring, suggesting a prominent role of land-atmosphere interactions on the inland precipitation regime during this period of the year. Local recycling ratios are the highest in spring and early summer, coinciding with those areas where this spring peak of rainfall represents the absolute maximum in the annual cycle. This confirms that recycling processes are crucial to explain the Iberian spring precipitation, particularly over the eastern and northeastern sectors. Average monthly recycling values range from 0.04 in December to 0.14 in June according to the numerical model and from 0.03 in December to 0.07 in May according to the analytical procedure. Our analysis shows that the highest values of recycling are limited by the coexistence of two necessary mechanisms: (1) the availability of sufficient soil moisture and (2) the occurrence of appropriate synoptic configurations favoring the development of convective regimes. The analyzed surplus of rainfall in spring has a critical impact on agriculture over large semiarid regions of the interior of Iberia.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.