Flux is continually emerging on the Sun, making its way from the solar interior up into the atmosphere. Emergence occurs on small-scales in the quiet Sun where magnetic fragments emerge, interact and cancel and on large-scales in active regions where magnetic fields emerge and concentrate to form sunspots. This thesis has been concerned with the large-scale emergence process and in particular the results from previous solar flux emergence modelling endeavours. Modelling uses numerical methods to evolve a domain representing simplified layers of the Sun’s atmosphere, within which the subsurface layer contains magnetic flux. The flux is initialised such that it will rises towards the surface at the start of the simulation. Once the flux reaches the solar surface, it can only emerge into the atmosphere if a magnetic buoyancy instability occurs, after which it expands rapidly both vertically and horizontally. The aim of this thesis is to test the robustness of these general findings from simulations to date upon the seed magnetic field. More explicitly, we have used three-dimensional numerical simulations to investigate how variations in the subsurface magnetic field modify the emergence process and the resulting atmospheric field. We initially consider a simple constant twist flux tube for the seed field and vary the tube’s magnetic field strength and degree of twist. Additionally, we have examined the effects of using non-constant twist flux tubes as the seed field by choosing two different profiles for the twist that are functions of the tube’s radius. Finally, we have investigated the effects of increasing the complexity of the seed field by positioning two flux tubes below the solar surface and testing two different configurations for the tubes. In both cases, the magnetic fields of the two tubes are such that, once the tubes come into contact with each other, reconnection occurs and a combined flux system is formed. From our investigations, we conclude that the general emergence results given by previous simulations are robust. However, for constant twist tubes with low field strength and twist, the buoyancy instability fails to be launched when the tubes reach the photosphere and they remain trapped in the low atmosphere. Similarly, when the non-constant twist profile results in a low tension force throughout the tube, we find that the buoyancy instability is not initialised.

Multi-component induction resistivity and sonic measurements acquired in high-angle wells can be strongly influenced by shoulder-bed effects, anisotropy resulting from sand-shale laminations, and presence of mud-filtrate invasion. Understanding the corresponding biasing effects aids in the interpretation of resistivity and sonic measurements and subsequently leads to more accurate and reliable formation evaluation. This dissertation describes numerical simulation studies examining the effects on multi-component induction and sonic measurements in a variety of complex formation models. Subsequently, a joint inversion scheme is presented that combines resistivity and sonic measurements to estimate in situ petrophysical and elastic properties in the presence of mud-filtrate invasion. To facilitate the simulation study of multi-component induction logs, I develop a new finite-difference algorithm for the numerical simulation of frequency-domain electromagnetic borehole measurements. The algorithm~uses a coupled scalar-vector potential formulation for arbitrary three-dimensional inhomogeneous and electrically anisotropic media. Simulations show that shoulder-bed anisotropy: enhances shoulder-bed effects across sand layers; and impacts invasion sensitivities to significantly alter the assessment of invasion in terms of invaded- and virgin-zone resistivities, radial length, and front shape. For the simulation study of sonic logs, I develop a three-dimensional, finite-difference time-domain algorithm that models elastic wave propagation in a fluid-filled borehole. Simulations show that presence of anisotropy not only alters the degree of dispersion observed in flexural and Stoneley waves, but also alters their responses to invasion. In addition, presence of a dipping shoulder bed can significantly distort flexural dispersion, making it difficult to identify the low frequency asymptote corresponding to formation shear wave velocity. Lastly, I consider a radial one-dimensional model in the development of a joint resistivity and sonic inversion algorithm. This scheme simultaneously inverts array-induction apparent conductivities and sonic flexural and Stoneley dispersions for the rock's elastic moduli and water saturation in the presence of mud-filtrate invasion. Inversions are performed on numerically simulated data for a variety of models reflecting soft and hard rock formations with presence of water- and oil-based mud-filtrate invasion. Results show the estimated invasion profiles display excellent agreement with the true models, and the elastic moduli are estimated to within a few percent of the true values. / text

Scientific research in areas of physics, chemistry, and biology traditionally depends purely on experimental and theoretical methods. Recently numerical simulation is emerging as the third way of science discovery beyond the experimental and theoretical approaches. This work describes some general procedures in numerical computation, and presents several applications of numerical modeling in bioheat transfer and biomechanics, jet diffusion flame, and bio-molecular interactions of proteins in blood circulation. A three-dimensional (3D) multilayer model based on the skin physical structure is developed to investigate the transient thermal response of human skin subject to external heating. The temperature distribution of the skin is modeled by a bioheat transfer equation. Different from existing models, the current model includes water evaporation and diffusion, where the rate of water evaporation is determined based on the theory of laminar boundary layer. The time-dependent equation is discretized using the Crank-Nicolson scheme. The large sparse linear system resulted from discretizing the governing partial differential equation is solved by GMRES solver. The jet diffusion flame is simulated by fluid flow and chemical reaction. The second-order backward Euler scheme is applied for the time dependent Navier-Stokes equation. Central difference is used for diffusion terms to achieve better accuracy, and a monotonicity-preserving upwind difference is used for convective ones. The coupled nonlinear system is solved via the damped Newton's method. The Newton Jacobian matrix is formed numerically, and resulting linear system is ill-conditioned and is solved by Bi-CGSTAB with the Gauss-Seidel preconditioner. A novel convection-diffusion-reaction model is introduced to simulate fibroblast growth factor (FGF-2) binding to cell surface molecules of receptor and heparan sulfate proteoglycan and MAP kinase signaling under flow condition. The model includes three parts: the flow of media using compressible Navier-Stokes equation, the transport of FGF-2 using convection-diffusion transport equation, and the local binding and signaling by chemical kinetics. The whole model consists of a set of coupled nonlinear partial differential equations (PDEs) and a set of coupled nonlinear ordinary differential equations (ODEs). To solve the time-dependent PDE system we use second order implicit Euler method by finite volume discretization. The ODE system is stiff and is solved by an ODE solver VODE using backward differencing formulation (BDF). Findings from this study have implications with regard to regulation of heparin-binding growth factors in circulation.

The greenhouse industry is facing significant challenges such as the demand for more efficient use of energy and natural resources and prevention of detrimental environmental impacts. Reducing negative environmental impacts can be achieved by utilizing recycled and environmentally friendly products and by optimizing the use of water and root zone substrates. New and advanced root zone substrates are currently tested as substitute for natural soils in greenhouse agriculture. They can be inert non-organic materials such as rockwool and perlite. These are mined products from the earth, and are difficult to dispose after use. Natural substrates such as peat are being consumed faster than being regenerated. A new potential substrate that consists of recycled foamed glass aggregates is considered an alternative, as it is environmentally friendly, non-toxic and disposable. Experiments with foamed glass aggregates and with foamed glass aggregate/coconut coir mixtures indicated that the yield of greenhouse tomatoes was not statistically significant different (α=0.05) when compared to rockwool. To investigate the potential application of recycled glass as a root zone substrate, physical and hydraulic properties were measured. For comparison, the same measurements were completed for rockwool, coconut coir, perlite, and PET/PE fibers as well as for a mixture of coconut coir and recycled glass. The water characteristics (WC) determined for each substrate exhibited distinct air entry potentials, which provided information for irrigation scheduling, water storage and aeration for optimum plant growth conditions. Coconut coir and rockwool exhibited a unimodal shaped water retention curve, while foamed glass aggregates and perlite exhibited bimodal shaped curves. The obtained substrate properties were used as input paramaters for HYDRUS- 2D/3D model to simulate water mass balance and matric potential distributions within a typical growth container of foamed glass aggregates. The simulated matric potential and water content distributions were compared to tensiometer measurements of matric potential in the foamed glass aggregates. The simulations compared favorably with laboratory experiments measured under controlled environmental conditions.

This thesis presents numerical and analytical investigation of the geomechanics underlying longwall mining. It was tried out to study the disturbances induced by longwall mining in nearby rocks and their influence on the stability of the gates, pillars and main tunnels of longwall mines. The thesis consists of two major parts: numerical and analytical investigations. The study site is the Svea Nord coalmine, Svalbard, Norway. A novel algorithm was proposed for numerical simulation of the longwall mining process. In the proposed algorithm progressive cave-in and fracturing of the roof strata, consolidation of the cave-in materials and stress changes are simulated in detail. In order to outline the caved-in roof rocks a criterion based on maximum principal strain (in tension) was used. The critical tensile strain of roof cave-in was determined through back-calculation of the surface subsidence above a longwall panel at the mine. The results of the simulations were then used to analyse stress changes induced by longwall mining and the stability of gates. The simulations revealed that the stability of the gates and the loading to the rock bolts are closely related to the width of the chain pillars. With slender pillars, shear displacements along weak interlayers and bedding planes result in heavy loading to the rock bolts. Therefore, the locations of weakness zones should be taken into account in rock bolt design. The developed algorithm was implemented to study the loading and stability of the barrier pillar of the mine. The barrier pillars protect the main tunnels and border area of the mine from disturbances induced by longwall mining in the panels. The simulations show that the stresses in the barrier pillars fluctuate up and down during mining because of periodic cave-in events behind the longwall face. A failure zone of about 12 m exists in the wall of the barrier pillars. A large portion of the barrier pillar is still intact and is, thus, capable of protecting the border area. The results of the detailed simulations of longwall mining via the developed algorithm were, also, implemented in a large-scale numerical model. The model consists of all of the longwall panels and the border area of the mine. It is intended that the coal in the border area on the other side of the longwall panels will be mined after completion of the longwall mining. There is concern about how the longwall mining affects the stress state in the border area and how stress changes would affect future mining in the border area. A failure zone of about 20 m developed in the wall of the main tunnels on the side of the border area after all the longwall panels were mined out. The stress state in the remaining portion of the border area remains unchanged. Therefore, it will be possible to mine the border area in the future. In order to investigate the roof strata cave-in mechanism in detail a discontinuous numerical simulation of roof cave-in process was conducted by UDEC code. The block size in the roof strata and the mechanical parameters of the discontinuities were obtained through back-calculations. The back-calculations were conducted with a statistical method, Design of Experiment (DOE). Numerical simulations revealed that jointed voussoir beams formed in the roof strata before the first cave-in. Beam bending results in stress fluctuations in the roof strata. The maximum deflection of a roof stratum at the study site before the first cave-in is about 70% of the stratum thickness. The simulations and field measurements show no periodic weighting on the longwall shields in this mine. Numerical sensitivity analyses show, however, that periodic weighting may occur in strong roof strata. Roof strata with a high Young’s modulus and large joint spacing are not suitable for longwall mining. The maximum sustainable deflection of the roof strata before cave-in depends upon the horizontal in-situ stress state. It slightly increases with the in-situ horizontal stress in the stratum beams, but the horizontal stress would increase the possibility of rock-crushing in deflected roof beams. The implemented numerical method would be useful in assessment of the cavability of the roof strata and in selection of longwall shields with adequate load capacity. As shown through discontinuous numerical simulations, the roof strata above the underground opening constructed in the stratified rocks form voussoir beams. The stability of those beams is the major concern in the study of the gate stability and roof cave-in assessment in the longwall panels. Two different analytical methods were developed for cases with and without the in-situ horizontal stress acting along the beams. In the analytical model for the beams without horizontal stress a bilinear shape was assumed for the compression arch generated within the voussoir beams. The stability of the compression arch is governed by the energy method. The model requires an iterative procedure for convergence, and an algorithm was proposed for it. The analytical method was verified with numerical simulations by means of a discrete element code, UDEC. For the beams subjected to in-situ horizontal stress, the classic beam theory was employed to drive the analytical solution for it. The superposition method was used to obtain bending/deflection equations of the beam. The validity of both the assumptions and the developed method were, also, investigated by numerical simulations. The developed analytical method revealed that high Young’s modulus of a beam rock increases the stability of the beams against buckling but it causes higher stress within the compression arch which increases the probability of crushing failures in the beam abutments and midspan. In-situ horizontal stress along beams increases their stability against buckling and abutment sliding failure, but it raises the possibility of crushing failure at the abutments and the midspan.

<p>Surface energy-powered motion is useful for a variety of autonomous functions such as passive cooling and self-cleaning, where independence from external forces is highly desirable. Drop coalescence offers a convenient process to release surface energy, which can be harvested to power self-propelled fluid motion. </p><p>On superhydrophobic surfaces, out-of-plane jumping motion spontaneously results from drop coalescence. However, less than 4\% of the released surface energy is converted to useful kinetic energy giving rise to the jumping motion. Using three-dimensional interfacial flow simulations that are experimentally validated, we elucidate the mechanism of low energy conversion efficiency. The non-wetting substrate interferes with the expanding liquid bridge between the coalescing drops at a relatively late stage, forcing a small fraction of the merged drop to "bounce" back from the non-wetting substrate. The substrate breaks the symmetry of surface energy release, leading to self-propelled jumping that is perpendicular to the solid substrate. The intercepting substrate imparts a relatively small translational momentum on the overall merged drop, giving rise to a small energy conversion efficiency. </p><p>This mechanistic understanding has provided guidance on how to increase the energy conversion efficiency by changing the geometry of the intercepting solid surface, e.g. to a pillared substrate which has additional intercepting planes, or to a cylindrical fiber which interferes with the coalescence process at a much earlier stage. These topographical changes have already led to a 10-fold increase in energy conversion efficiency. The directional control of surface energy-powered motion is achieved by breaking the symmetry of oscillations induced by drop coalescence, such as by adding additional intercepting planes on pillared substrates. The work has applications ranging from self-sustained dropwise condensers, drop coalescers to ballistospore discharge in some fungi species in nature. </p><p> The ballistospore discharge process is powered by surface energy released from the coalescence between a spherical Buller's drop and an adaxial drop on the spore. The disturbance to the adaxial drop from coalescing Buller's drop results in the capillary-inertial oscillations of the liquid system. The oscillations redirect the mass and momentum transfer and yields a tensile force along the adaxial direction with negligible momentums in other directions, ensuring the preferable launching along the adaxial direction. The findings offer insights for applications of biomimicry involving self-propelled jumping with payloads which takes advantage of the high power density of the process.</p> / Dissertation

Depuis 1949, date à laquelle Bloembergen en introduisit le concept, la diffusion de spin nucléaire suscite un vif intérêt en résonance magnétique. La diffusion de spin, qui peut être définie comme le transfert de polarisation de spin induit par l’interaction dipolaire, est un mécanisme omniprésent dans les solides. Les mesures expérimentales de ce phénomène contiennent des informations sur la structure du système étudié. La diffusion de spin est cependant un problème quantique à N corps, ce qui rend sa description ab initio relativement difficile. L’objectif principal de cette thèse est d’obtenir une description quantitative et ab initio de la diffusion de spin, en modélisant de manière adéquate la dynamique à N corps sous-jacente. Tout d’abord, nous exploitons une approche existante, reposant sur l’utilisation d’une équation maître pour les polarisations, dans le cas de la diffusion de spin entre carbones permise par les protons (PDSD). Ensuite, nous introduisons une méthode permettant de simuler l’évolution temporelle d’un ensemble d’observables pour un système de spins nucléaires fortement couplés, en utilisant les corrélations de petit ordre dans l’espace de Liouville (LCL). Le modèle LCL fournit une description précise du transfert de polarisation pour les systèmes polycristallins soumis à la rotation à l’angle magique. Après avoir décrit le modèle, nous analysons plus en détail la réduction de l’espace de Liouville pour les solides, afin d’identifier les conditions dans lesquelles l’approximation LCL est valide. Enfin, nous effectuons des simulations de la diffusion de spin entre pro- tons (PSD) et entre carbones (PDSD), à partir de la structure des cristaux étudiés et sans aucun paramètre libre, et nous constatons pour des solides organiques polycristallins que leur accord avec les mesures expérimentales est excellent. / Since its introduction by Bloembergen in 1949, nuclear spin diffusion has been a topic of significant interest in magnetic resonance. Spin diffusion, which can be defined as the transfer of spin polarisation induced by the dipolar interaction, is a ubiquitous transport mechanism in solids. Experimental observations of spin diffusion contain structural information. However, the many-body nature of the problem makes it difficult to describe from first principles. The central goal of this thesis is to obtain a quantitative description of the spin diffusion phenomenon from first-principles, through the development of suitable models of the underlying many-body dynamics. To that end we first consider an extension of an existing approach that relies on a master equation to describe the polarisations, for the case of proton-driven carbon-13 spin diffusion (PDSD). Second, a novel approach is introduced for the simulation of the time evolution of selected observables for large strongly coupled nuclear spin systems, using low-order correlations in Liouville space (LCL). Following the introduction of this new simulation method, Liouville-space reduction in solids is analysed in more detail, in order to identify the conditions under which the LCL approximation is valid. Finally, using the LCL model, simulations of proton spin diffusion (PSD) and PDSD are performed, directly from crystal geometry and with no adjustable parameters, and are found to be in excellent agreement with experimental measurements for polycrystalline organic solids.

Einleitung Immer höhere Anforderungen an die Interdisziplinarität der virtuellen Produktentwicklung (VPE) erfordern qualifizierte Produktmodelle, die eine vollständige Integration und Verknüpfung aller relevanten Teilprozesse absichern. Gleichzeitig soll dabei für den Anwender das Produktverständnis, wie auch die Qualität des Produktes und des Prozesses erhöht werden. Eine Folge daraus sind kurze Innovationszyklen und eine Erhöhung der Transparenz des Prozesses. Die Anwendung numerischer Simulationsmethoden hat sich als dritter essentieller Bestandteil neben Konstruktion und Versuch in der VPE etabliert (Pährisch et al. 2012). Eine Absicherung durch virtuelle Prototypen in einer frühen Konzeptphase unterstützt dabei den Konstruktionsprozess. Ein Nachteil ist, dass die Verwendung virtueller Prototypen noch unzureichend in die übrigen Prozessschritte integriert und damit eine Sensibilisierung für eine vorausschauende Modellerzeugung noch nicht vorhanden ist. Ebenso ergab eine Studie, dass Berechnungsingenieure durchschnittlich 50% ihrer Arbeitszeit auf Datenbeschaffung verwenden müssen und nur jeweils 10% auf die Modellaufbereitung (Sendler et al. 2011). Dies liegt u. a. an der sog. Kommunikationsbarriere zwischen der Konstruktion und Simulation beschreibt. Eine Lösung dazu ist eine tiefergehende Integration dieser beiden Disziplinen in ein Produktmodell. Ein Lösungsansatz ist die Durchführung konstruktionsbegleitender Simulationen. Diese können mit in CAD-Systemen integrierten Simulationsmodulen durchgeführt werden. Die Integrationstiefe der gegebenen Verknüpfungen ist allerdings meist sehr gering. Dieser Beitrag befasst sich mit Techniken, welche einen systematischen Aufbau eines simulationsorientierten Produktmodells absichern. Umgesetzt wird dies durch die Verwendung simulationsgerechter Komponenten, Feature und Analysen. Diese unterstützen eine automatisierte Modelltransformation im CAD-Prozess, an der Schnittstelle von Konstruktion und Simulation. Damit wird die Prozesskette Konstruktion-Simulation verkürzt. Ebenso werden auch durch die Integration tiefgehender Inferenzmechanismen fortgeschrittene Simulationstechniken, wie auch die Definition und Informationsübergabe von Rand- und Lastbedingungen und weiteren Details auf höherer Instanz ermöglicht.

One-dimensional neural networks comprised of large numbers of Integrate-and-Fire neurons have been widely used to model electrical activity propagation in neural slices. Despite these efforts, the vast majority of these computational models have no analytical solutions. Consequently, my Ph.D. research focuses on a specific class of homogeneous Integrate-and-Fire neural network, for which analytical solutions of network dynamics can be derived. One crucial analytical finding is that the traveling wave acceleration quadratically depends on the instantaneous speed of the activity propagation, which means that two speed solutions exist in the activities of wave propagation: one is fast-stable and the other is slow-unstable. Furthermore, via this property, we analytically compute temporal-spatial spiking dynamics to help gain insights into the stability mechanisms of traveling wave propagation. Indeed, the analytical solutions are in perfect agreement with the numerical solutions. This analytical method also can be applied to determine the effects induced by a non-conductive gap of brain tissue and extended to more general synaptic connectivity functions, by converting the evolution equations for network dynamics into a low-dimensional system of ordinary differential equations. Building upon these results, we investigate how periodic inhomogeneities affect the dynamics of activity propagation. In particular, two types of periodic inhomogeneities are studied: alternating regions of additional fixed excitation and inhibition, and cosine form inhomogeneity. Of special interest are the conditions leading to propagation failure. With similar analytical procedures, explicit expressions for critical speeds of activity propagation are obtained under the influence of additional inhibition and excitation. However, an explicit formula for speed modulations is difficult to determine in the case of cosine form inhomogeneity. Instead of exact solutions from the system of equations, a series of speed approximations are constructed, rendering a higher accuracy with a higher order approximation of speed.

Lors de la fusion du verre, de nombreuses petites bulles de gaz sont produites. L’affinage du verre a pour objectif de faire disparaitre ces bulles par l’ajout d’espèces réactives contribuant à la résorption des bulles ou à une augmentation de leur taille. La modélisation de l’hydrodynamique et des transferts nécessite l’étude des couplages entre convection, diffusion et réaction. Une approche locale à l’échelle de la bulle (simulation directe du transfert réactif et de l’écoulement) est utilisée pour déterminer le transfert interfacial. Des mesures de la propagation de fronts d’oxydation dans la fonte ont permis de préciser certaines propriétés physiques des espèces réactives. L’ensemble de cette analyse multi-échelles a contribué à l’élaboration d’un modèle de simulation d’un nuage de bulles / Many bubbles are generated during glass production. Due to the high viscosity of molten glass, their rising velocity is extremely low. The refining step consists in adding reactive agents to improve the glass quality. Bubble release is enhanced by chemical reaction (iron and sulfate oxidation-reduction) which will favor shrinkage or growth of bubbles through interfacial mass transfer. Better understanding of bubble cloud behavior in molten glass requires studying the interplay between convection, diffusion and chemical reactions. The direct numerical simulation of the flow and reactive mass transfer provided new insights on modeling interfacial bubble gas fluxes. The acceleration factor has been determined for simple reversible reactions in order to validate the simulation tool. Different Péclet and Damkhöler numbers have been tested to map all the different regimes (diffusion, convection and reaction). Together with those simulations, we have carried out series of experiments in molten glass : propagation of oxidation fronts. At different temperatures and for various glass compositions, we have determined physical properties of reactive species. A theoretical model of reactive transport for instantaneous reactions has been proposed to interpret experimental data. The core of this multi-scale analysis contributed to elaborating an Euler- Lagrange model to simulate bubble clouds in reactive media. This model has been applied to specific processes related to glass industry and can easily be extended to any reactive bubbly flows