Appliquer un champ électrique ou un gradient de température à une solution colloïdale implique la migration des particules (soluté) en suspension. Ce déplacement n’est pas la conséquence de forces de volume comme dans le cas de la sédimentation mais de forces interfaciales agissant sur la double couche électrique présente à la surface des particules colloïdales chargées. Ces forces induisent un écoulement de surface qui à son tour engendre un champ de vitesse du fluide en 1/r³ autour des particules dans la direction opposée à leurs déplacements, où r distance au centre des particules. Dans ce travail on considère une situation différente où la suspension est confinée dans un demi-espace infini limité par une paroi rigide. Un colloïde, sous l’action d’un champ extérieur, se dépose le long de la surface rigide. Bien qu’immobile le colloïde continue de pomper le fluide environnant. Il apparaît alors un écoulement latéral le long du mur et en direction du colloïde. D’autres colloïdes insérés dans un tel écoulement subissent une force hydrodynamique de trainée à l’origine de la formation d’agrégats. De tels agrégats ont été observés aussi bien lors de déposition électrophorétique que plus récemment lors de déposition thermophorétique pour des particules micrométriques en solution aqueuse. Le champ de vitesse confiné prend une forme plus complexe que dans le cas infini : il doit satisfaire à la fois la condition limite fixée à la surface de la particule et sur le mur. Deux méthodes perturbatives, la méthode des réflexions et la méthode d’Oseen, sont utilisées pour résoudre l’équation de Stokes et trouver une solution exacte pour l’écoulement autour du colloïde confiné en puissance de e = a/h rapport du rayon de la particule sur sa distance au mur. La solution usuelle à l’ordre zéro en e donne de pauvres résultats alors que les corrections suivantes donnent de meilleurs conclusions en accord avec les récentes mesures expérimentales de potentiel hydrodynamique de paire entre colloïdes sous champ confinés le long d’un mur. / Applying a steady electric field or a constant thermal gradient to a colloidal suspension induces a finite velocity of the dispersed particles. The motion of particles is not due to a net body force like in sedimentation but to interfacial forces acting on the electric double layer at their surface. These forces involve a surface flow, which, in turn, results in a velocity field of the surrounding fluid in 1/r³ in the opposite direction of the particle displacement, with r the distance from the centre of the particle. In this work we consider a somewhat different situation, where the suspension is confined to a semi-infinite half space. The particle, under the action of the applied field, is trapped against the solid interface. Still, the creep flow remains; more precisely the particle continues to pump the fluid in the opposite direction. As a consequence there arises a lateral flow along the solid surface towards the particle. Thus others particles inserting themselves in this flow undergo drag forces and form clusters. Particles aggregation has been observed in Electrophoresis deposition and more recently in Thermophoresis deposition for micron sized polystyrene beads in aqueous solution. The total velocity field takes a form significantly more complicated than in the above mentioned unbounded cases; it must satisfy boundary conditions both at the particle surface and at the confining wall. Using the perturbative method of reflections or Oseen method based on Fourier transform we resolve the Stokes equation and find an analytic solution for the drag flow along the interface in powers of the ratio e=a/h of particle radius and wall distance. The usual solution at the zero order induces poor approximation, when following corrections in e involves better results in agreement with experimental measurements of hydrodynamic pair potential between two particles along a wall.

A novel type of precast, prestressed concrete structural element is being implemented in load-bearing systems in buildings. These structural elements combine the use of high-performance, self-consolidating concrete (HPSCC) and non-corroding carbon fibre reinforced polymer (CFRP) prestressing tendons; this produces highly optimized, slender structural elements with excellent serviceability and (presumed) extended service lives. More widely, the use of new construction techniques, innovative materials, and ground-breaking designs is increasingly commonplace in today's rapidly evolving building construction industry. However, the performance of these and other structural elements in fire is in general not well known and must be understood before these can be used with confidence in load-bearing applications where structural fire resistance is a concern. Structural fire testing has traditionally relied on the use of the standard fire resistance test (i.e. furnace test) for assuring regulatory compliance of structural elements and assemblies, and in many cases also for developing the scientific understanding of structural response to fire. Conceived in the early 1900s and fundamentally unchanged since then, the standard testing procedure is characterized by its high cost and low repeatability. A novel test method, the Heat-Transfer Rate Inducing System (H-TRIS), resulting from a mental shift associated with controlling the thermal exposure not by temperature (e.g. temperature measured by thermocouples) but rather by the time-history of incident heat flux, was conceived, developed, and validated within the scope of the work presented in this thesis. H-TRIS allows for experimental studies to be carried out with high repeatability, imposing rationally quantifiable thermal exposure, all at low economic and temporal cost. The research presented in this thesis fundamentally seeks to examine and understand the behaviour of CFRP prestressed HPSCC structural elements in fire, with emphasis placed on undesired 'premature' failure mechanisms linked to the occurrence of heat-induced concrete spalling and/or loss of bond between the pretensioned CFRP tendons and the concrete. Results from fire resistance tests presented herein show that, although compliant with testing standards, temperature distributions inside furnaces (5 to 10% deviation) appear to influence the occurrence of heat-induced concrete spalling for specimens tested simultaneously during a single test; fair comparison of test results is therefore questionable if thermal exposure variability is not explicitly considered. In line with the aims of the research presented in this thesis, H-TRIS is used to carry out multiple comprehensive studies on the occurrence of concrete spalling and bond behaviour of CFRP tendons; imposing a quantified, reproducible and rational thermal exposure. Test results led to the conclusion that a "one size fits all" approach for mitigating the risk of heat-induced concrete spalling (e.g. prescribed dose of polypropylene (PP) fibres included in fresh concrete), appears to be ineffective and inappropriate in some of the conditions examined. This work demonstrates that PP fibre cross section and individual fibre length can have an influence on the risk of spalling for the HPSCC mixes tested herein. The testing presented herein has convincingly shown, for the first time using multiple repeated tests under tightly controlled thermal and mechanical conditions, that spalling depends not only on the thermal gradients in concrete during heating but also on the size and restraint conditions of the tested specimen. Furthermore, observations from large scale standard fire resistance tests showed that loss of bond strength of pretensioned CFRP tendons occurred at a 'critical' temperature of the tendons in the heated region, irrespective of the temperature of the tendons at the prestress transfer length, in unheated overhangs. This contradicts conventional wisdom for the structural fire safety design of concrete elements pretensioned with CFRP, in which a minimum unheated overhang is generally prescribed. Overall, the research studies presented in this thesis showed that a rational and practical understanding of the behaviour of CFRP prestressed HPSCC structural elements during real fires is unlikely to be achieved only by performing additional standard fire resistance tests. Hence, H-TRIS presents an opportunity to help promote an industry-wide move away from the contemporary pass/fail and costly furnace testing environment. Recommendations for further research to achieve the above goal are provided.

La mise en œuvre de méthodes d'assimilation d'ensemble est une technique assez récente visant à simuler les erreurs d'analyse et de prévision d'un système d'assimilation de données. Cela permet d'une part d'estimer des covariances spatiales des erreurs de prévision, qui sont un ingrédient essentiel des systèmes d'assimilation de données, dans la mesure où elles permettent de filtrer et de propager spatialement l'information observée. La dépendance de ces covariances d'erreur à la situation météorologique devient ainsi accessible avec ces techniques d'ensemble. D'autre part, l'assimilation d'ensemble est également une méthode de plus en plus utilisée pour fournir des perturbations initiales aux systèmes de prévision d'ensemble. Une telle approche peut être mise en place non seulement dans un système modélisant l'atmosphère sur l'ensemble du globe, mais aussi dans un système régional à aire limitée, en utilisant dans ce cas des conditions limites latérales appropriées. Le sujet de thèse proposé consiste à examiner certaines propriétés de sensibilité de ces techniques d'assimilation d'ensemble dans ces deux types de contextes (à savoir global et régional, respectivement). Il s'agit premièrement d'étudier la sensibilité d'un système global d'assimilation d'ensemble à son initialisation. Cela sera mené en comparant une technique d'initialisation "à froid" (basée sur des perturbations initiales nulles) avec une méthode basée sur des perturbations initiales tirées d'un modèle de covariance. Dans une deuxième partie, la sensibilité d'une assimilation d'ensemble régionale aux conditions limites latérales sera examinée. Dans cette perspective, une comparaison entre différentes techniques de production des perturbations latérales sera réalisée. Il s'agit notamment de comparer les approches basées sur des perturbations latérales qui sont soit nulles, soit tirées d'un ensemble global, ou encore produites à l'aide d'un modèle de covariance. Ces études de sensibilité seront menées d'une part en utilisant des expérimentations avec les systèmes global Arpege et régional Aladin. Ce travail s'appuiera d'autre part sur une formalisation des équations qui gouvernent l'évolution des perturbations au sein d'une assimilation d'ensemble. Ces études devraient permettre de documenter les propriétés de ces assimilations d'ensemble, et de définir des stratégies de mise en œuvre en grandeur réelle pour l'assimilation de données ainsi qu'éventuellement pour la prévision d'ensemble. / The implementation of ensemble assimilation methods is a fairly recent technique used to simulate the analysis and forecast errors within a data assimilation system. On the one hand, this allows to estimate the spatial covariances of forecast errors, which are an essential component in data assimilation systems, insofar as they are used to filter and disseminate spatially the observed information. The dependence of such error covariances to the weather situation becomes accessible with these ensemble techniques. On the other hand, the ensemble assimilation is a method increasingly used to provide initial perturbations to ensemble prediction systems. Such approach may be implemented not only in a system modeling the atmosphere throughout the globe, but also in a regional system with limited area using suitable lateral boundary conditions. The proposed thesis consists on examining some sensitivity properties of these ensemble assimilation techniques in both contexts (global and regional, respectively). In the first part, the sensitivity of a global ensemble assimilation system to its initialization will be examined. This will be conducted by comparing a "cold" initialization technique (initial perturbations equal to zero) with a method based on initial perturbations drawn from a covariance model. In the second part, the sensitivity of a regional ensemble assimilation to lateral boundary conditions will be considered. In this context, a comparison between different techniques producing lateral boundaries will be achieved. It involves comparing approaches using lateral boundaries which are equal to zero or drawn from a global ensemble, or generated using a covariance model. These sensitivity studies will be conducted using experiments using the global and regional modeling systems, Arpège and Aladin respectively. Furthermore, this work will be based on a formalization of the equations governing the evolution of perturbations in an ensemble assimilation. These studies should help to document the ensemble assimilation properties, and develop strategies for implementing in real scale for data assimilation and possibly for ensemble prediction system.

In this thesis a multiscale mixed method aiming at the accurate approximation of velocity and pressure fields in heterogeneous porous media is proposed, the Multiscale Robin Coupled Method (MRCM). The procedure is based on a new domain decomposition method in which the local problems are subject to Robin boundary conditions. The method allows for the independent definition of interface spaces for pressure and flux over the skeleton of the decomposition that can be chosen with great flexibility to accommodate local features of the underlying permeability fields. Numerical simulations are presented aiming at illustrating several features of the new method. We illustrate the possibility to recover the multiscale solution of two wellknown methods of the literature, namely, the Multiscale Mortar Mixed Finite Element Method (MMMFEM) and the Multiscale Hybrid-Mixed (MHM) Finite Element Method by suitable choices of the parameter b in the Robin interface conditions. Results show that the accuracy of the MRCM depends on the choice of this algorithmic parameter as well as on the choice of the interface spaces. An extensive numerical assessment of the MRCM is conduct with two types of interface spaces, the usual piecewise polynomial spaces and the informed spaces, the latter obtained from sets of snapshots by dimensionality reduction. Different distributions of the unknowns between pressure and flux are explored. The results show that b, suitably nondimensionalized, can be fixed to unity to avoid any indeterminacy in the method. Further, with both types of spaces, it is observed that a balanced distribution of the interface unknowns between pressure and flux renders the MRCM quite attractive both in accuracy and in computational cost, competitive with other multiscale methods from the literature. The MRCM solutions are in general only global conservative. Two postprocessing procedures are proposed to recover local conservation of the multiscale velocity fields. We investigate the applicability of such methods in highly heterogeneous permeability fields in modeling the contaminant transport in the subsurface. These methods are compared to a standard procedure. Results indicate that the proposed methods have the potential to produce more accurate results than the standard method with similar or reduced computational cost. / Nesta tese é proposto um método misto multiescala visando a aproximação precisa de campos de velocidade e pressão em meios porosos altamente heterogêneos, o método Multiscale Robin Coupled Method (MRCM). Este procedimento é baseado em um novo método de decomposição de domínio no qual os problemas locais são definidos com condições de contorno de Robin. O método permite a definição independente de espaços de interface para pressão e fluxo sobre o esqueleto da decomposição que pode ser escolhida com grande flexibilidade para acomodar características locais dos campos de permeabilidade subjacentes. Simulações numéricas são apresentadas visando ilustrar várias características do novo método. Ilustramos a possibilidade de recuperar a solução multiescala de dois métodos bem conhecidos da literatura, a saber, o Multiscale Mortar Mixed Finite Element Method (MMMFEM) e o Multiscale Hybrid-Mixed (MHM) Finite Element Method por escolhas adequadas do parâmetro b nas condições da interface de Robin. Os resultados mostram que a precisão do MRCM depende da escolha deste parâmetro algorítmico, bem como da escolha dos espaços de interface. Uma extensa avaliação numérica do MRCM é conduzida com dois tipos de espaços de interface, os usuais espaços polinomiais por partes e os espaços informados, este último obtidos a partir da redução de dimensionalidade de conjutos de espaços de snapshots. Diferentes distribuições de incógnitas entre pressão e fluxo são exploradas. Os resultados mostram que b, adequadamente adimensionalizado, pode ser fixado em unidade para evitar qualquer indeterminação no método. Além disso, com ambos os tipos de espaços, observa-se que uma distribuição equilibrada de incógnita entre pressão e fluxo nas interfaces torna o MRCM bastante atraente tanto em precisão quanto em custo computacional, competitivo com outros métodos multiescala da literatura. As soluções MRCM são, em geral, apenas globalmente conservativas. Dois procedimentos de pós-processamento são propostos para recuperar a conservação local dos campos de velocidade multiescala. Investigamos a aplicabilidade de tais métodos em campos de permeabilidade altamente heterogêneos na modelagem do transporte de contaminantes na subsuperfície. Esses métodos são comparados a um procedimento padrão da literatura. Os resultados indicam que os métodos propostos têm o potencial de produzir resultados mais precisos do que o método padrão com custo computacional similar ou reduzido.

<p>The MIUU mesoscale model was further developed, in order to include information on large-scale atmospheric fields from global or regional atmospheric climate- and weather-prediction models. For this purpose, a new lateral boundary condition was developed and implemented into the model. The new lateral boundary condition is a combination of two existing conditions, namely the flow relaxation scheme and the tendency modification scheme.</p><p>Tests indicated that an optimum lateral boundary configuration would be obtained with moderate to strong flow relaxation at higher levels, small flow relaxation at lower levels (within the atmospheric boundary layer), upstream advection at the outermost 4 grid points, and 6% horizontal grid stretching starting at a substantial distance from the lateral boundaries. The flow relaxation coefficients should be specified carefully, in order to minimize the reflection of all kinds of waves at the lateral boundaries.</p><p>The summer thermal low in the mean-sea-level pressure field over North America is traditionally analyzed over the northern end of the Gulf of California. The position of this low is influenced by the application of the so-called plateau correction in obtaining mean-sea-level pressure values from highly elevated stations in North America. A model study indicated that the low should be located approximately 450 km to the north and somewhat to the east of the above location. </p><p>A statistical comparison of model results from two mesoscale models against upper-air and surface measurements from several sites was carried out. Statistical methods, however, give only an insufficient picture of overall model performance. A comparison between predicted and measured tracer concentrations could be used to better evaluate the overall performance of different models.</p><p>Sound propagation in the atmosphere was predicted in a mountain valley using a mesoscale atmospheric model together with a sound propagation model. This suggests that forecasts of sound propagation should be possible in future.</p>

The MIUU mesoscale model was further developed, in order to include information on large-scale atmospheric fields from global or regional atmospheric climate- and weather-prediction models. For this purpose, a new lateral boundary condition was developed and implemented into the model. The new lateral boundary condition is a combination of two existing conditions, namely the flow relaxation scheme and the tendency modification scheme. Tests indicated that an optimum lateral boundary configuration would be obtained with moderate to strong flow relaxation at higher levels, small flow relaxation at lower levels (within the atmospheric boundary layer), upstream advection at the outermost 4 grid points, and 6% horizontal grid stretching starting at a substantial distance from the lateral boundaries. The flow relaxation coefficients should be specified carefully, in order to minimize the reflection of all kinds of waves at the lateral boundaries. The summer thermal low in the mean-sea-level pressure field over North America is traditionally analyzed over the northern end of the Gulf of California. The position of this low is influenced by the application of the so-called plateau correction in obtaining mean-sea-level pressure values from highly elevated stations in North America. A model study indicated that the low should be located approximately 450 km to the north and somewhat to the east of the above location. A statistical comparison of model results from two mesoscale models against upper-air and surface measurements from several sites was carried out. Statistical methods, however, give only an insufficient picture of overall model performance. A comparison between predicted and measured tracer concentrations could be used to better evaluate the overall performance of different models. Sound propagation in the atmosphere was predicted in a mountain valley using a mesoscale atmospheric model together with a sound propagation model. This suggests that forecasts of sound propagation should be possible in future.

This thesis describes the results of experimental work on polyelectrolyte gels and their interaction with oppositely charged surfactants, and presents two new algorithms applicable to the simulation of colloid and polymer systems. The model systems investigated were crosslinked poly(acrylate) (PA) and poly(styrene sulphonate) (PSS), and the surfactant was dodecyl trimethylammonium bromide (DoTAB). Pure gel materials were studied using dynamic light scattering. It was shown that the diffusion coefficient (D) increases with increasing degree of swelling and the concentration dependence is larger than predicted by scaling arguments. For gels at swelling equilibrium D increases with increasing degree of crosslinking. In subsequent studies on gel particles in DoTAB solution, Raman spectra were recorded at different positions in the gel. For both types of gels two distinct regions could be observed. For PA the surfactant is localised in the outer phase without any surfactant in the core, while for PSS the surfactant was distributed such that it had the same concentration relative to the polymer throughout the gel. In a second experiment, the kinetics for the deswelling of microscopic PSS particles in DoTAB solution was studied. It was found that the final volume varied linearly with the DoTAB concentration, and the rate of volume decrease could be fitted to a single exponential indicating stagnant layer diffusion to be the rate limiting process for the deswelling of the PSS particles. In the second part, I first describe an algorithm showing an efficient way to detect percolation in simulations, with periodic boundary conditions, using recursion. Spherical boundary conditions is an alternative to periodic boundary conditions for systems with long-range interactions. In the last part, the possibility to use the surface of a hypersphere in four dimensions for simulations of polymer systems is investigated, and algorithms for Monte Carlo and Brownian dynamics simulations are described.

An artificial neural network (ANN) method was developed for solving boundary value problems (BVPs) on an arbitrary irregular domain in such a manner that all Dirichlet and/or Neuman boundary conditions (BCs) are automatically satisfied. Exact satisfaction of BCs is not available with traditional numerical solution techniques such as the finite element method (FEM). The ANN is trained by reducing error in the given differential equation (DE) at certain points within the domain. Selection of these points is significantly simpler than the often difficult definition of meshes for the FEM. The approximate solution is continuous and differentiable, and can be evaluated at any location in the domain independent of the set of points used for training. The continuous solution eliminates interpolation required of discrete solutions produced by the FEM. Reducing error in the DE at a particular location in the domain does not necessarily imply improvement in the approximate solution there. A theorem was developed, proving that the solution will improve whenever error in the DE is reduced at all locations in the domain during training. The actual training of ANNs reasonably approximates the assumptions required by the proof. This dissertation offers a significant contribution to the field by developing a method for solving BVPs where all BCs are automatically satisfied. It had already been established in the literature that such automatic BC satisfaction is beneficial when solving problems on rectangular domains, but this dissertation presents the first method applying the technique to irregular domain shapes. This was accomplished by developing an innovative length factor. Length factors ensure BC satisfaction extrapolate the values at Dirichlet boundaries into the domain, providing a solid starting point for ANN training to begin. The resulting method has been successful at solving even nonlinear and non-homogenous BVPs to accuracy sufficient for typical engineering applications.

In this thesis, the boundary errors are defined for the NFM to explore the convergence rates, and the condition numbers are derived for simple cases to explore numerical stability. The optimal convergence (or exponential) rates are discovered numerically. This thesis is also devoted to seek better choice of locations for the field nodes of the FS expansions. It is found that the location of field nodes Q does not affect much on convergence rates, but do have influence on stability. Let £_ denote the distance of Q to ∂S. The larger £_ is chosen, the worse the instability of the NFM occurs. As a result, £_ = 0 (i.e., Q ∈ ∂S) is the best for stability. However, when £_ > 0, the errors are slightly smaller. Therefore, small £_ is a favorable choice for both high accuracy and good stability. This new discovery enhances the proper application of the NFM. However, even for the Dirichlet problem of Laplace¡¦s equation, when the logarithmic capacity (transfinite diameter) C_£F = 1, the solutions may not exist, or not unique if existing, to cause a singularity of the discrete algebraic equations. The problem with C_£F = 1 in the BEM is called the degenerate scale problems. The original explicit algebraic equations do not satisfy the conservative law, and may fall into the degenerate scale problem discussed in Chen et al. [15, 14, 16], Christiansen [35] and Tomlinson [42]. An analysis is explored in this thesis for the degenerate scale problem of the NFM. In this thesis, the new conservative schemes are derived, where an equation between two unknown variables must satisfy, so that one of them is removed from the unknowns, to yield the conservative schemes. The conservative schemes always bypasses the degenerate scale problem; but it causes a severe instability. To restore the good stability, the overdetermined system and truncated singular value decomposition (TSVD) are proposed. Moreover, the overdetermined system is more advantageous due to simpler algorithms and the slightly better performance in error and stability. More importantly, such numerical techniques can also be used, to deal with the degenerate scale problems of the original NFM in [15, 14, 16]. For the boundary integral equation (BIE) of the first kind, the trigonometric functions are used in Arnold [3], and error analysis is made for infinite smooth solutions, to derive the exponential convergence rates. In Cheng¡¦s Ph. Dissertation [18], for BIE of the first kind the source nodes are located outside of the solution domain, the linear combination of fundamental solutions are used, error analysis is made only for circular domains. So far it seems to exist no error analysis for the new NFM of Chen, which is one of the goal of this thesis. First, the solution of the NFM is equivalent to that of the Galerkin method involving the trapezoidal rule, and the renovated analysis can be found from the finite element theory. In this thesis, the error boundary are derived for the Dirichlet, the Neumann problems and its mixed types. For certain regularity of the solutions, the optimal convergence rates are derived under certain circumstances. Numerical experiments are carried out, to support the error made.

The coupled and uncoupled consolidation theories for saturated-unsaturated soils have been discussed. A new method for constructing the constitutive surfaces for saturated-unsaturated soils has been proposed. The consolidation processes for saturated-unsaturated soils have been explained by thermodynamic analogue. One dimensional consolidation theory for saturated-unsaturated soils is presented and a new method is proposed to calculate the immediate settlement, total settlement and the time history of the consolidation settlement manually in the same way as what we have done for saturated soils with a higher accuracy. It makes the consolidation theory of unsaturated soils as applicable as that of saturated soils. This method can also be used to perform uncoupled two or three dimensional consolidation calculation for both expansive soils and collapsible soils. From the analysis, the equivalent effective stress and excessive pore water pressure can be easily calculated. At the same time, the physical meanings for the parameters in the constitutive laws for saturated-unsaturated are illustrated. A new set of the differential equations for the coupled two or three dimensional consolidation of saturated-unsaturated soils are proposed, together with the corresponding method to solve the differential equations. It is also proved numerically and analytically that during the consolidation process the Mandel-Cryer effect exists for unsaturated expansive soils and there is a ??reverse?? Mandel-Cryer effect for unsaturated collapsible soils. A new method is proposed to estimate the volume change of expansive soils. A complete system is proposed for the numerical simulation of residential buildings on expansive soils. The strength of this method lies in its use of simple and readily available historic weather data such as daily temperature, solar radiation, relative humidity, wind speed and rainfall as input. Accurate three dimensional predictions are obtained by integrating a number of different analytical and numerical techniques: different simulation methods for different boundary conditions such as tree, grass, and bare soils, coupled hydro-mechanical stress analysis to describe deformation of saturated-unsaturated soils, jointed elements simulation of soil-structure interaction, analysis of structure stress moment by general shell elements, and to assess structural damage by the smeared cracking model. The real-time and dynamic simulation results are consistent with filed measurements.