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One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking. Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis. In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding. In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters. The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents. In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases. The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid. When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials). We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory. In the final chapter, we summarize the problems studied in this thesis and point out some future directions.

Le besoin pressant de substitution du plomb dans les alliages de soudure a conduit à une introduction très rapide de nouveaux alliages sans plomb dont la connaissance en termes de comportement n'est pas assez approfondie. En effet, d'autres problématiques sont apparues (l'augmentation de la température du procédé de soudage, trop grand choix disponible dans les alliages alternatifs) alors que les problèmes relatifs aux alliages actuels sont restés sans réponse (le changement incessant de la microstructure des alliages de soudure, la méthodologie empirique prédisant la durée de vie). Tous les paramètres cités ci-dessus modifient la stabilité et la fiabilité des performances spécifiques de l'alliage de soudure et par conséquence, de tout le module électronique.De plus, avec la miniaturisation de l'électronique et les conditions d'environnement de plus en plus sévères, ces obstacles deviennent critiques et les solutions actuelles ne sont plus compatibles. Les demandes de ce marché deviennent donc de plus en plus strictes en termes de prédiction de durée de vie et de contrôle de fiabilité.L'objectif de ce projet est de comprendre et de concevoir une nouvelle formulation d'alliage sans plomb afin de développer une alternative à l'alliage plombé haute température et un alliage pour les applications haute fiabilité et en accord avec les directives gouvernementales. Des approches expérimentales avancées comme la nano-indentation, le suivi de l'évolution de la microstructure par SEM et par EDS mapping, l'étude des effets du vieillissement thermique sur la croissance de la taille des grains avec de la lumière croisée polarisée de microscopie optique etc seront utilisées pour développer un alliage sans plomb qui convienne aux exigences des applications automobile et pipeline / The urgent need for removing lead from solder alloys led to the very fast introduction of lead-free solder alloys without a deep knowledge of their behaviour. As a consequence, additional issues raised (increased thermally induced problems during soldering process, a too wide range of possible available alternative alloy formulations), while problems related to current solder alloys remained unsolved (the constant change of the solder alloy microstructure, empirical predicting lifetime methodology). All the above mentioned issues alter stability and reliability of the application specific performances of the solder alloy, and subsequently of the whole electronic module. These problems become critical and are no longer compatible, as the market goes towards miniaturization and harsh environment conditions. These market trends now require stricter life time prediction and reliability control. Objective of this project is to understand and design a novel lead-free solder formulation to develop a potential alternative to lead-based high temperature melting point solder for high reliability requirements and in accordance with governmental directives. An advanced experimental approach like nanoindentation, microstructure evolution with SEM and EDS mapping, thermal aging effects on continuous grain size growth with cross polarized light of optical microscopy etc. would be implemented to develop doped-SAC lead-free solders for the best-fit to requirements in automotives and pipelines applications

<p>Cemented carbides (WC-Co) are powder metallurgical products produced by liquid phase sintering. WC-Co is widely used for making a large variety of cutting tools, such as drills and inserts turning applications, due to its great mechanical properties, where the hardness of the WC grains is combined with the toughness of the of the Co binder. WC grain size and grain size distribution are the two most important factors to control the mechanical properties of the products.</p><p>This study examined the grain growth dependence of different milling and sintering times. The resulting grain size and grain size distribution were measured using image analysis on scanning electron microscopy images (SEM) and by using electron backscatter diffraction (EBSD). In addition, the correlation between hardness and coercivity, the most common indirect measures of grain size, and different methods of calculating average grain radius were investigated. An attempt was also made to study the contribution of defects to grain growth. This work also includes an overview of various grain growth equations and a numerical implementation of these.</p><p>Experimental results show that for shorter sintering times, powders milled for short times (15 min and 1 h) have larger average grain radii. There is a crossover after 6 to 8 h of sintering, where the powders milled for a long time (40 h and 200 h), have larger average radii. The measured hardness values correlate well with the average grain radius calculated from the grain surface area and the coercivity correlates with the established equations. EBSD measurements detected boundaries that could not be detected by image analysis, and that were not Sigma 2 boundaries. It is likely that these boundaries are either low energy boundaries or boundaries between grains that are very closely oriented. Comparing heat-treated powder with the untreated resulted in a lower average grain size after sintering for the heat-treated powder. None of the growth equations investigated in this work could fully describe the experimental grain growth.</p><p>Through increased understanding of the grain growth, the growth can be controlled and the end product can have the desired tool properties. The occurrence of abnormal grains in cutting tool applications can cause breakage, which is especially important to avoid in applications such as PCB drills. A correlation between hardness and grain size provides further means for cheap and fast indirect measures of the grain size in production.</p> / <p>Hårdmetall är ett pulvermetallurgiskt material som tillverkas genom smältfassintring och som kännetecknas av hårdhet, styvhet och god slitstyrka. Volframkarbidens (WC) kornstorlek och kornstorleksfördelning är två viktiga faktorer för att kontrollera de mekaniska egenskaperna i hårdmetall.</p><p>I den här studien har korntillväxtens beroende på malning och sintring undersökts. WC-Co maldes och sintrades fyra olika tider och kornstorleksfördelningen mättes med bildanalys på svepelektronmikroskopbilder samt med ``electron backscatter diffraction'' (EBSD). I arbetet har även korrelationen mellan hårdhet, koercivitet och olika sätt att beräkna medelkornstorleken undersökts. Ett försök har också genomförts för att studera hur defekterna i det malda pulvret påverkar korntillväxten. I arbetet har även ett flertal olika tillväxtekvationer modellerats numeriskt och för och nackdelar med de olika tillväxtekvationerna har vägts mot varandra.</p><p>En lång maltid (40 h och 200 h) visade sig ge liten kornstorlek för sintring kortare än 6 h, men för sintringar längre än 8 h gav istället kort malning (15 min och 1 h) den mindre kornstorleken. Det visade sig att uppmätt hårdhet korrelerar bäst med den medelkornstorleksradie som räknats fram från kornytan. I EBSD mätningarna kunde man observera ett flertal korngränser, utöver Sigma 2 korngränser, som inte hade detekterats med bildanalys. Värmebehandlingen av det malda pulvret minskade korntillväxten under efterföljande sintring. Ingen av de undersökta tillväxtekvationerna kunde beskriva de experimentella resultaten fullt ut.</p><p>Genom ökad förståelse för korntillväxt kan man kontrollera tillväxten och slutprodukten kan få önskade egenskaper. Förekomsten av abnorm korntillväxt i skärverktyg i hårdmetall är en av de vanligaste kritiska defekterna och det är speciellt viktigt är undvika korntillväxt i tillverkning av små verktyg, som till exempel kretskortsborrar. Hårdhet och koercivitet är de vanligaste indirekta mätmetoderna för att mäta kornstorlek i produktion. En bra korrelation mellan kornstorlek och indirekta mätmetoder ger utökade verktyg för snabba och billiga mätningar.</p>

Sn-Pb solder has long been used in the Electronics industry. But, due to its toxic nature and environmental effects, certain restrictions are made on its use and therefore many researchers are looking to replace it. Sn-3.0Ag-0.5Cu (SAC) solders are suggested as lead-free replacements but their coarse microstructure and formation of hard and brittle Inter-Metallic Compounds (IMCs) like Ag₃Sn and Cu₆Sn₅ have limited their use in high temperature applications. In this research work, RE elements, mostly lanthanum (La), are used as potential additives to SAC alloys. They reduce the surface free energy, refine the grain size and improve the mechanical and wetting properties of SAC alloys. An extensive experimental work has been performed on the microstructure evolution, bulk mechanical properties, individual phase (matrix and IMCs) mechanical properties, creep behavior and wettability performance of the SAC and SAC-La alloys, with different (La) doping. SEM and EDS have been used to follow the continuous growth of the IMCs at 150°C and 200°C and thus provide a quantitative measure in terms of their size, spacing and volume fraction. Grain size is measured at regular intervals starting from 10 hours up to 200 hours of thermal aging using Optical Microscope with cross polarized light. Bulk mechanical properties are evaluated using tensile tests at low strain rates. Individual phase mechanical properties like Young's modulus, hardness, strain rate sensitivity index and bulge effects are characterized with nanoindentation from 100 µN up to 5000 µN loadings at different temperatures of 25°C, 45°C, 65°C and 85°C. Creep experiments are performed at elevated temperatures with good fitting of Dorn creep and back-stress creep models. Activation energy measurements are made at 40°C, 80°C and 120°C. Wettability testing on copper substrates is used for surface tension, wetting force and contact angle measurements of SAC and SAC-La doped alloys at 250°C and 260°C.

Cette thèse étudie l'application de méthodes de parallélisation en temps pour la simulation numérique directe des écoulements turbulents. Après une étude préliminaire, on choisit de se focaliser sur l'algorithme Parareal avec grossissement spatial. Le comportement de l'algorithme est étudié en premier lieu sur l'équation d'advection, comme simplification des équations de Navier-Stokes, par une analyse de Fourier et une série d'expériences numériques, afin d'en cerner les mécanismes et paramètres dimensionnants. L'algorithme est ensuite étudié dans un contexte HPC, à l'aide du code de simulation massivement parallèle Hybrid. Deux situations d'écoulements turbulents tridimensionnels sont à l'étude: la décroissance d'une turbulence homogène isotrope et l'écoulement de canal turbulent. Ce travail propose une première mesure de l'efficacité de la parallélisation combinée espace-temps, ainsi qu'une évaluation précise de la capacité de l'algorithme à représenter les propriétés physiques de la turbulence. / This thesis aims at studying the application of time-parallel integration methods for the Direct Numerical Simulation of turbulent flows. After a preliminary study, we choose to focus on the Parareal algorithm with spatial coarsening. The behavior of the algorithm is first studied on the advection equation, as a simplified model for the Navier-Stokes equations, using a Fourier analysis and numerical experiments, to understand its mechanisms and identify the relevant parameters. The algorithm is then studied in a HPC context, using the massively parallel CFD simulation code Hybrid. Two tri-dimensional turbulent flow problems are investigated : the decay of an Homogeneous Isotropic Turbulence and the Turbulent Channel Flow. This work offers a first evaluation of combined space-time parallel efficiency, and analyse the algorithm’s abilities to correctly reproduce the physical properties of turbulence.

Dendritic solidification has been the subject of continuous research, also because of its high importance in metal production. The challenge of predicting macroscopic material properties due to complex solidification processes is complicated by the multiple physical scales and phenomena involved. Practical modeling approaches are still subject to significant limitations due to remaining gaps in the systematic understanding of dendritic microstructure formation. The present work investigates some of these problems at the microscopic level of interfacial morphology using phase-field simulations. The employed phase-field models are implemented within a finite-element framework, allowing efficient and scalable computations on high-performance computing facilities. Particular emphasis is placed on the evolution and interaction of dendrite sidebranches in the broader context of dendrite fragmentation, varying and dynamical solidification conditions.

In this thesis, we consider two models from physics, which are characterized by the interplay of thermodynamical and fluid mechanical phenomena: demixing (spinodal decomposition) and Rayleigh--Bénard convection. In both models, we investigate the dependencies of certain intrinsic quantities on the system parameters. The first model describes a thermodynamically driven demixing process of a binary viscous fluid. During the evolution, the two components of the mixture separate into two domains of the different equilibrium volume fractions. One observes a clear tendency: Larger domains grow at the expense of smaller ones, and thus, the average domain sizes increases --- a phenomenon called coarsening. It turns out that two mechanisms are relevant for the coarsening process. At an early stage of the evolution, material transport is essentially mediated by diffusion; at a later stage, when the typical domain size exceeds a certain value, due to the viscosity of the mixture, a fluid flow sets in and becomes the relevant transport mechanism. In both regimes, the growth rates of the typical domain size obey certain power laws. In this thesis, we rigorously establish one-sided bounds on these growth rates via a priori estimates. The second model, Rayleigh--Bénard convection, describes the behavior of a fluid between two rigid horizontal plates that is heated from below and cooled from above. There are two competing heat transfer mechanisms in the system: On the one hand, thermodynamics favors a state in which temperature variations are locally minimized. Thus, in our model, the thermodynamical equilibrium state is realized by a temperature with a linearly decreasing profile, corresponding to pure conduction. On the other hand, due to differences in the densities of hot and cold fluid parcels, buoyancy forces act on the fluid. This results in an upward motion of hot parcels and a downward motion of cold parcels. We study the dependence of the average upward heat flux, measured in the so-called Nusselt number, on the temperature forcing encoded by the container height. It turns out that the efficiency of the heat transport is independent of the height of the container, and thus, the Nusselt number is a constant function of height. Using a priori estimates, we prove an upper bound on the Nusselt number that displays this dependency --- up to logarithmic errors. Further investigations on the flow pattern in Rayleigh--Bénard convection show a clear separation of length scales: Along the horizontal top and bottom plates one observes thin boundary layers in which heat is essentially conducted, whereas the large bulk is characterized by a convective heat flow. We give first rigorous results in favor of linear temperature profiles in the boundary layers, which indicate that heat is indeed essentially conducted close to the boundaries.:1 Introduction 2 Coarsening rates in binary viscous fluids 2.1 Background from physics 2.2 Background from mathematics 2.3 The model 2.4 The gradient flow structure 2.5 Heuristics 2.6 Numerical simulations 2.7 Main results 2.8 Preliminaries 2.9 Proof of upper bounds on coarsening rates 2.10 Appendix: Well-posedness and regularity of solutions 3 Scaling of the Nusselt number 3.1 Background from physics 3.2 The model and the Nusselt number 3.3 Heuristics 3.4 Main results 3.5 Scaling law in the linear regime 3.6 Preliminaries and review 3.7 Upper bound using the background field method 3.8 Upper bound using the maximum principle 3.9 Appendix: Some elementary estimates 4 The laminar boundary layer 4.1 Background, model, and motivation 4.2 Main results 4.3 Preparation: Bounds on the velocity field 4.4 On the energy distribution 4.5 Bounds on the second order derivatives of the temperature field 4.6 Bounds on the third order derivatives of the temperature field

Knowledge of the properties of single molecule diffusion is important for controlling dynamic self-assembly of molecular structures. A powerful experimental technique for determining diffusion coefficients is the recording of diffusion-induced signal fluctuations by a locally fixed point-like probe. Here, the signal becomes modified, whenever a molecule enters a certain detection area on the surface under the probe. The technique is minimal invasive and has a very good time resolution, enabling the investigation of highly mobile molecules. Theories are necessary for the analysis of the fluctuations and the extraction of diffusion properties. In this thesis, three methods are presented, which are based on the autocorrelation function, the distribution of peak widths and the distribution of interpeak intervals. Analytical expressions are derived for the distributions and the autocorrelation function in case of molecules, which can be described by circular or rectangular shapes. For rectangular shaped molecules, rotational diffusion can influence the recorded fluctuations. To allow for a simultaneous determination of rotational and translational diffusion coefficients the analytical treatment is extended. Furthermore, new methods are developed to determine the diffusion tensor for anisotropic stochastic molecular motion, using either one linearly extended probe or two individual probes. Coarse-graining the signal recorded by a point-like probe, which repeatedly moves on a line or a circle, is suggested for experimental implementation. All facets of the evaluation methods are verified against kinetic Monte Carlo simulations. Applications to experimental data, recorded by a locally fixed scanning tunneling microscope tip, are demonstrated for copperphthalocyanine and PTCDA molecules diffusing on Ag(100).