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We present a mathematical study of two conservative systems in fluid mechanics. First, we study a fragmentation model for sprays. The model takes into account the break-up of spray droplets due to drag forces. In particular, we establish the existence of global weak solutions to a system of incompressible Navier-Stokes equations coupled with a Boltzmann-like kinetic equation. We assume the particles initially have bounded radii and bounded velocities relative to the gas, and we show that those bounds remain as the system evolves. One interesting feature of the model is the apparent accumulation of particles with arbitrarily small radii. As a result, there can be no nontrivial hydrodynamical equilibrium for this system. Next, with an interest in understanding hydrodynamical limits in discontinuous regimes, we study a classical model for shock waves. Specifically, we consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L² perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L² norm of a perturbed solution relative to the shock wave is bounded above by the L² norm of the initial perturbation. Finally, we include some preliminary relative entropy estimates which are suitable for a study of shock wave solutions to n x n systems of conservation laws having a convex entropy. / text

No / A discrete particle model is described which simulates bedload transport over a flat bed of a unimodal mixed-sized distribution of particles. Simple physical rules are applied to large numbers of discrete sediment grains moving within a unidirectional flow. The modelling assumptions and main algorithms of the bedload transport model are presented and discussed. Sediment particles are represented by smooth spheres, which move under the drag forces of a simulated fluid flow. Bedload mass-transport rates calculated by the model exhibit a low sensitivity to chosen model parameters. Comparisons of the calculated mass-transport rates with well-established empirical relationships are good, strongly suggesting that the discrete particle model has captured the essential elements of the system physics. This performance provides strong justification for future interrogation of the model to investigate details of the small-scale constituent processes which have hitherto been outside the reach of previous experimental and modelling investigations.

The objectives of this dissertation are to measure and calculate surface free energies of soil particles, to understand the mechanical behavior of unsaturated silty sand through first studying the stress-strain relationship, the effects of matric suction and pore water chemistry and second to interpret the behavior by the critical state frame work, to develop a method to predict cone tip resistance in unsaturated soils, and to present the concept of pseudo strain and dissipated pseudo strain energy. Universal Sorption Device (USD) is developed to measure surface free energies of soil particles. The test results on a soil sample shows that specific surface area increased with decreasing particle size. The components of surface free energies and the work of adhesion increased with decreasing particle size. A servo controlled triaxial testing device is developed to test 15.24 cm in height and 7.62 cm in diameter, recompacted specimens of unsaturated soil under varying matric suction and different pore chemistry. During the test, the matric suction is maintained constant. Results from the triaxial drained tests are used for validation of the constitutive models proposed by Alonso et al. (1990). Predictions from the model are in good agreement with experimental results. The critical state model for unsaturated soil is used to calculate cone tip resistance in unsaturated silty sand. The calculated cone tip resistance is used to evaluate the liquefaction potential of unsaturated soils. The results from the stress based liquefaction potential analysis reveal that even in an unsaturated condition soil is susceptible to liquefaction. By applying the pseudo strain concept, it is possible to account for the viscous resistance of water during cyclic loading. The results of undrained cyclic triaxial tests are used to calculate pseudo-strain and dissipated pseudo strain energy. The results of calculated dissipated pseudo strain energy suggest that the effect of initial matric suction is evident. On the other hand, the effect of surface tension increase or decrease due to existence of chemical on the pore water is negligible.

Dans cette thèse, on étudie des systèmes de particules en interaction dont le comportement est lié à certaines équations aux dérivées partielles lorsque le nombre de particules tend vers l’infini. L’équation de Kuramoto-Sivashinsky modélise par exemple la propagation de certains fronts de flamme, la topographie de la surface d’une couche mince en cours de croissance, et fait apparaître des structures macroscopiques. Un modèle de particules en interaction par un couplage harmonique des vitesses, attractif aux premières vitesses voisines, répulsive aux secondes voisines, associée à des collisions élastiques, produit des profils de vitesses analogues aux fronts de flamme. On observe également la création et l’annihilation d’agrégats de particules. Un autre modèle, où les particules fusionnent lors des collisions en préservant masse et quantité de mouvement, et avec uniquement attraction au plus proche voisin, permet de retrouver un modèle de type gaz sans pression avec viscosité. Ces modèles sont étudiés théoriquement, en particulier les facteurs de mise à l’échelle des forces d’interaction sont précisés pour obtenir les équations correctes dans la limite du grand nombre de particules. Des simulations numériques confirment la validité et la pertinence des modèles. / This work is concerned by systems of interacting particles, which are linked to partial derivative equations when the particle number becomes large enough. The Kuramoto-Sivashinsky equation is actually modeling as well the front flame propagation as the morphology of growing interfaces, in deposition, for example. Moreover, surface periodical macroscopic structuring is occurring. An interacting particle model through an harmonic velocity coupling, attractive with the first velocity-neighbor and repulsive for the second neighbors, associated with elestic collisions. This model thus provides us with velocity profiles close to those of front flame propagation. Creation and annihilation of particle clusters is also observed. Another model, where particle are merging during collisions, while retaining mass and momentum conservation and with only nearest neighbor attraction, allows to recover a viscous pressureless gas model. These models are studied using mathematical tools. Especially interaction scaling factors are determined for obtaining the suitable equations in the large particle number limit. The numerical simulations confirm the relevance of the models.

Lagrangian particle models are useful for modelling pollutants in the atmosphere. They simulate the spread of pollutants by modelling trajectories of individual particles. However, to be useful, these models require a density estimate. The standard method to use has been boxcounting, but kernel density estimator (KDE) is an alternative. How KDE is used varies as there is no standard implementation. Primarily, it is the choice of kernel and bandwidth estimator that determines the model. In this report I have implemented a KDE for FOI’s Lagrangian particle model LPELLO. The kernel I have used is a combination between a uniform and Gaussian kernel. Four different bandwidth estimators has been tested, where two are global and two are variable. The first variable bandwidth estimator is based on the age of released particles, and the second is based on the turbulence history of the particles. The methods have then been tested against boxcounting, which by using an exceedingly large number of particles can be seen as the true concentration. The tests indicate that KDE method generally performs better than boxcounting at low particle numbers. The variable bandwidth estimators also performed better than both global bandwidth estimators. To achive a firmer conclusion, more testing is needed. The results indicate that KDE in general, and variable bandwidth estimators in specific, are useful tools for concentration estimate.

Syftet med denna studie är att bidra med ökade kunskaper om hur mellanstadielärare undervisar om partikelmodellen. Datainsamlingsmetoden var kvalitativa semistrukturerade intervjuer och åtta lärare intervjuades. Resultatet visar att partikelmodellen får lite utrymme i dagens kemiundervisning på mellanstadiet. Lärarna anger flera idéer men gör det utan att presentera en holistisk modell. Likaså lyfter de fram ett begränsat undervisningsinnehåll kopplat till partikelmodellen som inte speglar dess användbarhet eller ger eleverna förutsättningar till att utveckla en helhetsförståelse för vad modellen innebär. Lärarna har dessutom lättare för att ange varför och vad de undervisar om partikelmodellen än när och hur. Detta tyder på att de saknar strategier för hur de kan undervisa om partikelmodellen med en genomtänkt progression. En slutsats är att lärarna är medvetna om att partikelmodellen är viktig, men att detta inte speglas i deras undervisningspraktik. / The purpose of this study is to contribute with increased knowledge of how primary school teachers teach about the particle model. The data collection method was qualitative semi-structured interviews and eight teachers were interviewed. The result shows that the particle model has a small place in today’s chemistry teaching for pupils in age 10 to 12 years. The teachers mention several ideas that pupils should learn but without presenting a holistic model. Similarly, they emphasized a limited teaching content linked to the particle model which does not reflect its usefulness or provide students with the conditions to develop a holistic understanding of what the model means. In addition, teachers can more easily tell why and what they teach about the particle model than when and how. This indicates that they lack strategies for how to teach about the particle model with a progression. One conclusion is that teachers are aware of the importance of the particle model, but this is not reflected in their teaching practice.

<p>The single particle model was extended to include electrode and particle volume expansion effects observed in high capacity alloying electrodes. The model was used to predict voltage profiles in sodium ion batteries with tin and tin-phosphide negative electrodes. It was seen that the profiles predicted by the modified model were significantly better than the classical model. A parametric study was done to understand the impact of properties such as particle radius, diffusivity, reaction rate etc on the performance of the electrode. The model was also modified for incorporating particles having a cylindrical morphology. For the same material properties, it was seen that cylindrical particles outperform spherical particles for large L/R values in the cylinder due to the diffusion limitations at low L/R ratios. A lattice spring-based degradation model was used to observe crack formation and creep relaxation within the particle. It was observed that the fraction of broken bonds increases with an increase in strain rate. At low strain rates, it was seen that there was a significant expansion in particle volumes due to creep deformation. This expansion helped release particle stresses subsequently reducing the amount of fracture.</p>

This thesis presents the results of an effort to quantify the implications of using ultra-high performance concrete (UHPC) for shear walls in tall buildings considering structural efficiency and environmental sustainability. The Lattice Discrete Particle Model (LDPM) was used to simulate the response to failure of concrete shear walls without web steel bar reinforcement under lateral loading and constant axial compressive loading. The structural efficiency of UHPC with simulated compressive strength of f'c = 231 MPa was compared to that of a high-performance concrete (HPC) with f'c = 51.7 MPa simulated compressive strength. UHPC shear walls were found to have equal uncracked stiffness and superior post-cracking capacity at a thickness 58% of the HPC shear wall thickness, and at 59% of the HPC shear wall weight. Next, the environmental sustainability of UHPC with compressive strength f'c = 220-240 MPa was compared to that of an HPC with compressive strength f'c = 49 MPa with a life-cycle assessment (LCA) approach, using SimaPro sustainability software. At a thickness 58% of the HPC shear wall thickness, UHPC shear walls with 0% fiber by volume were found to have an environmental impact 6% to 10% worse than that of HPC shear walls, and UHPC shear walls with 2% fiber by volume were found to have an environmental impact 47% to 58% worse than that of HPC shear walls. The results detailed herein will allow for design guidelines to be developed which take advantage of UHPC response in shear. Additionally, this work may be implemented into topology optimization frameworks that incorporate the potential improvements in structural efficiency and sustainability through using UHPC. / Master of Science

This research develops and validates computational tools for the design and analysis of structural components and systems constructed with Ultra-High Performance Concrete (UHPC). The modeling strategy utilizes the Lattice Discrete Particle Model (LDPM) to represent UHPC material and structural member response, and extends a structural-level triaxial continuum constitutive law to account for the addition of discrete fibers. The approach is robust, general, and could be utilized by other researchers to expand the computational capability and simulate the behavior of different composite materials. The work described herein identifies the model material parameters by conducting a complete material characterization for UHPC, with and without fiber reinforcement, describing its behavior in unconfined compression, uniaxial tension, and fracture toughness. It characterizes the effect of fiber orientations, fiber-matrix interaction, and resolves the issue of multi-axial stress states on fiber pullout. The capabilities of the computational models are demonstrated by comparing the material test data that were not used in the parameter identification phase to numerical simulations to validate the models' predictive capabilities. These models offer a mechanics-based shortcut to UHPC analysis that can strategically support ongoing development of material and structural design codes and standards. / Ph. D. / This research develops and validates new computer-based methods to analyze and design civil infrastructure constructed with ultra-high performance concrete (UHPC), achieved when steel fibers are combined with a finely graded cement matrix. With superior performance characteristics in comparison to regular concrete, UHPC is studied herein for its strong potential to advance the durability, efficiency, and resiliency of new and existing infrastructure. The simulation-based methods are extensively verified with novel experiments that evaluate the material limits and failure modes when compressed, bent, or stretched, considering fiber volume and orientation. The computer-based tools can be used to realistically assess the structural performance of innovative UHPC applications in buildings, bridges, and tunnels under natural hazards, leading to surpassed levels of structural efficiency and resiliency across civil infrastructure.