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<p>This thesis describes the experimental results of liquid polymer droplets levelling on thin films of identical polymer liquid. Through varying the thickness of the underlying polymer film relative to the size of the droplet height, we have observed a crossover in the dynamics between droplets spreading on very thin films to droplets levelling on films thicker than the droplet itself. In the thin film regime, the underlying film behaves as a pre-existing precursor film and the droplet spreads according to the well-known Tanner's law where the droplet height, d₀, decreases in time as d₀ ~ t^-1/5. In the opposite regime, when the film thickness is much greater than the initial droplet height, the droplet levels with a much stronger time dependence compared to Tanner's law spreading, d₀ ~ t^-1/2. Not only have we observed the two extreme cases, we have also experimentally observed levelling behaviour of intermediate systems, where the droplet height and film height are on the same order. We have captured experimentally the crossover behaviour of droplets spreading on thin films to droplets levelling on thick films. In addition, we have developed a theoretical model that accurately captures the physics of this crossover using the lubrication approximation for thin film flows. The relevant background information will be presented as well as a detailed description of the sample preparation techniques required to fabricate spherical caps atop thin films of identical material.</p> / Master of Science (MSc)

This thesis is comprised of three parts. The first part describes a novel framework for computing importance measures on graph vertices. The concept of a D-spectrum is introduced, based on vertex ranks within certain chains of nested sub-graphs. We show that the D- spectrum integrates the degree distribution and coreness information of the graph as two particular such chains. We prove that these spectra are realized as fixed points of certain monotone and contractive SDSs we call t-systems. Finally, we give a vertex deletion algorithm that efficiently computes D-spectra, and we illustrate their correlation with stochastic SIR-processes on real world networks. The second part deals with the topology of the intersection nerve for a bi-secondary structure, and its singular homology. A bi-secondary structure R, is a combinatorial object that can be viewed as a collection of cycles (loops) of certain at most tetravalent planar graphs. Bi-secondary structures arise naturally in the study of RNA riboswitches - molecules that have an MFE binary structural degeneracy. We prove that this loop nerve complex has a euclidean 3-space embedding characterized solely by H2(R), its second homology group. We show that this group is the only non-trivial one in the sequence and furthermore it is free abelian. The third part further describes the features of the loop nerve. We identify certain disjoint objects in the structure of R which we call crossing components (CC). These are non-trivial connected components of a graph that captures a particular non-planar embedding of R. We show that each CC contributes a unique generator to H2(R) and thus the total number of these crossing components in fact equals the rank of the second homology group. / Doctor of Philosophy / This Thesis is divided into three parts. The first part describes a novel mathematical framework for decomposing a real world network into layers. A network is comprised of interconnected nodes and can model anything from transportation of goods to the way the internet is organized. Two key numbers describe the local and global features of a network: the number of neighbors, and the number of neighbors in a certain layer, a node has. Our work shows that there are other numbers in-between the two, that better characterize a node. We also give explicit means of computing them. Finally, we show that these numbers are connected to the way information spreads on the network, uncovering a relation between the network’s structure and dynamics on said network. The last two parts of the thesis have a common theme and study the same mathematical object. In the first part of the two, we provide a new model for the way riboswtiches organize themselves. Riboswitches, are RNA molecules within a cell, that can take two mutually opposite conformations, depending on what function they need to perform within said cell. They are important from an evolutionary standpoint and are actively studied within that context, usually being modeled as networks. Our model captures the shapes of the two possible conformations, and encodes it within a mathematical object called a topological space. Once this is done, we prove that certain numbers that are attached to all topological spaces carry specific values for riboswitches. Namely, we show that the shapes of the two possible conformations for a riboswich are always characterized by a single integer. In the last part of the Thesis we identify what exactly in the structure of riboswitches contributes to this number being large or small. We prove that the more tangled the two conformations are, the larger the number. We can thus conclude that this number is directly proportional to how complex the riboswitch is.

In this work, we develop an interface-preserving level-set method in the finite-element framework for interfacial flows with moving contact lines. In our method, the contact line is advected naturally by the flow field. Contact angle hysteresis can be easily implemented without explicit calculation of the contact angle or the contact line velocity, and meshindependent results can be obtained following a simple computational strategy. We have implemented the method in three dimensions and provide numerical studies that compare well with analytical solutions to verify our algorithm. We first develop a high-order numerical method for interface-preserving level-set reinitialization. Within the interface cells, the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. For the non-interface cells, we compute the gradient of the level set function by solving a Hamilton-Jacobi equation as a conservation law system using the discontinuous Galerkin method. This follows the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660-690]. The missing constant for these cells is recovered using the continuity of the level set function while taking into account the characteristics. To treat highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax-Friedrichs flux and a penalty flux. Our method is accurate for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N + 1)th order accuracy in the interface cells and Nth order accuracy in the whole domain are observed for smooth solutions when Nth degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We then develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E [Phys. Fluids, vol. 19, p. 022101, 2007], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN; βCL). This combination leads to a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method. Lastly, we extend our method to three-dimensional simulations, where an extension equation is solved on the wall boundary to obtain the boundary condition for level-set reinitializaiton with contact lines. Reinitialization of ellipsoidal interfaces is presented to show the accuracy and stability of our method. In addition, simulations of a drop on an inclined wall are presented that are in agreement with theoretical results. / Doctor of Philosophy / When a liquid droplet is sliding along a solid surface, a moving contact line is formed at the intersection of the three phases: liquid, air and solid. This work develops a numerical method to study problems with moving contact lines. The partial differential equations describing the problem are solved by finite element methods. Our numerical method is validated against experiments and theories. Furthermore, we have implemented our method in three-dimensional problems.

No / In the November issue (2001) of Neuroscience Letters, Holmin et al. (Neurosci. Lett. 314 (2001) 151) reported that the synthesis of the intermediate filament protein nestin was upregulated by potassium-induced depolarization in the rat cortex. In this letter, we provide supplementary evidence that repeated cortical spreading depression elicited by potassium induces a delayed upregulation of nestin. However, we argue against the authors' conclusion, Nestin expression was N-methyl-D-aspartate (NMDA)-receptor dependent since dizocilpine (MK-801) treatment abolished the response because spreading depression itself is very sensitive to NMDA-receptor block, and the drug treatment was initiated prior to potassium application to the cortex in Holmin et al.'s study.

Liquefaction-induced deformations associated with lateral spreading represent a significant hazard that can cause substantial damage during earthquakes. The ability to accurately predict lateral-spreading displacement is hampered by a lack of field data from previous earthquakes. Remote sensing via optical image correlation can fill this gap and provide data regarding liquefaction-induced lateral spreading displacements. In this thesis, deformations from three earthquakes (2010 Darfield, February 2011 Christchurch, and 2011 Tohoku Earthquakes) are measured using optical image correlation applied to 0.5-m resolution satellite imagery. The resulting deformations from optical image correlation are compared to the geologic conditions, as well as field observations and measurements of liquefaction. Measurements from optical image correlation are found to have a precision within 0.40 m in all three cases, and results agree well with field measurements. / text

In Nordic design of boiling water reactors, a deep water pool under the reactor vessel is employed for the core melt fragmentation and the long term cooling of decay heated corium debris in case of a severe accident. To assess the effectiveness of such accident management strategy the Risk-Oriented Accident Analysis Methodology has been proposed. The present work contributes to the further development of the methodology and is focused on the issue of ex-vessel debris coolability. The height and shape of the porous debris bed are among the most important factors that determine if the debris can be cooled by natural circulation of water. The bed geometry is formed in the process of melt release, fragmentation, sedimentation and packing of the debris in the pool. Bed shape is affected by the coolant flow that induces movement of particles in the pool and after settling on top of the bed. The later one is called debris bed self-leveling phenomenon. In this study, the self-leveling was investigated experimentally and analytically. Experiments were carried out in order to collect data necessary for the development of a numerical model with an empirical closure. The self-leveling model was coupled to a model for prediction of the debris bed dryout. Such coupled code allows to calculate the time necessary to have a coolable configuration of the bed. The influence of input parameters was assessed through sensitivity analysis in order to screen out the less influential parameters. Results of the risk analysis are reported as complementary cumulative distribution functions of the conditional containment failure probability (CCFP). Sensitivity analyses identified: effective particle diameter and debris bed porosity as the parameters that provide the largest contribution to the CCFP uncertainty. It is found that the effect of the initial maximum height of the bed on the CCFP is reduced by the self-leveling. / Kokvattenreaktorer av nordisk typ har en djup vattenbassäng under reaktorkärlet som kan utnyttjas för att kyla härdsmältan och de fragmenterade härdresterna vid ett svårt reaktorhaveri. För att bedöma effektiviteten av en sådan haverihantering har man föreslagit användande av en riskorienterad metodik för haverianalysen (ROAAM, från engelska ”Risk-Oriented Accident Analysis Methodology”). Föreliggande projekt fokuserar på kylbarhet hos härdresterna utanför reaktortanken och bidrar till den pågående vidareutvecklingen av ROAAM till ROAAM+. Höjden på och formen för den porösa ansamlingen av härdrester (här också kallad partikelbädd) är bland de viktigaste faktorerna som avgör om resteffekten kan kylas bort med hjälp av naturlig cirkulation av vattnet i bassängen. Ansamlingens geometriska form skapas under hela processen från utsläpp av  härdsmältan via fragmentering och sedimentering i bassängens botten. Formen kan sedan förändras med tiden genom att partiklar rör sig och omfördelas i kylflödet. Detta fenomen kallas en självnivellerande process. I detta arbete studeras denna självnivellerande process experimentellt och analytiskt. Experimenten utfördes i en särskild experimentuppställning utformad för att att samla in data och parametrar som behövs för att simulera fenomenet och utveckla en beräkningsmodell som sluts empiriskt. Denna modell kopplades sedan till en modell för beräkning av dryout i partikelbädden. Genom denna koppling av de två beräkningsprogrammen är det är möjligt att beräkna tiden för partikelbädden att nå en kylbar konfiguration. Inverkan av variationer i modellens indata studeras med hjälp av känslighetsanalys. Härigenom identifierades de minst inflytelserika parametrarna såsom effektiv drifttid, partikeldensitet, experimentell ovisshet i de empiriska samband som används för att sluta modellen, samt omlokaliseringstid efter det att reaktorn snabbstoppats (SCRAM).  Dessa parametrar avfördes sedan från den fortsatta känslighetsanalysen. Ett artificiellt neuralt nätverk tränades för att användas i stället för den kopplade koden och möjliggöra den beräkningseffektivitet som krävs för att studera hur osäkerheter i indata förs vidare i riskanalysen. Resultaten är presenterade i form av komplementära, kumulativa fördelningsfunktioner för den betingade sannolikheten för brott på reaktorinneslutningen (CCFP, från engelska ”conditional containment failure probability”). Det visas att CCFP kan variera inom ett brett område beroende på de valda kombinationerna av frekvensfunktioner för ingångsparametrarna. Resultaten visar att effektiv partikeldiameter och hög porositet är de två parametrar som ger de största bidragen till osäkerheten i CCFP. Vi har också funnit att fenomenet självnivellering har en gynnsam inverkan på CCFP och leder till lägre utsläppsrisk. Det vore värdefullt att förfina de modeller som beskriver bildandet av den initiala partikelbädden. Detta är särskilt viktigt i de scenarier där det finns kort tid för självnivellering innan partikelbädden börjar smälta igen, dvs när man har relativt hög initial temperatur i partikelbädden och/eller hög specifik värmeeffekt. / <p>QC 20170315</p> / APRI

Motivé par l'étude de tissus biologiques, ce travail contribue aux développements d'outils numériques permettant de prédire la réponse mécanique de matériaux hétérogènes non linéaires dans lesquels les énergies d'interfaces deviennent prépondérantes. Ainsi, une méthode d'homogénéisation multi échelle combinée à une technique de réduction de modèle basée sur la décomposition orthogonale aux valeurs propres est proposée dans un cadre thermique et hyperélastique. Les énergies d'interfaces entre les différentes phases des composites sont décrites par un modèle d'interface cohérent et prises en compte numériquement par une approche liant la méthode des éléments finis étendus et la méthode level-set. Une étude de l'étalement d'une cellule vivante entre deux lamelles fixes est ensuite réalisée. Les deux modèles utilisés pour les simulations montrent que l'assemblage cortex d'actine-membrane plasmique ne joue qu'un rôle minime dans la réponse mécanique cellulaire / Motivated by the study of biological tissues, this work contributes to developing numerical tools to predict the mechanical response of nonlinear heterogeneous materials in which the energies of interfaces can no longer be ignored. First, a computational homogenization strategy combined with a model reduction technique based on the proper orthogonal decomposition is implemented in the cases of large elastic deformations and highly nonlinear conduction. The interfaces between the different phases of a composite are described by means of a coherent interface model and taken into account numerically by an extended finite element method in tandem with a level-set technique. Finally, experimental results of single cell spreading between two fixed parallel microplates are exploited through finite element modelling. Our two models show that the bilayer membrane and the actin cortex do not play a significant role in the cell mechanical response

Mid-ocean ridge hydrothermal systems play an important role in the cycling of energy and mass between the solid earth and oceans. The on-axis low-temperature diffuse fluids (temperature lower than ~100 °C) carry ~90% of the on-axis heat fluxes, but diffuse fluids generation is poorly constrained. This study uses the abundance of the chalcophile elements, which form metal-sulphides in the rock record, to test models for diffuse fluids generation. These include mixing between seawater and high-temperature hydrothermal fluids and conductive cooling of high- temperature hydrothermal fluids. This thesis determined the concentrations of the elements of interest (As, Mo, Ag, Cd, Sn, and Tl) in geological reference materials using standard addition method in ICP-MS. These values were used to calibrate the analysis of samples from Pito Deep to trace the abundance of these elements within the upper oceanic crust. The results show that the Zn, Cu, As, Ag, Cd, Tl, and Pb are generally depleted in sheeted dikes and enriched in the lava unit and/or the transition zone, which is consistent with previous studies on fast-spreading EPR crust at Hole 504B, Hess Deep and Hole 1256D. The enrichment of these elements in the lava unit and/or the transition zone suggests that cooling high-temperature hydrothermal fluids to form diffuse fluids occurred in this iii iv area of the oceanic crust. Molybdenum and Sb are added into all units of the crust by recharging seawater. The concentrations of chalcophile elements in diffuse fluids were calculated by a mass balance. The results of this study favored a diffuse fluids generation model that involves mixing of seawater and high-temperature hydrothermal fluids. Results also show that the observed concentrations of Mo and Sb requires extra input source besides recharging seawater and oceanic crust, possibly particulates in seawater. / Graduate / juliatian2013@gmail.com