We explore the effect of multiscale structure on weakly interacting diffusions through two main projects. In the first, we consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit as the number of particles grow to infinity and the time-scale separation parameter goes to zero simultaneously. We make use of weak convergence methods providing a convenient representation for the large deviations rate function, which allow us to characterize the effective controlled mean field dynamics. In addition, we obtain equivalent representations for the large deviations rate function of the form of Dawson-Gartner which hold even in the case where the diffusion matrix depends on the empirical measure and when the particles undergo averaging in addition to the propagation of chaos. In the second, we consider a fully-coupled slow-fast system of McKean-Vlasov SDEs with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy-Problem on the Wasserstein space that are of independent interest.

Yes / In this article we briefly review the Boxed Molecular Dynamics (BXD) method, which allows analysis of thermodynamics and kinetics in complicated molecular systems. BXD is a multiscale technique, in which thermodynamics and long-time dynamics are recovered from a set of short-time simulations. In this article, we review previous applications of BXD to peptide cyclization, diamond etching, solution-phase organic reaction dynamics, and desorption of ions from self-assembled monolayers (SAMs). We also report preliminary results of simulations of diamond etching mechanisms and protein unfolding in AFM experiments. The latter demonstrate a correlation between the protein’s structural motifs and its potential of mean force (PMF). Simulations of these processes by standard molecular dynamics (MD) is typically not possible, since the experimental timescales are very long. However, BXD yields well-converged and physically meaningful results. Compared to other methods of accelerated MD, our BXD approach is very simple; it is easy to implement, and it provides an integrated approach for simultaneously obtaining both thermodynamics and kinetics. It also provides a strategy for obtaining statistically meaningful dynamical results in regions of configuration space that standard MD approaches would visit only very rarely. / DRG is grateful for funding from a Royal Society Research Fellowship. JB and DVS acknowledge the support of EPSRC (Grant No EP/E009824/1). E.M.-N. and S.A.V. are grateful to the “Centro de Supercomputación de Galicia (CESGA)” for the use of its computational resources, as well as to “Ministerio de Economía y Competitividad” (Grant No. CTQ2009-12588) for financial support. DS and E.M.-N. acknowledge the Leverhulme Trust for funding the E.M.-N. visit to Leeds by the grant “Accelerated classical and quantum molecular dynamics and its applications” (Grant No. VP1-2012-013).

The rapid increase in computational power over the last decade has unlocked the possibility of providing patient-specific healthcare via simulation and data assimilation. In the past 2 decades, computational approaches to simulating cardiovascular flows have advanced significantly due to intense research and adoption of methods in medical device companies. A significant source of friction in porting these tools to the hospital and getting in the hands of surgeons is due to the expertise required to handle the geometry pre-processing and meshing of models. Meshless meth- ods reduce the amount of corner cases which makes it easier to develop robust tools surgeons need. To accurately simulate modifications to a region of vasculature as in surgical planning, the entire system must be modeled. Unfortunately, this is computationally prohibitive even on to- day’s machines. To circumvent this issue, the Radial-Basis Function Finite Difference (RBF-FD) method for solution of the higher-dimensional (2D/3D) region of interest is tightly-coupled to a 0D Lumped-Parameter Model (LPM) for solution of the peripheral circulation. The incompress- ible flow equations are updated by an explicit time-marching scheme based on a pressure-velocity correction algorithm. The inlets and outlets of the domain are tightly coupled with the LPM which contains elements that draw from a fluid-electrical analogy such as resistors, capacitors, and in- ductors that represent the viscous resistance, vessel compliance, and flow inertia, respectively. The localized RBF meshless approach is well-suited for modeling complicated non-Newtonian hemo- dynamics due to ease of spatial discretization, ease of addition of multi-physics interactions such as fluid-structure interaction of the vessel wall, and ease of parallelization for fast computations. This work introduces the tight coupling of meshless methods and LPMs for fast and accurate hemody- namic simulations. The results show the efficacy of the method to be used in building robust tools to inform surgical decisions and further development is motivated.

L'érosion de contact est un type d'érosion interne qui se développe à l'interface entre deux couches de matériaux de granulométries différentes. Les particules d'un sol fin (sable, limon, argile…) sont détachées par l'écoulement et entraînées à travers les pores du sol grossier au contact (gravier…). Bien que l'on suspecte sa présence dans de nombreux ouvrages, ce processus d'érosion a été peu étudié jusqu'à présent. Aussi ce travail de thèse s'est attaché à mieux le comprendre pour parvenir à le modéliser. A l'échelle du pore, l'écoulement à l'interface entre deux milieux poreux a été caractérisé, grâce à un dispositif expérimental développé au Cemagref d'Aix-en-Provence qui combine fluorescence induite par laser, méthode PIV et milieu iso-indice. L'importance de la variabilité des sollicitations hydrauliques a ainsi été soulignée. A l'échelle de l'échantillon, des essais sur sols réels et sols reconstitués ont été menés au LTHE, afin d'identifier les phénomènes en jeu. Ont également été obtenues sur ce dispositif des mesures du taux d'érosion en fonction de l'intensité de l'écoulement, pour différents types de sols fins et de sols grossiers. Une modélisation stochastique de ces essais a ensuite été proposée. Enfin, des essais à grande échelle ont été conduits au laboratoire de la Compagnie Nationale du Rhône pour étudier l'éventuelle influence d'effets d'échelle ainsi que les conséquences de cette érosion de contact sur le comportement global et l'intégrité d'un ouvrage. Il a ainsi été mis en évidence la possibilité qu'une érosion de conduit soit initiée par érosion de contact. Cette thèse a été réalisée dans le cadre du projet ERINOH (ERosion INterne dans les Ouvrages Hydrauliques), en convention CIFRE avec le Centre d'Ingénierie Hydraulique d'EDF. / Contact erosion is a type of internal erosion which occurs at the interface between two soil layers of different particle sizes. Particles from the fine soil (sand, silt, clay…) are pulled and driven by the flow through the pores of the surrounding coarse soil (gravel ...). Although its presence is suspected in many earthfill embankments, this process has been little studied so far. The aim of this thesis was to better understand and, possibly, to model contact erosion. At pore scale, the flow at the interface between two porous media was characterized thanks to an experimental device, developed in Cemagref, combining Planar Laser Induced Fluorescence, PIV method and Refractive Index Matching. The spatial variability of flow shear stress has been emphasized. At sample scale, several tests on real and reconstituted soils were carried out in LTHE, in order to identify the phenomena involved in contact erosion. Erosion rates as a function of flow magnitude have also been measured for different types of fine and coarse soils. Then, a stochastic model was proposed to account for these experiments. Finally, large scale tests were conducted in the laboratory of Compagnie National du Rhône, to study the influence of scale effects as well as the consequences of contact erosion on global behavior and integrity of the embankment structure. The possibility of piping initiation by contact erosion was underlined. This thesis is part of the project ERINOH project and was funded by EDF-CIH.

The main focus of the present thesis is on the homogenization of some selected elliptic and parabolic problems. More precisely, we homogenize: non-periodic linear elliptic problems in two dimensions exhibiting a homothetic scaling property; two types of evolution-multiscale linear parabolic problems, one having two spatial and two temporal microscopic scales where the latter ones are given in terms of a two-parameter family, and one having two spatial and three temporal microscopic scales that are fixed power functions; and, finally, evolution-multiscale monotone parabolic problems with one spatial and an arbitrary number of temporal microscopic scales that are not restricted to be given in terms of power functions. In order to achieve homogenization results for these problems we study and enrich the theory of two-scale convergence and its kins. In particular the concept of very weak two-scale convergence and generalizations is developed, and we study an application of this convergence mode where it is employed to detect scales of heterogeneity. / Huvudsakligt fokus i avhandlingen ligger på homogeniseringen av vissa elliptiska och paraboliska problem. Mer precist så homogeniserar vi: ickeperiodiska linjära elliptiska problem i två dimensioner med homotetisk skalning; två typer av evolutionsmultiskaliga linjära paraboliska problem, en med två mikroskopiska skalor i både rum och tid där de senare ges i form av en tvåparameterfamilj, och en med två mikroskopiska skalor i rum och tre i tid som ges i form av fixa potensfunktioner; samt, slutligen, evolutionsmultiskaliga monotona paraboliska problem med en mikroskopisk skala i rum och ett godtyckligt antal i tid som inte är begränsade till att vara givna i form av potensfunktioner. För att kunna uppnå homogeniseringsresultat för dessa problem så studerar och utvecklar vi teorin för tvåskalekonvergens och besläktade begrepp. Speciellt så utvecklar vi begreppet mycket svag tvåskalekonvergens med generaliseringar, och vi studerar en tillämpningav denna konvergenstyp där den används för att detektera förekomsten av heterogenitetsskalor.

No description available.

In this thesis, we introduce a new approach to wavefront phase reconstruction in Adaptive Optics (AO) from the low-resolution gradient measurements provided by a wavefront sensor, using a non-linear approach derived from the Microcanonical Multiscale Formalism (MMF). MMF comes from established concepts in statistical physics, it is naturally suited to the study of multiscale properties of complex natural signals, mainly due to the precise numerical estimate of geometrically localized critical exponents, called the singularity exponents. These exponents quantify the degree of predictability, locally, at each point of the signal domain, and they provide information on the dynamics of the associated system. We show that multiresolution analysis carried out on the singularity exponents of a high-resolution turbulent phase (obtained by model or from data) allows a propagation along the scales of the gradients in low-resolution (obtained from the wavefront sensor), to a higher resolution. We compare our results with those obtained by linear approaches, which allows us to offer an innovative approach to wavefront phase reconstruction in Adaptive Optics.

It is perhaps paradoxical that many material properties arise from the absence of material rather than the presence of it. For example, the strength, stiffness, and toughness of a concrete are related to its pore structure. Furthermore, the volume, size distribution, and interconnectivity of porosity is important for understanding permeability, diffusivity, and capillary action occurring in concrete, which are necessary for predicting service lives in aggressive environments. This research advances the state-of-the-art of multiscale characterization of cement-based materials, and uses this characterization information to model the material behavior under competing durability concerns. In the first part of this research, a novel method is proposed to characterize the entrained air void system. In the second and third parts of this research, microstructural characterization is used in tandem with mechanical models to investigate the behavior of cementitious materials when exposed to rapid rates of loading and to cyclic freezing and thawing. First, a novel analytical technique is presented which reconstructs the 3D entrained air void distribution in hardened concrete using 2D image analysis. This method proposes a new spacing factor, which is believed to be more sensitive to microstructural changes than the current spacing factor commonly utilized in practiced, and specified in ASTM C457, as a measure of concrete's ability to resist to damage under cyclic freeze/thaw loading. This has the potential to improve economy by improving the quality of petrographic assessment and reducing the need for more expensive and time-consuming freeze/thaw tests, while also promoting the durability of concrete. Second, quantitative measurements of the sizes, shapes, and spatial arrangements of flaws which are through to drive failure at strain rates above 100/s were obtained in order to model mortar subjected to high strain-rate loading (i.e., extremes in load rate). A micromechanics model was used to study the ways in which flaw geometry and flaw interaction govern damage. A key finding suggests that dynamic strength may be multimodal, with larger flaws shifting the dynamic strength upwards into the highest strength failure mode. Third, a robust theoretical approach, based upon poroelasticity, is presented to further validate the utility of the novel spacing factor proposed this research. The model is truly multiscale, using in its formulation pore size data ranging from the nanoscale to the micro-scale, entrained air data from the micro-scale to the millimeter scale, and infers a representative volume element on the centimeter scale. The results provide an underlying physical basis for the performance of the novel spacing factor. Furthermore, the framework could be used as a forensic tool, or as a tool to optimize the entrained air void system against freeze/thaw damage.

An understanding of the mechanical properties of viral capsids (protein assemblies forming shell containers) has become necessary as their perceived use as nano-materials for targeted drug delivery. In this thesis, a heterogeneous, spatially detailed model of the viral capsid is considered. This model takes into account the increased degrees of freedom between the capsomers (capsid sub-structures) and the interactions between them to better reflect their deformation properties. A spatially realistic finite element multi-domain decomposition of viral capsid shells is also generated from atomistic PDB (Protein Data Bank) information, and non-linear continuum elastic simulations are performed. These results are compared to homogeneous shell simulation re- sults to bring out the importance of non-homogenous material properties in determining the deformation of the capsid. Finally, multiscale methods in structural analysis are reviewed to study their potential application to the study of nanoindentation of viral capsids. / text

Modeling the competition between drying and curing processes in polymerizing films is of great importance to many existing and developing materials synthesis processes. These processes involve multiple length and time scales ranging from molecular to macroscopic, and are challenging to fully model in situations where the polymerization is non-ideal, such as sol-gel silica thin film formation. A comprehensive model of sol-gel silica film formation should link macroscopic flow and drying (controlled by process parameters) to film microstructure (which dictates the properties of the films). This dissertation describes a multiscale model in which dynamic Monte Carlo (DMC) polymerization simulations are coupled to a continuum model of drying. Unlike statistical methods, DMC simulations track the entire molecular structure distribution to allow the calculation not only of molecular weight but also of cycle ranks and topological indices related to molecular size and shape. The entire DMC simulation (containing 106 monomers) is treated as a particle of sol whose position and composition are tracked in the continuum mass transport model of drying. The validity of the multiscale model is verified by the good agreement of the conversion evolution of DMC and continuum simulations for ideal polycondensation and first shell substitution effect (FSSE) cases. Because our model allows cyclic and cage-like siloxanes to form, it is better able to predict the silica gelation conversion than other reported kinetic models. By studying the competition between molecular growth and cyclization, and the competition between mass transfer (drying) and reaction (gelation) on the drying process of the sol-gel silica film, we observe that cyclization delays gelation, shrinks the molecular size, increases the likelihood of skin formation, and leads to a molecular structure gradient inside the film. We also find that compared with a model with only 3-membered rings, the molecular structure is more complicated and the structure gradients in the films are larger with 4- membered rings. We expect that our simulation will allow better prediction of the formation of structure gradients in sol-gel derived ceramics and other nonideal multifunctional polycondensation products, and that this will help in developing procedures to reduce coating defects.