Turbulence transport with nonlocal interactions

This preliminary report describes a variety of issues in turbulence transport analysis with particular emphasis on closure procedures that are nonlocal in wave-number and/or physical space. Anomalous behavior of the transport equations for large scale parts of the turbulence spectrum are resolved by including the physical space nonlocal interactions. Direct and reverse cascade processes in wave-number space are given a much richer potential for realistic description by the nonlocal formulations. The discussion also describes issues, many still not resolved, regarding new classes of self-similar form functions

Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study

We study an approximation scheme for a variational theory of cohesive fracture in a one-dimensional setting. Here, the energy functional is approximated by a family of functionals depending on a small parameter $0 < \varepsilon \ll 1$ and on two fields: the elastic part of the displacement field and an eigendeformation field that describes the inelastic response of the material beyond the elastic regime. We measure the inelastic contributions of the latter in terms of a non-local energy functional. Our main result shows that, as $\varepsilon \to 0$, the approximate functionals $\Gamma$-converge to a cohesive zone model.Comment: Comments are welcome

Multilevel Schwarz methods for multigroup radiation transport problems

The development of advanced discretization methods for the radiation transport equation is of fundamental importance, since the numerical effort of modeling increasingly complex multidimensional problems with increasing accuracy is extremely challenging. Different expressions of this equation arise in several science fields, from nuclear fission and fusion to astrophysics, climatology and combustion. Mathematically, the radiation intensity is usually a rapidly changing function, causing a considerable loss in accuracy for many discretization methods. Depending on the coefficient ranges, the equation behaves like totally different equation types, making it very difficult to find a discretization method that is efficient in all regimes. Computationally, the huge amount of unknowns involved demands not only extremely powerful computers, but also efficient numerical methods and optimized implementations. Today, solvers covering all the coefficient ranges and still being robust in the diffusion dominated case are very scarce. In the last 20 years, Discontinous Galerkin (DG) methods have been studied for the monoenergetic problem, unsuccessfully, due to lack of stability for diffusion-dominated cases. Recently, new mathematical developments have fully explained the instability and provided a remedy by using a numerical flux depending on the scattering cross section and the mesh size. The new formulation has proven to be stable and allows the application of multigrid, matrix-free methods, reducing the memory needed for such an amount of unknowns. We use these numerical methods to address the solution of a energy dependent problem with a multigroup approach. We study the diffusion approximation to the transport problem, obtaining convergence proofs for the symmetric scattering case and advances in the nonsymmetric case, using field of values analysis. For the full transport case, we discretize by means of an asymptotic preserving, weakly penalized discontinuous Galerkin method that we solve with a multigrid preconditioned GMRES solver, using nonoverlapping Schwarz smoothers for the energy and direction dependent radiative transfer problem. To address the local thermodynamic equilibrium (LTE) constraint, we use a nonlinear additive Schwarz method to precondition the Newton solver. By solving full local radiative transfer problems for each grid cell, performed in parallel on a matrix-free implementation, we achieve a method capable to address large scale calculations arising from applications such as astrophysics, atmospheric radiation calculations and nuclear applications. To the best of our knowledge, this is the first time this preconditioner combination has been used in LTE radiation transport and in several tests we show the robustness of the approach for different mesh sizes, cross sections, energy distributions and anisotropic regimes, both in the linear and nonlinear cases

Phonon Transport Analysis of Thermal Conductivity in Particulate Nanocomposites

Les modèles théoriques ont été présentés pour la prédiction de la conductivité thermique de composites constitués de particules sphériques. Parmi ces modèles, seuls quelques-uns d'entre eux sont en mesure de prédire correctement la conductivité thermique de nanocomposites. La difficulté à modéliser correctement cette propriété physique origine de la différence entre la conductivité de la matrice et des particules à l'état pur par rapport à leurs valeurs respectives dans le composite. En conséquence, la résistance thermique à l'interface entre la matrice et les particules devient une variable importante de la conductivité thermique des matériaux nanocomposites. Dans ce projet, l'analyse de l'échange des phonons thermiques dans les milieux hétérogènes est réalisée et une formule générale de la conductivité thermique effective de nanocomposites est présentée. Dans la première étape du travail, le transport de phonons à l'interface entre la matrice et des nanoparticules est étudié. Cette investigation vise à présenter la résistance thermique sous une nouvelle forme. Les deux types de transport de phonons sur l'interface particule-matrice, soient diffus et spéculaire, sont pris en compte dans le calcul de la conductivité thermique effective pour les nanocomposites particulaires. Dans un deuxième temps, le modèle proposé est évalué en regard de résultats numériques et expérimentaux disponibles dans la littérature. Cette évaluation tend à prouver que le modèle proposé est capable de prédire la conductivité thermique effective pour un large éventail de fractions volumiques et de tailles de particules.---------- Theoretical models have been presented for predicting the thermal conductivity of composites consisting of spherical particles. Among these models, only a few of them are able to predict the thermal conductivity of nanocomposites. This is because the matrix and particle thermal conductivities in nanocomposites are not equal to their bulk values due to increased interface scattering. The boundary scattering becomes important when the characteristic length of the media is smaller than the bulk mean free path of phonons. The thermal boundary resistance at the interface between matrix and suspended particles is affected on the thermal conductivity of nanocomposites. In this work, the phonon viewpoint of heat transport in heterogeneous media is investigated and a general formula for the effective thermal conductivity of particulate nanocomposites is presented. In the first step of this project, the phonon scattering at the interface between matrix and nanoparticles is investigated. This study aims to present the thermal boundary resistance in a new form. Both diffuse and specular types of scattering of phonons on the particle-matrix interface are taken into account in the derivation of the effective thermal conductivity for the particulate nanocomposites. In the next step, the proposed model is evaluated with numerical and experimental results available in literature. This evaluation is done to prove that the proposed model is able to predict the effective thermal conductivity in a wid

Segmentation and quantification of spinal cord gray matter–white matter structures in magnetic resonance images

This thesis focuses on finding ways to differentiate the gray matter (GM) and white matter (WM) in magnetic resonance (MR) images of the human spinal cord (SC). The aim of this project is to quantify tissue loss in these compartments to study their implications on the progression of multiple sclerosis (MS). To this end, we propose segmentation algorithms that we evaluated on MR images of healthy volunteers. Segmentation of GM and WM in MR images can be done manually by human experts, but manual segmentation is tedious and prone to intra- and inter-rater variability. Therefore, a deterministic automation of this task is necessary. On axial 2D images acquired with a recently proposed MR sequence, called AMIRA, we experiment with various automatic segmentation algorithms. We first use variational model-based segmentation approaches combined with appearance models and later directly apply supervised deep learning to train segmentation networks. Evaluation of the proposed methods shows accurate and precise results, which are on par with manual segmentations. We test the developed deep learning approach on images of conventional MR sequences in the context of a GM segmentation challenge, resulting in superior performance compared to the other competing methods. To further assess the quality of the AMIRA sequence, we apply an already published GM segmentation algorithm to our data, yielding higher accuracy than the same algorithm achieves on images of conventional MR sequences. On a different topic, but related to segmentation, we develop a high-order slice interpolation method to address the large slice distances of images acquired with the AMIRA protocol at different vertebral levels, enabling us to resample our data to intermediate slice positions. From the methodical point of view, this work provides an introduction to computer vision, a mathematically focused perspective on variational segmentation approaches and supervised deep learning, as well as a brief overview of the underlying project's anatomical and medical background

From the nano- to the macroscale – bridging scales for the moving contact line problem

The moving contact line problem is one of the main unsolved fundamental problems in fluid mechanics, with relevant physical phenomena spanning multiple scales, from the molecular to the macroscopic scale. In this thesis, at the macroscale, it is shown that classical asymptotic analysis is applicable at the moving contact line. This allows for a direct matching procedure between the inner (nanoscale) region and the outer (macroscale) region, therefore simplifying the analysis presented to date in the literature. At the mesoscale, a unified derivation for single and binary fluid diffuse interface models is presented, consolidating two models present in the literature. Results from an asymptotic analysis of the sharp interface limit of the binary fluid diffuse interface model are compared with numerical computations of the inner region in the vicinity of a moving contact line. Finally, the nanoscale structure of the density profile in the vicinity of the con- tact line is studied using density functional theory (DFT). At equilibrium, an effective disjoining pressure is extracted and results are compared with coarse-grained Hamiltonian theory. A derivation of Navier-Stokes like dynamic DFT equations is presented. Results for the moving contact line are compared with predictions from molecular kinetic theory. Computations for both DFT and diffuse interface approaches are performed using pseudospectral methods mapped to unbounded domains. The numerical scheme is presented, and the inclusion of hard-sphere effects via a fundamental measure theory is discussed.Open Acces

Surface Layers in the Gravity/Hydrodynamics Correspondence

The AdS/hydrodynamics correspondence provides a 1-1 map between large wavelength features of AdS black branes and conformal fluid flows. In this Thesis we consider boundaries between nonrelativistic flows, applying the usual boundary conditions for viscous fluids. We find that a naive application of the correspondence to these boundaries yields a surface layer in the gravity theory whose stress tensor is not equal to that given by the Israel matching conditions. In particular, while neither stress tensor satisfies the null energy condition and both have nonvanishing momentum, only Israel's tensor has stress. The disagreement arises entirely from corrections to the metric due to multiple derivatives of the flow velocity, which violate Israel's finiteness assumption in the thin wall limit

Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program

The focus of the program was on the use of direct numerical simulations of turbulent flow for study of turbulence physics and modeling. A special interest was placed on turbulent mixing layers. The required data for these investigations were generated from four newly developed codes for simulation of time and spatially developing incompressible and compressible mixing layers. Also of interest were the structure of wall bounded turbulent and transitional flows, evaluation of diagnostic techniques for detection of organized motions, energy transfer in isotropic turbulence, optical propagation through turbulent media, and detailed analysis of the interaction of vortical structures