Title Abstract "Accounting for Complex Structure in Diffusion Weighted Imaging Data using Volume Fraction Representations (Rekening houden met complexe structuur in diffusie gewogen beeldvorming data door gebruik van volume fractie representaties)" "The domain of diffusion weighted imaging (DWI) has come a long way since its initial development in the mid-1980s. Over the years, we have gained a better understanding of the accompanying techniques and necessary processing steps involved, furthermore leading to a wealth of new insights in the complex workings of the (human) brain. The introduction of diffusion tensor imaging (DTI) has played a crucial role in thisprocess, as it provided the first model intended to deal with anisotropic diffusion; a particular feature observed in the white matter (WM), asopposed to the other most common 'tissue' types found in the human brain, i.e. the gray matter (GM) and cerebrospinal fluid (CSF). During the last decade, however, we have come to realize that the DTI model is severely lacking in its possibilities to represent voxels that contain so called 'crossing fibers', a general name that is often used to refer to a range of complex geometric fiber configurations caused by the partial volume effect. In this PhD thesis, we intended to design certain representations of (information extracted from) DWI data that take into account the aforementioned variety of complex geometrical configurations. Our proposed novel representations aim to offer a greater flexibility that should inherently render many existing difficult problems (e.g. segmentation and registration) trivial; yet make as little assumptions aspossible on the nature of the data or the properties of the underlying structures. A first major contribution is a generic framework for multi-shell multi-tissue (MSMT) representations, and a specific implementation tailored to represent WM, GM and CSF in the human brain. This representation was specifically designed to render the retransformation problem trivial. The latter was easily solved by a newly introduced preservation of principal volume fractions (PPVF) retransformation strategy. A second major contribution is a more tangible track orientation distribution (TOD) representation for complex fiber track distributions. Our newly developed method to obtain such a TOD, is termed track orientation density imaging (TODI). This technique allowed us to gain further understanding in the amplitude of a short-tracks TOD, which can now be interpreted as a measure of track-like local support (TLS). Furthermore, we showed that employing the latter for TOD-based tractography results in guiding the tracks along directions that are morelikely to correspond to continuous structure over a longer distance; i.e. track-like structure! Both representations (MSMT and the TOD) forthcoming from these major contributions, also allow for increased insightin many other aspects of the data they describe, and provide a large range of opportunities for future research." "The Dependency of Diffusion Coefficients and Geometric Factor on the Size of the Diffusing Molecule: Observations for Different Clay-Based Materials" "Elke Jacops, Rudy Swennen" "Copyright © 2017 Elke Jacops et al. In order to investigate in more detail the relation between the size of diffusing molecules and their diffusion coefficients (and geometric factors), diffusion experiments with gases of different size and tritiated water (HTO) have been performed on different clayey samples (Boom Clay, Eigenbilzen Sands, Opalinus Clay, Callovo-Oxfordian Clay, and bentonite with different dry densities). We observed that, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. The variation of the geometric factor can also be described by an exponential function. The observed experimental relations can be used to estimate diffusion coefficients; by measuring experimentally in clay the effective diffusion coefficient of two unreactive dissolved gases with a different size, the diffusion coefficients of other dissolved gases (with a size in between the two measured gases) can be estimated by using the fitted exponential relationship." "Measurement of the molecular diffusion coefficient and the effective longitudinal diffusion under supercritical fluid chromatography conditions in packed bed columns" "Timothy Januarius, Ken Broeckhoven" "The improvement of supercritical fluid chromatography (SFC) instrumentation enhanced its reliability and utility over the past decade. The further development of high speed and high resolution separations is however obstructed by the lack of accurate models for axial dispersion in SFC. This work is a first step to tackle this by developing more reliable methods to measure molecular (Dmol) and longitudinal diffusion (Deff) in SFC, as these affect all aspects of separation efficiency. In the present contribution, we report on an improved method, to enable more flexible, reliable and accurate measurements of Dmol in SFC using commercial instrumentation. A two-column variant of the stopped-flow experiment is proposed as an adapted set-up for measuring the effective longitudinal diffusion coefficient Deff in SFC-conditions. Using the set-ups for a number of test-compounds, it has been found that Deff, and the coefficients describing its constituent sub-processes (cf. particle diffusion Dpart and surface diffusion γsDs), all vary in a linearly proportional way with the bulk diffusion coefficient Dmol within a high degree of accuracy. It has also been found that Deff decreases much more sharply with increasing retention factor compared to LC. By applying the effective medium theory, it was found that the relative surface diffusion coefficient γsDs/Dmol decreases strongly with retention factor for the investigated solutes and column, in contrary to what is typically observed in reversed phase liquid chromatography. Results indicate that this might be related to a change in retention behavior of the analytes. Obviously, more analytes and conditions need to be explored to complete this picture and the extend range of applicability of these observations." "Drift diffusion equations with fractional diffusion on compact Lie groups" "Duvan Cardona Sanchez, Julio Delgado, Michael Ruzhansky" "In this work we investigate the well-posed for diffusion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The diffusion by strongly elliptic operators is considered as a special case and in particular the fractional diffusion with respect to the Laplacian. The general case is studied within the Hormander classes associated to a sub-Riemannian structure on the group (encoded by a Hormander system of vector fields). Applications to diffusion equations for fractional sub-Laplacians, fractional powers of more general subelliptic operators and the corresponding quasi-geostrophic model with drift D are investigated. Examples on SU(2) for diffusion problems with fractional diffusion are analysed." "Differential diffusion effects in numerical simulations of laminar, axi-symmetric H-2/N-2-air diffusion flames" "Georgios Maragkos, Pieter Rauwoens, Bart Merci" "Perpendicular diffusion of solar energetic particles: When is the diffusion approximation valid?" "Nicolas Wijsen" "Multi-spacecraft observations of widespread solar energetic particle (SEP) events indicate that perpendicular (to the mean field) diffusion is an important SEP transport mechanism. However, this is in direct contrast to so called spike and drop-out events, which indicate very little lateral transport. To better understand these seemingly incongruous observations, we discuss the recent progress made towards understanding and implementing perpendicular diffusion in transport models of SEP electrons. This includes a re-derivation of the relevant focused transport equation, a discussion surrounding the correct form of the pitch-angle dependent perpendicular diffusion coefficient and what turbulence quantities are needed as input, and how models lead to degenerate solutions of the particle intensity. Lastly, we evaluate the validity of a diffusion approach to SEP transport and conclude that it is valid when examining a large number of (an ensemble of) events, but that individual SEP events may exhibit coherent structures related to the magnetic field turbulence at short timescales that cannot be accounted for in this modelling approach." "Numerical study on the importance of the turbulent inlet boundary condition and differential diffusion in a turbulent H2/N2/air jet diffusion flame" "Alessandro D'Ausilio, Ivana Stankovic, Bart Merci" "Robust estimation of diffusion tensor and diffusion kurtosis imaging parameters" "Quinten Collier, Jan Sijbers, Jelle Veraart" "Investigation of the diffusion behavior in Sn-xAg-yCu/Cu solid state diffusion couples" "Yuan Yuan, Nele Moelans" "The interfacial reactions and growth behavior of the Cu3Sn and Cu6Sn5 phases in Sn-3.0%Ag-0.5%Cu/Cu and Sn-3.5%Ag-0.7%Cu/Cu diffusion couples were investigated at 130 °C, 150 °C, 170 °C and 200 °C and compared with those in binary Sn/Cu diffusion couples using identical experimental conditions. The Ag solubility in the Cu3Sn and Cu6Sn5 phases was found to be quite small. The parabolic growth constants of Cu3Sn and Cu6Sn5 in Sn-xAg-yCu/Cu diffusion couples were calculated. A transient stage for the growth of Cu3Sn was observed. A pseudo-binary method was proposed and performed to obtain the integrated interdiffusion coefficients and activation energies for diffusion of the intermetallics with limited solubility in one of the elements. The growth of Cu3Sn in Sn-xAg-yCu/Cu diffusion couples was found to be a little slower than that in binary Sn/Cu diffusion couples. The growth rate of the Cu6Sn5 phase in ternary Sn-xAg-yCu/Cu diffusion couples is quite close to that in Sn/Cu diffusion couples. The Cu addition in the Sn-based end-member is expected to favor the growth of Cu6Sn5 providing instantly available Cu atoms for the formation of Cu6Sn5. The Ag addition is suggested to slightly decrease the thermodynamic activity of Sn and further decrease the diffusion of Sn. These interpretations were confirmed by a study of the diffusion behavior in Sn-3.5%Ag/Cu and Sn-1.0%Cu/Cu diffusion couples. The calculated activation energy for interdiffusion in the Cu3Sn and Cu6Sn5 phases in Sn-xAg-yCu/Cu diffusion couples are quite close to those obtained for binary Cu/Sn couples. The obtained conclusions are informative for the Ag-Cu-Sn solder design." "Investigation of diffusion behavior in Cu–Sn solid state diffusion couples" "Yuan Yuan, Yuanyuan Guan, Nele Moelans" "The diffusion behaviors and diffusion parameters of intermetallic compounds (IMCs) formed in Cu-Sn diffusion couples were investigated at the temperature range of 130 °C–200 °C. Interdiffusion coefficients of IMCs were calculated based on the measured composition profiles of the diffusion zones. Considering the wavy type of the diffusion layers and the narrow homogeneity range of the IMCs (Cu₃Sn and Cu₆Sn₅), the integrated method was performed to evaluate the integrated interdiffusion coefficients based on the measured thicknesses of the IMCs layers. The transient initial growth stage was excluded by considering two diffusion times where the growths of both IMCs are in the diffusion control stage. The activation energies for diffusion of the IMCs were evaluated from the integrated diffusion coefficients. The growth behavior of Cu₃Sn suggested the existence of a transient growth regime for Cu₃Sn at the initial stage in cold-bonded Cu-Sn diffusion couple. The intrinsic diffusion coefficients of Cu and Sn in Cu₆Sn₅ were estimated based on the integrated diffusion coefficients. Sn was found to be the faster diffusion component in the Cu₆Sn₅ phase. Phase-field simulations combined with the experimentally measured diffusion coefficients and steady-state growth-rate coefficients were performed to estimate the homogeneity range of IMCs. The estimated results are consistent with the experimental results from this study as well as those from literature experimental values and showed that the homogeneity ranges of Cu₃Sn and Cu₆Sn₅ phases in the Cu-Sn system are almost temperature independent."