NMR T2 distribution measurement is our chosen everyday method for NMR logging while drilling oil and gas wells. This method yields straightforward preparation and execution of the job as well as a normally easy interpretation of the measured data. For instance, gas and light oil discrimination against water is feasible by direct observation of the T2 distribution. A condition for this measurement method is a NMR logging tool that hardly moves while drilling and in addition uses a small static magnetic field gradient and short inter-echo time TE to be motion tolerant. Using data compression techniques, we can transmit by mud pulse telemetry the T2 distribution in real time from the borehole to the surface. This enables the drilling operator to use the NMR data for real-time decisions such as geosteering.

Extraction of accurate quantitative parameters to characterize water diffusion in complex porous media like brain tissue in neuroimaging is a challenging inverse problem, that depends on medium\'s structural and geometrical factors [1,3]. If the role of membranes is generally invoked, probe collisions with the insoluble cytoskeleton network and water hydrodynamic interactions with dissolved macromolecules and cytoskeleton occur as well [2]. The latter two interactions have been shown to determine the phenomenological “anomalous diffusion” of probes in the cytoplasm [4,5,6,7,8]. Additionally, the diffusion of small solutes in cytoplasm could be slowed by the local micro-viscosity of the aqueous phase, a phenomenon generally not taken into account in simulations. We suggest that the Grey and White Matter contrast in Diffusion Decay Imaging (DDI) could be caused by differences in cytoskeleton structures, composed respectively of actin and tubulin that could act by the elimination of one possible water diffusion pathlength by the volume occupied by the network phase. This could explain why anomalous DDI signal has been shown to be independent of membrane integrity [9]. Cytoplasm is able to rapidly shift from a sol (aqueous solutions embedded with insolubles particles) to a gel state (a colloidal solutions with a structured semi-solid and an aqueous fluid phase) or to a viscous solution when the insoluble particles become soluble. Does water have the ability of being a sensor of its local “self-viscosity” ? What is the length of the water diffusion\'s path compared to cells size ? Compared to this path length, how many cellular structures should be probed by water\'s translational diffusion ? We try to respond to these questions by investigating Diffusion Decay Imaging models and their effects on the hypothese-free q-space diffusion propagator shape [3], containing all informations concerning viscosity-slowed gaussian diffusion, structural informations [3] and restricted diffusion [1].

It is shown that internal gradient combined with the restricted diffusion effect can significantly influence the D-T2 cross plots, which are widely used for fluid typing in Nuclear Magnetic Resonance (NMR) well-logging applications. By using models that capture the most important features of the internal gradient in the sedimentary rocks, such effects can be accounted for in the D-T2 inversion process, making fluid typing more accurate.

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This study focuses on the derivation of a general effective diffusion coefficient to describe the twodimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width that lies on a curved surface, in the simple diffusional motion of noninteracting point-like particles under no external field. To this end we extend the generalization of the Kalinay-Percus’ projection method [J. Chem. Phys. 122, 204701 (2005); Phys. Rev. E 74, 041203 (2006)] for the asymmetric channels introduced in [J. Chem. Phys. 137, 024107 (2012)], to project the anisotropic 2D diffusion equation on a smooth curved manifold into an effective one-dimensional generalized Fick-Jacobs equation which is modified due to the curvature of the surface. The lowest order in the perturbation parameter, corresponding to the Fick-Jacobs equation, contains an extra term that accounts for the curvature of the surface. We found explicitly the first order correction for the invariant effective concentration, which is defined as the correct marginal concentration in one variable, and we obtain the first approximation to the effective diffusion coefficient analogous to Bradley’s coefficient [Phys. Rev. E 80, 061142 (2009)] as a function of metric elements of the surface. Straightforwardly we study the perturbation series up to the n-th order, and we derive the full effective diffusion coefficient for 2D diffusion in a narrow asymmetric channel, which have modifications due to the curved metric. Finally, as an example we show how to use our formula to calculate the effective diffusion coefficient considering the case of an asymmetric conical channel embedded on a torus.

We numerically investigate random walks (RWs) and self-avoiding random walks (SAWs) on critical percolation clusters, basic models for diffusion and flexible polymers in disordered media. While this can be easily done for RWs using a simple enumeration method, it is difficult for long SAWs due to the long-range correlations. We employed a sophisticated algorithm that makes use of the self-similar structure of the critical clusters and allows exact enumeration of several thousand SAW steps. We also investigate a kinetic version of the SAW, the so-called kinetic growth (self-avoiding) walk (KGW), as well static averaging over all RW conformations, which describes the so-called ideal chain. For the KGW, we use a chain-growth Monte Carlo method which is inspired by the pruned-enriched Rosenbluth method. The four walk types are found to be affected in different ways by the fractal, disordered structure of the critical clusters. The simulations were carried out in two and three dimensions.

A method for rapid characterization of emulsions is presented. From the proposed setup we are able to measure the droplet size distribution of brine or water droplets confined by an oil phase, even though there is complete overlap in relaxation times and/or molecular mobility between the water and the oil phases. A PFG-NMR sequence is presented that applies the spoiler recovery method for significant reduction in acquisition time, and the method is used for rapid characterization of emulsions.