The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells

Personality Gaze Patterns Unveiled via Automatic Relevance Determination

Understanding human gaze behaviour in social context, as along a face-to-face interaction, remains an open research issue which is strictly related to personality traits. In the effort to bridge the gap between available data and models, typical approaches focus on the analysis of spatial and temporal preferences of gaze deployment over specific regions of the observed face, while adopting classic statistical methods. In this note we propose a different analysis perspective based on novel data-mining techniques and a probabilistic classification method that relies on Gaussian Processes exploiting Automatic Relevance Determination (ARD) kernel. Preliminary results obtained on a publicly available dataset are provided