Displacement propagators of brine flowing within different types of sedimentary rock

This paper explores the correlation between different microstructural characteristics of porous sedimentary rocks and the flow properties of a Newtonian infiltrating fluid. Preliminary results of displacement propagator measurements of brine solution flowing through two types of sedimentary rock cores are reported. The two types of rocks, Bentheimer and Portland, are characterized by different porosities, pore-size distributions and permeabilities. Propagators have been measured for brine flow rates of 1 and 5 ml/min. Significant differences are seen between the propagators recorded for the two rocks, and these are related to the spatial distribution of porosity within these porous media.     

MR-u: Material Characterization Using 3D Displacement-Encoded Magnetic Resonance and the Virtual Fields Method

Experimental Mechanics - Experimental, fully three-dimensional mechanical characterization of opaque materials with arbitrary geometries undergoing finite deformations is generally challenging. We...     

A cumulant analysis for non-Gaussian displacement distributions in Newtonian and non-Newtonian flows through porous media

We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S(q) of flow displacement distributions P(zeta) with mean displacement (zeta) for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln(S(q)). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P(zeta), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15.6+/-2.3% enhancement of the variance sigma(2) of displacement distributions when compared to flow experiments with water.     

Spatial and temporal coarse graining for dispersion in randomly packed spheres

The propagator for molecular displacements P(zeta, t) and its first three cumulants were measured for Stokes flow in monodisperse bead packs with different sphere sizes d and molecular diffusion coefficients D(m). We systematically varied the normalized mean displacement /d and diffusion length L(D)=sqrt[2D(m)t]/d. The experimental results map onto each other with this scaling. For L(D)/d<0.2 the propagator remains non-Gaussian, and thus an advection diffusion equation is not obeyed, for mean displacements measured up to 10d. A Gaussian shape is approached for large mean displacements when L(D)>0.3d.     

Minimizers of Higher Order Gauge Invariant Functionals

We introduce higher order variants of the Yang–Mills functional that involve \((n-2)\)-th order derivatives of the curvature. We prove coercivity and smoothness of critical points in Uhlenbeck gauge in dimensions \(\mathrm {dim}M\le 2n\). These results are then used to establish the existence of smooth minimizers on a given principal bundle \(P\rightarrow M\) for subcritical dimensions \(\mathrm {dim}M<2n\). In the case of critical dimension \(\mathrm {dim}M=2n\) we construct a minimizer on a bundle which might differ from the prescribed one, but has the same Chern classes \(c_1,\ldots ,c_{n-1}\). A key result is a removable singularity theorem for bundles carrying a \(W^{n-1,2}\)-connection. This generalizes a recent result by Petrache and Rivière.