Wetting Phase Bridges Establish Capillary Continuity Across Open Fractures and Increase Oil Recovery in Mixed-Wet Fractured Chalk

The effect of fractures on oil recovery and in situ saturation development in fractured chalk has been determined at near neutral wettability conditions. Fluid saturation development was monitored both in the matrix and in the fractures and the mechanisms of fracture crossing were determined using high spatial resolution MRI. Capillary continuity across open oil-filled fractures was verified by imaging the water bridges established within the fracture. Despite an alternate escape fracture for the water, separate water bridges were shown to be stable for the entire duration of the experiments. The established capillary contact resulted in oil recovery exceeding the spontaneous imbibition potential in the outlet-isolated cores by ca. 10% PV. This is explained by viscous recovery provided by water bridges across open fractures. The size of the bridges seemed to be controlled by the wettability of the rock and not by the differential pressure applied across the open fracture.     

Local Lead–Lag Relationships and Nonlinear Granger Causality: An Empirical Analysis

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.     

Order-disorder transition in a system of magnetic holes

Polystyrene spheres of the same size (10–100μm) dispersed in ferrofluid produce voids, which have been denoted magnetic holes. A two-dimensional system of interacting magnetic holes confined between two glass plates and subject to rotating magnetic fields in the sample plane are studied in a light microscope. For low frequencies of the field rotation, the holes form pairs, which arrange themselves in a regular triangular lattice when stabilized with a weak constant field normal to the sample plane. By increasing the frequency of the rotating field, we observe that above a critical frequency, the steady forward rotation of the pairs is interrupted by backward rotations in short time intervals. Because the intervals of backward rotation occur at different times for each individual pair, disorder is introduced in the system, and the triangular lattice of pairs “melts” and forms a liquid-like structure at high rotation frequencies of the field. This “melting” transition is observed both directly and in light scattering experiments using a laser.     

Graph pegging numbers

In graph pegging, we view each vertex of a graph as a hole into which a peg can be placed, with checker-like “pegging moves” allowed. Motivated by well-studied questions in graph pebbling, we introduce two pegging quantities. The pegging number (respectively, the optimal pegging number) of a graph is the minimum number of pegs such that for every (respectively, some) distribution of that many pegs on the graph, any vertex can be reached by a sequence of pegging moves. We prove several basic properties of pegging and analyze the pegging number and optimal pegging number of several classes of graphs, including paths, cycles, products with complete graphs, hypercubes, and graphs of small diameter.     

Irreducibility of the punctual quotient scheme of a surface

It is shown that the punctual quotient schemeQ _l ^r parametrizing all zero-dimensional quotients of lengthl and supported at some fixed point O∈A ² in the plane is irreducible.