Magnetic Resonance Imaging of Hydrodynamic Dispersion in a Saturated Porous Medium

By using nuclear magnetic resonance imaging (NMRI) we have been able to analyse dispersion at the microscopic scale during steady-state flow through water-saturated glass beads. The flow rate through the porous medium was chosen high enough in order to neglect the influence of molecular diffusion on dispersion. Velocity statistics were measured, by NMRI, within slices of increasing thickness perpendicular to the direction of flow. It took more than two bead diameters before a representative elementary volume (REV) for the mean velocity was reached. This was in a region in the middle of the column that was not influenced by the boundary conditions. There the velocity variance decreased exponentially as a function of the slice thickness, due we consider to the formation of an interconnecting streamline network. The exponential decrease in the velocity variance reflects the transition from a local pattern of stochastic–convective flow to a convective–dispersion regime at the scale of the REV. We found that the point-like preferential influx and efflux boundary condition increased velocity variances and thus enhanced longitudinal hydrodynamic dispersion. Using the transverse correlation length of longitudinal velocity variance, we derived a mean transverse dispersivity that agreed well with Saffmans (1959) model. So we have been able to provide for the first time a direct observation verification of a part of Saffmans (1959) conjectures. By NMRI we observed this value to be independent of the observation scale of the slice thickness.     

A Generalization of Lerch’s Formula

We give higher-power generalizations of the classical Lerch formula for the gamma function.     

Analytic regularity for an operator with Treves curves

We study a partial differential operator with analytic coefficients, which is of the form “sum of squares”. is hypoelliptic on any open subset of , yet possesses the following properties: (1) is not analytic hypoelliptic on any open subset of that contains 0. (2) If u is any distribution defined near with the property that is analytic near 0, then u must be analytic near 0. (3) The point 0 lies on the projection of an infinite number of Treves curves (bicharacteristics).These results are consistent with the Treves conjectures. However, it follows that the analog of Treves conjecture, in the sense of germs, is false.As far as we know, is the first example of a “sum of squares” operator which is not analytic hypoelliptic in the usual sense, yet is analytic hypoelliptic in the sense of germs.     

A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities

We study the bifurcation diagrams of positive solutions of the two point boundary value problem

     

Total curvatures of a closed curve in Euclidean -space

A classical result by J. W. Milnor states that the total curvature of a closed curve in the Euclidean -space is the limit of the total curvatures of polygons inscribed in . In the present paper a similar geometric interpretation is given for all total curvatures , .

     

Cycle decompositions and train tracks

We prove that the disjoint cycle decomposition of the permutation consists of cycles of at most distinct lengths. The proof relies on the geometry and topology of simple closed curves and train tracks on a closed surface of genus .

     

The monopole equations and -holomorphic curves on weakly convex almost Kähler 4-manifolds

We prove that a weakly convex almost Kähler 4-manifold contains a compact, non-constant -holomorphic curve if the corresponding monopole invariant is not zero and if the corresponding line bundle is non-trivial.

     

Mechanical Properties of a Single Electrospun Fiber and Its Structures

Summary: A method to measure the Young's modulus of a single electrospun polyacrylonitrile (PAN) fiber is reported. The Young's modulus can be calculated from the force‐displacement curves obtained by the bending of a single fiber attached to an atomic force microscopy (AFM) cantilever. It is suggested that the high modulus of electrospun fibers is caused by the orientation of molecular chains, which is confirmed by wide‐angle X‐ray diffraction (WAXD) measurements. The communication will provide a basic understanding of the relationship between mechanical properties and structures of electrospun fibers.

A PAN fiber was attached to a contact mode cantilever to facilitate the measurement of force‐displacement curves and Young's modulus.     

Generalising a characterisation of Hermitian curves

This article proves a characterisation of the classical unital that is a generalisation of a characterisation proved in 1982 by Lefèvre-Percsy. It is shown that if is a Buekenhout-Metz unital with respect to a line in such that a line of not through meets in a Baer subline, then is classical. An immediate corollary is that if is a unital in PG such that is Buekenhout-Metz with respect to two distinct lines, then is classical. Received 5 August 1999; revised 15 February 2000.     

大型风力发电机组的功率曲线

介绍了国产化风机功率曲线的测量方法.