Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids

A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.     

Rigidity Result for Certain Three-Dimensional Singular Spaces and Their Fundamental Groups

In this paper, we introduce a particularly nice family of locally CAT(−1) spaces, which we call hyperbolic P-manifolds. For X³ a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of X³ are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometry rigidity for these spaces.     

Ditopic Calixcrowns with Inequivalent Crown Loops: Synthesis and Structural Characterisation of an Unsymmetrical Calix[4]arene biscrown-6

Consecutive base-catalysed reactions of calix[4]arene with the ditosylates of two different polyetherdiols result in the relatively efficient production of an unsymmetrical calix biscrown-6 which, after reduction of an ethoxycarbonyl substituent to an hydroxymethyl group, has been characterised structurally by a room-temperature, single crystal X-ray study of its chloroform solvate. Crystals of ( 4), C53H62O13... 0.57CHCl3, are triclinic, P¯1, a 18.95(3), b 12.394(9), c 11.756(7) Å 106.93(5), 101.77(8), 94.63(8)°, Z = 2; R was 0.088 for 2231 observed' (I > 3(I)) diffractometer data.