Density Correlations in the Two-Dimensional Coulomb Gas

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the Möbius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.     

Influence of solute mobility on dislocation motion I. Basic model

Dislocation motion in the real lattice of alloys is highly complex. In a certain temperature range the dynamic strain ageing phenomena have been reported. In this paper the influence of mobile solute atoms (as obstacles) on the motion of dislocation is analysed. Both processes are assumed to be thermally activated. A new model based on this assumption is proposed. The dislocation velocity and the friction stress (due to solute-dislocation interactions) are calculated. A change in the friction stress caused by solute mobility is discussed.     

On quasi-conformally flat weakly Ricci symmetric manifolds

The object of the present paper is to study quasi-conformally flat weakly Ricci symmetric manifolds.      

Asymptotic analysis of elastic curved rods

We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross‐sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non‐smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd.     

The critical probability for random Voronoi percolation in the plane is 1/2

We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ², and form the Voronoi tessellation of ℝ² with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These results are analogous to Kesten's results for bond percolation in ℤ². The result corresponding to Harris' Theorem for bond percolation in ℤ² is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting. For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof of Kesten's Theorem for ℤ²; we hope they will be applicable in other contexts as well. Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900 Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland     

Dehydration and dehydroxylation of reduced charge montmorillonite

Reduced charge montmorillonites (RCM) were prepared by the thermal treatment of lithiumsaturated montmorillonite. Samples prepared by mild thermal treatment with lithium contained more water sorbed than the original montmorrilonite. When RCMs were prepared, part of the lithium cations reacted with hydroxyl groups in the octahedral sheet and released protons, which reacted with the structure. Acid treatment probably enhanced the surface area. which was reflected in the amount of water sorbed. Deprotonation of hydroxyl groups was proved by the measurements of the ignition loss. The heating of lithium saturated montmorillonite at higher temperatures brough about the collapse of the interlayers and a decrease in the amount of water sorbed.     

Electrochemical characterization of composite membranes based on crown-ethers intercalated into montmorillonite

Oxyethylene macrocyclic compounds (crown-ethers) act as ligands of intracrystalline cations of certain layered silicates as montmorillonites. Stable intercalation materials are formed which are used to prepare organic-inorganic membranes by encapsulating these intercalation compounds with a poly-butadiene thin coating. Electrochemical Impedance Spectroscopy (EIS) is used to study the resulting composite membranes in contact with aqueous electrolytes. From the impedance plots, the ionic resistance of the membranes is obtained. The thickness of the polybutadiene coating is an important factor determining the ability of ions to pass across the membrane. Marked differences in the ionic resistance are observed as a function of the nature of the interlayer macrocyclic compound. For non-intercalated montmorillonite membranes, the ionic resistance is strongly reduced, whereas for some crown-ether intercalated materials such as 18-crown-6 and dibenzo 24-crown-8, iono-selective membranes are obtained. Concerning the nature of the electrolyte, cations exhibiting greater hydration energies show higher difficulties to pass through the membrane and, consequently, the ionic resistance increases.     

Charge-transfer chromatographic study of the interaction of anticancer drugs with acetyl-β-cyclodextrin

The interaction between 23 anticancer drugs and acetyl-β-cyclodextrin (acetyl-β-CD) was studied by reversed-phase charge-transfer thin-layer chromatography and the relative strength of interaction was calculated. Acetyl-β-CD formed inclusion complexes with 16 compounds, the complex always being more hydrophilic than the uncomplexed drug. The inclusion forming capacity of drugs differed considerably according to their chemical structure. The significant linear correlation between the hydrophobicity and specific hydrophobic surface area of anticancer drugs indicated that they can be considered as a homologous series of compounds, however, their chemical structures are highly different.     

On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.