A finite volume–multigrid method for flow simulation on stratified porous media on curvilinear co‐ordinate systems

This paper presents a numerical study of infiltration processes on stratified porous media. The study is carried out to examine the performance of a finite volume method on problems with discontinuous solutions due to the transmission conditions in the interfaces. To discretize the problem, a curvilinear co‐ordinate system is used. This permits matching the interface with the boundary of the control volumes that interchange fluxes between layers. The use of the multigrid algorithm for the resulting systems of equations allows problems involving a large number of nodes with low computational cost to be solved. Finally, some numerical experiments, which show the capillary barrier behaviour depending on the material used for the different layers and the geometric design of the interface, are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

On the axiomatization of the τ-value

Summary The τ-value is a solution concept for a subclass of games with transferable utility introduced and axiomatized by Tijs (1981, 1987). In this note an alternative characterization of the τ-value by means of five axioms is offered. Two of them are well-known: efficiency and translation equivalence; the other three relate the solution of a game with the minimal and maximal aspiration vectors involved in the definition of the τ-value. This work was partially supported by Universidad del País Vasco (projects UPV 036.321-H061/91 and UPV 036.321-HA186/92).     

Fresnel diffraction by deterministic fractal gratings: An experimental study

Experimental results are presented for light diffraction under the Fresnel regime by two types of fractal gratings: triadic Cantor bars and Vicsek fractals. It is shown that the evolution of the diffraction patterns in the Fresnel regions reveals the hierarchical structure of deterministic fractal gratings.     

Approximate preservation of quadratic first integrals by explicit Runge–Kutta methods

The approximate preservation of quadratic first integrals (QFIs) of differential systems in the numerical integration with Runge–Kutta (RK) methods is studied. Conditions on the coefficients of the RK method to preserve all QFIs up to a given order are obtained, showing that the pseudo-symplectic methods studied by Aubry and Chartier (BIT 98(3):439–461, 1998) of algebraic order p preserve QFIs with order q = 2p. An expression of the error of conservation of QFIs by a RK method is given, and a new explicit six-stage formula with classical order four and seventh order of QFI-conservation is obtained by choosing their coefficients so that they minimize both local truncation and conservation errors. Several formulas with algebraic orders 3 and 4 and different orders of conservation have been tested with some problems with quadratic and general first integrals. It is shown that the new fourth-order explicit method preserves much better the qualitative properties of the flow than the standard fourth-order RK method at the price of two extra function evaluations per step and it is a practical and efficient alternative to the fully implicit methods required for a complete preservation of QFIs.     

Biochemical analysis of a caveolae-enriched plasma membrane fraction from rat liver

We isolated and characterized a subcellular fraction derived from the blood-sinusoidal plasma membrane of hepatocytes enriched in caveolin and containing several of the molecular components described to be present in caveolae isolated from other cell types. A morphological study by electron microscopy revealed that it was composed of caveolae-attached membrane profiles. Immunoelectron microscopy of isolated fraction showed the specific labeling of internal caveolae membranes with anti-caveolin antibody. Finally, one- and two-dimensional electrophoresis and Western blotting were used for the biochemical analysis of this new rat liver plasma membrane fraction. From the biochemical and the morphological characterization, we conclude that the caveolae-enriched plasma membrane fraction is a plasma membrane fraction, which originates from specialized regions of the sinusoidal plasma membrane, enriched in caveolae.     

Surface-enhanced Raman spectrometry of amiloride on colloidal silver

Surface-enhanced Raman spectrometry (SERS) of the diuretic drug amiloride is discussed. The SERS-active substrate used is colloidal silver, which is prepared at room temperature by simple tetrahydroborate reduction of an aqueous solution of silver nitrate. SERS detection of amiloride in human urine is illustrated. The reproducibility of quantitative SERS data is supported by the simultaneous measurement of the scattering signal and transmitted light. Relative standard deviations at the 5% level are compatible with many practical analytical situations.     

Gadolinium and neodymium citrates: evidence for weak ferromagnetic exchange between gadolinium(III) cations

A new lanthanide citrate motif of general formula [Ln(Hcit)(H2O)2.H2O]n, where Ln = Gd (1) and Nd (2) and Hcit3- = C(OH)(COO-)(CH2COO-)2, has been synthesized hydrothermally from Ln2O3 and citric acid at 100 degrees C and characterized by elemental analysis, IR, TG-DTA, single-crystal X-ray diffraction, and magnetic measurements. The structures can be seen as "ladder chains" along the a axis, with dinuclear Ln2O2 units serving as "steps" and R-COO groups as "uprights", which are connected by H bonds. The magnetic susceptibility between 2 and 300 K and the magnetization at 2 K, as a function of magnetic field between 0 and 5 T, were measured for both compounds. By modeling the magnetic behavior of the Gd compound with a dinuclear Hamiltonian [symbol: see text](S) = gmu(B)(S(A) + S(B))B(o) - J(o)S(A)S(B) (S(A) = S(B) = 7/2), a ferromagnetic exchange interaction J(o) = 0.039 cm(-1) was evaluated between Gd ions situated at d(o) = 4.321 angstroms in dinuclear units bridged by two symmetry-related tridentate carboxylate oxygens. The EPR spectrum of the Gd compound is discussed. The temperature dependence of the susceptibility of the Nd compound is caused by the depopulation of the excited crystal-field levels when the temperature decreases. The magnetic-field dependence of the magnetization of 2 is attributed to the ground-state Kramers' doublet populated at 2 K. The g factor of this ground-state doublet is calculated from the data and compared with values for other compounds reported in the literature.