The thermal expansion and anisotropic magnetomiction of the R C q Laves phases were studied in the temperature range 4-500 K using the x-ray powder diffraction methcd.In the heavy RCo2 the magnetic moment of the itinerant d electron subsystem derived imm the magnetovolume effect was found to fit well with the magnetization curve of YCo2. A pronounced paraprocess above the metamagnetic m i t i o n has been observed when increasing the f-d exchange field. "%e type and temperature variation of the distortion of the njbic unit cell of the t h ~ compounds PrCol, NdCo2 and SmCoz have been studied in detail. The corresponding magnetostriction ~nslants 1111 or AIM were calculated. At 4 K the following values have been obtained: R c 0 2 . temgonai distortion. easy axes (100). AIM = -3.4 x SmCq, rhombohedral distortion, easy axes (Ill), A l l , r -4.6 x NdC4, teuagonal distortion and eaxy axes (100) for 42 K c I e T,. orthorhombic distortion and easy axes (110) for T c 42 K with 111111 = 1.9 x aid AIM = -4.0 x IO-' .

We found thal in TmCm the molecular held does not exceed the critical value necessary to induce long-range magnetic order in the CO d-electron subsystem, which is in c n n m t to the other heavy RCoz compounds. Below Tc = 3.8 K a firstader magnetic phase transition at 3.4 K exists, which is due to a r e m g e m e n l of the Tm 4f magnetic moments. When substituting Tm by Gd long-range magnetic order appears in the CO d subsystem. The onset of the magnetic order in the d-electron subsystem can most clearly be seen from thermal expansion measurements. There is an increasing positive volume anomaly with increasing Gd content below Tc.The estimated magnetostriction constant i l I I of TmCoz is -4.1 x io-), in agreement with the single-ion model.Pronounced discontinuities al Tc are characteristic for the transpon properties (resistivity and thermopower) for TmCo2 a well as for the pseudobinary Tmlp,Cd,C% compounds. At elevated temperatures the physical properties of all these compounds are dominated by spin fluctuations.

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An implicit flux-corrected transport (FCT) algorithm has been developed for a class of chemotaxis models. The coefficients of the Galerkin finite element discretization has been adjusted in such a way as to guarantee mass conservation and keep the cell density nonnegative. The numerical behaviour of the proposed highresolution scheme is tested on the blow-up problem for a minimal chemotaxis model with singularities. It has also been shown that the results for an Escherichia coli chemotaxis model are in good agreement with the experimental data reported in the literature. 2000 Mathematics Subject Classification: 35B36; 65N30; 92C15; 92C17.