REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS

61. IntroductionLet us consider the clajss of partial differential equations of the form--div(a.(x, Du.)) ~ f on fi, us E Wt,p(fl), (1.1)where a6 is increasingly oscillating as E -- 0, fi is an open bounded subset of R", 1 < p < cot1/p 1/q = 1 and f E W--"q(fl). The homogenization problem for (l.1) consists of the studyof the asymptotic behavior of solutions net as e - 0. In many important cases nE convergesweakly in WI'p(n) to the solution no of the homogenized problem--div(b(Duo)) = f …     

Stacking order and disorder in layered K3Me(CN)6 compounds studied by diffuse X-ray scattering: A realization of the ANNNI model?

Layered crystalline materials like K₃Me(CN)₆ with Me=Cr, Mn, Fe, Co may often exist in various polytypic forms, due to a variety of choices of layer stacking modes. For cases where the interlayer constellations can be limited to only two energetically almost equivalent ways, the buildup of the crystal may be described by a spin-1/2 Ising-like model. For the system presently being studied one can rationalize the layer stacking to a four-valued choice (i.e., a 1D 4-state Potts case), or use an Ising-like two-sublattice model. Previous diffraction studies of K₃Me(CN)₆ indicated that two long-range ordered structures prevailed, an orthohombic one named MDO₁, with one double layer per repetition unit, and a monoclinic one, MDO₂, with two double-layer units. Our studies reveal a more complex situation: The Fe material is for the most part of the MDO₂ type. But in addition, in some crystal samples, a hitherto unobserved phase also appears, with six double-layer repetition units, in fact a hybrid of MDO₁ and MDO₂. The Co material is for the most part of the MDO₂ type, but contains in addition a considerable contribution of stacking disorder, as evidenced by the presence of diffuse X-ray scattering lines. The lines do, however, contain distinct maxima, indicating the presence of several layer stacking modes with preference of two, three, four, five, and seven double-layer correlations. The findings can be qualitatively discussed in terms of the ANNNI model.     

A FILTER BINDING ASSAY FOR CHARACTERIZATION OF ANTIBODIES TOWARDS DAMAGED DNA

A nitrocellulose filter binding assay was used to characterize rabbit antibodies specific for UV-irradiated DNA. The dissociation constant for the UV-DNA-antibody complex was found to be 4.2 × 10⁻¹² M. No significant binding to unirradiated DNA was observed. Unlabelled single-stranded and double-stranded DNA competed with equal efficiency for the radioactively labelled antigen (UV-irradiated φX174 DNA). The antibodies also bound to OsO₄-treated DNA, suggesting that these polyclonal antibodies also recognize minor photoproducts. Caffeine efficiently decreased binding of the antibodies to UV-irradiated DNA.     

A deformation rig for synchrotron microtomography studies of geomaterials under conditions down to 10 km depth in the Earth

A hard X‐ray transparent triaxial deformation apparatus, called HADES, has been developed by Sanchez Technologies and installed on the microtomography beamline ID19 at the European Radiation Synchrotron Facility (ESRF). This rig can be used for time‐lapse microtomography studies of the deformation of porous solids (rocks, ceramics, metallic foams) at conditions of confining pressure to 100 MPa, axial stress to 200 MPa, temperature to 250°C, and controlled aqueous fluid flow. It is transparent to high‐energy X‐rays above 60 keV and can be used for in situ studies of coupled processes that involve deformation and chemical reactions. The rig can be installed at synchrotron radiation sources able to deliver a high‐flux polychromatic beam in the hard X‐ray range to acquire tomographic data sets with a voxel size in the range 0.7–6.5 µm in less than two minutes.     

Homogenization of a Class of Nonlinear Variational Inequalities with Applications in Fluid Film Flow

The authors consider the homogenization of a class of nonlinear variational inequalities, which include rapid oscillations with respect to a parameter. The homogenization of the corresponding class of differential equations is also studied. The results are applied to some models for the pressure in a thin fluid film fluid between two surfaces which are in relative motion. This is an important problem in the lubrication theory. In particular, the analysis includes the effects of surface roughness on both faces and the phenomenon of cavitation. Moreover, the fluid can be modeled as Newtonian or non-Newtonian by using a Rabinowitsch fluid model.     

Origin of lyotropic liquid crystalline mesophase formation and liquid crystalline to mesostructured solid transformation in the metal nitrate salt-surfactant systems

The zinc nitrate salt acts as a solvent in the ZnX-C(12)EO(10) (ZnX is [Zn(H(2)O)(6)](NO(3))(2) and C(12)EO(10) is C(12)H(25)(OCH(2)CH(2))(10)OH) lyotropic liquid crystalline (LLC) mesophase with a drastic dropping on the melting point of ZnX. The salt-surfactant LLC mesophase is stable down to -52 °C and undergoes a phase change into a solid mesostructured salt upon cooling below -52 °C; no phase separation is observed down to -190 °C. The ZnX-C(12)EO(10) mesophase displays a usual phase behavior with an increasing concentration of the solvent (ZnX) in the media with an order of bicontinuous cubic(V(1))-2D hexagonal(H(1))--a mixture of 2D hexagonal and micelle cubic(H(1) + I)-micelle cubic(I)-micelle(L(1)) phases. The phase behaviors, specifically at low temperatures, and the first phase diagram of the ZnX-C(12)EO(10) system was investigated using polarized optical microscopy (POM), X-ray diffraction (XRD), differential scanning calorimetry (DSC), Fourier transform infrared (FTIR), and Raman techniques and conductivity measurements.     

First principles studies of a Xe atom adsorbed on Nb(1 1 0) surface

We study adsorption sites of a single Xe adatom on Nb(1 1 0) surface using a density functional theory approach: the on-top site is the most favorable position for adsorption. We compare the binding features of the present study to earlier studies of a Xe adatom on close-packed (1 1 1) surfaces of face-centered cubic metals. The different features are attributed through a microscopic picture to the less than half filled d-states in Nb.