Numerical and theoretical study of a Dual Mesh Method using finite volume schemes for two phase flow problems in porous media

Summary. In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this problem with finite volume schemes. In a simplified case (elliptic - hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates for different test-cases. Received March 21, 1997 / Revised version received October 13, 1997     

Mössbauer study of small amounts of iron in graphite,around the diamond-graphite pressure-temperature stability region

An exploratory Mössbauer spectroscopy study of the Fe-C system in the C rich region, prepared by high pressure-high temperature treatment near the graphite-diamond stability line, was made. The results obtained for the different processing conditions give no evidence of Fe intercalation in graphite. The presence of some water in the cell produced hydrated Fe complexes, which can explain the deleterious effect of water or hydrogen in the high pressure diamond synthesis.     

Improved quantitation of 13-cis- and all-trans-acitretin in human plasma by normal-phase high-performance liquid chromatography.

A reliable analytical method has been developed for measurement of 13-cis- and all-trans-acitretin (Neotigason) in human plasma by normal-phase high-performance liquid chromatography, with ultraviolet detection. Human plasma was obtained after centrifugation of whole blood samples and deproteinized by ethanolic denaturation. After liquid-liquid extraction with water-n-hexane, and aliquot ws chromatographed on a silica column using isocratic elution with n-hexane-methylsalicylate-acetic acid (200:18:0.6, v/v). The wavelength was set at 360 nm, and for plasma samples a limit of quantification of 3-4 ng/ml was obtained. All manipulations were carried out under dim light conditions to prevent photoisomerization.     

The canalicular structure of compact bone in the rat at different ages.

Osteocytes communicate through a canalicular system that maintains the vitality and mineral metabolism of bone. Casting the vascular canals and canaliculi of compact bone with methacrylate and viewing them with scanning electron microscopy shows their extent and relationships. Confocal laser scanning microscopy of the same specimen before corrosion establishes the degree of calcification of the different tissue components. These methods were used to compare basal with alveolar compact bone in the rat mandible at different ages. Sections of the mandibular molar region were placed in a methacrylate resin. After polymerization and study with confocal microscopy, the organic matrix was removed. Juvenile rats had large irregular central vascular canals and lacunae that were more concentric in the basal than the alveolar bone. Cast lacunae were round, and the canaliculi from these lacunae were short and thick in both bones. Adult rats had regular concentrically arranged lacunae in the basal bone. Cast lacunae were ellipsoid and flatter in the basal bone than in the alveolar bone. The intercommunicating canaliculi were increased and canaliculi had more branching than the juvenile rats. The aged rats had fewer vascular canals, lacunae, and canaliculi and had osteoporotic changes. The cast lacunae were slender and flat especially in the basal bone. The porosity of the mandible became more pronounced in the alveolar than in the basal bone with aging. The canaliculi of mandibular compact bone thinned and developed extensive branching with adulthood but decreased in size and number with advanced age. Lacunae proceed from the large circular structures of youth to the flat forms of the aged. These studies show that the internal structure of compact bone changes with age and mirrors its functional state.     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

NMRON studies of ferromagnetic hcp and fcc Co

The high resolution hyperfine spectroscopy, modulated adiabatic passage of oriented nuclei (MAPON), has been applied for the first time to high purity, elemental systems. Detailed comparisons between the electric quadrupole hyperfine interactions (EQI’s) and, in particular, their distributions, are obtained for⁶⁰CoCo where the hosts are a single crystal of hcp cobalt and a polycrystalline cobalt foil of predominantly fcc character. For hcp Co, with the electronic magnetization, M, parallel to the c-axis, the mode value P/h=3e²qQ/4I(2I−1)h=−48.5(5) kHz. This fractional distribution implies the sharpest electric field gradient (efg) measured in a metal to date, using MAPON spectroscopy, in excess of two times sharper than that of the most dilute impurity efg in a crystallographically cubic ferromagnetic host. The mode efg is V_zz=−27.3(32)×10¹⁹ Vm⁻². For the polycrystalline, predominantly fcc foil, prepared by quenching, the EQI mode value is P/h=−6.2(4) kHz with a FWHM of 12.0(7) kHz yielding a mode efg of V_zz=−3.5(5)×10¹⁹ Vm⁻².     

Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities

We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W^{?1, p} spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain L^p estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd.     

Lines Tangent to Four Triangles in Three-Dimensional Space

We investigate the lines tangent to four triangles in R³. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.     

The magnetic properties of Be-codoped GaMnN grown via molecular beam epitaxy

GaMnN and Be-codoped GaMnN were grown via molecular beam epitaxy using a single GaN precursor and their structural and magnetic properties were examined. X-ray diffraction and superconducting quantum interference device (SQUID) measurements revealed that the grown layers are homogeneous without precipitates. The saturation magnetization of GaMnN has increased from ∼4 to ∼16 emu/cm³ via codoping of Be. The d–d exchange interaction between Mn atoms was discussed for the ferromagnetism of GaMnN.     

Enhanced cleaning of photoresist film on a transparent substrate by backward irradiation of a Nd:YAG laser

Laser cleaning of a photoresist (PR) on a glass substrate using ns-pulsed Nd:YAG laser was studied. The direction of the substrate facing the laser beam was varied as a main parameter as well as the power of the laser beam. The backward irradiation (BWI) of the third harmonic beam (355 nm) completely removed 1.2 μm thick PR layer with three pulses at 1.5 J/cm² leaving no residues behind; while the forward irradiation (FWI) at the same condition just partially cleaned it. To investigate the difference of removal mechanisms between irradiation directions, the size distributions of particulates generated during laser cleaning were observed using an optical particle counter. The concentration of micron-sized particulates increased with increasing laser fluence up to 1 J/cm² for FWI and 0.5 J/cm² for BWI and then decreased at higher fluences because the target was a very thin film. The concentration of larger particulates for BWI was much higher than that for FWI implying the difference in removal mechanisms. In consideration of the size characteristics of the particulates and the temperature profiles of the PR layer, the most probable distinct mechanism for the BWI would be a blasting due to high temperature at the PR/glass interface. The particulate number concentration decreased rapidly after the completion of cleaning, suggesting that the measurement of the particulate concentration could detect the progress of the cleaning. Our results demonstrated that the backward irradiation will be useful for the laser cleaning of film-type contaminants on an optically transparent substrate.