Robust convergence of multi point flux approximation on rough grids

This paper establishes the convergence of a multi point flux approximation control volume method on rough quadrilateral grids. By rough grids we refer to a family of refined quadrilateral grids where the cells are not required to approach parallelograms in the asymptotic limit. In contrast to previous convergence results for these methods we consider here a version where the flux approximation is derived directly in the physical space, and not on a reference cell. As a consequence, less regular grids are allowed. However, the extra cost is that the symmetry of the method is lost.     

Spatial correlations of pairing collective states

The properties of the low-energy nuclear spectrum are greatly affected by pairing correlations. We study these effects in the nucleus ²¹⁰Pb which has two particles moving outside closed shells. The configuration-mixed wave functions describe the motion of particles which are on the average closer together than they would be if the particles were confined to particular orbitals. Since the energy associated with pairing correlations is much smaller than the Fermi energy the width of the associated probability distribution is determined by the wavelength of single particles moving close to the Fermi surface. Despite the fact that the amplitudes associated with high-lying configurations are small, their net effect is important, typically changing the collectivity of the states by a factor of about two. The results of the microscopic calculations compare well with a semiclassical pairing transition density calculated on the basis of the Thomas-Fermi approximation.     

Probing the low angular momentum window in fusion reactions

The angular correlation between two alpha particles evaporated from the compound nucleus is sensitive to the initial spin population, and can thus be used to test the possible existence of angular momentum windows in the fusion cross section. A model calculation performed for the ²⁸Si + ²⁸Si fusion reaction at E_cm = 60 MeV is used as an illustration.     

Instability of Buckley-Leverett flow in a heterogeneous medium

We study the simultaneous one-dimensional flow of water and oil in a heterogeneous medium modelled by the Buckley-Leverett equation. It is shown both by analytical solutions and by numerical experiments that this hyperbolic model is unstable in the following sense: Perturbations in physical parameters in a tiny region of the reservoir may lead to a totally different picture of the flow. This means that simulation results obtained by solving the hyperbolic Buckley-Leverett equation may be unreliable.Symbols and Notation f fractional flow function varying withs andx - value off outsideI - value off insideI - local approximation off around¯x - f ^–,f ⁺ values of - f _j ⁿ value off atS _j ⁿ andx _j - g acceleration due to gravity [ms^–2] - I interval containing a low permeable rock - k dimensionless absolute permeability - k ^* absolute permeability [m²] - k _c ^* characteristic absolute permeability [m²] - k _ro relative oil permeability - k _rw relative water permeability - L ^* characteristic length [m] - L ₁ the space of absolutely integrable functions - L the space of bounded functions - P _c dimensionless capillary pressure function - P _c ^* capillary pressure function [Pa] - P _c ^* characteristic pressure [Pa] - S similarity solution - S _j ⁿ numerical approximation tos(x_j, t_n) - S ₁, S₂,S ₃ constant values ofs - s water saturation - value ofs at - s ^L left state ofs (wrt. ) - s ^R right state ofs (wrt. ) - s s for a fixed value of in Section 3 - T value oft - t dimensionless time coordinate - t ^* time coordinate [s] - t _c ^* characteristic time [s] - t _n temporal grid point,t _n=n t - v ^* total filtration (Darcy) velocity [ms^–1] - W, , v dimensionless numbers defined by Equations (4), (5) and (6) - x dimensionless spatial coordinate [m] - x ^* spatial coordinate [m] - x _j spatial grid piont,x _j=j x - discontinuity curve in (x, t) space - right limiting value of¯x - left limiting value of¯x - angle between flow direction and horizontal direction - t temporal grid spacing - x spatial grid spacing - length ofI - parameter measuring the capillary effects - argument ofS - _o dimensionless dynamic oil viscosity - _w dimensionless dynamic water viscosity - _c ^* characteristic viscosity [kg m^–1s^–1] - _o ^* dynamic oil viscosity [kg m^–1s^–1] - _w ^* dynamic water viscosity [k gm^–1s^–1] - _o dimensionless density of oil - _w dimensionless density of water - _c ^* characteristic density [kgm^–3] - _o ^* density of oil [kgm^–3] - _w ^* density of water [kgm^–3] - porosity - dimensionless diffusion function varying withs andx - ^* dimensionless function varying with s andx ^* [kg^–1m³s] - _j ⁿ value of atS _j ⁿ andx _j This research has been supported by VISTA, a research cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap a.s. (Statoil).     

Multigrid in H (div) and H (curl)

Summary. We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the Hilbert spaces and in three dimensions. We show that if appropriate finite element spaces and appropriate additive or multiplicative Schwarz smoothers are used, then the multigrid V-cycle is an efficient solver and preconditioner for the discrete operator. All results are uniform with respect to the mesh size, the number of mesh levels, and weights on the two terms in the inner products. Received June 12, 1998 / Revised version received March 12, 1999 / Published online January 27, 2000     

Erratum to: Almost complex structures in 6D with non-degenerate Nijenhuis tensors and large symmetry groups

We correct an error in the second part of Theorem 3 of our original paper.     

Millisecond dynamics in glutaredoxin during catalytic turnover is dependent on substrate binding and absent in the resting states

Conformational dynamics is important for enzyme function. Which motions of enzymes determine catalytic efficiency and whether the same motions are important for all enzymes, however, are not well understood. Here we address conformational dynamics in glutaredoxin during catalytic turnover with a combination of NMR magnetization transfer, R(2) relaxation dispersion, and ligand titration experiments. Glutaredoxins catalyze a glutathione exchange reaction, forming a stable glutathinoylated enzyme intermediate. The equilibrium between the reduced state and the glutathionylated state was biochemically tuned to exchange on the millisecond time scale. The conformational changes of the protein backbone during catalysis were followed by (15)N nuclear spin relaxation dispersion experiments. A conformational transition that is well described by a two-state process with an exchange rate corresponding to the glutathione exchange rate was observed for 23 residues. Binding of reduced glutathione resulted in competitive inhibition of the reduced enzyme having kinetics similar to that of the reaction. This observation couples the motions observed during catalysis directly to substrate binding. Backbone motions on the time scale of catalytic turnover were not observed for the enzyme in the resting states, implying that alternative conformers do not accumulate to significant concentrations. These results infer that the turnover rate in glutaredoxin is governed by formation of a productive enzyme-substrate encounter complex, and that catalysis proceeds by an induced fit mechanism rather than by conformer selection driven by intrinsic conformational dynamics.     

Application of supplementary flow in comprehensive 2D liquid chromatography combining SEC and RPC

A comprehensive two-dimensional HPLC system (SEC x RPC) was evaluated. Various model compounds with differing hydrophobicity (log D: -0.08 to 2.22) and size (MW: 194 to 66.0 x 10(3)) were used. In order to reduce the run time of the second dimension, and thereby optimize the number of runs per unit volume from the first dimension, short RPC columns were used (7.5 mm). This column size demanded a low concentration of methanol in the mobile phase from the first dimension, in order to avoid severe band broadening and solute loss. Secondary interactions on SEC make a high methanol concentration in the mobile phase a necessity. Up to 40% methanol was required to diminish non-ideal SEC behavior. These conditions were non-compatible with trapping of hydrophilic compounds on RPC. The use of a supplementary flow (0.1% TFA) mixed after the first dimension led to better peak shape and trapping of hydrophilic compounds in the second dimension. This demanded flow adjustment in SEC, which in turn caused performance improvement and an increase in analysis time, making more RPC separations possible. These factors contributed to a larger peak capacity.     

Multistep determination of enzyme activity by flow injection and sequential injection analysis. Assay of amyloglucosidase

A multi-point assay for determination of the activity of amyloglucosidase (AMG) by FIA and SIA is described. The assay is based on two consecutive reactions that are mutually incompatible. Both the FIA and SIA procedures allow these two reactions to be completely separated, whereby each of the processes can be individually optimized with respect to operational parameters. Special emphasis is placed on comparing the performance and applicability of the two procedures for this type of assay.