A comparative study of TVD‐limiters—well‐known limiters and an introduction of new ones

This paper gives a comparative study of TVD‐limiters for standard explicit Finite Volume schemes. In contrast to older studies, it includes also unsymmetrical limiter functions that depend on the local CFL‐number. We classify the limiters and show how to extend these families of limiters. We introduce a new member of the Superbee family, which is adapted to Roe's linear third‐order scheme. Based on an idea by Serna and Marquina, new smooth limiters are introduced, which turn the van Leer and van Albada limiters into complete classes of limiters. The comparison of the limiters is done with some standard test cases. The results clarify the influence of the chosen limiter on the quality of the numerical results. Compared with ENO or WENO schemes, they also show the high resolution, which can be obtained by a CFL‐number‐dependent limiter when the grid is not highly refined. Copyright © 2010 John Wiley & Sons, Ltd.     

On N1-free modules with trivial dual

In this paper we generalize the notion of Fountain-Gould order to the context of associative pairs. We give theorems about the existence and uniqueness of the left quotient pair and we obtain a Goldie-like haracterization which describes left orders in semiprime pairs coinciding with their socle.     

470—The proton pump at work: Part I. The basic concept of excess proton/defect proton translocation

The Nagle-Morowitz proton pump, which is based on proton transport in water and ice, is shown to be inapplicable to weakly H-bonded proton transport systems. It is demonstrated that in weakly or non H-bonded systems protons can migrate either as excess protons H using a high-lying proton conduction band or as defect protons H′ using intermediate energy levels. As H? the protons act as positive charge carriers endowed with a very high mobility. As H′ they act as negative charge carriers. The H′ transport mechanism involves thermally activated proton tunneling. Owing to the very large mobility differences between H? and H′, > 10⁶, very high potentials can be self-generated in any situation which creates a concentration gradient. Proton conductivity data on inorganic model compounds are presented. Applying these results to proton transport across biomembranes, transmembrane potentials U_m, acidification Δ pH and transient phenomena can be explained as result of H? and H′ translocation.     

Theoretical studies on the decarboxylation reaction in thiamin catalysis

The conformational behavior and the stability of thiazolium and thiamin diphosphate (ThDP) adducts formed by the C2 addition of the substrates pyruvate and glyoxylate to the corresponding thiamin systems are investigated within the force-field version PIMM 90 as well as the semiempirical AM 1 and PM 3 methods. Moreover, the reaction coordinate of the decarboxylation process of the adducts with respect to the C2α(SINGLEBOND)COO⁻ bond are calculated by PM 3 and AM 1. The calculations on the key intermediates of the Breslow mechanism are performed in order to study the steric aspects of both substrate adducts that show a different pathway in the catalytic cycle. The alternative structural findings for the decarboxylation products are compared with first 6–31C * studies on the corresponding thiazolium model systems. Especially, the PM 3 calculations show that the elimination of CO₂ is favored if the arrangement of the carboxylate group is nearly perpendicular to the plane of the thiazolium ring. These results support the least-motion maximum-overlap mechanism in the enzymatic decarboxylation reaction, proposed by Kluger. The most stable conformers of the ThDP adducts and its decarboxylation products are characterized by V-like structures and the formation of a significant intramolecular hydrogen bonding under participation of the 4′-aminopyrimidine ring. © 1996 John Wiley & Sons, Inc.     

Variational approach to contact problems in nonlinear elasticity

We use variational methods to study problems in nonlinear 3-dimensional elasticity where the deformation of the elastic body is restricted by a rigid obstacle. For an assigned variational problem we first verify the existence of constrained minimizers whereby we extend previous results. Then we rigorously derive the Euler-Lagrange equation as necessary condition for minimizers, which was possible before only under strong smoothness assumptions on the solution. The Lagrange multiplier corresponding to the obstacle constraint provides structural information about the nature of frictionless contact. In the case of contact with, e.g., a corner of the obstacle, we derive a qualitatively new contact condition taking into account the deformed shape of the elastic body. By our analysis it is shown here for the first time rigorously that energy minimizers really solve the mechanical contact problem. Received: 20 October 2000 / Accepted: 7 June 2001 / Published online: 5 September 2002     

Locking constraints for elastic rods and a curvature bound for spatial curves

The paper presents necessary conditions for curves in R³ subject to the nonholonomic constraint of an upper bound for curvature and suitable boundary conditions. The proof essentially uses a reformulation of the problem by means of framed curves. The Euler–Lagrange equations for nonlinearly elastic Cosserat rods subject to a general class of locking constraints is derived by similar methods. Mathematics Subject Classification (2000) 49K15, 51M16, 74B20, 74K10     

Comparison of agarose and dextran-grafted agarose strong ion exchangers for the separation of protein aggregates

The control of aggregate levels in recombinant protein based drugs is a primary concern during process development and manufacture. In recent years, a novel class of dextran-grafted ion exchange matrices has gained popularity for process scale protein purification due to increased mass transfer rates and higher dynamic binding capacity compared to conventional matrices. Using bovine serum albumin and a monoclonal antibody as model proteins, we studied Sepharose FF and Sepharose XL ion exchangers for the separation of protein aggregates. Experimental results comparing linear gradient elution, stepwise elution, and flow-through chromatography for aggregate separation are described. Differences in performance for the various ion exchangers are discussed and modeled. Strategies for the optimization of protein aggregate separation are provided.