Links of surface singularities and CR space forms

We classify 3-dimensional compact locally homogeneous non-degenerate CR-manifolds (“CR space-forms”). Most of them are links of normal complex surface singularities, and we classify these singularities. In memory of Peter Scherk Research partially supported by the NSF.     

Finite Swelling with Weakly Fulfilled Boundary Conditions

Biological soft tissues exhibit a swelling behaviour and consist of multiple phases, a solid phase composed of collgagen fibers and charged PGA chains and a fluid phase composed of the liquid solvent and the ions of dissolved salt. In this contribution, the Theory of Porous Media (TPM) model consists of four constituents, a charged solid and an aqueous solution composed of water and the ions of dissolved salt. The solid is modelled by a finite elasticity law accounting for the multiphasic micro structure, whereas the fluid is considered as a viscous Newtonian fluid. One finally ends up with the volume balance of the fluid, the concentration balance of the cations, the momentum balance of the overall mixture. The resulting set of partial differential equations is solved within the framework of the FEM. Therefore, the weak forms are derived and the resulting set of equations for the primary variables pore pressure p, cation concentration c and solid displacement u _S , is implemented into the FE tool PANDAS. Finally, a three dimensional example of a swelling hydrogel disc is shown. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Republication of: Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II

This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.     

Republication of: The geometry of free fall and light propagation

This is a reprinting of the paper by Jürgen Ehlers, Felix Pirani and Alfred Schild, first published in 1972 in a separate volume containing articles written in hounour of J. L. Synge. The original book is long out of print and almost forgotten by today. The authors present a method of deriving the Lorentzian geometry from compatible conformal and projective structures on a four dimensional manifold. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Andrzej Trautman.     

Computational Evaluation of Me2TCCP as Lewis Acid

Supramolecular adducts between dimethyl-2,2,3,3-tetracyanocyclopropane (Me₂TCCP) with 21 small (polar) molecules and 10 anions were computed with DFT (B3LYP-D3/def2-TZVP). Their optimized geometries were used to obtain interaction energies, and perform energy decomposition and ‘atoms-in-molecules’ analyses. A set of 38 other adducts were also evaluated for comparison purposes. Selected examples were further scrutinized by inspection of the molecular electrostatic potential maps, Noncovalent Interaction index plots, the Laplacian, the orbital interactions, and by estimating the Gibbs free energy of complexation in hexane solution. These calculations divulge the thermodynamic feasibility of Me₂TCCP adducts and show that complexation is typically driven by dispersion with less polarized partners, but by orbital interactions when more polarized or anionic guests are deployed. Most Me₂TCCP adducts are more stable than simple hydrogen bonding with water, but less stable than traditional Lewis adducts involving Me₃B, or a strong halogen bond such as with Br₂. Several bonding analyses showed that the locus of interaction is found near the electron poor sp³-hydridized (NC)₂C−C(CN)₂ carbon atoms. An empty hybrid σ*/π* orbital on Me₂TCCP was identified that can be held responsible for the stability of the most stable adducts due to donor-acceptor interactions.     

Could cell membranes produce acoustic streaming? Making the case for Synechococcus self-propulsion

Sir James Lighthill proposed in 1992 that acoustic streaming (AS) within the mammalian cochlea could play a role in the transmission of acoustic signals to the auditory sensory cells. Microelectromechanical devices for mixing and pumping, based on the acoustic streaming effect were introduced in the mid 1990s. Nature may have preceded this invention by 2.7 Gyr. We believe that acoustic streaming produced by nanometer scale membrane vibrations is widespread in cell biology. Flows generated by acoustic streaming could be produced along the “raphes” (central channels) of silica coated diatoms. Other possible instances are yeast cells and erythrocytes whose membranes generate nanoscale vibrations. We hypothesize that some of the most ancient organisms use acoustic streaming not only for self-propulsion but also to enhance their nutrient uptake. In this paper we focus on a motile strain of Synechococcus, a cyanobacterium whose mechanism for self-propulsion is not known. The calculations presented here show that a traveling surface acoustic wave (SAW) could account for the observed velocities. These SAWs would also produce a non-negligible Stokes layer surrounding the cell, motion within this region being essentially chaotic. Therefore, an AS mechanism would be biologically advantageous, enhancing localized diffusion processes and consequently, chemical reactions. Finally, we discuss possible experiments to support (or rule out) the AS model vs. other contending explanations for Synechococcus locomotion.