Coupling JOREK and STARWALL for Non-linear Resistive-wall Simulations

The implementation of a resistive-wall extension to the non-linear MHD-code JOREK via a coupling to the vacuum-field code STARWALL is presented along with first applications and benchmark results. Also, non-linear saturation in the presence of a resistive wall is demonstrated. After completion of the ongoing verification process, this code extension will allow to perform non-linear simulations of MHD instabilities in the presence of three-dimensional resistive walls with holes for limited and X-point plasmas.Comment: Contribution for "Theory Of Fusion Plasmas, Joint Varenna - Lausanne International Workshop, Villa Monastero, Varenna, Italy (27.-31.8.2012)", accepted for publication in Journal of Physics Conference Serie

Two-dimensional streptavidin crystals on giant lipid bilayer vesicles

Streptavidin was crystallized on giant bilayer vesicles (20-60 mum) in sucrose solution at various pH values. The streptavidin-coated vesicles exhibited unique roughened spherical and prolate ellipsoidal shapes, illustrating resistance to curvature of the two-dimensional crystals. Studies indicated that the spheroids and prolate ellipsoids correspond to different crystal morphologies. Through confocal microscopy, the various crystal morphologies on vesicle surfaces were observed under different solution conditions. Unlike two-dimensional (2D) streptavidin crystals grown in ionic buffer that assume the P1, P2, and C222 lattices at pH 4, 5.5, and 7, respectively (Wang et al. Langmuir 1999, 15, 154 1), crystals grown in sucrose with no added salt show only the lowest density C222 lattice due to strong electrostatic interactions

A minimal-length approach unifies rigidity in under-constrained materials

We present a novel approach to understand geometric-incompatibility-induced rigidity in under-constrained materials, including sub-isostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all these models a geometric criterion, represented by a minimal length $\bar\ell_\mathrm{min}$, determines the onset of prestresses and rigidity. This allows us to predict not only the correct scalings for the elastic material properties, but also the precise {\em magnitudes} for bulk modulus and shear modulus discontinuities at the rigidity transition as well as the magnitude of the Poynting effect. We also predict from first principles that the ratio of the excess shear modulus to the shear stress should be inversely proportional to the critical strain with a prefactor of three, and propose that this factor of three is a general hallmark of geometrically induced rigidity in under-constrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Lastly, our results may lay important foundations for ways to estimate $\bar\ell_\mathrm{min}$ from measurements of local geometric structure, and thus help develop methods to characterize large-scale mechanical properties from imaging data.Comment: 10 pages, 5 figure

NMR experiment factors numbers with Gauss sums

We factor the number 157573 using an NMR implementation of Gauss sums.Comment: 4 pages 5 figure