Foliations of Isonergy Surfaces and Singularities of Curves

It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the bifurcation set has singularities at the corresponding energy level. We formulate certain genericity assumptions for two degrees of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure

Cys-Ph-TAHA: a lanthanide binding tag for RDC and PCS enhanced protein NMR

Here we present Cys-Ph-TAHA, a new nonadentate lanthanide tag for the paramagnetic labelling of proteins. The tag can be easily synthesized and is stereochemically homogenous over a wide range of temperatures, yielding NMR spectra with a single set of peaks. Bound to ubiquitin, it induced large residual dipolar couplings and pseudocontact shifts that could be measured easily and agreed very well with the protein structure. We show that Cys-Ph-TAHA can be used to label large proteins that are biochemically challenging such as the Lac repressor in a 90 kDa ternary complex with DNA and inducer

Robust open cellular porous polymer monoliths made from cured colloidal gels of latex particles

The coagulation of oppositely charged latexes, prepared from the soap-free emulsion polymerisation of styrene using water as the reaction medium, resulted in the obtainment of colloidal gels that were porous in nature and held together by electrostatic interactions. Chemical crosslinking, involving the introduction of a water-soluble crosslinker, resulted in the obtainment of stronger chemical bonds between particles affording a rigid porous material known as a monolith. It was found that, in a simpler approach, these materials could be prepared using a single latex where the addition of ammonium persulfate both resulted in the formation of the colloidal gel and initiated the crosslinking process. The pore size of the resulting monoliths was predictable as this was observed to directly correlate to the particle diameter, with larger pores achieved using particles of increased size. All gels obtained in this work were highly mouldable and retained their shape, which allowed for a range of formats to be easily prepared without the requirement of a mould

Pre-sheath formation in an oblique magnetic field: fluid model and PIC simulation

We present some results of a one-dimensional fluid model with a floating electrode immersed in plasma with magnetic field applied at an oblique angle. The model equations are integrated numerically in order to find the space profiles of the ion velocities and electrostatic potential for various strenghts and angles of the magnetic field. We assume a collisionless magnetized pre-sheath with isothermal ions. The results are then compared with the spatial profiles obtained by a computer simulation. We use a BIT1 particle-in-cell code. The simulations input parameters are chosen in the way, that they resemble the fluid model as much as possible. Because the results of the simulation are given in the absolute SI units, they have to be normalized correctly. We evaluate the model results and compare them with the computer simulation results. Special attention is brought on formation of the pre-sheath with magnetic field applied at intermediate angles. The results of the simulation are in good qualitative agreement with the model