Using null strain energy functions in compressible finite elasticity to generate exact solutions

In this paper we characterize those strain energy functions in unconstrained nonlinear elasticity that satisfy the equations of equilibrium identically. The idea is to construct a useful, physically reasonable strain–energy function containing one or more components which are null, in such a way that exact solutions may be obtained from the resulting equilibrium equations. We show that the dilatation is a universal null energy while there may be others that depend on the actual problem. To obtain the null energies for a given problem it is often convenient to formulate the variational problem and look at the Euler–Lagrange equations. Specific examples are used to illustrate some of the potential uses of the method in finding exact solutions for physically meaningful constitutive models.     

Bifurcation of inflated circular cylinders of elastic material under axial loading—I. Membrane theory for thin-walled tubes

Bifurcations of circular cylindrical elastic tubes subjected to inflation combined with axial loading are analysed. Membrane tubes are considered in detail as a background to the more difficult analysis of thickwalled tubes described in the companion paper (Part II). Our results for membranes reinforce and extend those given by R.T. Shield and his co-workers.Two modes of bifurcation are investigated: firstly, a bulging (axisyrmmetric) mode; secondly, a prismatic mode in which the cross-section of the tube becomes non-circular. Necessary and sufficient conditions for the existence of modes of either type are given in respect of an arbitrary (incompressible isotropic) form of elastic strain-energy function. For a closed tube with a fixed axial loading many features of the results have close parallels with recent findings by D.M. Haughton and R.W. Ogden for spherical membranes. On the other hand, some results for tubes with fixed ends have no such parallel. In particular, bifurcation may, under certain conditions, occur before the inflating pressure reaches a maximum. A combination of the two modes is interpreted in terms of bending for a tube under axial compression, and the relative importance of the bending and bulging modes is discussed in relation to the length to radius ratio of the tube. The analytical results are illustrated for specific forms of strain-energy function. Corresponding analysis is given for thick-walled tubes in Part II.     

Effect of cyclization of N-terminal glutamine and carbamidomethyl-cysteine (residues) on the chromatographic behavior of peptides in reversed-phase chromatography

N-terminal loss of ammonia is a typical peptide modification chemical artifact observed in bottom-up proteomics experiments. It occurs both in vivo for N-terminal glutamine and in vitro following enzymatic cleavage for both N-terminal glutamine and cysteine alkylated with iodoacetamide. In addition to a mass change of −17.03 Da, modified peptides exhibit increased chromatographic retention in reversed-phase (RP) HPLC systems. The magnitude of this increase varies significantly depending on the peptide sequence and the chromatographic condition used. We have monitored these changes for extensive sets (more than 200 each) of tryptic Gln and Cys N-terminated species. Peptides were separated on 100 Å pore size C18 phases using identical acetonitrile gradient slopes with 3 different eluent compositions: 0.1% trifluoroacetic acid; 0.1% formic acid and 20 mM ammonium formate at pH 10 as ion-pairing modifiers. The observed effect of this modification on RP retention is the product of increased intrinsic hydrophobicity of the modified N-terminal residue, lowering or removing the effect of ion-pairing formation on the hydrophobicity of adjacent residues at acidic pHs; and possibly the increased formation of amphipathic helical structures when the positive charge is removed. Larger retention shifts were observed for Cys terminated peptides compared to Gln, and for smaller peptides. Also the size of the retention increase depends on the eluent conditions: pH 10 ? trifluoroacetic acid < formic acid. Different approaches for incorporation these findings in the peptide retention prediction models are discussed.     

Helium cosmic ray flux measurements at Mars

The helium energy spectrum in Martian orbit has been observed by the MARIE charged particle spectrometer aboard the 2001 Mars Odyssey spacecraft. The orbital data were taken from March 13, 2002 to October 28, 2003, at which time a very intense Solar Particle Event caused a loss of communication between the instrument and the spacecraft. The silicon detector stack in MARIE is optimized for the detection of protons and helium in the energy range below , which typically includes almost all of the flux during SPEs. This also makes MARIE an efficient detector for GCR helium in the energy range of 50–. We will present the first fully normalized flux results from MARIE, using helium ions in this energy range.     

Inner membrane lipids of Escherichia coli form domains

In prokaryotic cells, the hypothesis of the existence of lipid domains was considered. In order to test this hypothesis and study the organization of lipids in the inner membrane of Escherichia coli, we elaborated Langmuir films mimicking the inner leaflet of this membrane by considering lipids extracted from the inner membrane of E coli by Folch protocol.

Lipid monolayers were elaborated by using these extracts (Langmuir technique); the organization of the resulting films was studied at the air–water interface by Brewster angle microscopy and after transfer onto muscovite by atomic force microscopy. The existence of domains was demonstrated for different interfacial pressures of biological interest, and their stability was studied.     

Vortex merger near a topographic slope in a homogeneous rotating fluid

The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two-dimensional, quasi-geostrophic, incompressible fluid.When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times.For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process.Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones.Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.