Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude

Stability criteria have been derived and investigated in the last decades for many kinds of periodic traveling wave solutions to Hamiltonian PDEs. They turned out to depend in a crucial way on the negative signature of the Hessian matrix of action integrals associated with those waves. In a previous paper (Nonlinearity 2016), the authors addressed the characterization of stability of periodic waves for a rather large class of Hamiltonian partial differential equations that includes quasilinear generalizations of the Korteweg--de Vries equation and dispersive perturbations of the Euler equations for compressible fluids, either in Lagrangian or in Eulerian coordinates. They derived a sufficient condition for orbital stability with respect to co-periodic perturbations, and a necessary condition for spectral stability, both in terms of the negative signature - or Morse index - of the Hessian matrix of the action integral. Here the asymptotic behavior of this matrix is investigated in two asymptotic regimes, namely for small amplitude waves and for waves approaching a solitary wave as their wavelength goes to infinity. The special structure of the matrices involved in the expansions makes possible to actually compute the negative signature of the action Hessian both in the harmonic limit and in the soliton limit. As a consequence, it is found that nondegenerate small amplitude waves are orbitally stable with respect to co-periodic perturbations in this framework. For waves of long wavelength, the negative signature of the action Hessian is found to be exactly governed by the second derivative with respect to the wave speed of the Boussinesq momentum associated with the limiting solitary wave

Modulated equations of Hamiltonian PDEs and dispersive shocks

Motivated by the ongoing study of dispersive shock waves in non integrable systems , we propose and analyze a set of wave parameters for periodic waves of a large class of Hamiltonian partial differential systems-including the generalized Korteweg-de Vries equations and the Euler-Korteweg systems-that are well-behaved in both the small amplitude and small wavelength limits. We use this parametrization to determine fine asymptotic properties of the associated modulation systems, including detailed descriptions of eigenmodes. As a consequence, in the solitary wave limit we prove that modulational instability is decided by the sign of the second derivative-with respect to speed, fixing the endstate-of the Boussinesq moment of instability; and, in the harmonic limit, we identify an explicit modulational instability index, of Benjamin-Feir type

Intraclonal genome diversity of Pseudomonas aeruginosa clones CHA and TB.

International audienceBACKGROUND: Adaptation of Pseudomonas aeruginosa to different living conditions is accompanied by microevolution resulting in genomic diversity between strains of the same clonal lineage. In order to detect the impact of colonized habitats on P. aeruginosa microevolution we determined the genomic diversity between the highly virulent cystic fibrosis (CF) isolate CHA and two temporally and geographically unrelated clonal variants. The outcome was compared with the intraclonal genome diversity between three more closely related isolates of another clonal complex. RESULTS: The three clone CHA isolates differed in their core genome in several dozen strain specific nucleotide exchanges and small deletions from each other. Loss of function mutations and non-conservative amino acid replacements affected several habitat- and lifestyle-associated traits, for example, the key regulator GacS of the switch between acute and chronic disease phenotypes was disrupted in strain CHA. Intraclonal genome diversity manifested in an individual composition of the respective accessory genome whereby the highest number of accessory DNA elements was observed for isolate PT22 from a polluted aquatic habitat. Little intraclonal diversity was observed between three spatiotemporally related outbreak isolates of clone TB. Although phenotypically different, only a few individual SNPs and deletions were detected in the clone TB isolates. Their accessory genome mainly differed in prophage-like DNA elements taken up by one of the strains. CONCLUSIONS: The higher geographical and temporal distance of the clone CHA isolates was associated with an increased intraclonal genome diversity compared to the more closely related clone TB isolates derived from a common source demonstrating the impact of habitat adaptation on the microevolution of P. aeruginosa. However, even short-term habitat differentiation can cause major phenotypic diversification driven by single genomic variation events and uptake of phage DNA

Nanotrench for nano and microparticle electrical interconnects

We present a simple and versatile patterning procedure for the reliable and reproducible fabrication of high aspect ratio (10 4 ) electrical interconnects that have separation distances down to 20 nm and lengths of several hundreds of microns. The process uses standard optical lithography techniques and allows parallel processing of many junctions, making it easily scalable and industrially relevant. We demonstrate the suitability of these nanotrenches as electrical interconnects for addressing micro and nanoparticles by realizing several circuits with integrated species. Furthermore, low impedance metal-metal low contacts are shown to be obtained when trapping a single metal-coated microsphere in the gap, emphasizing the intrinsic good electrical conductivity of the interconnects, even though a wet process is used. Highly resistive magnetite-based nanoparticles networks also demonstrate the advantage of the high aspect ratio of the nanotrenches for providing access to electrical properties of highly resistive materials, with leakage current levels below 1 pA. © 2010 IOP Publishing Ltd

The Recent Star Formation History of NGC 5102

We present Hubble Space Telescope photometry of young stars in NGC 5102, a nearby gas-rich post-starburst S0 galaxy with a bright young stellar nucleus. We use the IAC-pop/MinnIAC algorithm to derive the recent star formation history in three fields in the bulge and disk of NGC 5102. In the disk fields, the recent star formation rate has declined monotonically and is now barely detectable, but a starburst is still in progress in the bulge and has added about 2 percent to the mass of the bulge over the last 200 Myr. Other studies of star formation in NGC 5102 indicate that about 20 percent of its stellar mass was added over the past Gyr. If this is correct, then much of the stellar mass of the bulge may have formed over this period. It seems likely that this star formation was fueled by the accretion of a gas-rich system with HI mass of about 2 x 10^9 Msol which has now been almost completely converted into stars. The large mass of recently formed stars and the blue colours of the bulge suggest that the current starburst, which is now fading, may have made a significant contribution to build the bulge of NGC 5102.Comment: 36 pages, 16 figures, accepted in A

Defect‐Driven Magnetization Configuration of Isolated Linear Assemblies of Iron Oxide Nanoparticles

International audienceThe magnetization state of one-dimensional magnetic nanoparticle chains plays a key role for a wide range of applications ranging from diagnosis and therapy in medicine to actuators, sensors and quantum recording media. The interplay between the exact particle orientation and the magnetic anisotropy is in turn crucial for controlling the overall magnetization state with high precision. Here, we report on a three-dimensional description of the magnetic structure of one-NP-wide chains. In this aim, we combined two complementary experimental techniques, magnetic force microscopy (MFM) and electronic holography (EH) which are sensitive to out-of-plane and in-plane magnetization components, respectively. We extended our approach to micromagnetic simulations which provided results in good agreement with MFM and EH. The findings are at variance with the known results on unidirectional nanoparticle assemblies, and show that magnetization is rarely strictly collinear to the chain axis. The magnetic structure of one-NP-wide chains can be interpreted as head-to-head magnetic domain structures with off-axis magnetization components, which is very sensitive to morphological defects in the chain structure such as minute size variation of NPs, tiny misalignment of NPs and/or crystal orientation with respect to easy magnetization axis

Functional Reconstitution into Liposomes of Purified Human RhCG Ammonia Channel

BACKGROUND: Rh glycoproteins (RhAG, RhBG, RhCG) are members of the Amt/Mep/Rh family which facilitate movement of ammonium across plasma membranes. Changes in ammonium transport activity following expression of Rh glycoproteins have been described in different heterologous systems such as yeasts, oocytes and eukaryotic cell lines. However, in these complex systems, a potential contribution of endogenous proteins to this function cannot be excluded. To demonstrate that Rh glycoproteins by themselves transport NH(3), human RhCG was purified to homogeneity and reconstituted into liposomes, giving new insights into its channel functional properties. METHODOLOGY/PRINCIPAL FINDINGS: An HA-tag introduced in the second extracellular loop of RhCG was used to purify to homogeneity the HA-tagged RhCG glycoprotein from detergent-solubilized recombinant HEK293E cells. Electron microscopy analysis of negatively stained purified RhCG-HA revealed, after image processing, homogeneous particles of 9 nm diameter with a trimeric protein structure. Reconstitution was performed with sphingomyelin, phosphatidylcholine and phosphatidic acid lipids in the presence of the C(12)E(8) detergent which was subsequently removed by Biobeads. Control of protein incorporation was carried out by freeze-fracture electron microscopy. Particle density in liposomes was a function of the Lipid/Protein ratio. When compared to empty liposomes, ammonium permeability was increased two and three fold in RhCG-proteoliposomes, depending on the Lipid/Protein ratio (1/300 and 1/150, respectively). This strong NH(3) transport was reversibly inhibited by mercuric and copper salts and exhibited a low Arrhenius activation energy. CONCLUSIONS/SIGNIFICANCE: This study allowed the determination of ammonia permeability per RhCG monomer, showing that the apparent Punit(NH3) (around 1x10(-3) microm(3)xs(-1)) is close to the permeability measured in HEK293E cells expressing a recombinant human RhCG (1.60x10(-3) microm(3)xs(-1)), and in human red blood cells endogenously expressing RhAG (2.18x10(-3) microm(3)xs(-1)). The major finding of this study is that RhCG protein is active as an NH(3) channel and that this function does not require any protein partner