Systematic Derivation of Amplitude Equations and Normal Forms for Dynamical Systems

We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from amplitudes to physical space. At any order, the relation provides explicit expressions for all the nonvanishing coefficients of the amplitude equation together with straightforward linear equations for the coefficients of the transformation. The recurrence relation therefore provides all the machinery needed to solve a given physical problem in physical terms through an amplitude equation. The new result applies to any local bifurcation of a flow or map for which all the critical eigenvalues are semisimple i.e. have Riesz index unity). The method is an efficient and rigorous alternative to more intuitive approaches in terms of multiple time scales. We illustrate the use of the method by deriving amplitude equations and associated transformations for the most common simple bifurcations in flows and iterated maps. The results are expressed in tables in a form that can be immediately applied to specific problems.Comment: 40 pages, 1 figure, 4 tables. Submitted to Chaos. Please address any correspondence by email to [email protected]

Radial sine-Gordon kinks as sources of fast breathers

We consider radial sine-Gordon kinks in two, three and higher dimensions. A full two dimensional simulation showing that azimuthal perturbations remain small allows to reduce the problem to the one dimensional radial sine-Gordon equation. We solve this equation on an interval $[r_0,r_1]$ and absorb all outgoing radiation. Before collision the kink is well described by a simple law derived from the conservation of energy. In two dimensions for $r_0 \le 2$, the collision disintegrates the kink into a fast breather while for $r_0 \ge 4$ we obtain a kink-breather meta-stable state where breathers are shed at each kink "return". In three and higher dimensions $d$ a kink-pulson state appears for small $r_0$. The three states then exist as shown by a study of the $(d,r_0)$ parameter space. On the application side, the kink disintegration opens the way for new types of terahertz microwave generators

Close binary evolution. III. Impact of tides, wind magnetic braking, and internal angular momentum transport

Massive stars with solar metallicity lose important amounts of rotational angular momentum through their winds. When a magnetic field is present at the surface of a star, efficient angular momentum losses can still be achieved even when the mass-loss rate is very modest, at lower metallicities, or for lower-initial-mass stars. In a close binary system, the effect of wind magnetic braking also interacts with the influence of tides, resulting in a complex evolution of rotation. We study the interactions between the process of wind magnetic braking and tides in close binary systems. We discuss the evolution of a 10 M$_\odot$ star in a close binary system with a 7 M$_\odot$ companion using the Geneva stellar evolution code. The initial orbital period is 1.2 days. The 10 M$_\odot$ star has a surface magnetic field of 1 kG. Various initial rotations are considered. We use two different approaches for the internal angular momentum transport. In one of them, angular momentum is transported by shear and meridional currents. In the other, a strong internal magnetic field imposes nearly perfect solid-body rotation. The evolution of the primary is computed until the first mass-transfer episode occurs. The cases of different values for the magnetic fields and for various orbital periods and mass ratios are briefly discussed. We show that, independently of the initial rotation rate of the primary and the efficiency of the internal angular momentum transport, the surface rotation of the primary will converge, in a time that is short with respect to the main-sequence lifetime, towards a slowly evolving velocity that is different from the synchronization velocity. (abridged).Comment: 11 pages, 13 figures, accepted for publication in Astronomy and Astrophysic

Regulation of releasable vesicle pool sizes by protein kinase A-dependent phosphorylation of SNAP-25

AbstractProtein kinase A (PKA) is a key regulator of neurosecretion, but the molecular targets remain elusive. We combined pharmacological manipulations of kinase and phosphatase activities with mutational studies on the exocytotic machinery driving fusion of catecholamine-containing vesicles from chromaffin cells. We found that constitutive PKA activity was necessary to maintain a large number of vesicles in the release-ready, so-called primed, state, whereas calcineurin (protein phosphatase 2B) activity antagonized this effect. Overexpression of the SNARE protein SNAP-25a mutated in a PKA phosphorylation site (Thr-138) eliminated the effect of PKA inhibitors on the vesicle priming process. Another, unidentified, PKA target regulated the relative size of two different primed vesicle pools that are distinguished by their release kinetics. Overexpression of the SNAP-25b isoform increased the size of both primed vesicle pools by a factor of two, and mutations in the conserved Thr-138 site had similar effects as in the a isoform

Deltaproteobacteria and Spirochaetes-Like Bacteria Are Abundant Putative Mercury Methylators in Oxygen-Deficient Water and Marine Particles in the Baltic Sea

Methylmercury (MeHg), a neurotoxic compound biomagnifying in aquatic food webs, can be a threat to human health via fish consumption. However, the composition and distribution of the microbial communities mediating the methylation of mercury (Hg) to MeHg in marine systems remain largely unknown. In order to fill this knowledge gap, we used the Baltic Sea Reference Metagenome (BARM) dataset to study the abundance and distribution of the genes involved in Hg methylation (thehgcABgene cluster). We determined the relative abundance of thehgcABgenes and their taxonomic identity in 81 brackish metagenomes that cover spatial, seasonal and redox variability in the Baltic Sea water column. ThehgcABgenes were predominantly detected in anoxic water, but somehgcABgenes were also detected in hypoxic and normoxic waters. Phylogenetic analysis identified putative Hg methylators within Deltaproteobacteria, in oxygen-deficient water layers, but also Spirochaetes-like and Kiritimatiellaeota-like bacteria. Higher relative quantities ofhgcABgenes were found in metagenomes from marine particles compared to free-living communities in anoxic water, suggesting that such particles are hotspot habitats for Hg methylators in oxygen-depleted seawater. Altogether, our work unveils the diversity of the microorganisms with the potential to mediate MeHg production in the Baltic Sea and pinpoint the important ecological niches for these microorganisms within the marine water column

Isotope effect in impure high T_c superconductors

The influence of various kinds of impurities on the isotope shift exponent \alpha of high temperature superconductors has been studied. In these materials the dopant impurities, like Sr in La_{2-x}Sr_xCuO_4, play different role and usually occupy different sites than impurities like Zn, Fe, Ni {\it etc} intentionally introduced into the system to study its superconducting properties. In the paper the in-plane and out-of-plane impurities present in layered superconductors have been considered. They differently affect the superconducting transition temperature T_c. The relative change of isotope shift coefficient, however, is an universal function of T_c/T_{c0} (T_{c0} reffers to impurity free system) {\it i.e.} for angle independent scattering rate and density of states function it does not depend whether the change of T_c is due to in- or out-of-plane impurities. The role of the anisotropic impurity scattering in changing oxygen isotope coefficient of superconductors with various symmetries of the order parameter is elucidated. The comparison of the calculated and experimental dependence of \alpha/\alpha_0, where \alpha_0 is the clean system isotope shift coefficient, on T_c/T_{c0} is presented for a number of cases studied. The changes of \alpha calculated within stripe model of superconductivity in copper oxides resonably well describe the data on La_{1.8}Sr_{0.2}Cu_{1-x}(Fe,Ni)_xO_4, without any fitting parameters.Comment: 8 pages, 6 figures, Phys. Rev. B67 (2003) accepte

Multi-Decadal Decline of Mercury in the North Atlantic Atmosphere Explained by Changing Subsurface Seawater Concentrations

[1] We analyze 1977–2010 trends in atmospheric mercury (Hg) from 21 ship cruises over the North Atlantic (NA) and 15 over the South Atlantic (SA). We find a steep 1990–2009 decline of −0.046 ± 0.010 ng m−3 a−1 (−2.5% a−1) over the NA (steeper than at Northern Hemispheric land sites) but no significant decline over the SA. Surface water Hg0 measurements in the NA show a decline of −5.7% a−1since 1999, and limited subsurface ocean data show an ∼80% decline from 1980 to present. We use a coupled global atmosphere-ocean model to show that the decline in NA atmospheric concentrations can be explained by decreasing oceanic evasion from the NA driven by declining subsurface water Hg concentrations. We speculate that this large historical decline of Hg in the NA Ocean could have been caused by decreasing Hg inputs from rivers and wastewater and by changes in the oxidant chemistry of the atmospheric marine boundary layer.Engineering and Applied Science