Almost sure existence of global weak solutions for super-critical Navier-Stokes equations

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which global energy bounds are proved. As a consequence, we obtain almost sure super-critical global weak solutions. We also show that in 2d these global weak solutions are unique.Comment: 22 pages, a revised argument in Section 5, the $d=3$ cas

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and \n u belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

Isotopic and velocity distributions of Bi produced in charge-pickup reactions of 208Pb at 1 A GeV

Isotopically resolved cross sections and velocity distributions have been measured in charge-pickup reactions of 1 A GeV 208Pb with proton, deuterium and titanium target. The total and partial charge-pickup cross sections in the reactions 208Pb + 1H and 208Pb + 2H are measured to be the same in the limits of the error bars. A weak increase in the total charge-pickup cross section is seen in the reaction of 208Pb with the titanium target. The measured velocity distributions show different contributions - quasi-elastic scattering and Delta-resonance excitation - to the charge-pickup production. Data on total and partial charge-pickup cross sections from these three reactions are compared with other existing data and also with model calculations based on the coupling of different intra-nuclear cascade codes and an evaporation code.Comment: 20 pages, 12 figures, background information on http://www-w2k.gsi.de/kschmidt

The gut microbiome variability of a butterflyfish increases on severely degraded Caribbean reefs.

Environmental degradation has the potential to alter key mutualisms that underlie the structure and function of ecological communities. How microbial communities associated with fishes vary across populations and in relation to habitat characteristics remains largely unknown despite their fundamental roles in host nutrition and immunity. We find significant differences in the gut microbiome composition of a facultative coral-feeding butterflyfish (Chaetodon capistratus) across Caribbean reefs that differ markedly in live coral cover (∼0-30%). Fish gut microbiomes were significantly more variable at degraded reefs, a pattern driven by changes in the relative abundance of the most common taxa potentially associated with stress. We also demonstrate that fish gut microbiomes on severely degraded reefs have a lower abundance of Endozoicomonas and a higher diversity of anaerobic fermentative bacteria, which may suggest a less coral dominated diet. The observed shifts in fish gut bacterial communities across the habitat gradient extend to a small set of potentially beneficial host associated bacteria (i.e., the core microbiome) suggesting essential fish-microbiome interactions may be vulnerable to severe coral degradation

Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDE

We study exchange of stability in the dynamics of solitary wave solutions under changes in the nonlinear balance in a 1+1 evolutionary partial differential equation related both to shallow water waves and to turbulence. We find that solutions of the equation $m_t + um_x +b u_xm = \nu m_{xx}$ with $m = u - \alpha^2 u_{xx}$ for fluid velocity $u(x,t)$ change their behavior at the special values $b=0,\pm1,\pm2,\pm3$.Comment: 15 pages, 8 figures. For this replacement of the original submission, we: (1) Introduced key explanations that clarify the differences between Figs 1 and 2, versus 3 and 4. (2) Expanded the introduction to provide added motivation and precise definitions. (3) Added section and subsection headings to make the plan of the paper more evident. (4) Added a brief summar

Coincidence measurement of residues and light particles in the reaction 56Fe+p at 1 GeV per nucleon with SPALADIN

The spallation of $^{56}$Fe in collisions with hydrogen at 1 A GeV has been studied in inverse kinematics with the large-aperture setup SPALADIN at GSI. Coincidences of residues with low-center-of-mass kinetic energy light particles and fragments have been measured allowing the decomposition of the total reaction cross-section into the different possible de-excitation channels. Detailed information on the evolution of these de-excitation channels with excitation energy has also been obtained. The comparison of the data with predictions of several de-excitation models coupled to the INCL4 intra-nuclear cascade model shows that only GEMINI can reasonably account for the bulk of collected results, indicating that in a light system with no compression and little angular momentum, multifragmentation might not be necessary to explain the data.Comment: 4 pages, 5 figures, revised version accepted in Phys. Rev. Let

Production of medium-mass neutron-rich nuclei in reactions induced by 136Xe projectiles at 1 A GeV on a beryllium target

Production cross sections of medium-mass neutron-rich nuclei obtained in the fragmentation of 136Xe projectiles at 1 A GeV have been measured with the FRagment Separator (FRS) at GSI. 125Pd was identified for the first time. The measured cross sections are compared to 238U fission yields and model calculations in order to determine the optimum reaction mechanism to extend the limits of the chart of the nuclides around the r-process waiting point at N=82.Comment: 9 pages, 6 figure

Measurement of residual nucleus cross sections and recoil energies in p + Fe collisions at 300, 500, 750, 1000 and 1500 MeV

The production of residual nuclei in p + Fe collisions has been measured at GSI on the FRS facility by means of the reverse kinematic techniques at 300, 500, 750, 1000 and 1500 MeV/A. The cross-sections larger than 0.01 mb of all isotopes with Z larger than 8 have been obtained. Velocity distributions were also measured. Comparisons to models describing spallation reactions and some empirical formulae often used in astrophysics are presented. These data are directly used to calculate impurety production and DPAs in a thin window as foreseen in spallation sources or accelerator-driven systems

Spallation Residues in the Reaction 56Fe + p at 0.3, 0.5, 0.75, 1.0 and 1.5 A GeV

The spallation residues produced in the bombardment of 56}Fe at 1.5, 1.0, 0.75, 0.5 and 0.3 A GeV on a liquid-hydrogen target have been measured using the reverse kinematics technique and the Fragment Separator at GSI (Darmstadt). This technique has permitted the full identification in charge and mass of all isotopes produced with cross-sections larger than 10^{-2} mb down to Z=8. Their individual production cross-sections and recoil velocities at the five energies are presented. Production cross-sections are compared to previously existing data and to empirical parametric formulas, often used in cosmic-ray astrophysics. The experimental data are also extensively compared to different combinations of intra-nuclear cascade and de-excitation models. It is shown that the yields of the lightest isotopes cannot be accounted for by standard evaporation models. The GEMINI model, which includes an asymmetric fission decay mode, gives an overall good agreement with the data. These experimental data can be directly used for the estimation of composition modifications and damages in materials containing iron in spallation sources. They are also useful for improving high precision cosmic-ray measurements.Comment: Submited to Phys. Rev. C (10/2006