Semi-groups, groups and Lyapunov stability of partial differential equations

Applications of group theory and Liapunov stability to partial differential equation

A Variable-Flavour Number Scheme for NNLO

At NNLO it is particularly important to have a Variable-Flavour Number Scheme (VFNS) to deal with heavy quarks because there are major problems with both the zero mass variable-flavour number scheme and the fixed-flavour number scheme. I illustrate these problems and present a general formulation of a Variable-Flavour Number Scheme (VFNS)for heavy quarks that is explicitly implemented up to NNLO in the strong coupling constant alpha_S, and may be used in NNLO global fits for parton distributions. The procedure combines elements of the ACOT(chi) scheme and the Thorne-Roberts scheme. Despite the fact that at NNLO the parton distributions are discontinuous as one changes the number of active quark flavours, all physical quantities are continuous at flavour transitions and the comparison with data is successful.Comment: 17 pages, 5 figures included as .ps files, uses axodraw. One additional explanatory sentence after eq. (25). Correction of typos and updated references. To be published in Phys. Rev.

Congener specific analysis of polychlorinated terphenyls

In order to identify and to quantify polychlorinated terphenyls (PCT) in environmental matrices, the chro- matographic behavior of coplanar and non-coplanar congeners was evaluated. A mixture of 16 single PCT congeners was used for method development. Four of these compounds were synthesized for the first time by SUZUKI-coupling reaction. These were p-PCT (2,200 ,6,600 -tetrachloro-, 20 ,3,300 ,4,400 ,50 ,-hexachloro-, 20 ,3,300 ,5,50 ,500 -hexachloro-) and m-PCT (2,200 ,3,300 ,5,500 -hexachloro-). They were characterized by NMR ( 1 H, 13 C) spectroscopy. By means of the new column chromatographic clean-up reported here, a good matrix removal and the separation of the coplanar PCT congeners from the non-coplanar ones was obtained. The recovery rates for all congeners were good for the PCT in different test matrices like fat, charcoal, and soil. The quality of the clean-up, the separation and the recovery rates were determined by GC/MS analysis. The method was applied for the first time to a real sample from a fire accident, where different PCT, obviously formed during the combustion process, were found. The conclusion is drawn that this method is suitable for the analysis of PCT in different environmental samples

Impingement of Water Droplets on NACA 65A004 Airfoil at 8 deg Angle of Attack

The trajectories of droplets in the air flowing past an NACA 65AO04 airfoil at an angle of attack of 8 deg were determined.. The amount of water in droplet form impinging on the airfoil, the area of droplet impingement, and the rate of droplet impingement per unit area on the airfoil surface were calculated from the trajectories and presented to cover a large range of flight and atmospheric conditions. These impingement characteristics are compared briefly with those previously reported for the same airfoil at an angle of attack of 4 deg

The last orbit of binary black holes

We have used our new technique for fully numerical evolutions of orbiting black-hole binaries without excision to model the last orbit and merger of an equal-mass black-hole system. We track the trajectories of the individual apparent horizons and find that the binary completed approximately one and a third orbits before forming a common horizon. Upon calculating the complete gravitational radiation waveform, horizon mass, and spin, we find that the binary radiated 3.2% of its mass and 24% of its angular momentum. The early part of the waveform, after a relatively short initial burst of spurious radiation, is oscillatory with increasing amplitude and frequency, as expected from orbital motion. The waveform then transitions to a typical `plunge' waveform; i.e. a rapid rise in amplitude followed by quasinormal ringing. The plunge part of the waveform is remarkably similar to the waveform from the previously studied `ISCO' configuration. We anticipate that the plunge waveform, when starting from quasicircular orbits, has a generic shape that is essentially independent of the initial separation of the binary.Comment: 5 pages, 5 figures, revtex

Dissociation rates of J/psi's with comoving mesons - thermal vs. nonequilibrium scenario

We study J/psi dissociation processes in hadronic environments. The validity of a thermal meson gas ansatz is tested by confronting it with an alternative, nonequilibrium scenario. Heavy ion collisions are simulated in the framework of the microscopic transport model UrQMD, taking into account the production of charmonium states through hard parton-parton interactions and subsequent rescattering with hadrons. The thermal gas and microscopic transport scenarios are shown to be very dissimilar. Estimates of J/psi survival probabilities based on thermal models of comover interactions in heavy ion collisions are therefore not reliable.Comment: 12 pages, 6 figure