Lyapunov Modes in Hard-Disk Systems

We consider simulations of a two-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lyapunov exponents. To this spectrum are associated eigen-directions, called Lyapunov modes. We carefully analyze these modes and show how they are naturally associated with vector fields over the container. We also show that the Lyapunov exponents, and the coupled dynamics of the modes (where it exists) follow linear laws, whose coefficients only depend on the density of the gas, but not on aspect ratio and very little on the boundary conditions.     

Fission lifetimes of Th nuclei measured by crystal blocking

Crystal blocking lifetime measurements have been made for highly excited Th nuclei with neutron number well removed from the stability line. Thin W crystals were bombarded with ³²S ions in the energy range 170-180 MeV and the yield of fission fragments was measured for emission close to a 〈111〉 axis. The fission blocking dips are compared to the appropriately scaled ones for elastic scattering of the ³²S beam ions and no significant difference is seen between the dips. This implies that the fraction of nuclei fissioning with lifetimes longer than 10 as is less than 2%. Fission lifetimes are increased by viscosity in the nuclear mass flow and comparison with a statistical model calculation indicates that the viscosity parameter, η, must be lower than for Th and U nuclei near β-stability. The effect of the N = 126 magic number is discussed. Received: 2 October 2002 / Accepted: 16 January 2003 / Published online: 29 April 2003     

Bending of high energy beams using axial and planar channeling

A very strong and dramatic bending effect has been found for 12 GeV/c positive particles channeled along crystal axes and planes. For a combination of axial and planar channeling the bending efficiency is 5–10%. The maximum bending angle was 52 mrad obtained over a 20 mm long 〈111〉 Si-crystal. The axial channeling is also able to bend negative particles.     

Ein beweis des Grauertschen bildgarbensatzes nach ideen von B. Malgrange

In 1960, H. Grauert proved the following coherence theorem [2]: Let X, Y be complex spaces and : X Y a proper holomorphic map. Then, for every coherent analytic sheaf J on X, all direct image sheaves Rⁿ*J are coherent. We give a new proof of this theorem, based on ideas of B. Malgrange. This proof does not use induction on the dimension of the base space Y and can be generalized to relative-analytic spaces X Y where Y belongs to a bigger category of ringed spaces, which contains in particular all complex spaces and differentiable manifolds.     

Über die Anzahl der Erzeugenden eines Ideals in einem Noetherschen Ring

Ohne Zusammenfassung