The Fubini-Furlan-Rossetti Sum Rule Revisited

The Fubini-Furlan-Rossetti sum rule for pion photoproduction on the nucleon is evaluated by dispersion relations at constant t, and the corrections to the sum rule due to the finite pion mass are calculated. Near threshold these corrections turn out to be large due to pion-loop effects, whereas the sum rule value is closely approached if the dispersion integrals are evaluated for sub-threshold kinematics. This extension to the unphysical region provides a unique framework to determine the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.Comment: 12 pages, 7 postscript figures, EPJ style files include

A Modification of the Social Force Model by Foresight

The motion of pedestrian crowds (e.g. for simulation of an evacuation situation) can be modeled as a multi-body system of self driven particles with repulsive interaction. We use a few simple situations to determine the simplest allowed functional form of the force function. More complexity may be necessary to model more complex situations. There are many unknown parameters to such models, which have to be adjusted correctly. The parameters can be related to quantities that can be measured independently, like step length and frequency. The microscopic behavior is, however, only poorly reproduced in many situations, a person approaching a standing or slow obstacle will e.g. show oscillations in position, and the trajectories of two persons meeting in a corridor in opposite direction will be far from realistic and somewhat erratic. This is inpart due to the assumption of instantaneous reaction on the momentary situation. Obviously, persons react with a small time lag, while on the other hand they will anticipate changing situations for at least a short time. Thus basing the repulsive interaction on a (linear) extrapolation over a short time (e.g. 1 s) eliminates the oscillations at slowing down and smoothes the patterns of giving way to others to a more realistic behavior. A second problem is the additive combination of binary interactions. It is shown that combining only a few relevant interactions gives better model performance.Comment: 6 pages, 5 figures, Preprint from PED 2008 (Wuppertal

Angular momentum and galaxy formation revisited

Motivated by new kinematic data in the outer parts of early-type galaxies (ETGs), we re-examine angular momentum (AM) in all galaxy types. We present methods for estimating the specific AM j, focusing on ETGs, to derive relations between stellar j_* and mass M_* (after Fall 1983). We perform analyses of 8 galaxies out to ~10 R_e, finding that data at 2 R_e are sufficient to estimate total j_*. Our results contravene suggestions that ellipticals (Es) harbor large reservoirs of hidden j_* from AM transport in major mergers. We carry out a j_*-M_* analysis of literature data for ~100 nearby bright galaxies of all types. The Es and spirals form parallel j_*-M_* tracks, which for spirals is like the Tully-Fisher relation, but for Es derives from a mass-size-rotation conspiracy. The Es contain ~3-4 times less AM than equal-mass spirals. We decompose the spirals into disks+bulges and find similar j_*-M_* trends to spirals and Es overall. The S0s are intermediate, and we propose that morphological types reflect disk/bulge subcomponents following separate j_*-M_* scaling relations -- providing a physical motivation for characterizing galaxies by mass and bulge/disk ratio. Next, we construct idealized cosmological models of AM content, using a priori estimates of dark matter halo spin and mass. We find that the scatter in halo spin cannot explain the spiral/E j_* differences, but the data are matched if the galaxies retained different fractions of initial j (~60% and ~10%). We consider physical mechanisms for j_* and M_* evolution (outflows, stripping, collapse bias, merging), emphasizing that the vector sum of such processes must produce the observed j_*-M_* relations. A combination of early collapse and multiple mergers (major/minor) may account for the trend for Es. More generally, the observed AM variations represent fundamental constraints for any galaxy formation model.Comment: ApJS, in press, 61 pages, 34 figures, abstract abridge