On Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis

We consider the phenomenon of collapse in the critical Keller-Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fruiting body development and biofilm formation. Also KS describes the collapse of a gas of self-gravitating Brownian particles. We find the fluctuation spectrum around the collapsing family of steady states for these equations, which is instrumental in derivation of the critical collapse law. To this end we develop a rigorous version of the method of matched asymptotics for the spectral analysis of a class of second order differential operators containing the linearized Keller-Segel operators (and as we argue linearized operators appearing in nonlinear evolution problems). We explain how the results we obtain are used to derive the critical collapse law, as well as for proving its stability.Comment: 22 pages, 1 figur

Two-pion Bose-Einstein correlations in nuclear collisions at 200 GeV per nucleon

Results of a pion interferometry analysis are presented for the reactions S+C, S+S, S+Cu, S+Ag, S+Au and O+Au at 200 GeV per nucleon. Correlation functions were measured for pairs of negative pions in narrow windows of transverse momentum and rapidity, as a function of the three components of the momentum difference vector in cylindrical coordinates. The measured two-pion correlation functions suggest a space-time evolution of the system which proceeds in the following way for central nucleus-nucleus collisions. After interpenetration of the incident nuclei, the pion source expands in a boost invariant way along the collision axis. Estimates for the proper time interval between the onset of expansion and pion decoupling, as well as for the duration of pion emission are ∼ 4 fm/c and <2 fm/c, respectively. The kT dependence observed for RS is consistent with the effect of resonance decays, alone or combined with slow transverse expansion. A linear dependence of the decoupling volume on the multiplicity is observed and indicates pion decoupling at a constant particle density. Presently available model predictions are briefly discussed © 1995 Springer-Verlag

Strange particle production in nuclear collisions at 200 GeV per nucleon

Multiplicities and spectra of strange particles ( Mathematical expression and K- produced in central32S+S,32S+Ag and32S+Au collisions at 200 GeV per nucleon are presented and compared with data on strange particle production in protonnucleus and nucleon-nucleon interactions. It is shown that strangeness production in32S+Ag collisions is enhanced by a factor of two, similar to that found previously in central32S+S collisions. © 1994 Springer-Verlag

The NA49 Data Acquisition System

NA49 is a fixed-target, heavy-ion experiment at the 200 GeV/nucleon Pb beam of the SPS at CERN, expected to take data in late 1994. Because of the unprecedented number of charged particles (up to 2000) emerging from a single Pb-induced nuclear reaction at these energies, the demands on various parts of the experimental setup are extreme. For the data acquisition system a burst input data rate of 750 Mbyte/sec from more than 150,000 electronic channels has to be buffered and compressed to allow the recording of events to magnetic media at rates around 15 Mbyte/sec with reasonable effort and cost. © 1994 IEEE