Nonequilibrium statistical mechanics of swarms of driven particles

As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation.Comment: 11 pages, 2 figure

An X-ray/optical study of the complex dynamics of the core of the massive intermediate-redshift cluster MACSJ0717.5+3745

Using CHANDRA, we investigate the spatial temperature distribution of the intracluster medium (ICM) within 700 kpc of the center of the massive merging cluster MACSJ0717.5+3745 at z=0.55. Combining the X-ray evidence with information about the distribution and velocities of the cluster galaxies near the core provides us with a snapshot of the three-dimensional geometry and dynamics of one of the most complex cluster studied to date. We find MACSJ0717.5+3745 to be an active triple merger with ICM temperatures exceeding 20 keV. Although radial velocity information and X-ray/optical offsets indicate that all three mergers proceed along distinctly different directions, the partial alignment of the merger axes points to a common origin in the large-scale filament south-east of the cluster core. Clear decrements in the ICM temperature observed near two of these subclusters identify the respective X-ray surface brightness peaks as remnants of cool cores; the compactness and low temperature of 5.7 keV of one of these features suggest that the respective merger, a high-velocity collision at 3,000 km/s, is still in its very early stages. Looking beyond the triple merger, we find the large-scale filament to not only provide a spatial as well as temporal arrow for the interpretation of the dynamics of the merger events near the cluster core; we also find tantalizing, if circumstantial, evidence for direct, large-scale heating of the ICM by contiguous infall of low-density gas from the filament.Comment: accepted by ApJL, 2 color figures, fix the typo of one author's nam

On the quantum statistics of bound states within the Rutherford model of matter

The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe - most of the relevant papers published in the Annalen der Physik, are discussed. Beyond this, the modern state of art is presented and new results are given which explain, why bound states according to a discrete part of the spectra occur only in a valley in the temperature-density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. The following transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities due to medium effects. Within the physical picture we calculate isotherms of pressure for Hydrogen in a broad density region and show that in the region between $20\, 000$ K and $100\, 000$ K and particle densities below $10^{22}$ cm$^{-3}$ the cross-over from full to partial ionization may be well described by the contributions of extended ring diagrams and ladder diagrams.Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1110.196

Radial index and Poincar\'e-Hopf index of 1-forms on semi-analytic sets

The radial index of a 1-form on a singular set is a generalization of the classical Poincar\'e-Hopf index. We consider different classes of closed semi-analytic sets in R^n that contain 0 in their singular locus and we relate the radial index of a 1-form at 0 on these sets to Poincar\'e-Hopf indices at 0 of vector fiels defined on R^n.Comment: 38 page

Strange duality of weighted homogeneous polynomials

We consider a mirror symmetry between invertible weighted homogeneous polynomials in three variables. We define Dolgachev and Gabrielov numbers for them and show that we get a duality between these polynomials generalizing Arnold's strange duality between the 14 exceptional unimodal singularities.Comment: 21 pages, 1 figur