9,507 research outputs found
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 K and K and particle
densities below cm 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
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