9,899 research outputs found
Graph-wreath products and finiteness conditions
A notion of \emph{graph-wreath product} is introduced. We obtain sufficient
conditions for these products to satisfy the topologically inspired finiteness
condition type . Under various additional assumptions we
show that these conditions are necessary. Our results generalise results of
Cornulier about wreath products in case . Graph-wreath products include
classical permutational wreath products and semidirect products of right-angled
Artin groups by groups of automorphisms amongst others.Comment: 12 page
Thermodynamics of rotating self-gravitating systems
We investigate the statistical equilibrium properties of a system of
classical particles interacting via Newtonian gravity, enclosed in a
three-dimensional spherical volume. Within a mean-field approximation, we
derive an equation for the density profiles maximizing the microcanonical
entropy and solve it numerically. At low angular momenta, i.e. for a slowly
rotating system, the well-known gravitational collapse ``transition'' is
recovered. At higher angular momenta, instead, rotational symmetry can
spontaneously break down giving rise to more complex equilibrium
configurations, such as double-clusters (``double stars''). We analyze the
thermodynamics of the system and the stability of the different equilibrium
configurations against rotational symmetry breaking, and provide the global
phase diagram.Comment: 12 pages, 9 figure
Multi-market minority game: breaking the symmetry of choice
Generalization of the minority game to more than one market is considered. At
each time step every agent chooses one of its strategies and acts on the market
related to this strategy. If the payoff function allows for strong fluctuation
of utility then market occupancies become inhomogeneous with preference given
to this market where the fluctuation occured first. There exists a critical
size of agent population above which agents on bigger market behave
collectively. In this regime there always exists a history of decisions for
which all agents on a bigger market react identically.Comment: 15 pages, 12 figures, Accepted to 'Advances in Complex Systems
Superconductivity in ropes of carbon nanotubes
Recent experimental and theoretical results on intrinsic superconductivity in
ropes of single-wall carbon nanotubes are reviewed and compared. We find strong
experimental evidence for superconductivity when the distance between the
normal electrodes is large enough. This indicates the presence of attractive
phonon-mediated interactions in carbon nanotubes, which can even overcome the
repulsive Coulomb interactions. The effective low-energy theory of rope
superconductivity explains the experimental results on the
temperature-dependent resistance below the transition temperature in terms of
quantum phase slips. Quantitative agreement with only one fit parameter can be
obtained. Nanotube ropes thus represent superconductors in an extreme 1D limit
never explored before.Comment: 19 pages, 9 figures, to appear in special issue of Sol. State Com
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