15,655 research outputs found
Stanilov-Tsankov-Videv Theory
We survey some recent results concerning Stanilov-Tsankov-Videv theory,
conformal Osserman geometry, and Walker geometry which relate algebraic
properties of the curvature operator to the underlying geometry of the
manifold.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Time scale competition leading to fragmentation and recombination transitions in the coevolution of network and states
We study the co-evolution of network structure and node states in a model of
multiple state interacting agents. The system displays two transitions, network
recombination and fragmentation, governed by time scales that emerge from the
dynamics. The recombination transition separates a frozen configuration,
composed by disconnected network components whose agents share the same state,
from an active configuration, with a fraction of links that are continuously
being rewired. The nature of this transition is explained analytically as the
maximum of a characteristic time. The fragmentation transition, that appears
between two absorbing frozen phases, is an anomalous order-disorder transition,
governed by a crossover between the time scales that control the structure and
state dynamics.Comment: 5 pages, 5 figures, figures 2 and 4 changed, tile changed, to be
published in PR
Divergent Time Scale in Axelrod Model Dynamics
We study the evolution of the Axelrod model for cultural diversity. We
consider a simple version of the model in which each individual is
characterized by two features, each of which can assume q possibilities. Within
a mean-field description, we find a transition at a critical value q_c between
an active state of diversity and a frozen state. For q just below q_c, the
density of active links between interaction partners is non-monotonic in time
and the asymptotic approach to the steady state is controlled by a time scale
that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma
Formation and Collapse of Quiescent Cloud Cores Induced by Dynamic Compressions
(Abridged) We present numerical hydrodynamical simulations of the formation,
evolution and gravitational collapse of isothermal molecular cloud cores. A
compressive wave is set up in a constant sub-Jeans density distribution of
radius r = 1 pc. As the wave travels through the simulation grid, a
shock-bounded spherical shell is formed. The inner shock of this shell reaches
and bounces off the center, leaving behind a central core with an initially
almost uniform density distribution, surrounded by an envelope consisting of
the material in the shock-bounded shell, with a power-law density profile that
at late times approaches a logarithmic slope of -2 even in non-collapsing
cases. The resulting density structure resembles a quiescent core of radius <
0.1 pc, with a Bonnor-Ebert-like (BE-like) profile, although it has significant
dynamical differences: it is initially non-self-gravitating and confined by the
ram pressure of the infalling material, and consequently, growing continuously
in mass and size. With the appropriate parameters, the core mass eventually
reaches an effective Jeans mass, at which time the core begins to collapse.
Thus, there is necessarily a time delay between the appearance of the core and
the onset of its collapse, but this is not due to the dissipation of its
internal turbulence as it is often believed. These results suggest that
pre-stellar cores may approximate Bonnor-Ebert structures which are however of
variable mass and may or may not experience gravitational collapse, in
qualitative agreement with the large observed frequency of cores with BE-like
profiles.Comment: Accepted for publication in ApJ. Associated mpeg files can be found
in http://www.astrosmo.unam.mx/~g.gomez/publica.htm
Modeling two-language competition dynamics
During the last decade, much attention has been paid to language competition
in the complex systems community, that is, how the fractions of speakers of
several competing languages evolve in time. In this paper we review recent
advances in this direction and focus on three aspects. First we consider the
shift from two-state models to three state models that include the possibility
of bilingual individuals. The understanding of the role played by bilingualism
is essential in sociolinguistics. In particular, the question addressed is
whether bilingualism facilitates the coexistence of languages. Second, we will
analyze the effect of social interaction networks and physical barriers.
Finally, we will show how to analyze the issue of bilingualism from a game
theoretical perspective.Comment: 15 pages, 5 figures; published in the Special Issue of Advances in
Complex Systems "Language Dynamics
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