63 research outputs found
Nonlinear Stochastic Differential Equations and Self-Organized Criticality
Several nonlinear stochastic differential equations have been proposed in
connection with self-organized critical phenomena. Due to the threshold
condition involved in its dynamic evolution an infinite number of
nonlinearities arises in a hydrodynamic description. We study two models with
different noise correlations which make all the nonlinear contribution to be
equally relevant below the upper critical dimension. The asymptotic values of
the critical exponents are estimated from a systematic expansion in the number
of coupling constants by means of the dynamic renormalization group.Comment: RevTeX 3.0, no figure
Dynamical properties of the Zhang model of Self-Organized Criticality
Critical exponents of the infinitely slowly driven Zhang model of
self-organized criticality are computed for with particular emphasis
devoted to the various roughening exponents. Besides confirming recent
estimates of some exponents, new quantities are monitored and their critical
exponents computed. Among other results, it is shown that the three dimensional
exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model
and that the dynamical exponent as computed from the correlation length and
from the roughness of the energy profile do not necessarily coincide as it is
usually implicitly assumed. An explanation for this is provided. The
possibility of comparing these results with those obtained from Renormalization
Group arguments is also briefly addressed.Comment: 8 pages, 12 PostScript figures, RevTe
Synchronization in dynamical networks of locally coupled self-propelled oscillators
Systems of mobile physical entities exchanging information with their
neighborhood can be found in many different situations. The understanding of
their emergent cooperative behaviour has become an important issue across
disciplines, requiring a general conceptual framework in order to harvest the
potential of these systems. We study the synchronization of coupled oscillators
in time-evolving networks defined by the positions of self-propelled agents
interacting in real space. In order to understand the impact of mobility in the
synchronization process on general grounds, we introduce a simple model of
self-propelled hard disks performing persistent random walks in 2 space and
carrying an internal Kuramoto phase oscillator. For non-interacting particles,
self-propulsion accelerates synchronization. The competition between agent
mobility and excluded volume interactions gives rise to a richer scenario,
leading to an optimal self-propulsion speed. We identify two extreme dynamic
regimes where synchronization can be understood from theoretical
considerations. A systematic analysis of our model quantifies the departure
from the latter ideal situations and characterizes the different mechanisms
leading the evolution of the system. We show that the synchronization of
locally coupled mobile oscillators generically proceeds through coarsening
verifying dynamic scaling and sharing strong similarities with the phase
ordering dynamics of the 2 XY model following a quench. Our results shed
light into the generic mechanisms leading the synchronization of mobile agents,
providing a efficient way to understand more complex or specific situations
involving time-dependent networks where synchronization, mobility and excluded
volume are at play
Modeling the Internet
We model the Internet as a network of interconnected Autonomous Systems which
self-organize under an absolute lack of centralized control. Our aim is to
capture how the Internet evolves by reproducing the assembly that has led to
its actual structure and, to this end, we propose a growing weighted network
model driven by competition for resources and adaptation to maintain
functionality in a demand and supply ``equilibrium''. On the demand side, we
consider the environment, a pool of users which need to transfer information
and ask for service. On the supply side, ASs compete to gain users, but to be
able to provide service efficiently, they must adapt their bandwidth as a
function of their size. Hence, the Internet is not modeled as an isolated
system but the environment, in the form of a pool of users, is also a
fundamental part which must be taken into account. ASs compete for users and
big and small come up, so that not all ASs are identical. New connections
between ASs are made or old ones are reinforced according to the adaptation
needs. Thus, the evolution of the Internet can not be fully understood if just
described as a technological isolated system. A socio-economic perspective must
also be considered.Comment: Submitted to the Proceedings of the 3rd International Conference
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Dynamical properties of model communication networks
We study the dynamical properties of a collection of models for communication
processes, characterized by a single parameter representing the relation
between information load of the nodes and its ability to deliver this
information. The critical transition to congestion reported so far occurs only
for . This case is well analyzed for different network topologies. We
focus of the properties of the order parameter, the susceptibility and the time
correlations when approaching the critical point. For no transition to
congestion is observed but it remains a cross-over from a low-density to a
high-density state. For the transition to congestion is discontinuous
and congestion nuclei arise.Comment: 8 pages, 8 figure
Synchronization of moving integrate and fire oscillators
We present a model of integrate and fire oscillators that move on a plane.
The phase of the oscillators evolves linearly in time and when it reaches a
threshold value they fire choosing their neighbors according to a certain
interaction range. Depending on the velocity of the ballistic motion and the
average number of neighbors each oscillator fires to, we identify different
regimes shown in a phase diagram. We characterize these regimes by means of
novel parameters as the accumulated number of contacted neighbors.Comment: 9 pages, 5 figure
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