619 research outputs found
Site-bond representation and self-duality for totalistic probabilistic cellular automata
We study the one-dimensional two-state totalistic probabilistic cellular
automata (TPCA) having an absorbing state with long-range interactions, which
can be considered as a natural extension of the Domany-Kinzel model. We
establish the conditions for existence of a site-bond representation and
self-dual property. Moreover we present an expression of a set-to-set
connectedness between two sets, a matrix expression for a condition of the
self-duality, and a convergence theorem for the TPCA.Comment: 11 pages, minor corrections, journal reference adde
On a property of random-oriented percolation in a quadrant
Grimmett's random-orientation percolation is formulated as follows. The
square lattice is used to generate an oriented graph such that each edge is
oriented rightwards (resp. upwards) with probability and leftwards (resp.
downwards) otherwise. We consider a variation of Grimmett's model proposed by
Hegarty, in which edges are oriented away from the origin with probability ,
and towards it with probability , which implies rotational instead of
translational symmetry. We show that both models could be considered as special
cases of random-oriented percolation in the NE-quadrant, provided that the
critical value for the latter is 1/2. As a corollary, we unconditionally obtain
a non-trivial lower bound for the critical value of Hegarty's
random-orientation model. The second part of the paper is devoted to higher
dimensions and we show that the Grimmett model percolates in any slab of height
at least 3 in .Comment: The abstract has been updated, discussion has been added to the end
of the articl
Solar source regions of 3HE-rich particle events
Hydrogen alpha X-ray, and metric and kilometric radio data to examine the solar sources of energetic 3He-rich particle events observed near earth in association with impulsive 2 to 100 keV electron events were applied. Each 3He/electron event is associated with a kilometric type 3 burst belonging to a family of such bursts characterized by similar interplanetary propagation paths from the same solar active region. The 3He/electron events correlate very well with the interplanetary low frequency radio brightnesses of these events, but progressively worse with signatures from regions closer to the Sun. When H alpha brightnings can be associated with 3He/electron events, they have onsets coinciding to within 1 min of that of the associated metric type 3 burst but are often too small to be reported. The data are consistent with the earlier idea that many type 3 bursts, the 3He/electron events, are due to particle acceleration in the corona, well above the associated H alpha and X-ray flares
Evolutionary dynamics on degree-heterogeneous graphs
The evolution of two species with different fitness is investigated on
degree-heterogeneous graphs. The population evolves either by one individual
dying and being replaced by the offspring of a random neighbor (voter model
(VM) dynamics) or by an individual giving birth to an offspring that takes over
a random neighbor node (invasion process (IP) dynamics). The fixation
probability for one species to take over a population of N individuals depends
crucially on the dynamics and on the local environment. Starting with a single
fitter mutant at a node of degree k, the fixation probability is proportional
to k for VM dynamics and to 1/k for IP dynamics.Comment: 4 pages, 4 figures, 2 column revtex4 format. Revisions in response to
referee comments for publication in PRL. The version on arxiv.org has one
more figure than the published PR
Hyperscaling in the Domany-Kinzel Cellular Automaton
An apparent violation of hyperscaling at the endpoint of the critical line in
the Domany-Kinzel stochastic cellular automaton finds an elementary resolution
upon noting that the order parameter is discontinuous at this point. We derive
a hyperscaling relation for such transitions and discuss applications to
related examples.Comment: 8 pages, latex, no figure
Dynamics of Majority Rule
We introduce a 2-state opinion dynamics model where agents evolve by majority
rule. In each update, a group of agents is specified whose members then all
adopt the local majority state. In the mean-field limit, where a group consists
of randomly-selected agents, consensus is reached in a time that scales ln N,
where N is the number of agents. On finite-dimensional lattices, where a group
is a contiguous cluster, the consensus time fluctuates strongly between
realizations and grows as a dimension-dependent power of N. The upper critical
dimension appears to be larger than 4. The final opinion always equals that of
the initial majority except in one dimension.Comment: 4 pages, 3 figures, 2-column revtex4 format; annoying typo fixed in
Eq.(1); a similar typo fixed in Eq.(6) and some references update
Survival, extinction and approximation of discrete-time branching random walks
We consider a general discrete-time branching random walk on a countable set
X. We relate local, strong local and global survival with suitable inequalities
involving the first-moment matrix M of the process. In particular we prove
that, while the local behavior is characterized by M, the global behavior
cannot be completely described in terms of properties involving M alone.
Moreover we show that locally surviving branching random walks can be
approximated by sequences of spatially confined and stochastically dominated
branching random walks which eventually survive locally if the (possibly
finite) state space is large enough. An analogous result can be achieved by
approximating a branching random walk by a sequence of multitype contact
processes and allowing a sufficiently large number of particles per site. We
compare these results with the ones obtained in the continuous-time case and we
give some examples and counterexamples.Comment: 32 pages, a few misprints have been correcte
- …