4,541 research outputs found
Analytic solutions for nonlinear waves in coupled reacting systems
We analyze a system of reacting elements harmonically coupled to nearest
neighbors in the continuum limit. An analytic solution is found for traveling
waves. The procedure is used to find oscillatory as well as solitary waves. A
comparison is made between exact solutions and solutions of the piecewise
linearized system, showing how the linearization affects the amplitude and
frequency of the solutions.Comment: 5 pages, 5 figures, RevTeX 4 styl
Compelled to do the right thing
We use a model of opinion formation to study the consequences of some
mechanisms attempting to enforce the right behaviour in a society. We start
from a model where the possible choices are not equivalent (such is the case
when the agents decide to comply or not with a law) and where an imitation
mechanism allow the agents to change their behaviour based on the influence of
a group of partners. In addition, we consider the existence of two social
constraints: a) an external authority, called monitor, that imposes the correct
behaviour with infinite persuasion and b) an educated group of agents that act
upon their fellows but never change their own opinion, i.e., they exhibit
infinite adamancy. We determine the minimum number of monitors to induce an
effective change in the behaviour of the social group, and the size of the
educated group that produces the same effect. Also, we compare the results for
the cases of random social interactions and agents placed on a network. We have
verified that a small number of monitors are enough to change the behaviour of
the society. This also happens with a relatively small educated group in the
case of random interactions.Comment: 8 pages, 9 figures, submitted to EPJ
Associative memory on a small-world neural network
We study a model of associative memory based on a neural network with
small-world structure. The efficacy of the network to retrieve one of the
stored patterns exhibits a phase transition at a finite value of the disorder.
The more ordered networks are unable to recover the patterns, and are always
attracted to mixture states. Besides, for a range of the number of stored
patterns, the efficacy has a maximum at an intermediate value of the disorder.
We also give a statistical characterization of the attractors for all values of
the disorder of the network.Comment: 5 pages, 4 figures (eps
Synchronization learning of coupled chaotic maps
We study the dynamics of an ensemble of globally coupled chaotic logistic
maps under the action of a learning algorithm aimed at driving the system from
incoherent collective evolution to a state of spontaneous full synchronization.
Numerical calculations reveal a sharp transition between regimes of
unsuccessful and successful learning as the algorithm stiffness grows. In the
regime of successful learning, an optimal value of the stiffness is found for
which the learning time is minimal
Long transients and cluster size in globally coupled maps
We analyze the asymptotic states in the partially ordered phase of a system
of globally coupled logistic maps. We confirm that, regardless of initial
conditions, these states consist of a few clusters, and they properly belong in
the ordered phase of these systems. The transient times necessary to reach the
asymptotic states can be very long, especially very near the transition line
separating the ordered and the coherent phases. We find that, where two
clusters form, the distribution of their sizes corresponds to windows of
regular or narrow-band chaotic behavior in the bifurcation diagram of a system
of two degrees of freedom that describes the motion of two clusters, where the
size of one cluster acts as a bifurcation parameter.Comment: To appear in Europhysics Letter
Sacks forcing does not always produce a minimal upper bound
AbstractTheorem. There is a countable admissible set, Ol, with ordinal ωCK1 such that if S is Sacks generic over Ol then ω1S > ωCK1 and S is a nonminimal upper bound for the hyperdegrees in Ol. (The same holds over Ol for any upper bound produced by any forcing which can be construed so that the forcing relation for Σ1 formulas is Σ1.) A notion of forcing, the “delayed collapse” of ωCK1, is defined. The construction hinges upon the symmetries inherent in how this forcing interacts with Σ1 formulas. It also uses Steel trees to make a certain part of the generic object Σ1 over the final inner model, Ol, and, indeed, over many generic extensions of Ol
Spatio-temporal patterns in the Hantavirus infection
We present a model of the infection of Hantavirus in deer mouse, Peromyscus
maniculatus, based on biological observations of the system in the North
American Southwest. The results of the analysis shed light on relevant
observations of the biological system, such as the sporadical disappearance of
the infection, and the existence of foci or ``refugia'' that perform as
reservoirs of the virus when environmental conditions are less than optimal.Comment: 6 pages, 5 inlined figures, RevTeX 4 forma
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