2,342 research outputs found
Efficient Monte Carlo Simulation of Biological Aging
A bit-string model of biological life-histories is parallelized, with
hundreds of millions of individuals. It gives the desired drastic decay of
survival probabilities with increasing age for 32 age intervals.Comment: PostScript file to appear in Int.J.Mod.Phys.
On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?
In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one
dimension, which is a simple cellular automata approach to consensus formation
among two opposite opinions (described by spin up or down). To elucidate the SM
dynamics, we first provide results of computer simulations for the
spatio-temporal evolution of the opinion distribution , the evolution of
magnetization , the distribution of decision times and
relaxation times . In the main part of the paper, it is shown that the
SM can be completely reformulated in terms of a linear VM, where the transition
rates towards a given opinion are directly proportional to frequency of the
respective opinion of the second-nearest neighbors (no matter what the nearest
neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow
your second-nearest neighbor''. The equivalence is demonstrated by extensive
computer simulations that show the same behavior between SM and VM in terms of
, , , , and the final attractor statistics. The
reformulation of the SM in terms of a VM involves a new parameter , to
bias between anti- and ferromagnetic decisions in the case of frustration. We
show that plays a crucial role in explaining the phase transition
observed in SM. We further explore the role of synchronous versus asynchronous
update rules on the intermediate dynamics and the final attractors. Compared to
the original SM, we find three additional attractors, two of them related to an
asymmetric coexistence between the opposite opinions.Comment: 22 pages, 20 figures. For related publications see
http://www.ais.fraunhofer.de/~fran
Static and dynamic heterogeneities in a model for irreversible gelation
We study the structure and the dynamics in the formation of irreversible gels
by means of molecular dynamics simulation of a model system where the gelation
transition is due to the random percolation of permanent bonds between
neighboring particles. We analyze the heterogeneities of the dynamics in terms
of the fluctuations of the intermediate scattering functions: In the sol phase
close to the percolation threshold, we find that this dynamical susceptibility
increases with the time until it reaches a plateau. At the gelation threshold
this plateau scales as a function of the wave vector as , with
being related to the decay of the percolation pair connectedness
function. At the lowest wave vector, approaching the gelation threshold it
diverges with the same exponent as the mean cluster size. These
findings suggest an alternative way of measuring critical exponents in a system
undergoing chemical gelation.Comment: 4 pages, 4 figure
Are the Tails of Percolation Thresholds Gaussians ?
The probability distribution of percolation thresholds in finite lattices
were first believed to follow a normal Gaussian behaviour. With increasing
computer power and more efficient simulational techniques, this belief turned
to a stretched exponential behaviour, instead. Here, based on a further
improvement of Monte Carlo data, we show evidences that this question is not
yet answered at all.Comment: 7 pages including 3 figure
Dynamical signatures of the vulcanization transition
Dynamical properties of vulcanized polymer networks are addressed via a
Rouse-type model that incorporates the effect of permanent random crosslinks.
The incoherent intermediate scattering function is computed in the sol and gel
phases, and at the vulcanization transition between them. At any nonzero
crosslink density within the sol phase Kohlrausch relaxation is found. The
critical point is signalled by divergence of the longest time-scale, and at
this point the scattering function decays algebraically, whereas within the gel
phase it acquires a time-persistent part identified with the gel fraction.Comment: 4 page
Intersection and mixing times for reversible chains
© 2017, University of Washington. All rights reserved. We consider two independent Markov chains on the same finite state space, and study their intersection time, which is the first time that the trajectories of the two chains intersect. We denote by tI the expectation of the intersection time, maximized over the starting states of the two chains. We show that, for any reversible and lazy chain, the total variation mixing time is O(tI). When the chain is reversible and transitive, we give an expression for tI using the eigenvalues of the transition matrix. In this case, we also show that tI is of order √nE[I], where I is the number of intersections of the trajectories of the two chains up to the uniform mixing time, and n is the number of states. For random walks on trees, we show that tI and the total variation mixing time are of the same order. Finally, for random walks on regular expanders, we show that tI is of order √n
Consensus Formation in Multi-state Majority and Plurality Models
We study consensus formation in interacting systems that evolve by
multi-state majority rule and by plurality rule. In an update event, a group of
G agents (with G odd), each endowed with an s-state spin variable, is
specified. For majority rule, all group members adopt the local majority state;
for plurality rule the group adopts the local plurality state. This update is
repeated until a final consensus state is generally reached. In the mean field
limit, the consensus time for an N-spin system increases as ln N for both
majority and plurality rule, with an amplitude that depends on s and G. For
finite spatial dimensions, domains undergo diffusive coarsening in majority
rule when s or G is small. For larger s and G, opinions spread ballistically
from the few groups with an initial local majority. For plurality rule, there
is always diffusive domain coarsening toward consensus.Comment: 8 pages, 11 figures, 2-column revtex4 format. Updated version: small
changes in response to referee comments. For publication in J Phys
Love kills: Simulations in Penna Ageing Model
The standard Penna ageing model with sexual reproduction is enlarged by
adding additional bit-strings for love: Marriage happens only if the male love
strings are sufficiently different from the female ones. We simulate at what
level of required difference the population dies out.Comment: 14 pages, including numerous figure
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