35,903 research outputs found
The structures underlying soliton solutions in integrable hierarchies
We point out that a common feature of integrable hierarchies presenting
soliton solutions is the existence of some special ``vacuum solutions'' such
that the Lax operators evaluated on them, lie in some abelian subalgebra of the
associated Kac-Moody algebra. The soliton solutions are constructed out of
those ``vacuum solitons'' by the dressing transformation procedure.Comment: Talk given at the I Latin American Symposium on High Energy Physics,
I SILAFAE, Merida, Mexico, November/96, 5 pages, LaTeX, needs aipproc.tex,
aipproc.sty, aipproc.cls, available from
ftp://ftp.aip.org/ems/tex/macros/proceedings/6x9
Strategies for Optimize Off-Lattice Aggregate Simulations
We review some computer algorithms for the simulation of off-lattice clusters
grown from a seed, with emphasis on the diffusion-limited aggregation,
ballistic aggregation and Eden models. Only those methods which can be
immediately extended to distinct off-lattice aggregation processes are
discussed. The computer efficiencies of the distinct algorithms are compared.Comment: 6 pages, 7 figures and 3 tables; published at Brazilian Journal of
Physics 38, march, 2008 (http://www.sbfisica.org.br/bjp/files/v38_81.pdf
Mean-field analysis of the majority-vote model broken-ergodicity steady state
We study analytically a variant of the one-dimensional majority-vote model in
which the individual retains its opinion in case there is a tie among the
neighbors' opinions. The individuals are fixed in the sites of a ring of size
and can interact with their nearest neighbors only. The interesting feature
of this model is that it exhibits an infinity of spatially heterogeneous
absorbing configurations for whose statistical properties we
probe analytically using a mean-field framework based on the decomposition of
the -site joint probability distribution into the -contiguous-site joint
distributions, the so-called -site approximation. To describe the
broken-ergodicity steady state of the model we solve analytically the
mean-field dynamic equations for arbitrary time in the cases n=3 and 4. The
asymptotic limit reveals the mapping between the statistical
properties of the random initial configurations and those of the final
absorbing configurations. For the pair approximation () we derive that
mapping using a trick that avoids solving the full dynamics. Most remarkably,
we find that the predictions of the 4-site approximation reduce to those of the
3-site in the case of expectations involving three contiguous sites. In
addition, those expectations fit the Monte Carlo data perfectly and so we
conjecture that they are in fact the exact expectations for the one-dimensional
majority-vote model
Dynamic Scaling of Non-Euclidean Interfaces
The dynamic scaling of curved interfaces presents features that are
strikingly different from those of the planar ones. Spherical surfaces above
one dimension are flat because the noise is irrelevant in such cases. Kinetic
roughening is thus a one-dimensional phenomenon characterized by a marginal
logarithmic amplitude of the fluctuations. Models characterized by a planar
dynamical exponent , which include the most common stochastic growth
equations, suffer a loss of correlation along the interface, and their dynamics
reduce to that of the radial random deposition model in the long time limit.
The consequences in several applications are discussed, and we conclude that it
is necessary to reexamine some experimental results in which standard scaling
analysis was applied
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