142 research outputs found
Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field
We consider two mean-field like models which belong to the universality class
of absorbing phase transitions with a conserved field. In both cases we derive
analytically the order parameter as function of the control parameter and of an
external field conjugated to the order parameter. This allows us to calculate
the universal scaling function of the mean-field behavior. The obtained
universal function is in perfect agreement with recently obtained numerical
data of the corresponding five and six dimensional models, showing that four is
the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.
Moment analysis of the probability distributions of different sandpile models
We reconsider the moment analysis of the Bak-Tang-Wiesenfeld and the Manna
sandpile model in two and three dimensions. In contrast to recently performed
investigations our analysis turns out that the models are characterized by
different scaling behavior, i.e., they belong to different universality
classes.Comment: 6 pages, 6 figures, accepted for publication in Physical Review
Nonequilibrium critical behavior of a species coexistence model
A biologically motivated model for spatio-temporal coexistence of two
competing species is studied by mean-field theory and numerical simulations. In
d>1 dimensions the phase diagram displays an extended region where both species
coexist, bounded by two second-order phase transition lines belonging to the
directed percolation universality class. The two transition lines meet in a
multicritical point, where a non-trivial critical behavior is observed.Comment: 11 page
Absorbing boundaries in the conserved Manna model
The conserved Manna model with a planar absorbing boundary is studied in
various space dimensions. We present a heuristic argument that allows one to
compute the surface critical exponent in one dimension analytically. Moreover,
we discuss the mean field limit that is expected to be valid in d>4 space
dimensions and demonstrate how the corresponding partial differential equations
can be solved.Comment: 8 pages, 4 figures; v1 was changed by replacing the co-authors name
"L\"ubeck" with "Lubeck" (metadata only
Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
We study probability distributions of waves of topplings in the
Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves
represent relaxation processes which do not contain multiple toppling events.
We investigate bulk and boundary waves by means of their correspondence to
spanning trees, and by extensive numerical simulations. While the scaling
behavior of avalanches is complex and usually not governed by simple scaling
laws, we show that the probability distributions for waves display clear power
law asymptotic behavior in perfect agreement with the analytical predictions.
Critical exponents are obtained for the distributions of radius, area, and
duration, of bulk and boundary waves. Relations between them and fractal
dimensions of waves are derived. We confirm that the upper critical dimension
D_u of the model is 4, and calculate logarithmic corrections to the scaling
behavior of waves in D=4. In addition we present analytical estimates for bulk
avalanches in dimensions D>=4 and simulation data for avalanches in D<=3. For
D=2 they seem not easy to interpret.Comment: 12 pages, 17 figures, submitted to Phys. Rev.
Fluctuations and correlations in sandpile models
We perform numerical simulations of the sandpile model for non-vanishing
driving fields and dissipation rates . Unlike simulations
performed in the slow driving limit, the unique time scale present in our
system allows us to measure unambiguously response and correlation functions.
We discuss the dynamic scaling of the model and show that
fluctuation-dissipation relations are not obeyed in this system.Comment: 5 pages, latex, 4 postscript figure
Activated Random Walkers: Facts, Conjectures and Challenges
We study a particle system with hopping (random walk) dynamics on the integer
lattice . The particles can exist in two states, active or
inactive (sleeping); only the former can hop. The dynamics conserves the number
of particles; there is no limit on the number of particles at a given site.
Isolated active particles fall asleep at rate , and then remain
asleep until joined by another particle at the same site. The state in which
all particles are inactive is absorbing. Whether activity continues at long
times depends on the relation between the particle density and the
sleeping rate . We discuss the general case, and then, for the
one-dimensional totally asymmetric case, study the phase transition between an
active phase (for sufficiently large particle densities and/or small )
and an absorbing one. We also present arguments regarding the asymptotic mean
hopping velocity in the active phase, the rate of fixation in the absorbing
phase, and survival of the infinite system at criticality. Using mean-field
theory and Monte Carlo simulation, we locate the phase boundary. The phase
transition appears to be continuous in both the symmetric and asymmetric
versions of the process, but the critical behavior is very different. The
former case is characterized by simple integer or rational values for critical
exponents (, for example), and the phase diagram is in accord with
the prediction of mean-field theory. We present evidence that the symmetric
version belongs to the universality class of conserved stochastic sandpiles,
also known as conserved directed percolation. Simulations also reveal an
interesting transient phenomenon of damped oscillations in the activity
density
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