376 research outputs found
Lane formation in a lattice model for oppositely driven binary particles
Oppositely driven binary particles with repulsive interactions on the square
lattice are investigated at the zero-temperature limit. Two classes of steady
states related to stuck configurations and lane formations have been
constructed in systematic ways under certain conditions. A mean-field type
analysis carried out using a percolation problem based on the constructed
steady states provides an estimation of the phase diagram, which is
qualitatively consistent with numerical simulations. Further, finite size
effects in terms of lane formations are discussed.Comment: 6 pages, 8 figures,v2; some corrections in the text have been mad
Morphology transition at depinning in a solvable model of interface growth in a random medium
We propose a simple, exactly solvable, model of interface growth in a random
medium that is a variant of the zero-temperature random-field Ising model on
the Cayley tree. This model is shown to have a phase diagram (critical
depinning field versus disorder strength) qualitatively similar to that
obtained numerically on the cubic lattice. We then introduce a specifically
tailored random graph that allows an exact asymptotic analysis of the height
and width of the interface. We characterize the change of morphology of the
interface as a function of the disorder strength, a change that is found to
take place at a multicritical point along the depinning-transition line.Comment: 7 pages, 6 figure
Critical fluctuations of time-dependent magnetization in a random-field Ising model
Cooperative behaviors near the disorder-induced critical point in a random
field Ising model are numerically investigated by analyzing time-dependent
magnetization in ordering processes from a special initial condition. We find
that the intensity of fluctuations of time-dependent magnetization, ,
attains a maximum value at a time in a normal phase and that
and exhibit divergences near the disorder-induced critical
point. Furthermore, spin configurations around the time are
characterized by a length scale, which also exhibits a divergence near the
critical point. We estimate the critical exponents that characterize these
power-law divergences by using a finite-size scaling method.Comment: 5 pages, 7 figure
Jamming transition in kinetically constrained models with reflection symmetry
A class of kinetically constrained models with reflection symmetry is
proposed as an extension of the Fredrickson-Andersen model. It is proved that
the proposed model on the square lattice exhibits a freezing transition at a
non-trivial density. It is conjectured by numerical experiments that the known
mechanism of the singular behaviors near the freezing transition in a
previously studied model (spiral model) is not responsible for that in the
proposed model.Comment: 14 pages, 12 figure
Stable Process Approach to Analysis of Systems Under Heavy-Tailed Noise: Modeling and Stochastic Linearization
The Wiener process has provided a lot of practically useful mathematical tools to model stochastic noise in many applications. However, this framework is not enough for modeling extremal events, since many statistical properties of dynamical systems driven by the Wiener process are inevitably Gaussian. The goal of this work is to develop a framework that can represent a heavy-tailed distribution without losing the advantages of the Wiener process. To this end, we investigate models based on stable processes (this term “stable” has nothing to do with “dynamical stability”) and clarify their fundamental properties. In addition, we propose a method for stochastic linearization, which enables us to approximately linearize static nonlinearities in feedback systems under heavy-tailed noise, and analyze the resulting error theoretically. The proposed method is applied to assessing wind power fluctuation to show the practical usefulness
Critical phenomena in globally coupled excitable elements
Critical phenomena in globally coupled excitable elements are studied by
focusing on a saddle-node bifurcation at the collective level. Critical
exponents that characterize divergent fluctuations of interspike intervals near
the bifurcation are calculated theoretically. The calculated values appear to
be in good agreement with those determined by numerical experiments. The
relevance of our results to jamming transitions is also mentioned.Comment: 4 pages, 3 figure
Emergent centrality in rank-based supplanting process
We propose a stochastic process of interacting many agents, which is inspired
by rank-based supplanting dynamics commonly observed in a group of Japanese
macaques. In order to characterize the breaking of permutation symmetry with
respect to agents' rank in the stochastic process, we introduce a
rank-dependent quantity, overlap centrality, which quantifies how often a given
agent overlaps with the other agents. We give a sufficient condition in a wide
class of the models such that overlap centrality shows perfect correlation in
terms of the agents' rank in zero-supplanting limit. We also discuss a
singularity of the correlation in the case of interaction induced by a Potts
energy.Comment: 31 pages, 8 figure
Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model
The dynamical behaviours of a kinetically constrained spin model
(Fredrickson-Andersen model) on a Bethe lattice are investigated by a
perturbation analysis that provides exact final states above the nonergodic
transition point. It is observed that the time-dependent solutions of the
derived dynamical systems obtained by the perturbation analysis become
systematically closer to the results obtained by Monte Carlo simulations as the
order of a perturbation series is increased. This systematic perturbation
analysis also clarifies the existence of a dynamical scaling law, which
provides a implication for a universal relation between a size scale and a time
scale near the nonergodic transition.Comment: 17 pages, 7 figures, v2; results have been refined, v3; A figure has
been modified, v4; results have been more refine
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