Discontinuous transition in a boundary driven contact process

Costa, André; Blythe, Richard A.; Evans, Martin R.

doi:10.1088/1742-5468/2010/09/p09008

Cited by 6 publications

(20 citation statements)

References 24 publications

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“…These results are consistent with those reported by Costa and his coworkers [43], where a heuristic argument supporting the results is also given. Indeed, one can see, from the inset of figure 4(b), that L(p; θ)/ tan θ takes very similar value among various θ, provided that p is same.…”

Section: Distance Dependence Of Order Parametersupporting

confidence: 93%

“…In most cases, the warm-up time W warm was long enough for the wave of the activity (similar to what was reported in Ref. [43]) to reach to the other side of the system. The simulation was repeated over 16 times to further improve statistics.…”

Section: Description Of the Modelsupporting

confidence: 84%

“…Since the crossover of the order parameter is not clearly observed unless the advection is sufficiently weak, it is desirable to find an alternative way to measure the remaining static critical exponent ν ⊥ . One of the possible candidates is the velocity v sup of the wave of activity in the high-density phase (hereafter referred to as "the supercritical wave velocity"), as studied by Costa et al [43]: It can be theoretically shown that v sup obeys the following functional form:…”

Section: Inactive Interval Distributionmentioning

confidence: 99%

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How to experimentally probe universal features of absorbing phase transitions using steady state

Tamai¹,

Sano²

2018

J. Stat. Mech.

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We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of duration/length of intervals of local inactive state in quasi-steady state, which has been very commonly used in experiments, in a case of the contact process. We show that the distributions obey the universal scaling ansatz expected from phenomenological scaling argument, but that care must be taken in order to suppress a bias caused by censoring due to a finite observation window. To demonstrate the latter point, we compare the distributions for the temporal intervals estimated through conventional histograms with those through the estimator which properly takes account of censoring and sampling bias. On the other hand, we also propose that, if a system is subject to uniform advection as is often the case with flowing systems, a correlation length and a correlation time near the transition point can be easily quantified by supplying the system with an active boundary condition. In order to support our proposal, we introduce a new model whose advection strength can be arbitrarily controlled. The results of numerical simulations on our model suggest that a correlation time, which is difficult to measure through the interval distributions without the aforementioned bias, can be measured through characteristic decay length of an order parameter. Crossovers between two different power-law behaviors are also identified in this case, and the universal scaling ansätze associated with the crossovers are discussed.

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Section: Distance Dependence Of Order Parametersupporting

confidence: 93%

Section: Description Of the Modelsupporting

confidence: 84%

Section: Inactive Interval Distributionmentioning

confidence: 99%

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How to experimentally probe universal features of absorbing phase transitions using steady state

Tamai¹,

Sano²

2018

J. Stat. Mech.

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“…Another highly relevant generalization are heterogeneous [69] and random [85] environments. Furthermore, the structure of the FKPP equation may be too restrictive which suggests to add transport/advection terms and active boundaries in which case discontinuous wave speed transitions have been reported [11]. Also the assumption of time-white or space-time-white noise is too restrictive and one should extend the view to spatiallycolored noise [25] and trace-class covariance operators.…”

Section: Discussionmentioning

confidence: 99%

Warning signs for wave speed transitions of noisy Fisher–KPP invasion fronts

Kuehn

2013

Theor Ecol

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Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The approach is based upon a detailed numerical study of various versions of the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation of this work is to contribute to the following question: how much information do statistics, collected by a stationary observer, contain about the speed and bifurcations of traveling waves? We suggest warning signs based upon closeness to carrying capacity, second-order moments and transients of localized initial invasions.

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“…different infection rates in the two directions) [21] the phase transition falls into the directed percolation universality class as in the unbiased model [22]. But, the breaking of the translation symmetry, for instance, by putting an active wall to the system, leads to differences compared to the unbiased case, such as the discontinuity of the velocity of the activity front across the transition [23]. So, one expects that in the simultaneous presence of a global bias and quenched disorder the nature of the phase transition is different from that of the homogeneous, biased contact process.…”

Section: Introductionmentioning

confidence: 99%

Disordered contact process with asymmetric spreading

Juhász

2013

Phys. Rev. E

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An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for the model by means of which it is shown that the local asymmetry of spreading is irrelevant on large scales if the model is globally (statistically) symmetric. Otherwise, in the presence of a global bias in either direction, the renormalization method predicts two distinct phase transitions, which are related to the spreading of activity in and against the direction of the bias. The latter is found to be described by an infinite randomness fixed point while the former is not.

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Discontinuous transition in a boundary driven contact process

Cited by 6 publications

References 24 publications

How to experimentally probe universal features of absorbing phase transitions using steady state

How to experimentally probe universal features of absorbing phase transitions using steady state

Warning signs for wave speed transitions of noisy Fisher–KPP invasion fronts

Disordered contact process with asymmetric spreading

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