Upper and lower bounds for the speed of pulled fronts with a cut-off

Benguria, Rafael D.; Depassier, M. C.; Loss, Michael

doi:10.1140/epjb/e2008-00069-1

Cited by 10 publications

(13 citation statements)

References 11 publications

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“…As it has been extensively applied in other works dealing with variational techniques for determining the wave front velocity [20], we now work in the phase space p = dθ /ds , so Eq. (40) reads p dp dθ…”

Section: A Region IImentioning

confidence: 99%

Analytical expressions for the flame front speed in the downward combustion of thin solid fuels and comparison to experiments

Pujol

Comas

2011

Phys. Rev. E

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We derive analytical expressions for the propagation speed of downward combustion fronts of thin solid fuels with a background flow initially at rest. The classical combustion model for thin solid fuels that consists of five coupled reaction-convection-diffusion equations is here reduced into a single equation with the gas temperature as the single variable. For doing so we apply a two-zone combustion model that divides the system into a preheating region and a pyrolyzing region. The speed of the combustion front is obtained after matching the temperature and its derivative at the location that separates both regions. We also derive a simplified version of this analytical expression expected to be valid for a wide range of cases. Flame front velocities predicted by our analytical expressions agree well with experimental data found in the literature for a large variety of cases and substantially improve the results obtained from a previous well-known analytical expression.

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Section: A Region IImentioning

confidence: 99%

Analytical expressions for the flame front speed in the downward combustion of thin solid fuels and comparison to experiments

Pujol

Comas

2011

Phys. Rev. E

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“…Travelling wave solutions for system (3), can thus be interpreted as heteroclinic trajectories of the dynamical system (9) in the four-dimensional phase space (η, θ, u, v), connecting the steady state E 1 = (0, ( / + 2), 0, 0) to the steady state E 2 = ((1/ ), ( / + 1), 0, 0).…”

Section: Travelling Wave Solutionsmentioning

confidence: 99%

“…In the next section, we present in details the numerical approximation of the reaction-diffusion system (3). The question of the numerical estimation of the travelling wave speed is also widely discussed.…”

Section: Travelling Wave Solutionsmentioning

confidence: 99%

“…Indeed, recent studies [3,10] prove that in presence of a cut-off on the solution, say tol, the velocity of the front is indeed shifted and is given byc =c(tol) = 2 − (π/ ln(tol)) 2 < c * . We present the numerical approximation of the Fisher equation by the MOL technique based on the D2ECDF methods of order p = 2, 4, 6 and some comparisons with results obtained by the Matlab function pdepe based on the finite-element method and more accurate in time (ode15s) than space (p = 2).…”

Section: Numerical Approximation By High Order Finite Difference Schemesmentioning

confidence: 99%

“…The effect of the cut-off on the travelling wave has been studied by many authors (see e.g. [11]) and in particular for the Fisher equation by [3,10]. In presence of this threshold, the reaction term in (19) has been defined as (20) and an estimate for the speed of the corresponding pulled front is given in [10] by c(u) ≈c =c(tol) := 2 − π 2 (ln tol) 2 (21) Moreover, in [3] the authors refine this estimate and give an upper and lower bound c LOW (tol) < c(u) ≤ c UP (tol), with…”

Section: Numerical Solution Of the Fisher Equationmentioning

confidence: 99%

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Travelling waves in a reaction-diffusion model for electrodeposition

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Lacitignola

Sgura

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Mathematics and Computers in Simulation

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Brunet-Derrida Behavior of Branching-Selection Particle Systems on the Line

Bérard

Gouéré

2010

Commun. Math. Phys.

143

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Abstract. We consider a class of branching-selection particle systems on R similar to the one considered by E. Brunet and B. Derrida in their 1997 paper "Shift in the velocity of a front due to a cutoff". Based on numerical simulations and heuristic arguments, Brunet and Derrida showed that, as the population size N of the particle system goes to infinity, the asymptotic velocity of the system converges to a limiting value at the unexpectedly slow rate (log N ) −2 . In this paper, we give a rigorous mathematical proof of this fact, for the class of particle systems we consider. The proof makes use of ideas and results by R. Pemantle, and by N. Gantert, Y. Hu and Z. Shi, and relies on a comparison of the particle system with a family of N independent branching random walks killed below a linear space-time barrier.

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Upper and lower bounds for the speed of pulled fronts with a cut-off

Cited by 10 publications

References 11 publications

Analytical expressions for the flame front speed in the downward combustion of thin solid fuels and comparison to experiments

Analytical expressions for the flame front speed in the downward combustion of thin solid fuels and comparison to experiments

Travelling waves in a reaction-diffusion model for electrodeposition

Brunet-Derrida Behavior of Branching-Selection Particle Systems on the Line

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