Reaction–diffusion fronts with inhomogeneous initial conditions

Bena, Ioana; Droz, Michel; Martens, Kirsten; Rácz, Zoltán

doi:10.1088/0953-8984/19/6/065103

Cited by 9 publications

(7 citation statements)

References 29 publications

(45 reference statements)

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“…Accordingly, the motion of these fronts, the spatial distribution of the rate of the production of C, and the width of the reaction zones have been much investigated. They are known theoretically for the case of neutral reagents 5,6,7,8,9,10 and the theories have been verified in experiments 11,12,13,14,15 .…”

Section: Introductionmentioning

confidence: 79%

Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

Martens,

Droz,

Rácz

2009

Preprint

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We investigate the effects of an electric current on the width of a stationary reaction zone in an irreversible A − +B + → C reaction-diffusion process. The ion dynamics of the electrolytes A ≡ (A + , A − ) and B ≡ (B + , B − ) is described by reaction-diffusion equations obeying local electroneutrality, and the stationary state is obtained by employing reservoirs of fixed electrolyte concentrations at the opposite ends of a finite domain. We find that the width of the reaction zone decreases when the current drives the reacting ions towards the reaction zone while it increases in the opposite case. The linear response of the width to the current is estimated by developing a phenomenological theory based on conservation laws and on electroneutrality. The theory is found to reproduce numerical solutions to a good accuracy.

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Section: Introductionmentioning

confidence: 79%

Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

Martens,

Droz,

Rácz

2009

Preprint

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“…It is remarkable that in both limits evolution of the radius of the island ρ f (T ) and particle distribution in it is described by the universal scaling laws Eqs. (16), (28) [37] with the Λ-dependent time of island collapse T c ∼ Λ 2/d . Substituting T c into Eqs.…”

Section: Quasi-1d Systemsmentioning

confidence: 99%

“…On the basis of the QSA a general description of spatiotemporal behavior of the system A + B → 0 has been obtained for arbitrary nonzero diffusivities [23] which was then generalized to the cases of anomalous diffusion [24], [25], diffusion in disordered systems [26], [27], diffusion in systems with inhomogeneous initial conditions [28], and to several more complex reactions. Following this approach, in most subsequent works the use of the QSA was traditionally restricted by the quasi-onedimensional sea-sea problem with A and B domains having an unlimited extension, i.e.…”

Section: Introductionmentioning

confidence: 99%

Diffusion-controlled coalescence, fragmentation, and collapse of d -dimensional A -particle islands in the B -particle sea

Shipilevsky¹

2019

Phys. Rev. E

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We present a systematic analysis of diffusion-controlled evolution and collapse of two identical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A + B → 0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ compared to their characteristic initial size and a relatively large initial ratio of concentrations island/sea the evolution dynamics of the island-seaisland system is determined unambiguously by the dimensionless parameter Λ = N0/NΩ, where N0 is the initial particle number in the island and NΩ is the initial number of sea particles in the volume Ω = (2ℓ) d . It is established that a) there is a d-dependent critical value Λ⋆ above which island coalescence occurs; b) regardless of d the centers of each of the islands move towards each other along a universal trajectory merging in a united center at the d-dependent critical value Λs ≥ Λ⋆; c) in one-dimensional systems Λ⋆ = Λs, therefore at Λ < Λ⋆ each of the islands dies individually, whereas at Λ > Λ⋆ coalescence is completed by collapse of a single-centered island in the system center; d) in two-and three-dimensional systems in the range Λ⋆ < Λ < Λs coalescence is accompanied by subsequent fragmentation of a two-centered island and is completed by individual collapse of each of the islands. We discuss a detailed picture of coalescence, fragmentation and collapse of islands focusing on evolution of their shape and on behavior of the relative width of the reaction front at the final collapse stage and in the vicinity of starting coalescence and fragmentation points. We demonstrate that in a wide range of parameters the front remains sharp up to a narrow vicinity of the coalescence, fragmentation and collapse points. PACS numbers: 05.70.Ln, 82.20.-w R = Jδ(x − x f ).

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“…whereas in the 1D case w acquires the k-independent form w ∼ (D/J) 1/2 [4], [5]. On the basis of the QSA a general description of spatiotemporal behavior of the system A + B → 0 has been obtained for arbitrary nonzero diffusivities [10] which was then generalized to anomalous diffusion [11], diffusion in disordered systems [12], diffusion in systems with inhomogeneous initial conditions [13], and to several more complex reactions. Following the simplest GR model [3] the main attention has been traditionally focused on the systems with A and B domains having an unlimited extension, i.e., with unlimited number of A ′ s and B ′ s particles, where asymptotically the stage of monotonous quasistatic front propagation is…”

mentioning

confidence: 99%

“…Making use then (13), for the distribution of particles (a = s(x < x f ), b = |s|(x > x f ) [14]) at ρ = 1 we obtain…”

mentioning

confidence: 99%

Diffusion-controlled death ofA-particle andB-particle islands at propagation of the sharp annihilation frontA+B→0

Shipilevsky

2008

Phys. Rev. E

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We consider the problem of diffusion-controlled evolution of the A -particle-island- B -particle-island system at propagation of the sharp annihilation front A+B-->0 . We show that this general problem, which includes as particular cases the sea-sea and island-sea problems, demonstrates rich dynamical behavior from self-accelerating collapse of one of the islands to synchronous exponential relaxation of both islands. We find a universal asymptotic regime of the sharp-front propagation and reveal the limits of its applicability for the cases of mean-field and fluctuation fronts.

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Reaction–diffusion fronts with inhomogeneous initial conditions

Cited by 9 publications

References 29 publications

Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

Diffusion-controlled coalescence, fragmentation, and collapse of d -dimensional A -particle islands in the B -particle sea

Diffusion-controlled death ofA-particle andB-particle islands at propagation of the sharp annihilation frontA+B→0

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