Self-similar evolution of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>-particle island–semi-infinite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-particle sea reaction-diffusion system

Shipilevsky, Boris M.

doi:10.1103/physreve.88.012133

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…where real, X m f = X − f , and imaginary, ̺ m f , semi-axes of the hyperbola (hyperboloid) first contract (T > 0), and then grow (T < 0) by the law (36) we find that evolution of island shape in the vicinity of coalescence and fragmentation points is described by the expression…”

Section: "Elastic" Reflection Of the Front At The Critical Point λ = λ⋆mentioning

confidence: 80%

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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Section: "Elastic" Reflection Of the Front At The Critical Point λ = λ⋆mentioning

confidence: 80%

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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“…If it happens that both species exhaust themselves in the mixing process, then the mixing is homogeneous (or efficient), otherwise it is inhomogeneous. For example, on an infinite one dimensional domain, if the total number of A species in a particular region is greater than (and surrounds) the number of B species then a rapid disappearance of the B species will eventuate from in-homogeneous mixing thus resulting in segregated island-type phenomenon [20]. For finite domains, the boundary of the domain will accentuate this mixing behavior.…”

Section: Introductionmentioning

confidence: 99%

MIXING TIME OF A + B− > 0 IN ONE DIMENSION

Haynes

2016

Fractals

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A mixing time density of A+B → 0 on a finite one dimensional domain is defined for general initial and boundary conditions in which A and B diffuse at the same rate. The density is a measure of the number of A and B particles that mix through the center of the reaction zone. It also corresponds to the reaction density for the special case in which A and B annihilate upon contact. An exact expression is found for the generating function of the mixing time. The analysis is extended to multiple reaction fronts and finitely ramified fractals. The full method involves using the kernel of the Laplace transform integral operator to map and analyze a moving homogeneous Dirichlet interior point condition.

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“…In real experiments, the solutions of reactants are, however, confined into a limited region of space leading to finite-size effects when the front reaches one of the system boundaries. Finite-size effects also naturally arise in the context of multiple A + B → C fronts when, for instance, the solution of one of the reactants is initially confined between solutions of the other reactant [24][25][26][27]. The formation of two or more localized reaction zones, randomly separated in space, is indeed expected to be much more likely than the formation of a single isolated one in natural environments.…”

mentioning

confidence: 99%

Complex dynamics of interacting fronts in a simpleA+B→Creaction-diffusion system

Tiani

Rongy

2019

Phys. Rev. E

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Pattern interaction has so far been restricted to systems with relatively complex reaction schemes, such as activator-inhibitor systems, that lead to rich spatio-temporal dynamics. Surprisingly, a simple second-order chemical reaction is capable of generating similar complex phenomena, such as attractive or repulsive interaction modes between the localized reaction zones (or fronts). We illustrate the latter statement both analytically and numerically with two initially separated A + B → C reaction-diffusion fronts when the solution of B is initially confined between two solutions of A. The nature of the front-front interaction changes from an attractive type to a repulsive one above a critical distance separating the two fronts initially. The complexity of the pattern dynamics emerges here due to finite-size effects. A scaling law relating the critical distance d c above which the repulsion occurs and kinetic parameters gives insights into (i) extracting those parameters from experiments for bimolecular reactions and (ii) the control strategy of periodic patterns.

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Self-similar evolution of theA-particle island–semi-infiniteB-particle sea reaction-diffusion system

Cited by 5 publications

References 15 publications

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

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

MIXING TIME OF A + B− > 0 IN ONE DIMENSION

Complex dynamics of interacting fronts in a simpleA+B→Creaction-diffusion system

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