Decay Process for Three - Species Reaction - Diffusion System

Kim, Kyungsik; Chang, Ki-Ho; Kong, Yu-Sik

doi:10.1143/jpsj.68.1450

Cited by 8 publications

(5 citation statements)

References 10 publications

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“…The results for scale-free networks, briefly reviewed above, are also counter-intuitive. Reactions between three species were studied on both square lattices [17] and scale-free networks [18]. Migration-driven growth has also been shown to behave differently on homogeneous [19] and non-homogeneous space [20].…”

Section: Discussionmentioning

confidence: 99%

The Third Spectrum of Tantalum (Ta III): Fine and Hyperfine Structure

et al. 2003

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We discuss recent work on reaction-diffusion processes that take place on complex networks. The inherent inhomogeneity of the substrate leads to a series of new phenomena, which bear only a small resemblance to the classical results of the field. The annihilation rate is abnormally high in such systems, while at the same time depletion zones are absent in the A + A → 0 reaction and no segregation is observed for the A + B → 0 reaction. These results are mainly attributed to the presence of network hubs and to the small network diameter of such systems.

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Section: Discussionmentioning

confidence: 99%

The Third Spectrum of Tantalum (Ta III): Fine and Hyperfine Structure

et al. 2003

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“…In the above expansion P α 1 α 2 (x; t|β, y; 0) is P (α 1 , α 2 , x 1 , x 2 ; t|β 1 , β 2 , y 1 , y 2 ; 0), f (p 1 , p 2 ) is the coefficient of expansion which in the second equality we choose it 1 (2π) 2 e −ip.y , and ǫ 2 = 2 − e −ip 1 − e −ip 2 (see (19)). Ψ(x 1 , x 2 ) is the two-particle wave function where from (17) and (22) we obtain Ψ(x 1 , x 2 ) = A 1 e i(p 1 x 1 +p 2 x 2 ) + A σ 1 e iσ 1 (p).x = A 1 e i(p 1 x 1 +p 2 x 2 ) + S 12 (p 1 , p 2 )A 1 e i(p 1 x 2 +p 2 x 1 ) .…”

Section: The Two-particle Conditional Probabilitiesmentioning

confidence: 99%

“…In this paper we are going to consider a class of integrable models in which there are two species of particles which can hop to their right neighboring sites if those are not occupied, and also the particles interact with each other if they are in adjacent sites. The details of this nearest-neighboring interaction depends on the specific considered model (see [17]- [19] for some recent works in two-and three-species reaction-diffusion processes). The important point in integrable reaction-diffusion processes with more than one type of particle is that, as we will show, the two-particle S-matrix of the reaction, which specify the N-point functions, must satisfy the Quantum Yang-Baxter Equation (QYBE).…”

Section: Introductionmentioning

confidence: 99%

Class of integrable diffusion-reaction processes

Alimohammadi

Ahmadi

2000

Phys. Rev. E

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We consider a process in which there are two types of particles, A and B, on an infinite one-dimensional lattice. The particles hop to their adjacent sites, like the totally asymmetric exclusion process (ASEP), and have also the following interactions: A+B-->B+B and B+A-->B+B, which all occur with equal rate. We study this process by imposing four boundary conditions on the ASEP master equation. It is shown that this model is integrable, in the sense that its N-particle S matrix is factorized into a product of two-particle S matrices and, more importantly, the two-particle S matrix satisfies the quantum Yang-Baxter equation. Using the coordinate Bethe-ansatz, the N-particle wave functions and the two-particle conditional probabilities are found exactly. Further, by imposing four reasonable physical conditions on two-species diffusion-reaction processes (where the most important ones are the equality of the reaction rates and the conservation of the number of particles in each reaction), we show that among the 4096 types of interactions which have these properties and can be modeled by a master equation and an appropriate set of boundary conditions, there are only 28 independent interactions which are integrable. We find all these interactions and also their corresponding wave functions. Some of these may be new solutions of the quantum Yang-Baxter equation.

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“…Different methods have been used to study these models, including analytical and asymptotic methods, mean field methods, and large-scale numerical methods. Systems with more than one species have also been studied [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Many of the arguments are based on simulation results.…”

Section: Introductionmentioning

confidence: 99%

Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions

2001

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Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for closedness of the evolution equations of the n-point functions are obtained. The average number of the particles at each site for one species and three-site interactions, and its generalization to the more-than-three-site interactions is explicitly obtained. Generalizations of the Glauber model in different directions, using generalized rates, generalized number of states at each site, and generalized number of interacting sites, are also investigated.

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Decay Process for Three - Species Reaction - Diffusion System

Cited by 8 publications

References 10 publications

The Third Spectrum of Tantalum (Ta III): Fine and Hyperfine Structure

The Third Spectrum of Tantalum (Ta III): Fine and Hyperfine Structure

Class of integrable diffusion-reaction processes

Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions

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