Effect of bias in a reaction-diffusion system in two dimensions

Mullick, Pratik; Sen, Parongama

doi:10.1103/physreve.99.052123

Cited by 6 publications

(6 citation statements)

References 36 publications

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“…α ≈ 1 (reported in the present paper). It may be added here that the bulk properties of some variants of the A + A → kA model with the above mentioned bias were recently studied in [25,26].…”

Section: Introductionmentioning

confidence: 99%

Tagged particle dynamics in one dimensional ${A+ A \to kA}$ models with the particles biased to diffuse towards their nearest neighbour

Roy¹,

Ray²,

Sen³

2020

J. Phys. A: Math. Theor.

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Dynamical features of tagged particles are studied in a one dimensional A + A → kA system for k = 0 and 1, where the particles A have a bias ǫ (0 ≤ ǫ ≤ 0.5) to hop one step in the direction of their nearest neighboring particle. ǫ = 0 represents purely diffusive motion and ǫ = 0.5 represents purely deterministic motion of the particles. We show that for any ǫ, there is a time scale t * which demarcates the dynamics of the particles. Below t * , the dynamics are governed by the annihilation of the particles, and the particle motions are highly correlated, while for t ≫ t * , the particles move as independent biased walkers. t * diverges as (ǫc − ǫ) −γ , where γ = 1 and ǫc = 0.5. ǫc is a critical point of the dynamics. At ǫc, the probability S(t), that a walker changes direction of its path at time t, decays as S(t) ∼ t −1 and the distribution D(τ ) of the time interval τ between consecutive changes in the direction of a typical walker decays with a power law as D(τ ) ∼ τ −2 .

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Section: Introductionmentioning

confidence: 99%

Tagged particle dynamics in one dimensional ${A+ A \to kA}$ models with the particles biased to diffuse towards their nearest neighbour

Roy¹,

Ray²,

Sen³

2020

J. Phys. A: Math. Theor.

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“…The model, in its deterministic limit, maps to a opinion dynamics model studied earlier [6]. The reaction diffusion model with parallel updating has also been studied in two dimensions recently [7].…”

Section: Introductionmentioning

confidence: 99%

$A+ A \to \emptyset$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension

Roy,

Sen

2020

Preprint

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Dynamics of a one dimensional A + A → ∅ system where the particles move towards their nearest neighbour with probability 0.5 + ǫ (0 ≤ ǫ ≤ 0.5) are well studied. We consider a negative bias (−0.5 ≤ ǫ < 0) so that the particles have a preference to move away from their nearest neighbour. Here ǫ = −0.5 = ǫc implies deterministic motion where the particles always move away from their nearest neighbour. Both the bulk properties and the tagged particle dynamics are studied in this system. We show that the negative bias changes drastically the behaviour of the fraction of surviving particles ρ(t) and persistence probability P (t) with time t. ρ(t) decays as a/(log t) b where b increases with ǫ − ǫc and P (t) is found to show a stretched exponential decay. The probability Π(x, t) that a tagged particle is at position x from its origin is found to be Gaussian for all ǫ < 0, where the scaling variable is x/t α , α is ǫ dependent, approaching the known limiting value 1/4 at ǫ → ǫc. Some additional features of the dynamics by tagging the particles are also studied.

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“…The A + A → ∅ system has been studied in the recent past where the particles A move with a bias towards or away from their nearest neighbours [3][4][5][6][7][8][9]. The annihilation process is not directly affected by the bias which governs only the direction of motion but this extension leads to drastic changes in the dynamical properties.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we report the results for the dynamical properties of the A + A → ∅ system in one dimension where a particle A diffuses towards its nearest neighbour with a probability 0.5 + ǫ with −0.5 ≤ ǫ ≤ 0.5 using parallel dynamics. A similar problem was studied in two dimensions with parallel updates where the bulk properties were considered [7]. Here we study both the macroscopic dynamical features as well as the tagged particle dynamics.…”

Section: Introductionmentioning

confidence: 99%

$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

Roy,

Sen,

Ray

2020

Preprint

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A one dimensional A + A → ∅ system where the direction of motion of the particles is determined by the position of the nearest neighours is studied. The particles move with a probability 0.5 + ǫ towards their nearest neighbours with −0.5 ≤ ǫ ≤ 0.5. This implies a stochastic motion towards the nearest neighbour or away from it for positive and negative values of ǫ respectively, with ǫ = ± 0.5 the two deterministic limits. The position of the particles are updated in parallel. The macroscopic as well as tagged particle dynamics are studied which show drastic changes from the diffusive case ǫ = 0. The decay of particle density shows departure from the usual power law behaviour as found in ǫ = 0, on both sides of ǫ = 0 and a scaling regime is obtained for ǫ > 0. The ǫ = 0.5 point is characterized by the presence of dimers, which are isolated pairs of particles in adjacent sites that are never annihilated. The persistence probability is also calculated that decays in a stretched exponential manner for ǫ < 0 and switches over to power law behaviour for ǫ ≥ 0, with different exponents for ǫ = 0 and ǫ > 0. For the tagged particle, the probability distribution Π(x, t) that it is at position x at time t shows the existence of a scaling variable x/t ν where ν = 0.55 ± 0.05 for ǫ > 0 and varies with ǫ for ǫ < 0. Finally, a comparative analysis for the behaviour of all the relevant quantities for the system using parallel and asynchronous dynamics (studied recently) shows that there are significant differences for ǫ > 0 while the results are qualitatively similar for ǫ < 0.

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Effect of bias in a reaction-diffusion system in two dimensions

Cited by 6 publications

References 36 publications

Tagged particle dynamics in one dimensional ${A+ A \to kA}$ models with the particles biased to diffuse towards their nearest neighbour

Tagged particle dynamics in one dimensional ${A+ A \to kA}$ models with the particles biased to diffuse towards their nearest neighbour

$A+ A \to \emptyset$ reaction for particles with a dynamic bias to move away from their nearest neighbour in one dimension

$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates

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