Multispecies extension of the solvable partially asymmetric reaction–diffusion processes

Alimohammadi, M.; Naimi, Yaghoob

doi:10.1063/1.1897664

Cited by 3 publications

(19 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different boundary conditions introduce different interactions for particles. Following the same argument given in [17], it can be easily seen that the master equation (4) leads to the following relation for two-particle probabilities…”

Section: Boundary Conditionmentioning

confidence: 99%

“…Following the same steps as [17], we first considerṖ α1α2 (x, x + 1). Using (4) and the type 1 boundary condition (6), it is founḋ…”

Section: P -Species Reaction-diffusion Systems With Pdhrmentioning

confidence: 99%

“…The effect of reactions has been coded in the boundary condition which is in fact the part of the master equation. Also the effect of annihilations has been coded in the modified constraint (17) or (18). 4 The Bethe ansatz solution…”

Section: Annihilation-diffusion Processesmentioning

confidence: 99%

“…partially asymmetric exclusion process (PASEP), has been studied and in [16], the one-species PASEP drop-push model has been described. The multi-species generalizations of PASEP models in which each particle hops to the right by rate D R and hops to the left by rate D L , have been studied in [17]. The D L = 0 case of the models studied in [17] leads to the previous mentioned TASEP models.…”

Section: Introductionmentioning

confidence: 99%

“…The multi-species generalizations of PASEP models in which each particle hops to the right by rate D R and hops to the left by rate D L , have been studied in [17]. The D L = 0 case of the models studied in [17] leads to the previous mentioned TASEP models.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Solvable multi-species reaction–diffusion processes with particle-dependent hopping rates

Naimi

Roshani

2009

J. Stat. Mech.

View full text Add to dashboard Cite

By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reactiondiffusion processes, with particle-dependent hopping rates, are investigated. In these models (i.e. reaction-diffusion and drop-push systems), we have the case of distinct particles where each particle Aα has its own intrinsic hopping rate vα. They also contain the parameters that control the annihilation-diffusion rates (including pair-annihilation and coagulation to the right and left). We obtain two distinct new models. It is shown that these models are exactly solvable in the sense of the Bethe anstaz. The two-particle conditional probabilities and the large-time behavior of such systems are also calculated.

show abstract

Section: Boundary Conditionmentioning

confidence: 99%

“…Following the same steps as [17], we first considerṖ α1α2 (x, x + 1). Using (4) and the type 1 boundary condition (6), it is founḋ…”

Section: P -Species Reaction-diffusion Systems With Pdhrmentioning

confidence: 99%

Section: Annihilation-diffusion Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solvable multi-species reaction–diffusion processes with particle-dependent hopping rates

Naimi

Roshani

2009

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

Solvable reaction-diffusion processes without exclusion

Alimohammadi

2006

Journal of Mathematical Physics

View full text Add to dashboard Cite

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master equation of the asymmetric diffusion process. The annihilation process is also added. The Bethe ansatz solution and the exact N-particle conditional probabilities are obtained.Comment: 13 pages, accepted for publication in Jour. Math. Phy

show abstract

Dynamic boundaries in asymmetric exclusion processes

Nowak¹,

Fok

Chou

2007

Phys. Rev. E

View full text Add to dashboard Cite

We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left-hand boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right-hand boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady-state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of nonequilibrium phases of the system, fluctuating boundary layers, and particle densities in the laboratory frame versus the frame of the fluctuating wall.

show abstract

Multispecies extension of the solvable partially asymmetric reaction–diffusion processes

Cited by 3 publications

References 30 publications

Solvable multi-species reaction–diffusion processes with particle-dependent hopping rates

Solvable multi-species reaction–diffusion processes with particle-dependent hopping rates

Solvable reaction-diffusion processes without exclusion

Dynamic boundaries in asymmetric exclusion processes

Contact Info

Product

Resources

About