Concentration for one and two species one-dimensional reaction - diffusion systems

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The coagulation (A+A to A) or the annihilation (A+A to 0) models can be mapped onto systems in which both processes are allowed. With the help of the coagulation-decoagulation model results for some death-decoagulation and annihilation-creation systems are given. We also find a reaction-diffusion system which is equivalent to the two-species annihilation model (A+B to 0). Besides we present numerical results of Monte Carlo simulations. An accurate description of the effects of the reaction rates on the concentration in one-species diffusion-annihilation model is made. The asymptotic behaviour of the concentration in the two-species annihilation system (A+B to 0) with symmetric initial conditions is studied.

References(27)

Figures(0)

[1]

D. ben-Avraham
,
M.A. Burschka
,
C.R. Doering

- J.Statist.Phys. 60 (1990) 695

[2]

A.A. Lushnikov

- Sov.Phys.JETP 64 (1986) 811

[3]

Reaction - diffusion processes, critical dynamics and quantum chains

- Annals Phys. 230 (1994) 250-302
•
e-Print:
- hep-th/9302112
•
DOI:
- 10.1006/aphy.1994.1026

[4]

K. Krebs
,
M.P. Pfannmüller
,
B. Wehefritz
,
H. Hinrichsen

- J.Statist.Phys. 78 (1995) 1429

[5]

S-Wave Cross Section for D (p, gamma) He-3

W. KOLOS
(
- Chicago U.
)

- Phys.Rev. 165 (1968) 165-167
•
DOI:
- 10.1103/PhysRev.165.165

[6]

R. Kopelman

- J.Statist.Phys. 42 (1986) 185

[7]

R. Kopelman
,
S.J. Parus
,
J. Prasad

- J.Chem.Phys. 128 (1988) 209

[8]

R. Kroon
,
H. Fleurent
,
R. Sprik

- Phys.Rev.E 47 (1993) 2462

[9]

W.J. Rodriguez
,
M.F. Herman
,
G.L. McPherson

- Phys.Rev.B 39 (1989) 18

[10]

Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension, preprint

D. Zhong
,
D. ben-Avraham

[11]

V. Privman
,
C.R. Doering
,
H.L. Frisch

- Phys.Rev.E 48 (1993) 846

[12]

V. Privman

- Phys.Rev.E 50 (1994) 50

[13]

K. Kang
,
S. Redner

- Phys.Rev.A 30 (1984) 2833

[14]

J. Spouge

- Phys.Rev.Lett. 60 (1988) 871

[15]

Scaling Approach for the Kinetics of Recombination Processes

K. Kang
(
- Boston U.
)
,
S. Redner
(
- Boston U.
)

- Phys.Rev.Lett. 52 (1984) 955-958
•
DOI:
- 10.1103/PhysRevLett.52.955

[16]

Particle- antiparticle annihilation in diffusive motion

D. Toussaint
,
F. Wilczek

- J.Chem.Phys. 78 (1983) 2642

[17]

Critical Behaviour in Non-Equilibrium Systems, Ph. D. Thesis University of California, Santa Barbara

B.P. Lee

[18]

J.-C. Lin

- Phys.Rev.A 44 (1991) 6706

[19]

Spectra of quantum chains without the Yang-Baxter equation

I. Peschel
(
- Dresden, Max Planck Inst. and
- Freie U., Berlin
)
,
V. Rittenberg
(
- Bonn U.
)
,
U. Schultze
(
- Paris U., VI-VII
)

- Nucl.Phys.B 430 (1994) 633-655
•
e-Print:
- cond-mat/9406047
•
DOI:
- 10.1016/0550-3213(94)90163-5

[20]

18

C.R. Doering
,
D. ben-Avraham

- Phys.Rev.Lett. 62 (1989) 2563

[21]

C.R. Doering
,
M.A. Burschka
,
W. Horsthemke

- J.Statist.Phys. 65 (1991) 953

[22]

Exponents Appearing in the Zero Temperature Dynamics of the 1d Potts Model, preprint

E. Derrida

[23]

D. ben-Avraham

- J.Chem.Phys. 88 (1988) 941

[24]

C.R. Doering
,
D. ben-Avraham

- Phys.Rev.A 38 (1988) 3035

[25]

K. Krebs
,
M. Pfannmüller
,
H. Simon
,
B. Wehefritz

- J.Statist.Phys. 78 (1995) 1471

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1
2
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