### Abstract

Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version[Figure not available: see fulltext.] where c_{t}=c_{1}(t) is the concentration of l-particle clusters at time t. We prove that for initial data satisfying c_{1}(0)>0 and the condition 0 =c_{l}(0) <A (1+?)^{-l}(A ?>0), the solutions behave asymptotically like c_{1}(t)~t^{-2}˜c(lt^{-1}) as t?8 with lt^{-1} kept fixed. The scaling function ˜c(?) is (1/gr)?, where {Mathematical expression}, a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation {Mathematical expression} where c(v, t) is the oncentration of clusters of size v. © 1994 Plenum Publishing Corporation.

Original language | English |
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Pages (from-to) | 389-407 |

Number of pages | 19 |

Journal | Journal of Statistical Physics |

Volume | 75 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - May 1994 |

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### Keywords

- cluster growth
- dynamical scaling
- kinetics of first-order phase transitions
- Smoluchowski's coagulation equations

### Cite this

*Journal of Statistical Physics*,

*75*(3-4), 389-407. https://doi.org/10.1007/BF02186868

}

*Journal of Statistical Physics*, vol. 75, no. 3-4, pp. 389-407. https://doi.org/10.1007/BF02186868

**Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel.** / Kreer, Markus; Penrose, Oliver.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel

AU - Kreer, Markus

AU - Penrose, Oliver

PY - 1994/5

Y1 - 1994/5

N2 - Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version[Figure not available: see fulltext.] where ct=c1(t) is the concentration of l-particle clusters at time t. We prove that for initial data satisfying c1(0)>0 and the condition 0 =cl(0) <A (1+?)-l(A ?>0), the solutions behave asymptotically like c1(t)~t-2˜c(lt-1) as t?8 with lt-1 kept fixed. The scaling function ˜c(?) is (1/gr)?, where {Mathematical expression}, a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation {Mathematical expression} where c(v, t) is the oncentration of clusters of size v. © 1994 Plenum Publishing Corporation.

AB - Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version[Figure not available: see fulltext.] where ct=c1(t) is the concentration of l-particle clusters at time t. We prove that for initial data satisfying c1(0)>0 and the condition 0 =cl(0) <A (1+?)-l(A ?>0), the solutions behave asymptotically like c1(t)~t-2˜c(lt-1) as t?8 with lt-1 kept fixed. The scaling function ˜c(?) is (1/gr)?, where {Mathematical expression}, a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation {Mathematical expression} where c(v, t) is the oncentration of clusters of size v. © 1994 Plenum Publishing Corporation.

KW - cluster growth

KW - dynamical scaling

KW - kinetics of first-order phase transitions

KW - Smoluchowski's coagulation equations

UR - http://www.scopus.com/inward/record.url?scp=21344485189&partnerID=8YFLogxK

U2 - 10.1007/BF02186868

DO - 10.1007/BF02186868

M3 - Article

VL - 75

SP - 389

EP - 407

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -