1991 Fiscal Year Final Research Report Summary
Stationary power-law distribution in a generalized aggregation system with injection
| Project/Area Number |
02804022
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | Kobe University |
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Principal Investigator |
TAKAYASU Hideki Kobe Univ. Dept. of Earth Sciences, 理学部, 助教授 (00183062)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Aggregation / power-low distribution / Practals / Landform Model |
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| Research Abstract |
In this research we studied a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For 1-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are constantly injected. The steady state charge distribution obeys a power law with exponent depending both on the type of the injection and the spatial dimension. The response of the system to a perturbation(i. e., relaxation)is characterized by either a power law decay or a compressed exponential decay.
As an application of this model we introduced a model of landform created by water erosion. Water flows aggregate making river networks and the earth's surface is eroded as a result. We showed that the landform automatically makes Practal geometry by the effect of erosion.
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