Scaling of Coalescing Random Walkers with Injection Obeying Nonlinear Conservation Law
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概要
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We study the scaling behaviour of the diameter s of coalescing particles obeying the nonlinear conservation law : s^Δ=s^Δ_1+s^Δ_2 in the coalescing random walker model with injection where s_1 and s_2 are the diameters of two particles before collision. The dynamic exponent z of the mean diameter s and the scaling exponent τ' of the cumulative size distribution are obtained by computer simulation. The exponents z and τ' depend strongly on the diameter exponent Δ. The scaling exponents z and τ' are given by z=3/2Δ and τ'=Δ/3 for Δ≤1.0. For Δ≥2.0, the exponents z and τ'are given by the mean-field values z=1 and τ'=1/2. At the upper critical value Δ_c=2.0, the scaling changes to the mean-field behaviour. For Δ≤1.0, the scaling relation (Δ-τ')^<-1>=z is satisfied. It is shown that the diameter-size distribution n_s(t) satisfies the dynamic scaling form n_s(t)≈s^<-(τ'+1)>f(s/t^z).
- 社団法人日本物理学会の論文
- 1994-10-15
著者
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Nagatani Takashi
College Of Engineering Shizuoka University
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Nagatani Takashi
College of Engineering, Shizuoka University
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