J. Phys. I France
Volume 1, Numéro 9, September 1991
Page(s) 1251 - 1261
DOI: 10.1051/jp1:1991204
J. Phys. I France 1 (1991) 1251-1261

Finite fractal diffusion-limited aggregates

M. Arturo López-Quintela and M. Carmen Buján-Núñez

Biodynamical Physics Group, Department of Physical Chemistry, University of Santiago de Compostela, E-15706 Santiago de Compostela, Spain

(Received 9 July 1990, accepted in final form 6 May 1991)

Particle-cluster aggregation has been studied by computer simulation. It has been observed that the fractal dimension of a diffusion-limited aggregate is only constant when the number N of its elementary units is sufficiently large. For small N, the fractal dimension is a function of N. The concept of a differential fractal dimension $D(N)=-d[\log n(\varepsilon/r_0,N)] /d[\log(\varepsilon/r_0)]$ allows the deviation from ideal behaviour to be quantified and interpreted. Introduction of D(N) in the scattering equations allows characterization of the deviation from linearity of plots of log I against $\log q$, where I is the scattering intensity and q the amplitude vector.

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