Physics and Fractal Structures

aerogels aggregation attractor behavior bond percolation bonds calculated Cantor set cluster-cluster colloids concentration conductivity correlation corresponds critical curve D₁ defined density dielectric diffusion front diffusion-limited diffusion-limited aggregation disordered distance distribution dynamic Editeurs elastic electrode equation example experimental exponent finite fluctuations fluid fractal dimension fractal structures fractional Brownian motion fracton fracture frequency function galaxies gels geometry GOUYET gradient growth sites Hausdorff Hausdorff dimension infinite cluster injection interaction interface iteration kinetics lattice length Lett Mandelbrot mass mean field measure membranes method monomers multifractal numerical simulation obtained P₁ parameter particles percolation cluster percolation model percolation threshold phenomena Phys physical Pietronero polymer pores porous medium power law probability radius régime region relation Sapoval scaling law self-affine self-similar shown in Fig Sierpinski gasket spectral surface temperature topological dimension transition turbulence viscosity Witten zero