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- W2057202557 abstract "The scaling behavior of the diffusion front, originated by the random motion of particles under a concentration gradient, is studied by means of the Monte Carlo method and solving the diffusion equation. Simulations are performed on the square lattice using confined geometries of size M×L, where the gradient is established along the M direction while periodic boundary conditions are set along the L direction. A dynamic scaling Ansatz is proposed such as the width of the front [w(M,t)] scales as w(M,t)∼Mαf(t/Mα/β), where α and β are the roughness and growing exponents, respectively. This proposal is based on the fact that the development of w is constrained by the gradient, that decays as M−1, in contrast to the standard Family–Vicsek scaling Ansatz where correlations are constrained by the lateral dimension of the sample. It is found that the roughness exponent exhibits a systematic dependence on the sample size that can be rationalized in terms of a finite-size correction. Extrapolation to the thermodynamic limit gives α=4/7, in excellent agreement with theoretical predictions linking the diffusion system to the percolation problem. The evaluation of the growing exponent gives β=0.30±0.02, leading us to the conjecture β=2/7 for the exact value." @default.
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- W2057202557 date "2004-06-18" @default.
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- W2057202557 title "A finite-size dynamic-scaling approach for the diffusion front of particles" @default.
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- W2057202557 doi "https://doi.org/10.1063/1.1756853" @default.
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