No abstract

Using a hierarchical ordering scheme, many off-lattice diffusion-limited-aggregation (DLA) clusters containing 10 particles are separated into branches of different orders. For each order we measure the number, mass, length, and width of the branches. All of these branch properties depend, with an exponential law, on the branch order. This means that for all of them the ratios between properties of subsequent branch orders are constant. By relating length, width, and mass to each other we find that the length and width of the whole branches both depend, with the same exponents vi =v, =0.60=P=1/D, on the mass of the branch. By measuring the ramification matrix R;I, of the clusters we find that the branches and stems are distributed in a self-similar way. Furthermore, we measure the angles enclosed by two branches. We find that this angle saturates to a finite value around 38'. All of these results indicate a statistical self-similarity between branches of different orders. This result is supported by a direct comparison of off-lattice DLA clusters of 10', 10, and 10' particles.PACS number(s): 82.20.Wt, 05.60.+ w, 36.40. +d

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Using both analytic and numerical methods, we study the radial growth probability distribution P (r, M ) for large scale off lattice diffusion limited aggregation (DLA) clusters. If the form of P (r, M ) is a Gaussian, we show analytically that the width ξ(M ) of the distribution can not scale as the radius of gyration R G of the cluster. We generate about 1750 clusters of masses M up to 500, 000 particles, and calculate the distribution by sending 10 6 further random walkers for each cluster. We give strong support that the calculated distribution has a power law tail in the interior (r ∼ 0) of the cluster, and can be described by a scaling Ansatz P (r, M ) ∝ r α ξ · g r−r 0 ξ , where g(x) denotes some scaling function which is centered around zero and has a width of order unity. The exponent α is determined to be ≈ 2, which is now substantially smaller than values measured earlier. We show, by including the power-law tail, that the width can scale as R G , if α > D f − 1.

In the recent Letter [1], the authors report the existence of a nove1 "fast" scaling regime in a molecu1ar dynamics (MD) simulation of a two-dimensional Lennard-Jones-like binary Quid mixture, in which the typical domain size R scales with time t as R t, with an exponent n = 0.65. Reference [1] also reports a slower growth regime preceding the faster growth, characterized by an exponent n = 1/4, as well as an early-time growth exponent n = 1/2. They base these conclusions on individual runs using a variety of MD simulation techniques.Here we argue that the scaling behavior they observed may be an artifact of their simulations. We find that although individual runs exhibit anomalous features of the sort found in [1], these features do not survive an averaging process over several independent realizations.We have repeated the MD simulations of [1] using the velocity rescaling technique (the technique used for "Run 8" in [1]) for 12 independent samples of 17 000 particles each. As in [1], we truncated the Lennard-Jones-like potentials between the diferent particle types at 4.2o and quenched each system from a high temperature to a low temperature A:IIT/e = 2 at a density po = 0.4. We took one time step to be 0.01 in reduced units and performed 60000 time steps for each sample. We ran our simulations on 16 nodes of a Connection Machine CM-5, using a M1MD algorithm implemented in CM Fortran, and consumed a total of 84 hours of CPU time. This algorithm achieves an update time of 25 ys per particle. Figure 1 shows the dependence on t of the typical domain size, R, as estimated by calculating the first zero of the pair correlation function g(r) [2]. Shown are selected data from individual runs as well as the average over all 12 runs. The figure shows that individual runs diKer significantly from one another. In fact, data setNo. 3 resembles that of run 8 in Ref.[1]. However, when we average over all 12 data sets, there is no evidence of either a fast growth regime with exponent a = Q.65 or a slow growth regime with n = 1/4, reported in [1]. Instead, we find an exponent rI = 0.49 over the entire range of data, consistent with the "hydrodynamic" prediction [3] of n = 1/2. We thank E. Velasco and S. Toxvaerd for their generous cooperation in resolving this issue, the Center for , Phys. Rev B. 37, 9638 (1988). [3] M. San Miguel, M. Grant, and 3. D. Gunton, Phys. Rev. A 81, 1001 (1985). FIG. 1, Typical domain size, R, plotted log-log versus time t. The topmost line of data points represent an average over 12 independent samples, while the other points indicate individual runs. The vertical axis is shifted for each set of data to allow for direct comparison. The solid line is the best 6t to the averaged data and has a slope 0.49.