ترغب بنشر مسار تعليمي؟ اضغط هنا

Diffusion-limited aggregation in channel geometry

186   0   0.0 ( 0 )
 نشر من قبل Ellak Somfai
 تاريخ النشر 2003
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Ellak Somfai




اسأل ChatGPT حول البحث

We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 +- 0.002 and its leading correction to scaling are the same as in the radial case. The average cluster, defined as the average conformal map, is similar but not identical to Saffman-Taylor fingers.

قيم البحث

اقرأ أيضاً

73 - E. Somfai , L. M. Sander , 1999
We discuss the scaling of characteristic lengths in diffusion limited aggregation (DLA) clusters in light of recent developments using conformal maps. We are led to the conjecture that the apparently anomalous scaling of lengths is due to one slow cr ossover. This is supported by an analytical argument for the scaling of the penetration depth of newly arrived random walkers, and by numerical evidence on the Laurent coefficients which uniquely determine each cluster. We find a single crossover exponent of -0.3 for all the characteristic lengths in DLA. This gives a hint about the structure of the renormalization group for this problem.
63 - Ellak Somfai 2002
Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.
We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a differe nt, but related, ensemble average, that of the conformal maps associated with random clusters, yields a non-trivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results.
The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe lattice. On a chain, this model is exactly solvable through the empty-interval method. This method can be extended to the Bethe lattice, in the ben-Avraham-Glasser approximation. On the Bethe lattice, the analysis of the Laplace-transformed time-dependent particle-density is analogous to the study of the stationary state, if a stochastic reset to a configuration of uncorrelated particles is added. In this stationary state logarithmic corrections to scaling are found, as expected for systems at the upper critical dimension. Analogous results hold true for the time-integrated particle-density. The crossover scaling functions and the associated effective exponents between the chain and the Bethe lattice are derived.
We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a l arger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) sim w^{-gamma}$ for small weight $w$. We obtain the exponent $gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا