Diffusion-limited aggregation as branched growth

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the cluster dimensionality, D \approx 1.66, which is close to numerically obtained values. In addition, the multifractal exponent \tau(3) = D in this theory, in agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary mail), Plain Te

Do method and species lifestyle affect measures of maximum metabolic rate in fish?

The rate at which active animals can expend energy is limited by their maximum aerobic metabolic rate (MMR). Two methods are commonly used to estimate MMR as oxygen uptake in fishes, namely during prolonged swimming or immediately following brief exhaustive exercise, but it is unclear whether they return different estimates of MMR or whether their effectiveness for estimating MMR varies among species with different lifestyles. A broad comparative analysis of MMR data from 121 fish species revealed little evidence of different results between the two methods, either for fishes in general or for species of benthic, benthopelagic or pelagic lifestyles

Multifractal Dimensions for Branched Growth

A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys. Rev. A46, 7793 (1992)], annealed average dimensions were computed for this model. In this paper, we compute the quenched average dimensions, which are expected to apply to typical members of the ensemble. We develop a perturbative expansion for the average of the logarithm of the multifractal partition function; the leading and sub-leading divergent terms in this expansion are then resummed to all orders. The result is that in the limit where the number of particles n -> \infty, the quenched and annealed dimensions are {\it identical}; however, the attainment of this limit requires enormous values of n. At smaller, more realistic values of n, the apparent quenched dimensions differ from the annealed dimensions. We interpret these results to mean that while multifractality as an ensemble property of random branched growth (and hence of DLA) is quite robust, it subtly fails for typical members of the ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl

Branched Growth with η≈4\eta \approx 4 Walkers

Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial dimensionality $d=2$, there is an upper critical $\eta_c=4$ above which the fractal dimensionality of the clusters is D=1. I compute the first order correction to $D$ for $\eta <4$, obtaining $D=1+{1/2}(4-\eta)$. The methods used can also determine multifractal dimensions to first order in $4-\eta$.Comment: 6 pages, 1 figur

Ernesto Caballero: Auto

Review of: Ernesto Caballero. Auto. Alicante, Instituto de Cultura Juan Gil-Albert, 1993, 72 pp

Effect of weak disorder in the Fully Frustrated XY model

The critical behaviour of the Fully Frustrated XY model in presence of weak positional disorder is studied in a square lattice by Monte Carlo methods. The critical exponent associated to the divergence of the chiral correlation length is found to be equal to 1.7 already at very small values of disorder. Furthermore the helicity modulus jump is found larger than the universal value expected in the XY model.Comment: 8 pages, 4 figures (revtex

Transfer across Random versus Deterministic Fractal Interfaces

A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cut-offs and the fractal dimension. Although the active zones are different for different geometries, the electrode reponses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer.Comment: 4 pages, 6 figure