ABSTRACT
We study the generalized diffusion-limited aggregates, grown from two proximal nucleation seeds placed at distance d lattice units and investigate the probability p(d) that these aggregates get connected. We vary the sticking probability to get a range of aggregate geometry from fractal to compact one. For fractal aggregates, p(d) decays rapidly with d , while for compact ones, the decay is so slow that p(d) approximately 1 for all practical distances. We experimentally demonstrate similar behavior for viscous fingering patterns with two injection points and electrochemical deposits grown on two cathodes. Our observations along with previous results on competitive growth suggest a common underlying principle.
ABSTRACT
The one-dimensional Ising model is analytically studied in a spatially periodic and oscillatory external magnetic field using the transfer-matrix method. For low enough magnetic field intensities the correlation between the external magnetic field and the response in magnetization presents a maximum for a given temperature. The phenomenon can be interpreted as a resonance phenomenon induced by the stochastic heat bath. This "spatial stochastic resonance" is realized in the equilibrium state and not as a dynamical response to the external time-periodic driving.
ABSTRACT
In spatially extended systems, intermediate-range interactions arise naturally in some physical contexts. To study them, we investigate a model of coupled map lattices (CML's) with intermediate-range coupling, and derive analytic conditions for its synchronization. We find that in these CML's, if the range of coupling is fixed, the law of large numbers applies for the mean field. The total normalized power in nonzero components of the power spectrum of the mean field goes to zero in the thermodynamic limit. We also show that in the same limit the relevant parameter for synchronization and coherence is the fraction of sites coupled, and not their number.
