Surface currents and slope selection in crystal growth

We face the problem to determine the slope dependent current during the epitaxial growth process of a crystal surface. This current is proportional to delta=(p+) + (p-), where (p+/-) are the probabilities for an atom landing on a terrace to attach to the ascending (p+) or descending (p-) step. If the landing probability is spatially uniform, the current is proved to be proportional to the average (signed) distance traveled by an adatom before incorporation in the growing surface. The phenomenon of slope selection is determined by the vanishing of the asymmetry delta. We apply our results to the case of atoms feeling step edge barriers and downward funnelling, or step edge barriers and steering. In the general case, it is not correct to consider the slope dependent current j as a sum of separate contributions due to different mechanisms.Comment: 6 pages. The text has been strongly revised and Fig.1 has been changed. Accepted for publication in the "Comptes Rendus Physique

Breakdown of metastable step-flow growth on vicinal surfaces induced by nucleation

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically step-flow growth. The breakdown of the metastable step-flow occurs through the formation of a mound of critical width proportional to L_c=1/sqrt(l_es), the length associated to the linear instability of a high-symmetry surface. The time required for the destabilization grows exponentially with L_c. Thermal detachment from steps or islands, or a steeper slope increase the instability time but do not modify the above picture, nor change L_c significantly. Standard continuum theories cannot be used to evaluate the activation energy of the critical mound and the instability time. The dynamics of a mound can be described as a one dimensional random walk for its height k: attaining the critical height (i.e. the critical size) means that the probability to grow (k->k+1) becomes larger than the probability for the mound to shrink (k->k-1). Thermal detachment induces correlations in the random walk, otherwise absent.Comment: 10 pages. Minor changes. Accepted for publication in Phys. Rev.

Deterministic reaction models with power-law forces

We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution function for the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker-Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished

Fracture precursors in disordered systems

A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with respect to the control parameter (reduced stress) exhibits a singular behaviour. Our results are nevertheless compatible with previous experimental findings, if one restricts the comparison to the (limited) range accessible in the experiment. A power-law avalanche distribution is also found with an exponent close to the experimental values.Comment: 4 pages, 5 figures. Submitted to Europhysics Letter

On the relationship between directed percolation and the synchronization transition in spatially extended systems

We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs to the directed percolation (DP) universality class. The analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold. We find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena. As a result of this analysis we conclude that the synchronization transition belongs to the DP class also in continuous models. The conclusions are supported by numerical checks on coupled map lattices too

Dynamic model of fiber bundles

A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under non-vanishing stress always breaks down in the presence of noise. Revealed in particular is the characteristic time evolution that the system tends to resist the stress for considerable time, followed by sudden complete rupture. The critical stress beyond which the complete rupture emerges is also obtained

ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS

A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is derived on the basis of this relationship. An approximate expression for the nonlinear velocity is also determined by extending the concept of Lyapunov exponent to growth rate of finite perturbations.Comment: Tex file without figures- Figures and text in post-script available via anonymous ftp at ftp://wpts0.physik.uni-wuppertal.de/pub/torcini/jpa_le

On the anomalous thermal conductivity of one-dimensional lattices

The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A possible explanation in the framework of linear-response theory is also presented, which traces back the physical origin of this anomaly to the slow diffusion of the energy of long-wavelength Fourier modes. Finally, the results of dynamical simulations are compared with the predictions of mode-coupling theory.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

Checkerboards, stripes and corner energies in spin models with competing interactions

We study the zero temperature phase diagram of Ising spin systems in two dimensions in the presence of competing interactions, long range antiferromagnetic and nearest neighbor ferromagnetic of strength J. We first introduce the notion of a "corner energy" which shows, when the antiferromagnetic interaction decays faster than the fourth power of the distance, that a striped state is favored with respect to a checkerboard state when J is close to J_c, the transition to the ferromagnetic state, i.e., when the length scales of the uniformly magnetized domains become large. Next, we perform detailed analytic computations on the energies of the striped and checkerboard states in the cases of antiferromagnetic interactions with exponential decay and with power law decay r^{-p}, p>2, that depend on the Manhattan distance instead of the Euclidean distance. We prove that the striped phase is always favored compared to the checkerboard phase when the scale of the ground state structure is very large. This happens for J\lesssim J_c if p>3, and for J sufficiently large if 2<p<=3. Many of our considerations involving rigorous bounds carry over to dimensions greater than two and to more general short-range ferromagnetic interactions.Comment: 21 pages, 3 figure

Coexistence of coarsening and mean field relaxation in the long-range Ising chain

We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance r decaying as r-α. For α = 0, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with α &gt; 1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0 &lt; α &lt; 1, we show that the system shows both features, with probability Pα(N) of having the latter one, with the different limiting behaviours limN→∞ Pα(N) = 0 (at fixed α &lt; 1) and limα→1 Pα(N) = 1 (at fixed finite N). We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time τα(N) ∼ Nα