Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition

Abstract

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a non-universal parameter, but its presence is universal. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.

arXiv comment16 pages, 16 figures, 77 references

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Cited by in corpus (15)

• Scaling in the crossover from random to correlated growth
• Universal and nonuniversal features in the crossover from linear to nonlinear interface growth
• Synchronization Landscapes in Small-World-Connected Computer Networks
• Exact scalings in competitive growth models
• Universal Scaling in Mixing Correlated Growth with Randomness
• Parameter free scaling relation for nonequilibrium growth processes
• Characterisation of non-equilibrium growth through global two-time quantities
• Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening
• Surface and bulk properties of ballistic deposition models with bond breaking
• Langevin equations for competitive growth models
• Crossover of interface growth dynamics during corrosion and passivation
• New method to study stochastic growth equations: a cellular automata perspective
• Comment on "Dynamic properties in a family of competitive growing models"
• Synchronization in Small-World-Connected Computer Networks
• Desynchronization and Speedup in an Asynchronous Conservative Parallel Update Protocol