Extremal-point Densities of Interface Fluctuations

Abstract

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface growth models. We show that in spite of the non-universal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic to the macroscopic observables of the system. The quantities investigated here present us with tools that give an entirely un-orthodox approach to the dynamics of surface morphologies: a statistical analysis from the short wavelength end of the Fourier decomposition spectrum. In addition to surface growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete event simulations, which are extensively used in Monte-Carlo type simulations on parallel architectures.

30 pages, 5 ps figures

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• Testing the Collective Properties of Small-World Networks through Roughness Scaling
• Synchronization Landscapes in Small-World-Connected Computer Networks
• Maximal and minimal height distributions of fluctuating interfaces
• Extreme fluctuations in noisy task-completion landscapes on scale-free networks
• Algorithmic scalability in globally constrained conservative parallel discrete event simulations of asynchronous systems
• On the topological classification of binary trees using the Horton-Strahler index
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• Nonequilibrium phase transition in surface growth
• Roughness Scaling in Cyclical Surface Growth
• Synchronization in Small-World-Connected Computer Networks
• Extremal-point density of scaling processes from fractal Brownian motion to turbulence in one dimension
• Universal distribution of the number of minima for random walks and Lévy flights