The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T . We find simple expressions for the mean global first passage time T for five fractals: the d-dimensional Sierpinski gasket, T-fractal, hierarchical percolation model, Mandelbrot-Given curve and a deterministic tree. We also find an exact expression for the second moment T 2 and show that the variance of the first passage time, Var(T ), scales with the number of nodes within the fractal N such that Var(T ) ∼ N 4/d , whered is the spectral dimension.
We settle a long-standing controversy about the exactness of the fractal Einstein and Alexander-Orbach laws by showing that the properties of a class of fractal trees violate both laws. A new formula is derived which unifies the two classical results by showing that if one holds, then so must the other, and resolves a puzzling discrepancy in the properties of Eden trees and diffusion-limited aggregates. We also conjecture that the result holds for networks which have no fractal dimension. The failure of the classical laws is attributed to anisotropic exploration of the network by a random walker. The occurrence of this newly revealed behavior means that the conventional laws must be checked if they, or numerous results which depend on them, are to be applied accurately.
A method to find the exact reaction rate density function of an A + B → 0 reaction on a finite 1D bar is derived. We consider the case where the A and B species diffuse at the same rate, have equal initial numbers, with the initial location of either species on the bar being arbitrary. The extension of the method to study A + B → 0 on fractals is also shown. Additionally, we introduce the notion of a continual (in time) reaction front and a ceasing (in time) reaction front and provide a physical criterion for when either occurs.
1] We perform a multicomponent sensitivity analysis of how the physical and dynamical parameters that characterize a meteor (in-fall) affect the ground overpressure and period of a plausible emitted N-wave signal. The nonlinear propagation model used throughout is based upon Whitham's nonlinearization method which is modified to take into account a stratified atmosphere. We use sensitivity indices, derived using a Fourier Amplitude Sensitivity Test, to measure how the meteor parameters' uncertainties affect the uncertainty in the overpressure and period of an emitted N-wave. The investigated parameters include the azimuth, entry angle, diameter, drag coefficient, density, and initial velocity of the meteor, as well as the atmosphere. The method is used to re-examine the crater-forming meteorite fall near Carancas, Peru (2007). We obtain good agreement between the simulated signals and observed waveforms. It is shown that ground overpressure uncertainty depends on the atmospheric uncertainties that are strongly correlated with the unknown trajectory, whereas the period is governed by the diameter uncertainties. Finally, we consider new waveform parameters that help characterize the meteor.Citation: Haynes, C. P., and C. Millet (2013), A sensitivity analysis of meteoric infrasound,
We show that the distance dependence of the source-to-target mean-first-passage time (MFPT) on a finite network with M links is approximately given by 2M times the target-to-shell resistance. For networks on which a random walker is transient the long-range MFPT is well approximated by the site-dependent resistance from the target to infinity. The result extends a recent scaling result for the MFPT to site-inhomogeneous lattices where the MFPT depends on the location of the source and targets and can be highly source-target asymmetric.
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