We have examined the response of multivariable linear systems to Lévy fluctuations. The characteristic function of the response is obtained explicitly as a function of time. Using the characteristic function, the fractional moments of the process are determined. The nature of the product rule...

A model of the permanent distortion of an elastic material due to high velocity projectile impact is described using a random walk model, with unusual temporal statistics, of the transport of dislocations. The biased motion of dislocations in a stress field and also in a random environment is...

We have determined the stability properties of nonlinear oscillators with fluctuating potential parameters and a fluctuating additive driving force. It is shown that nonlinearities in general stabilize moments known to diverge in the corresponding linear system.

We determine an approximate renormalized phase space evolution equation for an arbitrary multi-degree-of-freedom system externally driven by Gaussian parametric fluctuations having finite correlation times. Our method yields a second-order equation with a state- and time-dependent diffusion...

A newly developed technique for determining the statistical properties of random forces with long-range and long-time correlations is applied to the loading of ships and platforms by wind-generated water waves. Using empirical spectra for the vertical displacement of the sea surface we find that...

Scale invariance, the property relating time series across multiple scales, has provided a new perspective of physiological phenomena and their underlying control systems. The traditional “signal plus noise” paradigm of the engineer was first replaced with a model in which biological time...

The allometric relationship between the basal metabolic rate B and total body mass M is B = aMb, where the allometry coefficient a and the allometry exponent b have been fit to various data sets for over 150 years. The best fit of the allometry exponent to 391 mammalian species is given by...

We examine the stability properties of equilibrium moments of all orders for the damped mechanical oscillator with a delta correlated fluctuating frequency. A Markovian master equation is derived startimg from a frequency fluctuation process with finite correlation time τc and the limit τc→0...

A formally exact expression for a lattice model of the perturbed strain field in a grainy polycrystalline material is constructed using a discrete T-matrix. The matrix elements of T are expressed in terms of a self-consistent lattice Green's function and the “effective”, i.e., renormalized,...

We determine an approximate renormalized equation of evolution for an arbitrary nonlinear single-degree-of-freedom system externally driven by Gaussian parametric fluctuations of finite correlation time. The renormalization scheme used here gives a second order equation with a...