Douglas A. Kurtze

Corrugation of roads

We present a one dimensional model for the development of corrugations in roads subjected to compressive forces from a flux of cars. The cars are modeled as damped harmonic oscillators translating with constant horizontal velocity across the surface, and the road surface is subject to diffusive relaxation. We derive dimensionless coupled equations of motion for the positions of the cars and the road surface H(x,t), which contain two phenomenological variables: an effective diffusion constant Δ(H) that characterizes the relaxation of the road surface, and a function a(H) that characterizes the plasticity or erodibility of the road bed. Linear stability analysis shows that corrugations grow if the speed of the cars exceeds a critical value, which decreases if the flux of cars is increased. Modifying the model to enforce the simple fact that the normal force exerted by the road can never be negative seems to lead to restabilized, quasi-steady road shapes, in which the corrugation amplitude and phase velocity remain fixed.

Surface instability in windblown sand.

We investigate the formation of ripples on the surface of windblown sand based on the one-dimensional model of Nishimori and Ouchi [Phys. Rev. Lett. 71, 197 (1993)], which contains the processes of saltation and grain relaxation. We carry out a nonlinear analysis to determine the propagation speed of the restabilized ripple patterns, and the amplitudes and phases of their first, second, and third harmonics. The agreement between the theory and our numerical simulations is excellent near the onset of the instability. We also determine the Eckhaus boundary, outside which the steady ripple patterns are unstable.

Chaotic behavior in computer mediated network communication

Abstract The work examines the use of chaos theory in modelling time series data generated by computer mediated communication (CMC). Data generated by CMC bulletin boards is examined for the presence of chaotic behavior and to assess the variance which can be accounted for by the deterministic mechanism. The study regards the time series data generated from a CMC discussion group as the sum of two components. One is a deterministic “signal” which presumably obeys some unknown chaotic dynamics. The other component is truly random “noise”. The studys overall goal is to assess the relative importance of these two components, using techniques devised by Procaccia and Grassberger for studying chaos in time series data. Chaotic time series data had increasingly larger fractions of noise added until chaotic behavior was no longer found. Analysis of the data with added noise indicates that from 20 to 30% of the variation in the data is the result of noise. Conversely, 70 to 80% of the variation in the data can be accounted for by deterministic chaos. Implications for future research using chaos and CMC are discussed.