Nonlinear Measures for Characterizing Rough Surface Morphologies

We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops, and the exponent that characterizes their size distribution. Scaling formulas are derived and used to relate these two geometrical exponents to the roughness exponent of a self-affine surface, thus providing independent measurements of this important quantity. Furthermore, we define the scale dependent curvature and demonstrate that by measuring its third moment departures of the height fluctuations from Gaussian behavior can be ascertained. These nonlinear measures are used to characterize the morphology of computer generated Gaussian rough surfaces, surfaces obtained in numerical simulations of a simple growth model, and surfaces observed by scanning-tunneling-microscopes. For experimentally realized surfaces the self-affine scaling is cut off by a correlation length, and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to [email protected]

The calcareous brown alga Padina pavonica in southern Britain: population change and tenacity over 300 years

Understanding long-term persistence and variability in species populations can help to predict future survival, growth and distribution; however, sustained observations are exceedingly rare. We examine and interpret a remarkable record of the calcareous brown alga Padina pavonica (Phaeophyceae) at its northern limit on the south coast of England (50°N, 1–3°W) from 1680 to 2014, which is probably the longest compilation and review of any marine algal species. Over this period, which extends from the middle of the Little Ice Age to the present, there has been considerable variability in temperature and storminess. We identified a significant number of site extinctions in the second half of the nineteenth century, which coincided with cooler conditions and stormier weather. To interpret thesechanges, we measured recruitment, growth and production of tetraspores at sheltered and exposed sites in 2012–2014, years which had low and high spring temperatures. Potential spore production was greater at the sheltered site due to a longer growing period and survival of larger fronds. Delayed growth in the cooler spring resulted in smaller fronds and lower potential production of tetraspores by early summer. Yet in the warmer year, rapid initial growth caused higher sensitivity to damage and dislodgement by summer storms, which also limited potential spore production. Antagonistic responses to multiple stressors and disturbances make future predictions of survival and distribution difficult. Fronds of Padina pavonica are sensitive to both temperature and physical disturbances, yet vegetative perennation appears to have enabled population persistence and explained the longevity of remaining populations