Asymptotic Series and Precocious Scaling

Some of the basic concepts regarding asymptotic series are reviewed. A heuristic proof is given that the divergent QCD perturbation series is asymptotic. By treating it as an asymptotic expansion we show that it makes sense to keep only the first few terms. The example of e^+e^- annihilation is considered. It is shown that by keeping only the first few terms one can get within a per cent (or smaller) of the complete sum of the series even at very low momenta where the coupling is large. More generally, this affords an explanation of the phenomena of precocious scaling and why keeping only leading order corrections generally works so well

Predicting Whole Forest Structure, Primary Productivity, and Biomass Density From Maximum Tree Size and Resource Limitations

In the face of uncertain biological response to climate change and the many critiques concerning model complexity it is increasingly important to develop predictive mechanistic frameworks that capture the dominant features of ecological communities and their dependencies on environmental factors. This is particularly important for critical global processes such as biomass changes, carbon export, and biogenic climate feedback. Past efforts have successfully understood a broad spectrum of plant and community traits across a range of biological diversity and body size, including tree size distributions and maximum tree height, from mechanical, hydrodynamic, and resource constraints. Recently it was shown that global scaling relationships for net primary productivity are correlated with local meteorology and the overall biomass density within a forest. Along with previous efforts, this highlights the connection between widely observed allometric relationships and predictive ecology. An emerging goal of ecological theory is to gain maximum predictive power with the least number of parameters. Here we show that the explicit dependence of such critical quantities can be systematically predicted knowing just the size of the largest tree. This is supported by data showing that forests converge to our predictions as they mature. Since maximum tree size can be calculated from local meteorology this provides a general framework for predicting the generic structure of forests from local environmental parameters thereby addressing a range of critical Earth-system questions.Comment: 26 pages, 4 figures, 1 Tabl

A New Approach to y-scaling and the Universal Features of Scaling Functions and Nucleon Momentum Distributions

Some systematic general features of y-scaling structure functions, which are essentially independent of detailed dynamics, are pointed out. Their physical interpretation in terms of general characteristics, such as a mean field description and nucleon-nucleon correlations, is given and their relationship to the momentum distributions illustrated. A new relativistic scaling variable is proposed which incorporates the momentum dependence of the excitation energy of the (A-1) system, with the resulting scaling function being closely related to the longitudinal momemtum distributions and being free from removal-energy scaling violating effects.Comment: 17 pages, RevTeX, 4 ps Figures, to appear in Physics Letters