A similarity criterion for forest growth curves

Comparison of forest growth curves has led many to the conclusion that there is a similarity between forest stands growing in different conditions. Here we treat the same subject from the viewpoint of similarity theory. Our goal is to form a dimensionless ratio of biophysical entities that could parameterize the diversity of forest growth curves. (Such ratios are called similarity criteria.) Pursuing this goal, we focus on the analogy between tree crown growth and atomic explosion. A blast wave is formed when the rate of energy release is much higher than the rate of energy dissipation. The difference between the rates of energy release and dissipation is the essence of this phenomenon. The essential feature of crown growth is the difference between the rates of non-structural carbohydrate supply and demand. Since the rate of supply is much higher than the rate of demand, the flow of non-structural carbohydrates achieves the tips of branches and enables the radial growth of crown. Proceeding from these ideas, we derived the similarity criterion which supposedly captures the “essence of growth” that emerges from the geometric similarity of tree crowns

Random moves equation Kolmogorov-1934. A unified approach for description of statistical phenomena of nature

The paper by A.N. Kolmogorov 1934 "Random Moves", hereinafter ANK34, uses a Fokker-Planck-type equation for a 6-dimensional vector with a total rather than a partial derivative with respect to time, and with a Laplacian in the space of velocities. This equation is obtained by specifying the accelerations of the particles of the ensemble by Markov processes. The fundamental solution was used by A M Obukhov in 1958 to describe a turbulent flow in the inertial interval. Already recently it was noticed that the Fokker-Planck-type equation written by Kolmogorov contains a description of the statistics of other random natural processes, earthquakes, sea waves, and others. This theory, containing the results of 1941, paved the way for more complex random systems containing enough parameters to form an external similarity parameter. This leads to a change in the characteristics of a random process, for example, to a change in the slope of the time spectrum, as in the case of earthquakes and in a number of other processes (sea waves, cosmic ray energy spectrum, flood zones during floods, etc.). A review of specific random processes studied experimentally provides a methodology for how to proceed when comparing experimental data with the ANK34 theory. Thus, empirical data illustrate the validity of the fundamental laws of probability theory.Comment: 23 pages, 4 figure