 |
| FIG. 1. One dimensional arrangement of masses forming strings in tension. |
Topics: Astrophysics, Classical Mechanics, Kinematics, Planetary Science
Abstract
Here we show that bodies of the same size suspended uniformly in space constitute a system (a “suspension”) in a state of uniform volumetric tension because of mass-to-mass forces of attraction. The system “snaps” hierarchically, and evolves faster to a state of reduced tension when the bodies coalesce spontaneously nonuniformly, i.e., hierarchically, into few large and many small bodies suspended in the same space. Hierarchy, not uniformity, is the design that emerges, and it is in accord with the constructal law. The implications of this principle of physics in natural organization and evolution are discussed.
Introduction
Recent progress on the physics basis of evolutionary organization in nature1,2 continues to bring together phenomena that were previously considered unrelated. To the animate and inanimate examples (animal locomotion, river basins, turbulence) that were unified as a phenomenon of free-morphing flow design for greater access over time,1–18 we are now adding examples that belonged traditionally to solid mechanics. For example, the natural occurrence of hexagonal basalt columns is attributed to a principle of maximum energy release.19 The occurrence of cracks in solids is based on the same principle.20–22 Soil cracking under the drying wind was explained as a phenomenon of evolutionary design that enhances mass flow and accelerates drying.23 The aggregation of dust particles into clusters and dendrites was shown to be the result of the same tendency, to relieve electrostatic forces of attraction faster, through the evolutionary design of configuration.24
Here we add to this growing list of evolutionary phenomena the natural occurrence of multi-size hierarchy of bodies suspended in space. The hierarchy of sizes is researched intensely and described regularly in planetary science and astrophysics.25–31 Hierarchy emerges in two ways, through accretion (coalescence) and fragmentation resulting from collisions. Viewed from thermodynamics,32 the system of bodies in space is in a state of internal tension because of gravitational attraction between neighboring bodies. This system “snaps” freely by flowing internally and changing its configuration. Bodies coalesce into larger bodies, and their collision (with fragmentation) dissipates the tension and resulting kinetic energy, en route to reduced body-body attraction throughout the system. This phenomenon has been studied in celestial mechanics under several scenarios,25–27 and is recognized as the basis for the formation process of planets and the asteroid belt.
Sizes increase over all scales through accretion.31 Yet, the natural phenomenon is not only the growth of the body sizes but also the spontaneous hierarchy. The fundamental question that we address here is why “hierarchy” happens spontaneously, and why a uniform distribution of bodies of the same (growing) size does not happen. We show that the gravitational effect alone does not explain the hierarchy of sizes of bodies in space. The additional physics principle is the natural evolution (selection) of flow configuration during accretion such that the flow and evolution to equilibrium are facilitated.1,2
Journal of Applied Physics: The physics origin of the hierarchy of bodies in space
A. Bejan1,a) and R. W. Wagstaff1
1 Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708-0300, USA
Comments