Applications of Pattern Formation in Diffusive Instability Field on Modeling of Clod and Root System Formations

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Finding general aspects and descriptions of both root system and tilled clod formations is a main issue in this work. This study is a challenge to bio-physically clarifying the behavior of soil-Plant systems such as the plant growth under interactions with environment, and it has been an issue of wide interest in phytotechnology. The objectives of this work were as follows :1)to confirm that the configurations of both corn root systems and tilled clods are a kind of fractal patterns.2)to explain the development of soil cracks like elastic materials by the use of pattern formation under diffusive instability in viscoelastic strain field.3)to produce a branching growth model for a root system based upon L systems.4)to find control parameters of pattern formation on root systems and tilled clods. The results were as follows.1)Clods of heavy clay formed by rotary tillage showed power-scaling on their contours, cracks, and crack area distribution, and they were confirmed to be fractal patterns. Moreover high-frequency blade vibration was related to crack intervals on the clods.2)The root system of corn followed anisotropic power distribution like a self-affine fractal.3)Non-linear coupled diffusion equations including elastic strain and plastic flow terms were proposed for giving expression to viscoelastic behavior of soil, and local accumulation of elastic strain was simulated under diffusive instability.4)Hierarchical modeling of a corn root system provided a new type of root growth model and broke through a limit of traditional L-system methodology.5)General aspects of both clod and root system formations such as fractal were derived, and this would provide one avenue for investigators on soil-plant system-dynamics.