Biomedical subjects
Publications and source records attributed to A C Newell.
We prove the finite-time collapse of a system of N classical fields, which are described by N coupled nonlinear Schrödinger equations. We derive the conditions under which all of the fields experiences this finite-time collapse. Finally, for two-dimensional systems, we derive constraints on the number of particles associated with each field that are necessary to prevent collapse.
We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.
Many studies have shown that nonintegrable systems with modulational instabilities constrained by more than one conservation law exhibit universal long time behavior involving large coherent structures in a sea of small fluctuations. We show how this behavior can be explained in detail by simple thermodynamic arguments.
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