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We expose analogies between turbulence in a fluid heated from below (Rayleigh-Bénard (RB) flow) and shear flows: The unifying theory for RB flow (S.Grossmann and D.Lohse, J.Fluid Mech. 407, 27-56 (2000) and subsequent refinements) can be extended to the flow between rotating cylinders (Taylor-Couette flow) and pipe flow. We identify wind dissipation rates and momentum fluxes that are analogous to the dissipation rate and heat flux in RB flow. The proposed unifying description for the three cases is consistent with the experimental data.
Aside from the increasing, impressive evidence on chemical identification of graded molecules involved, it is the capability of axons for approaching the target position from different aspects in a two-dimensional field which is per se a strong indication for the involvement of gradients. Targeting requires, in the target field, counter-graded effects, either by antagonistic gradients, or by a single gradient in each dimension exerting attractive effects at low, reverting to inhibitory (repulsive) effects at high concentrations. A further requirement for mapping is the modulation of the counter-graded effects by components of the growth cone itself which depends on the origin of the corresponding axon.Transduction and processing of graded signals in the navigating growth cones are proposed to be strongly enhanced by intra-growth-cone pattern formation. The concept also encompasses regulatory and branching processes including the formation of the terminal arbors.
The paper addresses the formation of striking patterns within originally near-homogenous tissue, the process prototypical for embryology, and represented in particularly puristic form by cut sections of hydra regenerating a complete animal with head and foot. Essential requirements are autocatalytic, self-enhancing activation, combined with inhibitory or depletion effects of wider range - “lateral inhibition”. Not only de-novo-pattern formation, but also well known, striking features of developmental regulation such as induction, inhibition, and proportion regulation can be explained on this basis. The theory provides a mathematical recipe for the construction of molecular models with criteria for the necessary non-linear interactions. It has since been widely applied to different developmental processes.