Non-deterministic dynamics of a mechanical system

A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces to a wheel mounted on a turntable. In certain configurations the friction force is not uniquely determined. When the dynamics evolves past the singularity and the mechanism slips, the future state becomes uncertain up to a set of possible values. For certain parameters the system repeatedly returns to the singularity, giving recurrent yet unpredictable behaviour that constitutes non-deterministic chaotic dynamics. The robustness of the phenomenon is such that we expect it to persist with more sophisticated friction models, manifesting as extreme sensitivity to initial conditions, and complex global dynamics attributable to a local loss of determinism in the limit of discontinuous friction.Comment: 22 pages, 8 figure

Ground and flight test experience with a triple redundant digital fly by wire control system

A triplex digital fly by wire flight control system was developed and installed in an F-8C aircraft to provide fail operative, full authority control. Hardware and software redundancy management techniques were designed to detect and identify failures in the system. Control functions typical of those projected for future actively controlled vehicles were implemented

Characteristic matrices for linear periodic delay differential equations

Copyright © 2011 Society for Industrial and Applied MathematicsSzalai, Stépán, and Hogan [SIAM J. Sci. Comput., 28 (2006), pp. 1301–1317] gave a general construction for characteristic matrices for systems of linear delay differential equations with periodic coefficients. First, we show that matrices constructed in this way can have a discrete set of poles in the complex plane, which may possibly obstruct their use when determining the stability of the linear system. Then we modify and generalize the original construction such that the poles get pushed into a small neighborhood of the origin of the complex plane

Influence of salicylic acid on phytochelatin synthesis in Zea mays during Cd stress

Abstract: Presoaking maize (Zea mays) seeds in salicylic acid (SA) reduces damage caused by cadmium. In the present work the possible role of phytochelatins (PCs) in SA-mediated protection against Cd toxicity was investigated. Seeds were presoaked in 0.5 mM SA, and seedlings were grown in hydroponic solution containing 0, 0.01, 0.015, or 0.025 mM Cd. Treatment with Cd increased the PC levels in maize roots, but only slight changes were observed in the leaves. Long-term exposure to Cd decreased the phytochelatin synthase (PCS) activity in the roots and led to an increase in PCS and glutathione reductase (GR) activities in maize leaves. Although presoaking seeds in SA solution before exposure to Cd may reduce the level of heavy metal injury and has an effect on the composition of individual PCs, this protection is not directly connected with the altered regulation of PCs

On the origins of the compressive cochlear nonlinearity

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analysed. The models are assessed against their ability to explain the compressive nonlinear response of the basilar membrane. The speci fic models considered are: phenomenological Hopf and cusp normal forms, a recently-proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a new model highlighting the importance of the coupling between the nonlinear transduction current and somatic motility. The overall conclusion is that neither a Hopf bifurcation nor cusp bifurcation are necessary for realistic compressive nonlinearity. Moreover, two physiological models are discussed showing compressive nonlinearities similar to experimental observations without the need for tuning near any bifurcation