Different aspects of the long-period oscillations of tribological parameters in the wear process of metals under constant heavy duty sliding conditions are theoretically investigated on the basis of ...the previously constructed mathematical model. The obtained asymptotic formula for the period of oscillations agrees with the quantitative predictions known in the literature. The period of oscillations is suggested as a diagnostic parameter in assessing the health of operating tribosystem. An approximate formula for the phase of oscillations of relaxation type in the Lotka–Volterra nonlinear mathematical model is derived by the relaxation oscillation method.
Periodic chronic myelogenous leukemia and cyclical neutropenia are two hematological diseases that display oscillations in circulating cell numbers with a period far in excess of what one might ...expect based on the stem cell cycle duration. Motivated by this observation and a desire to understand how long period oscillations can arise, we analytically prove the existence and stability of long period oscillations in a $G_{0}$ phase cell cycle model described by a nonlinear differential delay equation. This periodic oscillation $p_{\infty }$ can be analytically constructed when the proliferative control is of a "bang-bang" type (the Hill coefficient involved in the nonlinear feedback is infinite). We further obtain a contractive return map (for the semiflow generated by the functional differential equation) in a closed and convex cone containing $p_{\infty }$ when the proliferative control is smooth (the Hill coefficient is large but finite). The fixed point of this contractive map gives the long period oscillation previously observed both numerically and experimentally.
We present a mathematical model of an aquatic community, where the size-and-age structure of hydrobiont populations is taken into account and the corresponding trophic interactions between ...zooplankton, peaceful fish, and predatory fish are described. We show that interactions between separate components of the aquatic community can give rise to long-period oscillations in fish population size. The period of these oscillations is on the order of decades. With this model we also show that an increase in the zooplankton growth rate may entail a sequence of bifurcations in the fish population dynamics: steady states → regular oscillations → quasicycles → dynamic chaos.
The PICARD microsatellite mission will provide 2 to 6 years simultaneous measurements of the solar diameter, differential rotation and solar constant to investigate the nature of their relations and ...variabilities. The 100 kg satellite has a 40 kg payload consisting of 3 instruments which will provide an absolute measure (better than 10 milliarcsec) of the diameter and the solar shape, a measure of total solar irradiance, and UV and visible flux in selected wavelength bands. Now in Phase B, PICARD is expected to be launched before mid-2003. The engineering model of the diameter telescope will be used on ground simultaneously with the satellite to investigate the atmospheric bias and state on the possible accuracy of the ground measurements carried up to now. We review the scientific goals linked to the diameter measurement, present the payload, and give a brief overview of the program aspects.PUBLICATION ABSTRACT
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