The limit case response of the archetypal oscillator for smooth and discontinuous dynamics

In this paper, the limit case of the SD (smooth and discontinuous) oscillator is studied. This system exhibits standard dynamics governed by the hyperbolic structure associated with the stationary state of the double-well. The substantial deviation from the standard dynamics is the non-smoothness of the velocity in crossing from one well to another, caused by the loss of local hyperbolicity due to the discontinuity. Without dissipation, the KAM structure on the Poincaré section is constructed with generic KAM curves and a series of fixed points associated with surrounded islands of quasi-periodic orbits and the chaotic connection orbits. It is found that, for a fixed set of parameters, a special chaotic orbit exits there which fills a finite region and connects a series of islands dominated by different chains of fixed points. As one adds weak dissipation, the periodic solutions in this finite region remain unchanged while the quasi-periodic solutions (isolated islands) are converted to the corresponding periodic solutions. The relevant dynamics for the system with weak dissipation under external excitation is shown having period doubling bifurcation leading to chaos, and multi-stable solutions.     

An optimized protocol for anthraquinones isolation from Rhamnus frangula L.

Different from works described in the literature, which use expansive analytical methods to separation of anthraquinones derivatives (AQs), this communication reported a simple and inexpensive methodology to get them. In this way, the expensive commercial AQs: Chrysophanol, physcione and emodine were extracted from plant material (Rhamnus frangula L.) and isolated by classical column chromatography technique under optimised binary mobile phase gradients (CHCl₃ : AcOEt(a), a = 1 to 5%) in excellent yields.     

Exogenous crimes and the assessment of public safety efficiency and effectiveness

Annals of Operations Research - This work discusses the issue on how to include data about property and violent crimes in the production technology for the assessment of police technical...     

Conditions for the abrupt bifurcation to chaotic scattering

One of the generic ways in which chaotic scattering can come about as a system parameter is varied is the so-called "abrupt bifurcation" in which the scattering is nonchaotic on one side of the bifurcation and is chaotic and hyperbolic on the other side. Previous work demonstrating the abrupt bifurcation [S. Bleher et al., Phys. Rev. Lett. 63, 919 (1989); Physica D 46, 87 (1990)] was primarily for the case where the scattering potential had maxima ("hilltops") which had locally circular isopotential contours. Here we extend these considerations to the more general case of locally elliptically shaped isopotential contours at the hilltops. It turns out that the conditions for the abrupt bifurcation change drastically as soon as even a small amount of noncircularity is included (i.e., the circular case is singular). The illustrative case of scattering from three isolated potential hills is dealt with in detail. One interesting result is a simple geometrical sufficient condition for an abrupt bifurcation in the case of large enough ellipticity of the hill with lowest potential at its hilltop.     

Production of antitumoral retamycin during fed-batch fermentations of Streptomyces olindensis

Fed-batch runs were performed in order to correlate the production of retamycin, an anthracycline antibiotic produced by Streptomyces olindensis in submerged cultures, with the specific growth rate. Maximum retamycin production was achieved with an exponential feed rate, controlling the specific growth rate at a low value (0.03h⁻¹, about 10% of the maximum specific growth rate). Control of the specific growth rate at higher values (0.10 and 0.17 h⁻¹) caused a decrease in antibiotic production. Morphology, assessed by image analysis, was shown to be highly relevant in this process. Cell growth mainly in the form of clumps (90% clumps and 10% free filaments) led to better results than growth as clumps (75%) and free filaments (25%).     

The goodness of ergodic adiabatic invariants

For a slowly time-dependent Hamiltonian system exhibiting chaotic motion that ergodically covers the energy surface, the phase space volume enclosed inside this surface is an adiabatic invariant. In this paper we examine, both numerically and theoretically, how the error in this ergodic adiabatic invariant scales with the slowness of the time variation of the Hamiltonian. It is found that under certain circumstances, the error is diffusive and scales likeT ^–1/2, whereT is the characteristic time over which the Hamiltonian changes. On the other hand, for other cases (where motion in the Hamiltonian has a long-time 1/t tail in a certain correlation function), the error scales like [T ^–1 ln(T)]^1/2. Both of these scalings are verified by numerical experiments. In the situation where invariant tori exist amid chaos, the motion may not be fully ergodic on the entire energy surface. The ergodic adiabatic invariant may still be useful in this case and the circumstances under which this is so are investigated numerically (in particular, the islands have to be small enough).