RESUMO
The study of the dynamical properties of vortex systems is an important and topical research area, and is becoming of ever increasing usefulness to a variety of physical applications. In this paper, we present a study of a model of a rotational singularity which obeys a logarithmic potential interacting with a bluff body in a uniform inviscid laminar flow, e.g., a line vortex interacting with a cylinder in three dimensions or a point vortex with a circular boundary in two dimensions. We show that this system is Hamiltonian and simple enough to be solved analytically for the stagnation points and separatrices of the flow, and a bifurcation diagram for the relevant parameters and classification of the various types of motion is given. We also show that, by introducing a periodic perturbation to the body, chaotic motion of the vortex can be readily generated, and we present analytic criteria for the generation of chaos using the Poincare-Melnikov-Arnold method. This leads to an important dynamical effect for the model, i.e., that the possibility exists for the vortex to be chaotically captured around the body for periods of time which are extremely sensitive to initial conditions. The basic mechanism for this capture is due to the chaotic dynamics and is similar to that of other chaotic scattering phenomena. We show numerically that cases exist where the vortex can be captured around an elliptic point external to (and possibly far from) the body, and the existence of other very complicated motions are also demonstrated. Finally, generalizations of the problem of the vortex-body interaction are indicated, and some possible applications are postulated such as the interaction of line vortices with aircraft wings.
RESUMO
The effect of the mitochondria-targeted, plastoquinone-containing antioxidant SkQ1 on the lifespan of outbred mice and of three strains of inbred mice was studied. To this end, low pathogen (LP) or specific pathogen free (SPF) vivaria in St. Petersburg, Moscow, and Stockholm were used. For comparison, we also studied mole-voles and dwarf hamsters, two wild species of small rodents kept under simulated natural conditions. It was found that substitution of a LP vivarium for a conventional (non-LP) one doubled the lifespan of female outbred mice, just as SkQ1 did in a non-LP vivarium. SkQ1 prevented age-dependent disappearance of estrous cycles of outbred mice in both LP and non-LP vivaria. In the SPF vivarium in Moscow, male BALB/c mice had shorter lifespan than females, and SkQ1 increased their lifespan to the values of the females. In the females, SkQ1 retarded development of such trait of aging as heart mass increase. Male C57Bl/6 mice housed individually in the SPF vivarium in Stockholm lived as long as females. SkQ1 increased the male lifespan, the longevity of the females being unchanged. SkQ1 did not change food intake by these mice. Dwarf hamsters and mole-voles kept in outdoor cages or under simulated natural conditions lived longer if treated with SkQ1. The effect of SkQ1 on longevity of females is assumed to mainly be due to retardation of the age-linked decline of the immune system. For males under LP or SPF conditions, SkQ1 increased the lifespan, affecting also some other system(s) responsible for aging.