In this paper, we consider the minimum-time reorientation problem of an axi-symmetric rigid spacecraft with two independent control torques mounted perpendicular to the spacecraft symmetry axis. The spacecraft is allowed to spin about its symmetry axis. All possible control structures, including both singular and nonsingular arcs, are studied completely by deriving the corresponding formulae, a...

We describe the characterization of axi 1, a tobacco gene isolated by activation T-DNA tagging which apparently plays a role in auxin action. Upon deregulated expression, axi 1 confers on protoplasts the ability to grow in culture not only in the absence of auxin but also in high auxin concentrations where maximal frequencies of cell division are not observed in wild-type protoplasts. In wild-t...

In this paper, results are presented on asymmetric sloshing in partially filled circular cylinders subjected to horizontal, periodic forcing, as well as geyser formation and the subsequent axi-symmetric sloshing that is caused by a sudden change in Bond number. Asymmetric sloshing is controlled by three parameters that are the liquid depth parameter, the frequency offset (depending on forcing f...

An unsolved problem in step-wise core-accretion planet formation is that rapid radial drift in gasrich protoplanetary disks should drive mm-/meter-sized particles inward to the central star before large bodies can form. One promising solution is to confine solids within small scale structures. Here we investigate dust structures in the (sub)mm continuum emission of four disks (TW Hya, HL Tau, H...

For the axi-symmetric incompressible Euler equations, we prove linear in time filamentation near Hill’s vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining recent nonlinear orbital stability obtained by first author with a dynamical bootstrapping scheme particle trajectories. These results rigorously confirm numerical simulatio...