PMC

Settling and orbital velocity versus water depth. The solid line represents the orbital velocity function related to the water depth. The intersection between settling velocity of a single specimen and bottom orbital velocity marks the suspension–deposition boundary (A). Accumulation of tests may occur at water depth where bottom orbital velocity is always lower than the settling velocity of the tests (B).

a Computational simulation of simple fluid dynamics to compare the rheological parameters during stirring by orbital mixing, or vertical mixing at a mixing speed of 45, 60, or 75 mm/s. The average value of each parameter is shown in the thumbnail of each panel. Flow velocity and shear stress of orbital mixing were higher than that of vertical mixing. Turbulent energy and energy dissipation, which are related to the status of the stirring force, of vertical mixing were higher than those of orbital mixing. b Computational simulation of solid–liquid transient analysis by using a discrete phase model to compare the movement of spheres (white circles) under orbital mixing or vertical mixing. Spheres in orbital mixing were unevenly distributed along with the wall of the culture dish, gradually translocated toward the center, and gathered with each other, while spheres in vertical mixing were equally dispersed throughout the culture bottle. c Comparison of three-dimensional flow velocity between orbital mixing (blue line) and vertical mixing (red line). The movement of spheres in orbital mixing showed higher velocity in X- and Y-direction than that in vertical mixing. In contrast, the movement of spheres only in vertical mixing showed rhythmic Z-directional velocity. The drag force applied to the spheres in orbital mixing is also higher than that in vertical mixing.

Models of possible ring configurations in the (x, y) (top panels) and (l, v) (bottom panels) space. In all the models, the bar major axis is always aligned with the axis x = 0 and the angle between the bar major axis and the Sun-Galactic Centre line is 20°. In the first column from the left, the ring minor axis is aligned with the bar major axis and the orbital velocity, v_orb, varies across the orbit. This configuration corresponds to the one produced in our simulation. In the second column, the ring minor axis is aligned with the bar major axis and the orbital velocity is constant. In the third column, the ring major axis is aligned with the bar major axis and the orbital velocity is variable. In the forth column, the ring major axis is aligned with the bar major axis and the orbital velocity is constant. The orbital velocity is shown in the top panels with vectors, whose length is proportional to the velocity magnitude. The different colours indicate the distance of each point from the Sun.

Regulation of orbital radius and velocity via rotational magnetomotility. a Evolution of three rotational modes of AR-2 amid half turn rotation upon magnetic speed manipulation. b Transferable orbital maneuver in a two-body system, including overlaid images (top) and y-axis displacement (bottom). c Time-lapsed trajectory showing that a faster spinbot catches up to a slightly slower spinbot via 27 orbital motions (top). The solid line in the graph refers to y = R sin(θ), when R is the average orbital radius of the spinbots and θ is the radian over time (bottom)