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It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control.

The Quadrangles Av-11 and Av-12 on Vesta are located at the northern rim of the giant Rheasilvia south polar impact basin. The primary geologic units in Av-11 and Av-12 include material from the Rheasilvia impact basin formation, smooth material and different types of impact crater structures (such as bimodal craters, dark and bright crater ray material and dark ejecta material). Av-11 and Av-12 exhibit almost the full range of mass wasting features observed on Vesta, such as slump blocks, spur-and-gully morphologies and landslides within craters. Processes of collapse, slope instability and seismically triggered events force material to slump down crater walls or scarps and produce landslides or rotational slump blocks. The spur-and-gully morphology that is known to form on Mars is also observed on Vesta; however, on Vesta this morphology formed under dry conditions.

A variety of geologic landforms and features are observed within quadrangle Av-13 Tuccia in the southern hemisphere of Vesta. The quadrangle covers parts of the highland Vestalia Terra as well as the floors of the large Rheasilvia and Veneneia impact basins, which results in a substantial elevation difference of more than 40 km between the northern and the southern portions of the quadrangle. Measurements of crater size–frequency distributions within and surrounding the Rheasilvia basin indicate that gravity-driven mass wasting in the interior of the basin has been important, and that the basin has a more ancient formation age than would be expected from the crater density on the basin floor alone. Subsequent to its formation, Rheasilvia was superimposed by several mid-sized impact craters. The most prominent craters are Tuccia, Eusebia, Vibidia, Galeria, and Antonia, whose geology and formation ages are investigated in detail in this work. These impact structures provide a variety of morphologies indicating different sorts of subsequent impact-related or gravity-driven mass wasting processes. Understanding the geologic history of the relatively young craters in the Rheasilvia basin is important in order to understand the even more degraded craters in other regions of Vesta.

In this paper we present a time-stratigraphic scheme and geologic time scale for the protoplanet Vesta, based on global geologic mapping and other analyses of NASA Dawn spacecraft data, complemented by insights gained from laboratory studies of howardite–eucrite–diogenite (HED) meteorites and geophysical modeling. On the basis of prominent impact structures and their associated deposits, we propose a time scale for Vesta that consists of four geologic time periods: Pre-Veneneian, Veneneian, Rheasilvian, and Marcian. The Pre-Veneneian Period covers the time from the formation of Vesta up to the Veneneia impact event, from 4.6 Ga to >2.1 Ga (using the asteroid flux-derived chronology system) or from 4.6 Ga to 3.7 Ga (under the lunar-derived chronology system). The Veneneian Period covers the time span between the Veneneia and Rheasilvia impact events, from >2.1 to 1 Ga (asteroid flux-derived chronology) or from 3.7 to 3.5 Ga (lunar-derived chronology), respectively. The Rheasilvian Period covers the time span between the Rheasilvia and Marcia impact events, and the Marcian Period covers the time between the Marcia impact event until the present. The age of the Marcia impact is still uncertain, but our current best estimates from crater counts of the ejecta blanket suggest an age between ∼120 and 390 Ma, depending upon choice of chronology system used. Regardless, the Marcia impact represents the youngest major geologic event on Vesta. Our proposed four-period geologic time scale for Vesta is, to a first order, comparable to those developed for other airless terrestrial bodies.

We report on a preliminary global geologic map of Vesta, based on data from the Dawn spacecraft’s High-Altitude Mapping Orbit (HAMO) and informed by Low-Altitude Mapping Orbit (LAMO) data. This map is part of an iterative mapping effort; the geologic map has been refined with each improvement in resolution. Vesta has a heavily-cratered surface, with large craters evident in numerous locations. The south pole is dominated by an impact structure identified before Dawn’s arrival. Two large impact structures have been resolved: the younger, larger Rheasilvia structure, and the older, more degraded Veneneia structure. The surface is also characterized by a system of deep, globe-girdling equatorial troughs and ridges, as well as an older system of troughs and ridges to the north. Troughs and ridges are also evident cutting across, and spiraling arcuately from, the Rheasilvia central mound.

However, no volcanic features have been unequivocally identified. Vesta can be divided very broadly into three terrains: heavily-cratered terrain; ridge-and-trough terrain (equatorial and northern); and terrain associated with the Rheasilvia crater. Localized features include bright and dark material and ejecta (some defined specifically by color); lobate deposits; and mass-wasting materials. No obvious volcanic features are evident. Stratigraphy of Vesta’s geologic units suggests a history in which formation of a primary crust was followed by the formation of impact craters, including Veneneia and the associated Saturnalia Fossae unit. Formation of Rheasilvia followed, along with associated structural deformation that shaped the Divalia Fossae ridge-and-trough unit at the equator. Subsequent impacts and mass wasting events subdued impact craters, rims and portions of ridge-and-trough sets, and formed slumps and landslides, especially within crater floors and along crater rims and scarps. Subsequent to the formation of Rheasilvia, discontinuous low-albedo deposits formed or were emplaced; these lie stratigraphically above the equatorial ridges that likely were formed by Rheasilvia. The last features to be formed were craters with bright rays and other surface mantling deposits.

Executed progressively throughout data acquisition, the iterative mapping process provided the team with geologic proto-units in a timely manner. However, interpretation of the resulting map was hampered by the necessity to provide the team with a standard nomenclature and symbology early in the process. With regard to mapping and interpreting units, the mapping process was hindered by the lack of calibrated mineralogic information. Topography and shadow played an important role in discriminating features and terrains, especially in the early stages of data acquisition.

Vesta is a unique, intermediate class of rocky body in the Solar System, between terrestrial planets and small asteroids, because of its size (average radius of ∼263 km) and differentiation, with a crust, mantle and core. Vesta’s low surface gravity (0.25 m/s²) has led to the continual absence of a protective atmosphere and consequently impact cratering and impact-related processes are prevalent. Previous work has shown that the formation of the Rheasilvia impact basin induced the equatorial Divalia Fossae, whereas the formation of the Veneneia impact basin induced the northern Saturnalia Fossae. Expanding upon this earlier work, we conducted photogeologic mapping of the Saturnalia Fossae, adjacent structures and geomorphic units in two of Vesta’s northern quadrangles: Caparronia and Domitia. Our work indicates that impact processes created and/or modified all mapped structures and geomorphic units. The mapped units, ordered from oldest to youngest age based mainly on cross-cutting relationships, are: (1) Vestalia Terra unit, (2) cratered highlands unit, (3) Saturnalia Fossae trough unit, (4) Saturnalia Fossae cratered unit, (5) undifferentiated ejecta unit, (6) dark lobate unit, (7) dark crater ray unit and (8) lobate crater unit. The Saturnalia Fossae consist of five separate structures: Saturnalia Fossa A is the largest (maximum width of ∼43 km) and is interpreted as a graben, whereas Saturnalia Fossa B-E are smaller (maximum width of ∼15 km) and are interpreted as half grabens formed by synthetic faults. Smaller, second-order structures (maximum width of <1 km) are distinguished from the Saturnalia Fossae, a first-order structure, by the use of the general descriptive term ‘adjacent structures’, which encompasses minor ridges, grooves and crater chains. For classification purposes, the general descriptive term ‘minor ridges’ characterizes ridges that are not part of the Saturnalia Fossae and are an order of magnitude smaller (maximum width of <1 km vs. maximum width of ∼43 km). Shear deformation resulting from the large-scale (diameter of <100 km) Rheasilvia impact is proposed to form minor ridges (∼2 km to ∼25 km in length), which are interpreted as the surface expression of thrust faults, as well as grooves (∼3 km to ∼25 km in length) and pit crater chains (∼1 km to ∼25 km in length), which are interpreted as the surface expression of extension fractures and/or dilational normal faults. Secondary crater material, ejected from small-scale and medium-scale impacts (diameters of <100 km), are interpreted to form ejecta ray systems of grooves and crater chains by bouncing and scouring across the surface. Furthermore, seismic shaking, also resulting from small-scale and medium-scale impacts, is interpreted to form minor ridges because seismic shaking induces flow of regolith, which subsequently accumulates as minor ridges that are roughly parallel to the regional slope. In this work we expand upon the link between impact processes and structural features on Vesta by presenting findings of a photogeologic, structural mapping study which highlights how impact cratering and impact-related processes are expressed on this unique, intermediate Solar System body.

We produced a geologic map of the Av-9 Numisia quadrangle of asteroid Vesta using Dawn spacecraft data to serve as a tool to understand the geologic relations of surface features in this region. These features include the plateau Vestalia Terra, a hill named Brumalia Tholus, and an unusual “dark ribbon” material crossing the majority of the map area. Stratigraphic relations suggest that Vestalia Terra is one of the oldest features on Vesta, despite a model crater age date similar to that of much of the surface of the asteroid. Cornelia, Numisia and Drusilla craters reveal bright and dark material in their walls, and both Cornelia and Numisia have smooth and pitted terrains on their floors suggestive of the release of volatiles during or shortly after the impacts that formed these craters. Cornelia, Fabia and Teia craters have extensive bright ejecta lobes. While diogenitic material has been identified in association with the bright Teia and Fabia ejecta, hydroxyl has been detected in the dark material within Cornelia, Numisia and Drusilla. Three large pit crater chains appear in the map area, with an orientation similar to the equatorial troughs that cut the majority of Vesta. Analysis of these features has led to several interpretations of the geological history of the region. Vestalia Terra appears to be mechanically stronger than the rest of Vesta. Brumalia Tholus may be the surface representation of a dike-fed laccolith. The dark ribbon feature is proposed to represent a long-runout ejecta flow from Drusilla crater.

We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.

We investigate the dynamics of ferrofluidic wavy vortex flows in the counter-rotating Taylor-Couette system, with a focus on wavy flows with a mixture of the dominant azimuthal modes. Without external magnetic field flows are stable and pro-grade with respect to the rotation of the inner cylinder. More complex behaviors can arise when an axial or a transverse magnetic field is applied. Depending on the direction and strength of the field, multi-stable wavy states and bifurcations can occur. We uncover the phenomenon of flow pattern reversal as the strength of the magnetic field is increased through a critical value. In between the regimes of pro-grade and retrograde flow rotations, standing waves with zero angular velocities can emerge. A striking finding is that, under a transverse magnetic field, a second reversal in the flow pattern direction can occur, where the flow pattern evolves into pro-grade rotation again from a retrograde state. Flow reversal is relevant to intriguing phenomena in nature such as geomagnetic reversal. Our results suggest that, in ferrofluids, flow pattern reversal can be induced by varying a magnetic field in a controlled manner, which can be realized in laboratory experiments with potential applications in the development of modern fluid devices.

Asteroids provide fundamental clues to the formation and evolution of planetesimals. Collisional models based on the depletion of the primordial main belt of asteroids predict 10–15 craters >400 km should have formed on Ceres, the largest object between Mars and Jupiter, over the last 4.55 Gyr. Likewise, an extrapolation from the asteroid Vesta would require at least 6–7 such basins. However, Ceres’ surface appears devoid of impact craters >∼280 km. Here, we show a significant depletion of cerean craters down to 100–150 km in diameter. The overall scarcity of recognizable large craters is incompatible with collisional models, even in the case of a late implantation of Ceres in the main belt, a possibility raised by the presence of ammoniated phyllosilicates. Our results indicate that a significant population of large craters has been obliterated, implying that long-wavelength topography viscously relaxed or that Ceres experienced protracted widespread resurfacing.