Can aerosols be trapped in open flows?

The fate of aerosols in open flows is relevant in a variety of physical contexts. Previous results are consistent with the assumption that such finite-size particles always escape in open chaotic advection. Here we show that a different behavior is possible. We analyze the dynamics of aerosols both in the absence and presence of gravitational effects, and both when the dynamics of the fluid particles is hyperbolic and nonhyperbolic. Permanent trapping of aerosols much heavier than the advecting fluid is shown to occur in all these cases. This phenomenon is determined by the occurrence of multiple vortices in the flow and is predicted to happen for realistic particle-fluid density ratios.Comment: Animation available at http://www.pks.mpg.de/~rdvilela/leapfrogging.htm

More than I expected: a qualitative exploration of participants’ experience of an online adoptive parent-toddler group

The question of how best to support adoptive parents has been attracting increasing attention in recent years. This paper aims to explore participants’ experience of a new online intervention for adoptive parents and toddlers, which was adapted from an existing psychoanalytic Parent-Toddler Group (PTG) model. Participants were recruited from the parents attending the intervention, and four took part in a semi-structured post-intervention interview, aimed at exploring their experience of the PTG. Findings showed that, despite difficulties with the online setting of this intervention, participants overall experienced it positively, and particularly valued the supportive element of the group and the improvements in the parent-child relationship. However, challenges included engaging toddlers in the online setting, and participants’ confusion over the expectations and outcomes of the group. Based on these findings, suggestions were made for further research and adaptations of this model for future adoptive parenting interventions and support

Dust Grain Orbital Behavior Around Ceres

Many asteroids show indications they have undergone impacts with meteoroid particles having radii between 0.01 m and 1 m. During such impacts, small dust grains will be ejected at the impact site. The possibility of these dust grains (with radii greater than 2.2x10-6 m) forming a halo around a spherical asteroid (such as Ceres) is investigated using standard numerical integration techniques. The orbital elements, positions, and velocities are determined for particles with varying radii taking into account both the influence of gravity, radiation pressure, and the interplanetary magnetic field (for charged particles). Under the influence of these forces it is found that dust grains (under the appropriate conditions) can be injected into orbits with lifetimes in excess of one year. The lifetime of the orbits is shown to be highly dependent on the location of the ejection point as well as the angle between the surface normal and the ejection path. It is also shown that only particles ejected within 10 degrees relative to the surface tangential survive more than a few hours and that the longest-lived particles originate along a line perpendicular to the Ceres-Sun line.Comment: 8 pages, Presented at COSPAR '0

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4Comment: Accepted for publication in ApJ. Some minor changes due to referee report, most notably that the clumping mechanism has been identified as the streaming instability of Youdin & Goodman (2005). Movies of the simulations are still available at http://www.mpia.de/homes/johansen/research_en.ph

An explicit KO-degree map and applications

The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-homotopy theory of the unit map from the motivic sphere spectrum to the Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We show that "Suslin matrices", which are explicit maps from odd dimensional split smooth affine quadrics to geometric models of the spaces appearing in Bott periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit map. As applications, we deduce that $K^{MW}_i(F) = GW^i_i(F)$ for $i \leq 3$, which can be thought of as an extension of Matsumoto's celebrated theorem describing $K_2$ of a field. These results provide the first step in a program aimed at computing the sheaf $\pi_{n}^{{\mathbb A}^1}({\mathbb A}^n \setminus 0)$ for $n \geq 4$.Comment: 36 Pages, Final version, to appear Journal of Topolog

An analysis of the transit times of CoRoT-1b

I report the results from a study of the transit times for CoRoT-1b, which was one of the first planets discovered by CoRoT. Analysis of the pipeline reduced CoRoT light curve yields a new determination of the physical and orbital parameters of planet and star, along with 35 individual transit times at a typical precision of 36 s. I estimate a planet-to-star radii ratio of 0.1433 +/- 0.0010, a ratio of the planet's orbital semimajor axis to the host star radius of 4.751 +/- 0.045, and an orbital inclination for the planet of 83.88 +/- 0.29 deg. The observed transit times are consistent with CoRoT-1b having a constant period and there is no evidence of an additional planet in the system. I use the observed constancy of the transit times to set limits on the mass of a hypothetical additional planet in a nearby, stable orbit. I ascertain that the most stringent limits (4 M_earth at 3 sigma confidence) can be placed on planets residing in a 1:2 mean motion resonance with the transiting planet. In contrast, the data yield less stringent limits on planets near a 1:3 mean motion resonance (5 M_jup at 3 sigma confidence) than in the surrounding parameter space. In addition, I use a simulation to investigate what sensitivity to additional planets could be obtained from the analysis of data measured for a similar system during a CoRoT long run (100 sequential transit times). I find that for such a scenario, planets with masses greater than twice that of Mars (0.2 M_earth) in the 1:2 mean motion resonance would cause high-significance transit time deviations. Therefore, such planets could be detected or ruled out using CoRoT long run data. I conclude that CoRoT data will indeed be very useful for searching for planets with the transit timing method.Comment: accepted for publication in A&A; v2 replaces with accepted versio

A Progress Report: Agricultural Research at the Range Field Station, South Dakota State College Experiment Station, Cottonwood, S.D.

South Dakota, west of the Missouri River, may be divided into three distinct regions. The most northerly of these is a series of benches, plateaus, and isolated buttes underlain by both sandstone and shale. These soils range from sandy loams to clays but are predominantly loamy. The most southerly region is a series of plateaus and broad benches underlain by silty, sandy, and clayey strata. These soils range from very sandy on the Nebraska border to silty and clayey at the southern tributaries of the White River. Between the two just described lies the third region. This is the region of the State represented by the Cottonwood Range Field Station. It is called the Pierre hills and is underlain by shaly strata which weather to dark clayey soils that are sticky when wet. These shaly strata do not form benches and plateaus like the younger strata to the north and south. Rather, they are reduced by weathering to a series of smooth grassy hills and ridges with convex tops. In the central region the major rivers, and the other two as well, Bow east. Stream valleys are entrenched several hundred feet and the rivers in them pursue meandering courses. Cottonwood trees flourish in the stream channels. (See more in text

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio