The effect of the Coriolis force on Kelvin-Helmholtz-driven mixing in protoplanetary disks

We study the stability of proto-planetary disks with vertical velocity gradients in their equilibrium rotation rates; such gradients are expected to develop when dust settles into the midplane. Using a linear stability analysis of a simple three-layer model, we show that the onset of instability occurs at a larger value of the Richardson number, and therefore for a thicker layer, when the effects of Coriolis forces are included. This analysis also shows that even-symmetry (midplane-crossing) modes develop faster than odd-symmetry ones. These conclusions are corroborated by a large number of nonlinear numerical simulations with two different parameterized prescriptions for the initial (continuous) dust distributions. Based on these numerical experiments, the Richardson number required for marginal stability is more than an order of magnitude larger than the traditional 1/4 value. The dominant modes that grow have horizontal wavelengths of several initial dust scale heights, and in nonlinear stages mix solids fairly homogeneously over a comparable vertical range. We conclude that gravitational instability may be more difficult to achieve than previously thought, and that the vertical distribution of matter within the dust layer is likely globally, rather than locally, determined.Comment: Accepted for publication in Ap

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

NN-body Simulation of Planetesimal Formation Through Gravitational Instability of a Dust Layer

We performed N-body simulations of a dust layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of non-axisymmetric wake-like structures, the creation of aggregates, and the collisional growth of the aggregates. Finally, a few large aggregates and many small aggregates are formed. The mass of the largest aggregate is larger than the mass predicted by the linear perturbation theory. We examined the dependence of system parameters on the planetesimal formation. We found that the mass of the largest aggregates increase as the size of the computational domain increases. However the ratio of the aggregate mass to the total mass $M_\mathrm{aggr}/M_\mathrm{total}$ is almost constant $0.8-0.9$. The mass of the largest aggregate increases with the optical depth and the Hill radius of particles.Comment: 34 pages, 11 figures. Accepted for publication in Ap

Possible association between moderate intellectual disability and weight gain in valproic acid–treated patients with epilepsy

Yukiko Tanamachi,1 Junji Saruwatari,1 Madoka Noai,1 Ryoko Kamihashi,1 Hiromi Soraoka,1 Yuki Yoshimori,1 Naoki Ogusu,1 Kentaro Oniki,1 Norio Yasui-Furukori,2 Takateru Ishitsu,3,4 Kazuko Nakagawa1,5 1Division of Pharmacology and Therapeutics, Graduate School of Pharmaceutical Sciences, Kumamoto University, Kumamoto, Japan; 2Department of Neuropsychiatry, Hirosaki University School of Medicine, Hirosaki, Japan; 3Kumamoto Saishunso National Hospital, Koshi, Japan; 4Kumamoto Ezuko Ryoiku Iryo Center, Kumamoto, Japan; 5Center for Clinical Pharmaceutical Sciences, Kumamoto University, Kumamoto, Japan Background: Although patients with moderate intellectual disability (ID) are known to have higher rates of being overweight and obese than those without ID, there are no current data regarding the relationship between ID and weight gain in epilepsy patients treated with valproic acid (VPA). Patients and methods: The possible association between moderate ID and an overweight status at the time of initiation of VPA therapy (baseline) was investigated using a logistic regression analysis in 143 patients with epilepsy. Among the 119 nonoverweight patients at baseline, the longitudinal association between moderate ID and the weight status during VPA therapy was retrospectively examined using a Cox hazards regression analysis and the generalized estimating equations approach, while also paying careful attention to associations with other patient characteristics. Results: The proportion of patients with moderate ID was 52.4% among the 143 study subjects. The presence of moderate ID was not associated with an overweight status at baseline (P=0.762). Among the nonoverweight patients at baseline, 16 subjects were newly diagnosed as being overweight during treatment with VPA (3.6±2.1 years). The presence of moderate ID was significantly associated with the incidence of an overweight status after starting VPA therapy (adjusted hazard ratio =6.72, P=0.007). The patient age at baseline and treatment with co-administered carbamazepine, clobazam, and zonisamide significantly influenced the degree of weight fluctuation during VPA therapy among the patients with moderate ID (P<0.001, P<0.001, P=0.002, and P=0.028, respectively), whereas only patient age at baseline affected this parameter among the patients without moderate ID (P=0.022). Conclusion: The present findings suggest that the weight status should be carefully monitored in VPA-treated patients with moderate ID, especially those receiving other co-administered antiepileptic drugs that facilitate weight gain, such as carbamazepine. Keywords: overweight, weight status, obesity, antiepileptic drug, longitudinal analysis&nbsp