Planetesimal disk evolution driven by embryo-planetesimal gravitational scattering

The process of gravitational scattering of planetesimals by a massive protoplanetary embryo is explored theoretically. We propose a method to describe the evolution of the disk surface density, eccentricity, and inclination caused by the embryo-planetesimal interaction. It relies on the analytical treatment of the scattering in two extreme regimes of the planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and dispersion-dominated (dynamically ``hot''). In the former, planetesimal scattering can be treated as a deterministic process. In the latter, scattering is mostly weak because of the large relative velocities of interacting bodies. This allows one to use the Fokker-Planck approximation and the two-body approximation to explore the disk evolution. We compare the results obtained by this method with the outcomes of the direct numerical integrations of planetesimal orbits and they agree quite well. In the intermediate velocity regime an approximate treatment of the disk evolution is proposed based on interpolation between the two extreme regimes. We also calculate the rate of embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that it is in agreement with both the simulations and earlier calculations. Finally we discuss the question of the direction of the embryo-planetesimal interaction in the dispersion-dominated regime and demonstrate that it is repulsive. This means that the embryo always forms a gap in the disk around it, which is in contrast with the results of other authors. The machinery developed here will be applied to realistic protoplanetary systems in future papers.Comment: 40 pages, 9 figures, submitted to A

Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log \Delta)$ bits per node and $O(nD)$ respectively, where $\Delta$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

An ab initio study of magneto-electric coupling of YMnO3\rm YMnO_3

The present paper proposes the direct calculation of the microscopic contributions to the magneto-electric coupling, using ab initio methods. The electrostrictive and the Dzyaloshinskii-Moriya contributions were evaluated individually. For this purpose a specific method was designed, combining DFT calculations and embedded fragments, explicitely correlated, quantum chemical calculations. This method allowed us to calculate the evolution of the magnetic couplings as a function of an applied electric field. We found that in $\rm YMnO_3$ the Dzyaloshinskii-Moriya contribution to the magneto-electric effect is three orders of magnitude weaker than the electrostrictive contribution. Strictive effects are thus dominant in the magnetic exchange evolution under an applied electric field, and by extension on the magneto-electric effect. These effects remain however quite small and the modifications of the magnetic excitations under an applied electric field will be difficult to observe experimentally. Another important conclusion is that the amplitude of the magneto-electric effect is very small. Indeed, it can be shown that the linear magneto-electric tensor is null due to the inter-layer symmetry operations.Comment: J. Phys. Cond. Matter 201

Density functional study of two-dimensional He-4 clusters

Binding energies and density profiles of two-dimensional systems of liquid He-4 with different geometries are studied by means of a zero-range density functional adjusted to reproduce the line tension obtained in a previous diffusion Monte Carlo calculation (lambda_{DMC}=0.121 K/A). It is shown that this density functional provides accurate results for the binding energy of large clusters with a reasonable computational effort.Comment: RevTeX4, 11 pages + 2 tables + 6 figure

Magnetic topology and surface differential rotation on the K1 subgiant of the RS CVn system HR 1099

We present here spectropolarimetric observations of the RS CVn system HR 1099 (V711 Tau) secured from 1998 February to 2002 January with the spectropolarimeter MuSiCoS at the Telescope Bernard Lyot (Observatoire du Pic du Midi, France). We apply Zeeman-Doppler Imaging and reconstruct brightness and magnetic surface topologies of the K1 primary subgiant of the system, at five different epochs. We confirm the presence of large, axisymmetric regions where the magnetic field is mainly azimuthal, providing further support to the hypothesis that dynamo processes may be distributed throughout the whole convective zone in this star. We study the short-term evolution of surface structures from a comparison of our images with observations secured at close-by epochs by Donati et al. (2003) at the Anglo-Australian Telescope. We conclude that the small-scale brightness and magnetic patterns undergo major changes within a timescale of 4 to 6 weeks, while the largest structures remain stable over several years. We report the detection of a weak surface differential rotation (both from brightness and magnetic tracers) indicating that the equator rotates faster than the pole with a difference in rotation rate between the pole and the equator about 4 times smaller than that of the Sun. This result suggests that tidal forces also impact the global dynamic equilibrium of convective zones in cool active stars.Comment: accepted by MNRA