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

Good rotations

Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in the representation of the sine s and cosine c of the angle theta. In a computer, one generally gets c^2 + s^2 1, resulting in a mapping that is slightly contracting or expanding. In the present paper we present a method to find pairs of representable real numbers s and c such that c^2 + s^2 is as close to 1 as possible. We show that this results in a drastic decrease of the systematic error, making it negligible compared to the random error of other operations. We also verify that this approach gives good results in a realistic celestial mechanics integration.Comment: 24 pages, 3 figure

Laser frequency combs and ultracold neutrons to probe braneworlds through induced matter swapping between branes

This paper investigates a new experimental framework to test the braneworld hypothesis. Recent theoretical results have shown the possibility of matter exchange between branes under the influence of suitable magnetic vector potentials. It is shown that the required conditions might be achieved with present-day technology. The experiment uses a source of pulsed and coherent electromagnetic radiation and relies on the Hansch frequency comb technique well-known in ultrahigh-precision spectroscopy. A good matter candidate for testing the hypothesis is a polarized ultracold neutron gas for which the number of swapped neutrons is measured.Comment: 14 pages, 4 figures. Published version. Published in Phys. Rev.

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

Robustness: a New Form of Heredity Motivated by Dynamic Networks

We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this definition using two different settings of dynamic networks. The first corresponds to networks of low dynamicity, where some links may be permanently removed so long as the network remains connected. The second corresponds to highly-dynamic networks, where communication links appear and disappear arbitrarily often, subject only to the requirement that the entities are temporally connected in a recurrent fashion ({\it i.e.} they can always reach each other through temporal paths). Each context induces a different interpretation of the notion of robustness. We start by motivating the definition and discussing the two interpretations, after what we consider the notion independently from its interpretation, taking as our focus the robustness of {\em maximal independent sets} (MIS). A graph may or may not admit a robust MIS. We characterize the set of graphs \forallMIS in which {\em all} MISs are robust. Then, we turn our attention to the graphs that {\em admit} a robust MIS (\existsMIS). This class has a more complex structure; we give a partial characterization in terms of elementary graph properties, then a complete characterization by means of a (polynomial time) decision algorithm that accepts if and only if a robust MIS exists. This algorithm can be adapted to construct such a solution if one exists

The measured compositions of Uranus and Neptune from their formation on the CO iceline

The formation mechanisms of the ice giants Uranus and Neptune, and the origin of their elemental and isotopic compositions, have long been debated. The density of solids in the outer protosolar nebula is too low to explain their formation, and spectroscopic observations show that both planets are highly enriched in carbon, very poor in nitrogen, and the ices from which they originally formed might had deuterium-to-hydrogen ratios lower than the predicted cometary value, unexplained properties observed in no other planets. Here we show that all these properties can be explained naturally if Uranus and Neptune both formed at the carbon monoxide iceline. Due to the diffusive redistribution of vapors, this outer region of the protosolar nebula intrinsically has enough surface density to form both planets from carbon-rich solids but nitrogen-depleted gas, in abundances consistent with their observed values. Water rich interiors originating mostly from transformed CO ices reconcile the D/H value of Uranus and Neptune's building blocks with the cometary value. Finally, Our scenario generalizes a well known hypothesis that Jupiter formed on an iceline (water snowline) for the two ice giants, and might be a first step towards generalizing this mechanism for other giant planets.Comment: The Astrophysical Journal (in press), 8 pages, 5 figure

Predicting spinor condensate dynamics from simple principles

We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these non-linear systems is explained by surprisingly simple principles: minimization of energy at zero temperature, and maximization of entropy at high temperature. Our analytical results for the homogeneous case are corroborated by numerical simulations for confined condensates in a wide variety of initial conditions. These predictions compare qualitatively well with recent experimental observations and can, therefore, serve as a guidance for on-going experiments.Comment: 4 pages, 2 figures. v3: matches version appeared in PR