Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

Global Solutions for Incompressible Viscoelastic Fluids

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data. The results hold in both two and three dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial dat

Radiative Corrections to One-Photon Decays of Hydrogenic Ions

Radiative corrections to the decay rate of n=2 states of hydrogenic ions are calculated. The transitions considered are the M1 decay of the 2s state to the ground state and the E1(M2) decays of the $2p_{1/2}$ and $2p_{3/2}$ states to the ground state. The radiative corrections start in order $\alpha (Z \alpha)^2$, but the method used sums all orders of $Z\alpha$. The leading $\alpha (Z\alpha)^2$ correction for the E1 decays is calculated and compared with the exact result. The extension of the calculational method to parity nonconserving transitions in neutral atoms is discussed.Comment: 22 pages, 2 figure

Towards Controlling the Acceptance Factors for a Collaborative Platform in Engineering Design

International audienceThis paper might serve as a guide to take step towards a better acceptance of computer-based Knowledge management (KM) tools in institutional setting. At first time, it investigates a set of factors with different origins which are proved to have an effect on usage decision. Secondly, we set a list of candidate factor which are supposed to influence future users of a collaborative KM platform (Dimocode). At the end, we develop a methodology to take into account the selected factors and master their positive or negative impacts. The contents of this paper would be an appropriate framework in the way of Knowledge management systems (KMS) deployment

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone

Partonic flow and ϕ\phi-meson production in Au+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We present first measurements of the $\phi$-meson elliptic flow ($v_{2}(p_{T})$) and high statistics $p_{T}$ distributions for different centralities from $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at RHIC. In minimum bias collisions the $v_{2}$ of the $\phi$ meson is consistent with the trend observed for mesons. The ratio of the yields of the $\Omega$ to those of the $\phi$ as a function of transverse momentum is consistent with a model based on the recombination of thermal $s$ quarks up to $p_{T}\sim 4$ GeV/$c$, but disagrees at higher momenta. The nuclear modification factor ($R_{CP}$) of $\phi$ follows the trend observed in the $K^{0}_{S}$ mesons rather than in $\Lambda$ baryons, supporting baryon-meson scaling. Since $\phi$-mesons are made via coalescence of seemingly thermalized $s$ quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC.Comment: 6 pages, 4 figures, submit to PR

Anomalous diffusion and the first passage time problem

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.Comment: 25 pages, 4 figure

Star Formation and Dynamics in the Galactic Centre

The centre of our Galaxy is one of the most studied and yet enigmatic places in the Universe. At a distance of about 8 kpc from our Sun, the Galactic centre (GC) is the ideal environment to study the extreme processes that take place in the vicinity of a supermassive black hole (SMBH). Despite the hostile environment, several tens of early-type stars populate the central parsec of our Galaxy. A fraction of them lie in a thin ring with mild eccentricity and inner radius ~0.04 pc, while the S-stars, i.e. the ~30 stars closest to the SMBH (<0.04 pc), have randomly oriented and highly eccentric orbits. The formation of such early-type stars has been a puzzle for a long time: molecular clouds should be tidally disrupted by the SMBH before they can fragment into stars. We review the main scenarios proposed to explain the formation and the dynamical evolution of the early-type stars in the GC. In particular, we discuss the most popular in situ scenarios (accretion disc fragmentation and molecular cloud disruption) and migration scenarios (star cluster inspiral and Hills mechanism). We focus on the most pressing challenges that must be faced to shed light on the process of star formation in the vicinity of a SMBH.Comment: 68 pages, 35 figures; invited review chapter, to be published in expanded form in Haardt, F., Gorini, V., Moschella, U. and Treves, A., 'Astrophysical Black Holes'. Lecture Notes in Physics. Springer 201

The STAR Time Projection Chamber: A Unique Tool for Studying High Multiplicity Events at RHIC

The STAR Time Projection Chamber (TPC) is used to record collisions at the Relativistic Heavy Ion Collider (RHIC). The TPC is the central element in a suite of detectors that surrounds the interaction vertex. The TPC provides complete coverage around the beam-line, and provides complete tracking for charged particles within +- 1.8 units of pseudo-rapidity of the center-of-mass frame. Charged particles with momenta greater than 100 MeV/c are recorded. Multiplicities in excess of 3,000 tracks per event are routinely reconstructed in the software. The TPC measures 4 m in diameter by 4.2 m long, making it the largest TPC in the world.Comment: 28 pages, 11 figure