Where the Jobs Are: Identification and Analysis of Local Employment Opportunities

A practitioner\u27s guide to local labor market analysis.https://research.upjohn.org/up_press/1127/thumbnail.jp

Probing rare physical trajectories with Lyapunov weighted dynamics

The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition, atypical structures like the first chaotic regions to appear, or the last regular islands to survive, play a crucial role in many physical situations. For instance, resonances and separatrices determine the fate of planetary systems, and localised objects like solitons and breathers provide mechanisms of energy transport in nonlinear systems such as Bose-Einstein condensates and biological molecules. Unfortunately, despite the fundamental progress made in the last years, most of the numerical methods to locate these 'rare' trajectories are confined to low-dimensional or toy models, while the realms of statistical physics, chemical reactions, or astronomy are still hard to reach. Here we implement an efficient method that allows one to work in higher dimensions by selecting trajectories with unusual chaoticity. As an example, we study the Fermi-Pasta-Ulam nonlinear chain in equilibrium and show that the algorithm rapidly singles out the soliton solutions when searching for trajectories with low level of chaoticity, and chaotic-breathers in the opposite situation. We expect the scheme to have natural applications in celestial mechanics and turbulence, where it can readily be combined with existing numerical methodsComment: Accepted for publication in Nature Physics. Due to size restrictions, the figures are not of high qualit

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

Relativistic Celestial Mechanics with PPN Parameters

Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.Comment: 71 page

Global Symplectic Polynomial Approximation of Area-Preserving Maps

International audienc

Graphical Evolution of the Arnold Web: From Order to Chaos

International audienc

Numerical investigation of the break-down threshold for a restricted three-body problem

Transition to chaos in the planar, circular, restricted three body problem is investigated. In particular, a model Hamiltonian suitable for the description of the motion of the asteroid Ceres is introduced. The break-down threshold of invariant surfaces (nearby the position of Ceres in phase space) is computed by means of different numerical methods, which allow to detect the transition from regular to chaotic motion. The experiments show that in the proximity of the location of the asteroid, invariant surfaces cease to exist for a mass ratio (between the perturbing body, Jupiter and the primary, the Sun) between 0.002 and 0.004. We remind that the real value of the above mass ratio is about 0.001 as derived from astronomical observations