Formation and tidal evolution of hot super-Earths in multiple planetary systems

Hot super-Earths are exoplanets with masses < 10 Earth masses and orbital periods < 20 days. Around 8 hot super-Earths have been discovered in the neighborhood of solar system. In this lecture, we review the mechanisms for the formation of hot super-Earths, dynamical effects that play important roles in sculpting the architecture of the multiple planetary systems. Two example systems (HD 40307 and GJ 436) are presented to show the formation and evolution of hot super-Earths or Neptunes.Comment: 12 pages, 4 color figures, Lecture in 'Extrasolar planets in Multi-Body systems: Theory and Observation',Torun (Poland), August 25-29, 2008, to appear in European Astronomical Society Publication Serie

On Relaxed Averaged Alternating Reflections (RAAR) Algorithm for Phase Retrieval from Structured Illuminations

In this paper, as opposed to the random phase masks, the structured illuminations with a pixel-dependent deterministic phase shift are considered to derandomize the model setup. The RAAR algorithm is modified to adapt to two or more diffraction patterns, and the modified RAAR algorithm operates in Fourier domain rather than space domain. The local convergence of the RAAR algorithm is proved by some eigenvalue analysis. Numerical simulations is presented to demonstrate the effectiveness and stability of the algorithm compared to the HIO (Hybrid Input-Output) method. The numerical performances show the global convergence of the RAAR in our tests.Comment: 17 pages, 26 figures, submitting to Inverse Problem