A mid-IR interferometric survey with MIDI/VLTI: resolving the second-generation protoplanetary disks around post-AGB binaries

We present a mid-IR interferometric survey of the circumstellar environment of a specific class of post-Asymptotic Giant Branch (post-AGB) binaries. For this class the presence of a compact dusty disk has been postulated on the basis of various spatially unresolved measurements. Our interferometric survey was performed with the MIDI instrument on the VLTI. In total 19 different systems were observed using variable baseline configurations. Combining all the visibilities at a single wavelength at 10.7 micron, we fitted two parametric models to the data: a uniform disk (UD) and a ring model mimicking a temperature gradient. We compared our observables of the whole sample, with synthetic data computed from a grid of radiative transfer models of passively irradiated disks in hydrostatic equilibrium. These models are computed with a Monte Carlo code that has been widely applied to describe the structure of protoplanetary disks around young stellar objects (YSO). The spatially resolved observations show that the majority of our targets cluster closely together in the distance-independent size-colour diagram, and have extremely compact N-band emission regions. The typical uniform disk diameter of the N-band emission region is about 40 mass which corresponds to a typical brightness temperature of 400-600~K. The resolved objects display very similar characteristics in the interferometric observables and in the spectral energy distributions. Therefore, the physical properties of the disks around our targets must be similar. The grid of protoplanetary disk models covers very well the observed objects. Much like for young stars, the spatially resolved N-band emission region is determined by the hot inner rim of the disk. Continued comparisons between post-AGB and protoplanetary disks will help to understand grain growth and disk evolution processes,Comment: 30 pages, 21 figures, in press in Astronomy and Astrophysic

Class of self-limiting growth models in the presence of nonlinear diffusion

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.Comment: RevTex, 13 pages, 5 figures. To appear in Physical Review

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion