Affine Toda model coupled to matter and the string tension in QCD2_{2}

The $sl(2)$ affine Toda model coupled to matter (ATM) is shown to describe various features, such as the spectrum and string tension, of the low-energy effective Lagrangian of QCD$_{2}$ (one flavor and $N$ colors). The corresponding string tension is computed when the dynamical quarks are in the {\sl fundamental} representation of SU(N) and in the {\sl adjoint} representation of SU(2).Comment: LaTex, 10 pages. Revised version to appear in Phys. Rev.

Moving lattice kinks and pulses: an inverse method

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an inverse method - to acoustic solitons in chains with nonlinear intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion equations and to discrete nonlinear Schr\"odinger systems. Potential functions can be found in at least a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure

Toward an Autonomous Lunar Landing Based on Low-Speed Optic Flow Sensors

International audienceFor the last few decades, growing interest has returned to the quite chal-lenging task of the autonomous lunar landing. Soft landing of payloads on the lu-nar surface requires the development of new means of ensuring safe descent with strong final conditions and aerospace-related constraints in terms of mass, cost and computational resources. In this paper, a two-phase approach is presented: first a biomimetic method inspired from the neuronal and sensory system of flying insects is presented as a solution to perform safe lunar landing. In order to design an au-topilot relying only on optic flow (OF) and inertial measurements, an estimation method based on a two-sensor setup is introduced: these sensors allow us to accu-rately estimate the orientation of the velocity vector which is mandatory to control the lander's pitch in a quasi-optimal way with respect to the fuel consumption. Sec-ondly a new low-speed Visual Motion Sensor (VMS) inspired by insects' visual systems performing local angular 1-D speed measurements ranging from 1.5 • /s to 25 • /s and weighing only 2.8 g is presented. It was tested under free-flying outdoor conditions over various fields onboard an 80 kg unmanned helicopter. These pre-liminary results show that the optic flow measured despite the complex disturbances encountered closely matched the ground-truth optic flow