Performing quantitative MFM measurements on soft magnetic nanostructures.

We have extended our previous work (Rawlings et al 2010 Phys. Rev. B 82 085404) on simulating magnetic force microscopy (MFM) images for magnetically soft samples to include an accurate representation of coated MFM tips. We used an array of square 500 nm nanomagnets to evaluate our improved MFM model. A quantitative comparison between model and experiment was performed for lift heights ranging from 20 to 100 nm. No fitting parameters were used in our comparison. For all lift heights the qualitative agreement between model and experiment was significantly improved. At low lift heights, where the magnetic signal was strong, the difference between theory and experiment was less than 30%.

Quantitative convergence analysis of multi-agent systems

We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions of contractiveness and (weak) connectedness (across an interval.) Convergence is shown to be exponential when either the system or the function characterizing the contraction is linear. Copyright © 2007 IFAC.