Removal of singularities and Gromov compactness for symplectic vortices

We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i Riera and Tian for circle actions to the case of arbitrary compact Lie groups. Our argument relies on an a priori estimate for vortices that allows us to apply techniques used by McDuff and Salamon in their proof of Gromov compactness for pseudoholomorphic curves. As an intermediate result we prove a removable singularity theorem for vortices.Comment: Minor changes and correction

Optimal prediction for positive self-similar Markov processes

This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in Glover et al. (2013) under the assumption that X is a positive transient diffusion. We extend their result to the class of positive self-similar Markov processes by establishing a link to Baurdoux and van Schaik (2013), where the same question is studied for a Levy process drifting to minus infinity. The connection to Baurdoux and van Schaik (2013) relies on the so-called Lamperti transformation which links the class of positive self-similar Markov processes with that of Levy processes. Our approach will reveal that the results in Glover et al. (2013) for Bessel processes can also be seen as a consequence of self-similarity

Experimental evidence of reduced sticking of nanoparticles on a metal grid

Filtering of NaCl, CaCl2, (NH4)2SO4 and NiSO4 aerosol particles 7–20 nm in diameter by a stainless steel grid was studied in order to find out if there is perfect sticking or partial rebound. Our experiment used particles from a spray-drying process, the majority of which were electrically neutral. Penetration through the grid was measured by comparing the concentration downstream of the grid with the upstream concentration under otherwise identical conditions. Size selection was done with a scanning mobility particle sizer (SMPS). Filter penetration P as function of the particle diameter dp was expressed by View the MathML source . The values of x determined were smaller than the theoretical value of 1.29, indicating enhanced penetration of small particles and deviation from the classical filtration model. Because of possible systematic errors in the size selection, we focus on the differences of x from material to material, which indicate different sticking probabilities. We apply a statistical test, which yields a 90% confidence level for the result. There is a sticking probability of <100% at least for NaCl particles and even more so for NiSO4. This result is in contrast to former findings using metal and/or charged particles, and we speculate that the discrepancy is due to the smaller Hamaker constant of salts and that particle charge is important for the sticking probability