On the Kropholler conjecture

This short note, produced for the volume of conjectures produced on the occasion of Guido Mislin's retirement, describes the status of the Kropholle conjecture which may be viewed as a far reaching generalisation of Stallings' theorem on groups with more than one end

Aerosol particle molecular spectroscopy

The molecular spectroscopy of a solution particle by structure resonance modulation spectroscopy is discussed [S. Arnold and A. B. Pluchino, "Infrared Spectrum of a Single Aerosol Particle by Photothermal Modulation of Structure Resonances," Appl. Opt. 21, 4194 (1982); S. Arnold et al., "Molecular Spectroscopy of a Single Aerosol Particle," Opt. Lett. 9, 4 (1984)]. Analytical equations are derived for time dependence of the particle radius as it interacts with a low intensity IR source (<20 mW/cm^2). This formalism is found to be in good agreement with pulsed experiments. Working equations for the spectroscopy are derived for both constant and periodic IR excitation

Particle sizing in the electrodynamic balance

We report a new technique for sizing particles in the electrodynamic balance. In this technique, the trajectory of a falling particle is followed with a photomultiplier tube. Particle velocities are measured by placing a mask between the particle and the detector. The masked region in the particle trajectory is roughly 0.6 mm wide. Output from the PMT is sampled every millisecond by an A/D converter and stored in a computer. Flight times of several hundred milliseconds are measured and the size is then computed from the particle's terminal velocity. With a modification of the mask, the technique is used to verify the uniformity of the electric field through which the particle is falling. In the present work we use the technique to determine size of polystryrene latex microspheres having nominal diameters of 10 and 20 µ. The technique can be used on any size particle, independent of its charge-to-mass ratio, and provides the size information in a short time