The paper “An integro-differential equation with variable delay arising in machine tool vibration” co-authored by Feng-Bin Wang (Chang Gung University, Taiwan), Stephen Gourley, and Yanyu Xiao (University of Cincinnati), has been published in the SIAM Journal of Applied Mathematics. The paper rigorously derives and analyzes an integro-differential equation as a model for the possible onset of regenerative chatter during a turning process using a lathe.  The published online version is available here.  The figure below shows the governing equation derived in the paper.