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Explore the complex dynamics of phase boundaries in cylindrical polyelectrolyte gels through this 27-minute research lecture from the Erwin Schrödinger International Institute for Mathematics and Physics. Examine how competition between mono- and divalent counterions in polyelectrolyte gels creates reversible transitions between swollen and collapsed phases, focusing specifically on the emergence and propagation of boundaries that separate these phases in cylindrical polyacrylate gels. Learn about the distinction between overall calcium-induced contraction and axial progression phenomena, and discover how researchers use object detection algorithms to determine boundary propagation rates. Investigate the influence of key factors including calcium concentration, external voltage, and gel diameter on both formation time and propagation velocity of phase boundaries. Understand how increased calcium concentration in adjacent baths, application of external voltage, and decreased gel diameter contribute to shorter formation times and higher propagation velocities, providing crucial insights into the sophisticated dynamics governing phase boundaries in cylindrical polyelectrolyte gel systems.