In addition to his teaching duties during his years at UCSB, Muller conducted numerous research studies, funded partly by four National Science Foundation grants, on allelopathic mechanisms in California plant communities and systematics and evolution of the species Quercus.
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During World War II, he worked for the Bureau of Plant Industry on the Special Guayule Research Project on a series of experiments on root development.
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The library at UCSB's Cheadle Center for Biodiversity and Ecological Restoration is named in his honor.
Herman Melville | Woody Herman | Herman's Hermits | Cornelius Vanderbilt | Cornelius | Adolfo Müller-Ury | Herman Wouk | Max Müller | Johannes Peter Müller | Herman Hollerith | Heiner Müller | Edward S. Herman | Renate Müller | Herman Daly | Gerhard Müller (rower) | Gerhard Müller | Herman Van Rompuy | Pope Cornelius | Lucius Cornelius Cinna | Johannes Müller | Herta Müller | Gerd Müller | Cornelius Cardew | Müller | Herman Dune | Herman Brood | Cornelius Vanderbilt Whitney | Cornelius Lanczos | Sophie Muller | Peter von Cornelius |