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In this research, the totally asymmetric exclusion process without particlenumber conservation is discussed. Based on the mean field approximation and theRankine-Hugoniot condition, the necessary and sufficient conditions of theexistence of the domain wall have been obtained. Moreover, the properties ofthe domain wall, including the location and height, have been studiedtheoretically. All the theoretical results are demonstrated by the computersimulations.

Domain wall of the totally asymmetric exclusion process without particle number conservation