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Universality class for a nonequilibrium state of matter: A d=4-ε expansion study of Malthusian flocks
Leiming Chen1, Chiu Fan Lee2, John Toner3
1School of Materials Science and Physics, China University of Mining and Technology, Xuzhou Jiangsu 221116, People's Republic of China.
Abstract:
We show that "Malthusian flocks"-i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion-belong to a new universality class in spatial dimensions d>2. We calculate the universal exponents and scaling laws of this new universality class to O(ε) in a d=4-ε expansion and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of 2
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