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Moving, Reproducing, and Dying Beyond Flatland: Malthusian Flocks in Dimensions d>2
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 an ε=4-d 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 in d>2. Our expansion should be quite accurate in d=3, allowing precise quantitative comparisons between our theory, simulations, and experiments.
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