Universality class for a nonequilibrium state of matter: A d=4-ε expansion study of Malthusian flocks.

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<d≤4. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real space (r) between two regions in which the equal-time density correlation 〈δρ(r,t)δρ(0,t)〉 has opposite signs. Our expansion should be quite accurate in d=3, allowing precise quantitative comparisons between our theory, simulations, and experiments.

• Publication year

  2020

• Venue

  Physical Review E

• Publication date

  2020-03-31

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PHYSREVE.102.022610arXiv 2004.00129PMID 32942483
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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