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Following your nose: Autochemotaxis and other mechanisms for spinodal decomposition in flocks (2401.10391v1)
Published 4 Jan 2024 in cond-mat.soft
Abstract: We develop the hydrodynamic theory of dry, polar ordered, active matter (flocking") with autochemotaxis; i.e., self-propelled entities moving in the same direction, each emitting a substance which attracts the others (e.g., ants). We find that sufficiently strong autochemotaxis leads to an instability to phase separation into one high and one low density band. This is very analogous to both equilibrium phase separation, andmotility induced phase separation" (``MIPS") and can occur in flocks due to any microscopic mechanism (e.g., sufficiently strong attractive interactions) that makes the entities cohere.
- E. F. Keller and L. A. Segel, Journal of Theoretical Biology 30, 225 (1971a).
- E. F. Keller and L. A. Segel, Journal of Theoretical Biology 26, 399 (1970).
- E. F. Keller and L. A. Segel, Journal of Theoretical Biology 30, 235 (1971b).
- D. Horstmann, Jahresbericht der Deutschen Mathematiker-Vereinigung 105, 103 (2003).
- H. Stark, Acc. Chem. Res. 51, 2681 (2018).
- J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995).
- J. Toner and Y. Tu, Phys. Rev. E 58, 4828 (1998).
- J. Toner, Phys. Rev. E 86, 031918 (2012).
- N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
- T. Bertrand and C. F. Lee, Phys. Rev. Res. 4, L022046 (2022).
- M. E. Cates and J. Tailleur, Annual Review of Condensed Matter Physics 6, 219 (2015).
- P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, 1995).
- Note that, in contrast to the approach of the Toner-Tu equation, the field v𝑣vitalic_v we are using in equation (2) is not the “true” or full velocity field 𝐯truesubscript𝐯true\mathbf{v}_{\rm true}bold_v start_POSTSUBSCRIPT roman_true end_POSTSUBSCRIPT, in the sense that it is not the field that is related to the number current of birds by the exact continuity equation 𝐉=ρ𝐯true𝐉𝜌subscript𝐯true{\bf J}=\rho\mathbf{v}_{\rm true}bold_J = italic_ρ bold_v start_POSTSUBSCRIPT roman_true end_POSTSUBSCRIPT. Instead, we have chosen to work with a velocity field defined by 𝐯=v0𝐩^𝐯subscript𝑣0^𝐩\mathbf{v}=v_{0}{\bf\hat{p}}bold_v = italic_v start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT over^ start_ARG bold_p end_ARG, where 𝐩^^𝐩{\bf\hat{p}}over^ start_ARG bold_p end_ARG is the local “polarization”’; that is, a unit vector along the direction in which the local flockers are pointing. This fact then requires that we include the symmetry allowed k1, k1a, k2 and k2a terms. See the Associated Long Paper Miller and Toner for a further discussion.
- T. Hillen and K. J. Painter, Journal of Mathematical Biology 58, 183 (2009).
- M. Miller and J. Toner, Associated long paper.