Active matter refers to systems composed of self-propelled agents, e.g., flock of birds, school of fish, etc. Active nematic (e.g., microtubule-motor protein mixtures, cell populations, etc.) is a class of active matter whose constituents have anisotropic shape and exhibit nematic (i.e. head-tail symmetric) orientational order. Topological defect is a singularity of the orientation field. It is a robust structure which cannot be removed by continuum deformations and has a great effect on the orientational structure of active nematic. To enhance the understanding of the behavior of active nematic, we investigate the defect configuration under spatial confinements. In this seminar, let us discuss two cases, (i) a circular obstacle is introduced in active nematic, (ii) active nematic is confined in a circular domain. When we consider passive nematic liquid crystals, the defect configuration can be identified exactly by an analytical calculation in both cases, (i) (Ref. [1]) and (ii) (Ref. [2]). However, in the case of active nematic, the analytical calculation becomes complicated because of the flow field induced by the activity of constituents. In Ref. [3], we have derived a formula to identify the defect configuration in case (i), including the flow field. Then, we have solved the formula numerically and compared the results with those of continuum simulations. It has been shown that the analytical formula can, at least qualitatively, reproduce the continuum-simulation results. Now we are trying to derive the formula to identify the defect configuration in case (ii) [4] and let me share the progress of this study.

References
[1] J. Fukuda & H. Yokoyama (2001) Euro. Phys. J. E 4, 389–396.
[2] Duclos et al. (2017) Nat. Phys. 13, 58-62.
[3] H. Matsukiyo & J. Fukuda (2026) Phys. Rev. E 113, 025409.
[4] H. Matsukiyo & J. Fukuda, in preparation.