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Article Contents

# A continuum model for nematic alignment of self-propelled particles

• * Corresponding author: Pierre Degond
• A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or anti-parallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to the modeling of myxobacteria is outlined.

Mathematics Subject Classification: 35L60, 35K55, 35Q70, 82C05, 82C22, 82C70, 92D50.

 Citation:

• Figure 1.  $M_0(\theta)$ for $\kappa=0.5, 2,10$ (red-dotted, black-solid, blue-dashed).

Figure 2.  $g(\theta)$ for $\kappa=0.5, 2,10$ (red-dotted, black-solid, blue-dashed).

Figure 3.  Local dynamics for $\lambda(\rho)$ given by 82. The arrows mark the flow field in the $(\rho_+,\rho_-)$ plane. The red-dotted and green-dashed lines show the values for which $\lambda(\rho_+)\rho_--\lambda(\rho_-)\rho_+=0$. The blue-solid line shows the threshold values $\rho_++\rho_-=2\sqrt{\frac{\lambda_0}{\lambda_1}}$.

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