Explain the anomalous longitudinal density correlations in confined flocks

Explain the origin of the anomalous longitudinal density-correlation scaling and corresponding effective mass term in transversely confined Vicsek flocks, including the observed dependence on the confinement width.

Background

For transversely confined polar flocks, the thesis derives scaling forms for velocity correlations and observes numerically that longitudinal density correlations follow an anomalous algebraic form characterized by an exponent approximately equal to 0.9. The associated confinement-induced effective mass scales as a negative power of the wall separation. Although the behavior is measured numerically, its theoretical origin is not identified.

References

Density correlation in the longitudinal direction, however, seem to be characterized by an anomalous effective mass term $\Sigma \sim L_\perp{-\gamma}$, with $\gamma \approx 0.9$ an empirical scaling factor of unknown origin.

— Boundary and bulk perturbations in vectorial active matter  (2609.28593 - Fava, 23 Sep 2026) in Chapter 4, Section 4, subsection “Discussion”