Every in-flowing mode is paired with a mode flowing out by time-reversal symmetry (TRS). (a) Ungapped time-reversal-symmetric system. Insets in (a)–(d) show different bulk (green) and interface (red) dispersion relations. In a region of space (gray circle), we count the number of in- and out-flowing modes (black arrows) and apply the pigeonhole principle. The incoming wave has parameters Ω B T = 1 / 5 and ω T = q L = π / 30. Time t ̃ = t / T and space x ̃ = x / L are nondimensionalized by L ≡ | ν o | / c and T ≡ | ν o | / c 2, using the odd viscosity parameter ν o ∼ Ω A (see text).

Density differences δ ρ around an equilibrium density ρ 0 are shown in color, and the velocity field is portrayed by white arrows. (c) The pulse hits the no-slip wall (solid line). (b) The right-moving pulse along the fluid-fluid interface (dotted line). The interface between the two fluids supports right-moving edge modes, one of which is shown in (b)–(d). The bulk is gapped with topological invariant C = sgn ( Ω A ) + sgn ( Ω B ). Each particle spins with rotational speed ± Ω A and is subject to a Coriolis force density ± Ω B v *, where v * is the velocity v rotated by 90 ∘. (a) Schematic of a two-dimensional system of two chiral active fluids composed of counter-rotating particles. Instead of making efficient waveguides, our paper shows how topology can be exploited for applications towards acoustic absorption, shielding, and soundproofing.Ĭompletely absorbed interface mode in a chiral active fluid.

We then conclude that energy dissipation is sped up by mode trapping. Solving the fluid equations of motion, we find explicit expressions for the disappearing modes. In these fluids, chiral edge states disappear, which implies non-Hermiticity and leads to an interplay between topology and energy dissipation. As a realization, we present a model system of two topological fluids composed of counter-spinning particles, which are separated by a boundary that transitions from a fluid-fluid interface into a no-slip wall. Here we design interfaces that host a net flux of the number of modes into a region, trapping incoming energy. However, in continuum systems, the number of states at an interface can depend on boundary conditions. Chiral edge states can transmit energy along imperfect interfaces in a topologically robust and unidirectional manner when protected by bulk-boundary correspondence.

Waves 9 complete