One-dimensional simulations of a dust ring. All setups included radiation pressure with β_{1 μm}=0.4, and are shown after 150 orbits at r₀. Left: simulation without gas. The horizontal line indicates the minimum particle size for which the dust remains on bound orbits, and the shaded area marks the initial radial range of the dust particles. Centre: includes gas density specified by Eq. (1), with gas density (Σ_g, blue curve) normalised to its maximum value, which was set to represent a gas ring of 10 M_⊕, representing a primordial scenario. The dust-to-gas ratio is 0.01. The dashed curve shows where β=η. Right: same as the centre panel, but with M_gas=0.1 M_⊕, and a dust-to-gas ratio of unity, reflecting a scenario of secondary gas origin. Large particles are affected by neither radiation pressure nor gas drag, and they remain on their initial circular Keplerian orbits. For sizes ≲100 μm, both gas drag and radiation pressure become efficient, and the particles move outward. The momentum feedback from the dust changes the gas density profile from its initial distribution (transparent blue line).