  We analyse the general features of localisation of fermions and scalars in
smoothed field-theoretical versions of the type 2 Randall- Sundrum braneworld
model. A scalar field domain-wall forms the brane, inducing warped gravity, and
we study the mass spectra of the matter fields in the dimensionally reduced
theory. We demonstrate explicitly that both scalar and fermion fields exhibit a
continuum of properly normalisable modes starting at zero mass. If discrete
bound modes are present in the gravity-free case, these become resonances in
the continuum, while off-resonant modes are highly suppressed on the brane. We
describe briefly how another scalar field can be used to break a symmetry on
the domain-wall while leaving it unbroken far from the wall, as has already
been done in the flat space case. Finally we present numerical calculations for
a toy model which demonstrates the decoupling of continuum modes at low
energies, so the theory becomes four dimensional.
