  The diffusion of finite-size hard-core interacting particles in two- or
three-dimensional confined domains is considered in the limit that the
confinement dimensions become comparable to the particle's dimensions. The
result is a nonlinear diffusion equation for the one-particle probability
density function, with an overall collective diffusion which depends on both
the excluded-volume and the narrow confinement. By including both these effects
the equation is able to interpolate between severe confinement (for example,
single-file diffusion) and unconfined diffusion. Numerical solutions of both
the effective nonlinear diffusion equation and the stochastic particle system
are presented and compared. As an application, the case of diffusion under a
ratchet potential is considered, and the change in transport properties due to
excluded-volume and confinement effects is examined.
