  We study the transport process of interacting Brownian particles in a tube of
varying cross section. To describe this process we introduce a modified
Fick-Jacobs equation, considering particles that interact through a hard-core
potential. We were able to solve the equation with numerical methods for the
case of symmetric and asymmetric cavities. We focused in the concentration of
particles along the direction of the tube. We also preformed Monte Carlo
simulations to evaluate the accuracy of the results, obtaining good agreement
between theory and simulations.
