Diffusion in the presence of a local attracting factor: Theory and some   interdisciplinary applications
  We study a simple model of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned space-dependent "attractiveness function", a situation frequently encountered in the study of various diffusion problems. The corresponding drift-diffusion equation and the explicit expressions for the velocity field and the diffusion coefficient are obtained and discussed. We consider some examples of applications of the results obtained to chemotactic diffusion processes and social dynamics. 
Hardi Veerm\"ae and Marco Patriarca
cond-mat.stat-mech