Sandpile model on a quenched substrate generated by kinetic   self-avoiding trails
  Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net outflow of grains from a toppling site and the total inflow of grains to the same site when all its neighbors topple once is maintained at all sites. Within numerical accuracy this model behaves in the same way as the multiscaling BTW model. 
R. Karmakar and S. S. Manna