The existence of a critical gradient is an important feature of many t
ransport models. [M. Kotschenreuther er nl., Phys, Plasmas 2, 2381 (19
95)], However, fundamental differences exist in the dynamics near marg
inal stability, depending on whether the transport phenomena are contr
olled by strict (linear) marginal stability or by a self-organized cri
ticality. One of the most striking differences is in the stiffness of
the profiles, In this paper, a sand pile model is used to gain some ba
sic understanding of the stiffness of the profile under different dyna
mics. (C) 1998 American Institute of Physics.