The transport of particles or heat against the driving gradient is studied by employing a probabilistic transport model with a characteristic particle step length that depends on the local concentration and heat gradient. When the gradient is larger than a prescribed critical value, the standard deviation of the step size is large compared to its value when the gradient is below critical. For symmetric as well as asymmetric off-axis fuelling, the model is capable of producing profiles peaking

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... the axis. Additionally, profile consistency is obtained over a broad ranges of source strengths. These results supplement recent works by van Milligen et al. (Phys. Plasmas 11, 3787 (2004)), which applied Lévy distributed step sizes in the case of super critical gradients to obtain the up-gradient transport.