Mean Response Function Research Articles

Diffusion of passive-scalar and magnetic fields by helical turbulence

Computer simulations of fluid-element trajectories in mirror-symmetric and maximally helical turbulence are used to evaluate Moffatt's (1974) formulae for the magnetic diffusivity η(t) and the coefficient κ(t) of the alpha-effect. The passive-scalar diffusivity κ(t) and the mean response functions of scalar and magnetic field wave-vector modes are also computed. The velocity field is normal, stationary, homogeneous and isotropic with spectrum $E(k) = \frac{3}{2}v^2_0\delta(k - k_0)$ and time correlation exp [−1/2ω2/0(t-t)2]. The cases ω0 = O (frozen turbulence), ω = vo k0 and ω0 = 2v0 k0 are followed to t = 4/v0 k0. In the ω0 > 0 cases with maximal helicity, κ(t) and a(t) approach steady-state values of order vo/k0 and v0, respectively. They behave anomalously for ω0 = 0. In the mirror-symmetric: cases, q(t) and κ(t) differ very little from each other. At all the ω0 values, is bigger in the helical than in the mirror-symmetric case. The difference is marked for ω0 = 0. The simulation results imply that κ(t) becomes negative in non-normal mirror-symmetric turbulence with strong helicity fluctuations that persist over several correlation lengths and times. The computations of response functions indicate that asymptotic expressions for these functions, valid for k [Lt ]; k0, retain good accuracy for k ∼ k0. The mean-square magnetic field is found to grow exponentially, and its kurtosis also grows apidly with t, indicating rapid development of a highly intermittent distribution of magnetic field.

Probability tracking of a linear periodic reinforcement schedule

The prediction of Estes’ generalized statistical learning theory was verified in a condition in which probability of reinforcement was a noncontingent, linear, periodic function of trials. A strong “probability tracking” effect in which the mean response function approximated the reinforcing event function with a constant tracking “lag” was obtained as expected. An estimate of the stimulus sampling ratio, a parameter of theoretical importance, was obtained from the data.