Thermodynamics of MHD flows with axial symmetry

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation

Misconceptions About Incline Speed for Nonlinear Slopes

In 3 experiments, college students provided qualitative predictions about a marble\u27s speed along nonlinear inclines. When predicting the outcome of a race between identical marbles along differently shaped ramps, most students predicted incorrectly that the shorter path was necessarily quicker (the shorter-quicker belief). When comparing instantaneous speed at 2 points, most students predicted incorrectly that incline speed depended on the slope at that point (the slope-speed belief). A final experiment provides evidence that the slope-speed belief reflects a deeper fallacy regarding the resistance encountered while traversing inclines and lifting objects. This fallacy also predicts the prevalent belief that heavier objects fall faster than lighter objects during incline descent or free fall