Nonuniversality and Finite Dissipation in Decaying Magnetohydrodynamic Turbulence.

A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cϵ=Cϵ,∞+C/R-+O(1/R-(2)), where R- is a generalized Reynolds number. The constant Cϵ,∞ describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of Cϵ,∞ is not universal. Direct numerical simulations were conducted on up to 2048(3) grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems.

Targeting Epilepsy Through the Foremen Ovale: How Many Helical Needles are Needed?

Laser ablation of the hippocampus offers medically refractory epilepsy patients an alternative to invasive surgeries. Emerging commercial solutions deliver the ablator through a burr hole in the back of the head. We recently introduced a new access path through the foremen ovale, using a helical needle, which minimizes the amount of healthy brain tissue the needle must pass through on its way to the hippocampus, and also enables the needle to follow the medial axis of the hippocampus more closely. In this paper, we investigate whether helical needles should be designed and fabricated on a patient-specific basis as we had previously proposed, or whether a small collection of pre-defined needle shapes can apply across many patients. We propose a new optimization strategy to determine this needle set using patient data, and investigate the accuracy with which these needles can reach the the medial axis of the hippocampus. We find that three basic tube shapes (mirrored as necessary for left vs. right hippocampi) are all that is required, across 20 patient datasets (obtained from 10 patient CT scans), to reduce worst-case maximum error below 2 mm.