Context. Supersonic turbulence is ubiquitous in the interstellar medium and plays an important role in contemporary star formation. Aims. We performed high-resolution numerical simulations of supersonic isothermal turbulence driven by compressive large-scale forcing and analyse various statistical properties. Methods. The compressible Euler equations with an external stochastic force field dominated by rotation-free modes are solved with the piecewise parabolic method. Both a static grid and adaptive mesh refinement is used with an effective resolution N = 768 3 . Results. After a transient phase dominated by shocks, turbulence evolves into a steady state with root mean square Mach number ≈2.5, in which cloud-like structures of over-dense gas are surrounded by highly rarefied gas. The index of the turbulence energy spectrum function is β ≈ 2.0 in the shock-dominated phase. As the flow approaches statistical equilibrium, the spectrum flattens, with β ≈ 1.9. For the scaling exponent of the root mean square velocity fluctuation, we obtain γ ≈ 0.43 from the velocity structure functions of second order. These results are well within the range of observed scaling properties for the velocity dispersion in molecular clouds. Calculating structure functions of order p = 1, . . . , 5, we find significant deviations from the Kolmogorov-Burgers model proposed by Boldyrev for all scaling exponents. Our results are very well described by a general log-Poisson model with a higher degree of intermittency, which implies an influence by the forcing on the scaling properties. The spectral index of the quadratic logarithmic density fluctuation is β δ ≈ 1.8. In contrast to previous numerical results for isothermal turbulence, we obtain a skewed probability density function of the mass density fluctuations that is not consistent with log-normal statistics and entails a substantially higher fraction of mass in the density peaks than implied by the Padoan-Nordlund relation between the variance of the density fluctuations and the Mach number. Conclusions. Even putting aside further complexity due to magnetic fields, gravity, or thermal processes, we question the notion that Larson-type relations are a consequence of universal supersonic turbulence scaling. For a genuine understanding, it seems necessary to account for the production mechanism of turbulence in the ISM.

ObjectiveTo quantify atrophy, demyelination, and iron accumulation over 2 years following acute spinal cord injury and to identify MRI predictors of clinical outcomes and determine their suitability as surrogate markers of therapeutic intervention.MethodsWe assessed 156 quantitative MRI datasets from 15 patients with spinal cord injury and 18 controls at baseline and 2, 6, 12, and 24 months after injury. Clinical recovery (including neuropathic pain) was assessed at each time point. Between-group differences in linear and nonlinear trajectories of volume, myelin, and iron change were estimated. Structural changes by 6 months were used to predict clinical outcomes at 2 years.ResultsThe majority of patients showed clinical improvement with recovery stabilizing at 2 years. Cord atrophy decelerated, while cortical white and gray matter atrophy progressed over 2 years. Myelin content in the spinal cord and cortex decreased progressively over time, while cerebellar loss decreases decelerated. As atrophy progressed in the thalamus, sustained iron accumulation was evident. Smaller cord and cranial corticospinal tract atrophy, and myelin changes within the sensorimotor cortices, by 6 months predicted recovery in lower extremity motor score at 2 years. Whereas greater cord atrophy and microstructural changes in the cerebellum, anterior cingulate cortex, and secondary sensory cortex by 6 months predicted worse sensory impairment and greater neuropathic pain intensity at 2 years.ConclusionThese results draw attention to trauma-induced neuroplastic processes and highlight the intimate relationships among neurodegenerative processes in the cord and brain. These measurable changes are sufficiently large, systematic, and predictive to render them viable outcome measures for clinical trials.