Given a velocity field u(x,t), we consider the evolution of passive tracer θ governed by ∂tθ+u⋅∇θ=Δθ+g with time-independent source g(x). When u is small in some sense, Batchelor, Howells and Townsend (Batchelor et al., 1959) predicted that spectrum scales as |θk|2∝|k|−4|uk|2. Following our recent work for two-dimensional case, this paper prove BHT59 scaling does hold probabilistically, asympto...

Introduction: Diffusion MRI was the first imaging modality to allow the visualization of white matter fibre paths in vivo, and non-invasively. The process by which the white matter tracts are reconstructed from diffusion tensor data is called tractography. Tensor interpolation methods have often been used to improve the reproducibility and reliability of tractography results (e.g [1]). In this ...

In this issue of the Journal, Batchelor et al. (1) compare the diagnostic yield of coronary angiography in the U.S. and Canadian patients enrolled in the Global Use of Strategies to Open Occluded Arteries in Acute Coronary Syndromes (GUSTO-1) trial. They defined yield as severe coronary artery disease (CAD), more specifically left-main or threevessel disease. The rates of angiography on the ind...

The similarity form of the scalar-variance spectrum at high Schmidt numbers is investigated for nonstationary turbulence. Theoretical arguments show that Batchelor scaling may apply only at high Reynolds numbers. At low Reynolds numbers, Batchlor scaling is not possible unless the turbulence is stationary or the enstrophy decays asymptotically as t. When this latter condition is satisfied, it i...

Our understanding of turbulent boundary layer scaling and structure has advanced greatly in the past 20 to 30 years. On computational side, direct numerical simulations large-eddy have made extraordinary contributions as methods resources advanced, while on experimental side major advances instrumentation available new imaging quantitative techniques that provide unprecedented accuracy detail. ...