An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfa...

Abstract Study aim : The study aimed to assess the differences in magnitude of anterior-posterior spinal curvatures depending on sex children aged 5 and 9 years. Material method s: This prospective longitudinal observational included 67 (29 girls 38 boys) pre-school-age school-age phases (the first examination at years old second old). Measurements body weight height were recorded. computerized...

We study principal curvatures of fibers and Heeagaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minimally embedded fiber or Heegaard surface and a lower bound on the injectivity...

Suppose that S is given a generic Riemannian metric with sectional curvatures which satisfy a suitable pinching condition formulated in terms of complex sectional curvatures. This pinching condition is satisfied by manifolds whose real sectional curvatures Kr(σ) satisfy 1/2 < Kr(σ) ≤ 1. Then the number of minimal two spheres of Morse index λ, for n − 2 ≤ λ ≤ 2n− 6, is at least p3(λ− n+ 2), wher...

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces’ areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature.We dis...