On the competition of anti-lift-up mechanism and Reynolds stress mechanism in Spiral Poiseuille flow

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in Spiral Poiseuille flow (SPF). The Poiseuille number [Formula: see text], representing the dimensionless axial pressure gradient, is varied from 0 to 20,000. The results show that for the axisymmetric case, with the increase of axial shear, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the inner cylinder, and a second peak appears near the outer cylinder for both velocity components. Viewing the time evolution of azimuthal shear contribution [Formula: see text] and axial shear contribution [Formula: see text] to the kinetic energy growth of the optimal perturbation, while [Formula: see text] is large enough ([Formula: see text], 20,000), the Reynolds stress mechanism in the meridional plane [Formula: see text] is dominant for the transient growth behavior in SPF relative to anti-lift-up mechanism, which is dominant in the absence of axial flow for co-rotating Taylor–Couette flow with wide gap. For the oblique mode with azimuthal wave number [Formula: see text], which becomes the optimal azimuthal mode over a wide range of azimuthal wave number ([Formula: see text]–10) when [Formula: see text] is large enough, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the outer cylinder, opposite to the axisymmetric case.

Modeling of Stiffness and Strength of Bone at Nanoscale

Two distinct geometrical models of bone at the nanoscale (collagen fibril and mineral platelets) are analyzed computationally. In the first model (model I), minerals are periodically distributed in a staggered manner in a collagen matrix while in the second model (model II), minerals form continuous layers outside the collagen fibril. Elastic modulus and strength of bone at the nanoscale, represented by these two models under longitudinal tensile loading, are studied using a finite element (FE) software abaqus. The analysis employs a traction-separation law (cohesive surface modeling) at various interfaces in the models to account for interfacial delaminations. Plane stress, plane strain, and axisymmetric versions of the two models are considered. Model II is found to have a higher stiffness than model I for all cases. For strength, the two models alternate the superiority of performance depending on the inputs and assumptions used. For model II, the axisymmetric case gives higher results than the plane stress and plane strain cases while an opposite trend is observed for model I. For axisymmetric case, model II shows greater strength and stiffness compared to model I. The collagen–mineral arrangement of bone at nanoscale forms a basic building block of bone. Thus, knowledge of its mechanical properties is of high scientific and clinical interests.

Icosahedral Symmetry and Quantum Gravity

In this note we will show that Theta functions are a solution of the icosahedron equation and also a solution of the Ernst equation for the stationary axisymmetric case of Einstein’s gravitational equation.

Two-dimensional planar plumes: non-Boussinesq effects

In an accompanying paper (van den Bremer & Hunt, J. Fluid Mech., vol. 750, 2014, pp. 210–244) closed-form solutions, describing the behaviour of two-dimensional planar turbulent rising plumes from horizontal planar area and line sources in unconfined quiescent environments of uniform density, that are universally applicable to Boussinesq and non-Boussinesq plumes, are proposed. This universality relies on an entrainment velocity unmodified by non-Boussinesq effects, an assumption that is derived in the literature based on similarity arguments and is, in fact, in contradiction with the axisymmetric case, in which entrainment is modified by non-Boussinesq effects. Exploring these solutions, we show that a non-Boussinesq plume model predicts exactly the same behaviour with height for a pure plume as would a Boussinesq model, whereas the effects on forced and lazy plumes are opposing. Non-intuitively, the non-Boussinesq model predicts larger fluxes of volume and mass for lazy plumes, but smaller fluxes for forced plumes at any given height compared to the Boussinesq model. This raises significant questions regarding the validity of the unmodified entrainment model for planar non-Boussinesq plumes based on similarity arguments and calls for detailed experiments to resolve this debate.