We report on a three-dimensional direct numerical simulation study of flow structure and heat transport in the annular centrifugal Rayleigh-Bdnard convection (ACRBC) system, with cold inner and hot outer cylinders corotating axially, for the Rayleigh number range Ra is an element of [10(6), 10(8)] and radius ratio range eta = R-i/R-o is an element of [0.3, 0.9] (R-i and R-o are the radius of the inner and outer cylinders, respectively). This study focuses on the dependence of flow dynamics, heat transport and asymmetric mean temperature fields on the radius ratio eta. For the inverse Rossby number Ro(-1) = 1, as the Coriolis force balances inertial force, the flow is in the inertial regime. The mechanisms of zonal flow revolving in the prograde direction in this regime are attributed to the asymmetric movements of plumes and the different curvatures of the cylinders. The number of roll pairs is smaller than the circular roll hypothesis as the convection rolls are probably elongated by zonal flow. The physical mechanism of zonal flow is verified by the dependence of the drift frequency of the large-scale circulation (LSC) rolls and the space- and time-averaged azimuthal velocity on eta. The larger eta is, the weaker the zonal flow becomes. We show that the heat transport efficiency increases with eta. It is also found that the bulk temperature deviates from the arithmetic mean temperature and the deviation increases as eta decreases. This effect can be explained by a simple model that accounts for the curvature effects and the radially dependent centrifugal force in ACRBC.

We introduce the notion of pseudo-N´eron model and give new examples of varieties admitting pseudo-N´eron models other than Abelian varieties. As an application of pseudo-N´eron models, given a scheme admitting a finite morphism to an Abelian scheme over a positive-dimensional base, we prove that for a very general genus-0, degree-d curve in the base with d sufficiently large, every section of the scheme over the curve is contained in a unique section over the entire base.

Flow reversals in two-dimensional Rayleigh-Benard convection led by non-Oberbeck-Boussinesq (NOB) effects due to large temperature differences arc studied by direct numerical simulation. Perfect gas is chosen as the working fluid and the Prandtl number is 0.71 for the reference state. 11 NOB effects are included, the flow pattern P-11 with only one dominant roll often becomes unstable by the growth of the cold corner roll, which sometimes results in cession-led flow reversals. By exploiting the vorticity transport equation, it is found that the asymmetries of buoyancy and viscous forces are responsible for the growth of the cold corner roll because both such asymmetries cause an imbalance between the corner rolls and the large-scale circulation (I.SC). The buoyancy force near the cold wall increases and decreases near the hot wall originating from the temperature-dependent isobaric thermal expansion coefficient alpha = 1/T if NOB effects are included; Moreover, the decreased dissipation due to lower viscosity is favourable for the growth of the cold corner roll, while the increased viscosity further suppresses the growth of the hot corner roll. Finally, it is found that the boundary layer near the cold wall plays an important role in the mass transport from LSC to corner rolls subject to mass conservation.

In this work, we show that for a certain class of threefolds in positive characteristics, rational-chain-connectivity is equivalent to supersingularity. The same result is known for K3 surfaces with elliptic fibrations. And there are examples of threefolds that are both supersingular and rationally chain connected.

For a fixed geometric configuration, hydrodynamic instabilities and bifurcation processes of laminar isothermal planar opposed jet flows with symmetric and slightly asymmetric inlet boundary conditions are investigated numerically using a high-resolution approach based on spectral element method. In current configuration, when inlet boundary conditions are symmetric, in the range of the Reynolds number considered (Re <= 200), multiple new symmetry-breaking bifurcations are observed and four new flow patterns are identified. Their hydrodynamic characteristics are analyzed, in particular their symmetries. In addition, the case that inlet boundary conditions are slightly asymmetric is investigated. It is found that bifurcation processes are extremely sensitive to this small symmetry-breaking imperfection and much different from those in the symmetric case. Furthermore, model equations are constructed by symmetry consideration to explain the numerical results based on hydrodynamic equations.