We derive upper bounds for the Nusselt number in innnite Prandtl-number rotating convection. The bounds decay algebraically with Taylor number to the conductive heat transport value; the decay rate depends on boundary conditions. We show moreover that when the rotation is fast enough the purely conductive solution is the globally and nonlinearly attractive xed point; the critical rotation rate ...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

We consider the initial-boundary value problem of two-dimensional inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary. Under slip boundary condition of velocity and the homogeneous Dirichlet boundary condition for temperature, we show that there exists a unique global smooth solution to the initial-boundary value problem for H i...

The existence and stability of travelling waves are typically investigated on unbounded domains even though the domains in experiments or numerical simulations are bounded. We are interested in the eeects that the truncation of the unbounded to a large but bounded domain has on the stability properties of a nonlinear wave. These eeects depend upon the boundary conditions that are imposed on the...

Grain rotation is a well-known phenomenon during high (homologous) temperature deformation and recrystallization of polycrystalline materials. In recent years, grain rotation has also been proposed as a plasticity mechanism at low temperatures (for example, room temperature for metals), especially for nanocrystalline grains with diameter d less than ~15 nm. Here, in tensile-loaded Pt thin films...

Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fixed-parameter tractable, in the parameter, k, the rotation distance. The proof relies on the kern...