Related papers: Algebraic Bounds on the Rayleigh-B\'enard attracto…
The dynamics of heat transfer in a model system of Rayleigh-B\'enard (RB) convection reduced to its essential, here dubbed Burgers-Rayleigh-B\'enard (BRB), is studied. The system is spatially one-dimensional, the flow field is compressible…
A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a p-form field strength. This requires the introduction of appropriate surface terms -- also known as `boundary counterterms' -- in the…
This article is concerned with the second boundary value problem of the Lagrangian mean curvature type equation arising from special Lagrangian geometry. By the parabolic method, we consider a fully nonlinear parabolic equation with oblique…
We use Ratner's theorem to compute the asymptotics of the number of (cylinders of) periodic trajectories in a rectangle with a barrier, assuming that the location p/q of the barrier is rational. We also show that as q tends to infinity, the…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
Bounds for the poloidal and toroidal kinetic energies and the heat transport are computed numerically for rotating convection at infinite Prandtl number with both no slip and stress free boundaries. The constraints invoked in this…
In this second work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations with Dirichlet boundary data on a finite timelike boundary, provided the Brown-York stress tensor of the boundary is a…
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \rightarrow \infty$, and find that the form of the boundary stress tensor is the…
Inertialess anisotropic particles in a Rayleigh-B\'enard turbulent flow show maximal tumbling rates for weakly oblate shapes, in contrast with the universal behaviour observed in developed turbulence where the mean tumbling rate…
Numerical simulations of rotating Rayleigh-B\'enard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly…
The effect of a perfectly conducting planar boundary on the average linear momentum (LM), angular (momentum (AM), and power of a time-harmonic statistically isotropic random field is analyzed. These averages are purely imaginary and their…
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…
We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma--vacuum interface. We establish the…
We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…
We study a viscous two-layer quasi-geostrophic beta-plane model that is forced by imposition of a spatially uniform vertical shear in the eastward (zonal) component of the layer flows, or equivalently a spatially uniform north-south…
We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical sample with aspect ratio (diameter over height) of 0.50, both in the classical and in the…
Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…
We argue that a natural boundary condition for gravity in asymptotically AdS spaces is to hold the {\em renormalized} boundary stress tensor density fixed, instead of the boundary metric. This leads to a well-defined variational problem, as…
We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion…