We obtain an upper bound on the convective heat transport in a heated from below horizontal fluid layer of infinite Prandtl number with rigid lower boundary and stress-free upper boundary. Because of the asymmetric boundary conditions the solutions of the Euler-Lagrange equations of the corresponding variational problem are also asymmetric with different thicknesses of the boundary layers on th...

In this paper we combine elements of the b-calculus and elliptic boundary problems to solve the decomposition problem for the (regularized) ζ-determinant of the Laplacian on a manifold with cylindrical end into the ζ-determinants of the Laplacians with Dirichlet conditions on the manifold with boundary and on the half infinite cylinder. We also compute all the contributions to this formula expl...

Absorbing boundary conditions have been developed for various types of problems to truncate infinite domains in order to perform computations. But absorbing boundary conditions have a second, recent and important application: parallel computing. We show that absorbing boundary conditions are essential for a good performance of the Schwarz waveform relaxation algorithm applied to the wave equati...

Introduction Compared to ultrasonic bulk waves that travel in infinite media with no boundary influence, guided waves require a structural boundary for propagation. As an example, some guided wave possibilities are illustrated in Figure 1 for a Rayleigh surface wave, a Lamb wave, and a Stonely wave at an interface between two materials.

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically.The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-...

On any given compact manifold M with boundary ∂M , it is proved that the moduli space E of Einstein metrics on M , if non-empty, is a smooth, infinite dimensional Banach manifold, at least when π1(M,∂M) = 0. Thus, the Einstein moduli space is unobstructed. The usual Dirichlet and Neumann boundary maps to data on ∂M are smooth, but not Fredholm. Instead, one has natural mixed boundary-value prob...

We consider a general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the ”star-genvalue” equation and to the time evolution equation. These corrections can be cast in the form of a boundary potential contributing to the total Hamiltonian. Moreover, in this context, it is the boundary potential that...

Using singular spectral theory, a boundary-initial value problem is solved for the interfacial concentration of a surfactant on a liquid droplet oscillating in a surrounding second immiscible liquid phase. Besides being of value to the specific application the methodology of this paper is useful for a variety of boundary-initial value problems of interest to chemical engineers in which material...

A reduced shallow water model under constant, non-zero advection in the infinite channel is considered. High-order (Givoli–Neta) non-reflecting boundary conditions are introduced in various configurations to create a finite computational space and solved using a spectral element formulation with high-order time integration. Numerical examples are used to demonstrate the synergy of using high-or...