Boundary-layer receptivity for a parabolic leading edge

The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius, rn, enters the theory through a Strouhal number, S = ?rn/U, where ? is the frequency of the acoustic wave and U is the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord

Mean drift forces on arrays of bodies due to incident long waves

The scattering of long water waves by an array of bodies is investigated using the method of matched asymptotic expansions. Two particular geometries are considered, these are a group of vertical cylinders extending throughout the depth and a group of floating hemispheres. From these solutions, the low-frequency limit of the ratio of the mean drift force on a group of N bodies to that on a single body is calculated. For a wide range of circumstances this drift force ratio is N2 which is in agreement with previous numerical work. Further drift force enhancement is possible for certain configurations of vertical cylinders

On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy

This version deposited at arxiv 02-10-12 arXiv:1210.0730v1. Subsequently published in Physical Review D as Phys. Rev. D 87, 063517 (2013) http://link.aps.org/doi/10.1103/PhysRevD.87.063517. Copyright American Physical Society (APS).11 pages11 pages11 pages11 pagesThe problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems may not be compatible with late-time acceleration driven by anything other than a constant term of the form f(0), which acts like a cosmological constant. For theories with f(R)=R^n we find that no known spherically symmetric vacuum solutions can be matched to an expanding FLRW background. This includes the absence of any Einstein-Straus-like embeddings of the Schwarzschild exterior solution in FLRW spacetimes

Sharp interface limits of phase-field models

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface limit'' from phase field models which have interfaces that are diffuse on a length scale $\xi$. In particular,phase-field equations are mapped onto sharp interface equations in the limits $\xi \kappa \ll 1$ and $\xi v/D \ll 1$, where $\kappa$ and $v$ are respectively the interface curvature and velocity and $D$ is the diffusion constant in the bulk. The calculations provide one general set of sharp interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation and the Kardar-Parisi-Zhang equation.Comment: 17 pages, 9 figure

Sharp interface limits of phase-field models

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the ``sharp interface limit'' from phase field models which have interfaces that are diffuse on a length scale $\xi$. In particular,phase-field equations are mapped onto sharp interface equations in the limits $\xi \kappa \ll 1$ and $\xi v/D \ll 1$, where $\kappa$ and $v$ are respectively the interface curvature and velocity and $D$ is the diffusion constant in the bulk. The calculations provide one general set of sharp interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation and the Kardar-Parisi-Zhang equation.Comment: 17 pages, 9 figure