Steady two-dimensional free surface flow past a semi-infinite flat plate is considered. The vorticity in the flow is assumed to be constant. For large values of the Froude number F, an analytical relation between F, the vorticity parameter ω and the steepness s of the waves in the far field is derived. In addition numerical solutions are calculated by a boundary integral equation method.

We consider the effect the competing mechanisms of buoyancy-driven acceleration (arising from heating a surface) and streamline curvature (due to curvature of a surface) have on the stability of boundary-layer flows. We confine our attention to vortex type instabilities (commonly referred to as Görtler vortices) which have been identified as one of the dominant mechanisms of instability in both centrifugally and buoyancy driven boundary layers. The particular model we consider consists of the boundary-layer flow over a heated (or cooled) curved rigid body. In the absence of buoyancy forcing the flow is centrifugally unstable to counter-rotating vortices aligned with the direction of the flow when the curvature is concave (in the fluid domain) and stable otherwise. Heating the rigid plate to a level sufficiently above the fluid's ambient (free-stream) temperature can also serve to render the flow unstable. We determine the level of heating required to render an otherwise centrifugally stable flow unstable and likewise, the level of body cooling that is required to render a centrifugally unstableflow stable.

This paper considers a cell population model with a general maturation rate. This model is described by a nonlinear PDE. We use the theory of operator semigroups to stud the problem under simple hypotheses on the growth function and the nonlinear term. By showing that a related operator generates a strongly continuous semigroup, we prove the existence of a classical solution of the nonlinear problem and its positivity. It is also proved that under simple hypotheses, the problem generates a semiflow. The invariance of the semiflow is studied as well.

A rapid spherical harmonic calculation method is used for the design of Nuclear Magnetic Resonance shim coils. The aim is to design each shim such that it generates a field described purely by a single spherical harmonic. By applying simulated annealing techniques, coil arrangements are produced through the optimal positioning of current-carrying circular arc conductors of rectangular cross-section. This involves minimizing the undesirable harmonics in relation to a target harmonic. The design method is flexible enough to be applied for the production of coil arrangements that generate fields consisting significantly of either zonal or tesseral harmonics. Results are presented for several coil designs which generate tesseral harmonics of degree one.

In this paper we use classical linear stability theory to analyse the onset of steady and oscillatory Bénard-Marangoni convection in a horizontal layer of fluid in the more physically-relevant case when both the non-dimensional Rayleigh and Marangoni numbers are linearly dependent. We present examples of situations in which there is competition between modes at the onset of convection when the layer is heated from below.

In this article, we use the method of Foias and Temam to show that the strong solutions of the time-dependent magnetohydrodynamics equations in a periodic domain are analytic in time with values in a Gevrey class of functions. As immediate corollaries we find that the solutions are analytic in Hr-norms and that the solutions become smooth immediately after the initial time.

We consider the nonlinear evolution of a disturbance to a mixing layer, with the base profile given by u0(y) = tanh3y rather than the more usual tanh y, so that the first two derivatives of u0 vanish at y = 0. This flow admits three neutral modes, each of which is singular at the critical layer. Using a non-equilibrium nonlinear critical layer analysis, equations governing the evolution of the disturbance are derived and discussed. We find that the disturbance cannot exist on a linear basis, but that nonlinear effects inside the critical layer do permit the disturbance to exist. We also present results of a direct numerical simulation of this flow and briefly discuss the connection between the theory and the simulation.

A numerical method for calculation of the generalized Chakalov-Popoviciu quadrature formulae of Radau and Lobatto type, using the results given for the generalized Chakalov-Popoviciu quadrature formula, is given. Numerical results are included. As an application we discuss the problem of approximating a function f on the finite interval I = [a, b] by a spline function of degree m and variable defects dv, with n (variable) knots, matching as many of the initial moments of f as possible. An analytic formula for the coefficients in the generalized Chakalov-Popoviciu quadrature formula is given.

We show that a sequence of generalized eigenfunctions of a one-dimensional linear thermoelastic system with Dirichiet-Dirichlet boundary conditions forms a Riesz basis for the state Hilbert space. This develops a parallel result for the same system with Dirichlet-Neumann or Neumann-Dirichlet boundary conditions.