M. J. Baines

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A new family of mathematical functions to fit longitudinal growth data is described. All members derive from the differential equation dh/dt = s(t). (h1-h) where h1 is adult size and s(t) is a function of time. The form of s(t) is given by one of many functions, all solutions of differential equations, thus generating a family of different models. Three(More)
A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations(More)
This paper discusses the problem of constructing a locally optimal mesh for the best L2 approximation of a given function by discontinuous piecewise polynomials. In the one-dimensional case, it is shown that, under certain assumptions on the approximated function, Baines’ algorithm [M. J. Baines, Math. Comp., 62 (1994), pp. 645-669] for piecewise linear or(More)
Deformable models of elastic structures have been proposed for use in image analysis. Previous work has used a variational approach, based on the EulerLagrange theory. In this paper an alternative mathematical treatment is introduced, based on a direct minimisation of the underlying energy integral using the Finite Element Method. The method is outlined and(More)
In this paper a direct variational approach (with nonstandard variations) is used to generate algorithms to determine optimal discontinuous piecewise linear and piecewise constant L2 fits to a continuous function of one or two variables with adjustable nodes. In the one-variable case the algorithm is fast and robust, the mesh cannot tangle, and the(More)
  • M J Baines
  • Clinical oncology (Royal College of Radiologists…
  • 2002
Malignant spinal cord compression is recognized as an oncological emergency. In spite of this, treatment in the U.K. varies widely from one area of the country to another. The reported survey shows that this variation is especially noticeable at weekends. Palliative care physicians and clinical nurse specialists working in the community are trained in the(More)
We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The(More)
The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this Letter, we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime, the liquid is mostly found within the grain(More)