A comparative study on applying the method of fundamental solutions to the backward heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the backward heat conduction problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct heat conduction problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

A method of fundamental solutions for transient heat conduction in layered materials

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction in layered materials, where the thermal diffusivity is piecewise constant. Recently, in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction. Eng Anal Boundary Elem 2008;32:697–703], a MFS was proposed with the sources placed outside the space domain of interest, and we extend that technique to numerically approximate the heat flow in layered materials. Theoretical properties of the method, as well as numerical investigations are included.

The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.

Method of detecting a significant change of scene

A significant change of scene in a gradually changing scene is detected with the aid of a least one camera means for capturing digital images of the scene. A current image of the scene is formed together with a present weighted reference image which is formed from a plurality of previous images of the scene. Cell data is established based on the current image and the present weighted reference image. The cell data is statistically analysed so as to be able to identify at least one difference corresponding to a significant change of scene. When identified, an indication of such significant change of scene is provided.

A transient method of measuring thermal contact conductance between metal-plastic surfaces

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Some obstacles to the establishment of a universal method of education for parenthood by the P.N.E.U

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Comparison of a preferred and actual method of selecting and implementing computerised control systems in a manufacturing environment

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Evaluation of the activity and stability of alkali-doped metal oxide catalysts for application to an intensified method of biodiesel production

A series of alkali-doped metal oxide catalysts were prepared and evaluated for activity in the transesterification of rapeseed oil to biodiesel. Of those evaluated, LiNO3/CaO, NaNO3/CaO, KNO3/CaO and LiNO3/MgO exhibited >90% conversion in a standard 3 h test. There was a clear correlation between base strength and activity. These catalysts appeared to be promising candidates to replace conventional homogeneous catalysts for biodiesel production as the reaction times are low enough to be practical in continuous processes and the preparations are neither prohibitively difficult nor costly. However, metal leaching from the catalyst was detected, and this resulted in some homogeneous activity. This would have to be resolved before these catalysts would be viable for large-scale biodiesel production facilities.

Structure of dysprosium and holmium phosphate glasses by the method of isomorphic substitution in neutron diffraction

The relative distribution of rare-earth ions R3+ (Dy3+ or Ho3+) in the phosphate glass RAl0.30P3.05O9.62 was measured by employing the method of isomorphic substitution in neutron diffraction and, by taking the role of Al into explicit account, a self-consistent model of the glass structure was developed. The glass network is found to be made from corner sharing PO4 tetrahedra in which there are, on average, 2.32(9) terminal oxygen atoms, OT, at 1.50(1) Å and 1.68(9) bridging oxygen atoms, OB, at 1.60(1) Å. The network modifying R3+ ions bind to an average of 6.7(1) OT and are distributed such that 7.9(7) R–R nearest neighbours reside at 5.62(6) Å. The Al3+ ion also has a network modifying role in which it helps to strengthen the glass through the formation of OT–Al–OT linkages. The connectivity of the R-centred coordination polyhedra in (M2O3)x(P2O5)1−x glasses, where M3+ denotes a network modifying cation (R3+ or Al3+), is quantified in terms of a parameter fs. Methods for reducing the clustering of rare-earth ions in these materials are then discussed, based on a reduction of fs via the replacement of R3+ by Al3+ at fixed total modifier content or via a change of x to increase the number of OT available per network modifying M3+ cation.

Structure of lanthanum and cerium phosphate glasses by the method of isomorphic substitution in neutron diffraction

Neutron diffraction was used to measure the total structure factors for several rare-earth ion R3+ (La3+ or Ce3+) phosphate glasses with composition close to RAl0.35P3.24O10.12. By assuming isomorphic structures, difference function methods were employed to separate, essentially, those correlations involving R3+ from the remainder. A self-consistent model of the glass structure was thereby developed in which the Al correlations were taken into explicit account. The glass network was found to be made from interlinked PO4 tetrahedra having 2.2(1) terminal oxygen atoms, OT, at 1.51(1) Angstrom, and 1.8(1) bridging oxygen atoms, OB, at 1.60(1) Angstrom. Rare-earth cations bonded to an average of 7.5(2) OT nearest neighbors in a broad and asymmetric distribution. The Al3+ ion acted as a network modifier and formed OT-A1-OT linkages that helped strengthen the glass. The connectivity of the R-centered coordination polyhedra was quantified in terms of a parameter f(s) and used to develop a model for the dependence on composition of the A1-OT coordination number in R-A1-P-O glasses. By using recent 17 A1 nuclear-magnetic-resonance data, it was shown that this connectivity decreases monotonically with increasing Al content. The chemical durability of the glasses appeared to be at a maximum when the connectivity of the R-centered coordination polyhedra was at a minimum. The relation of f(s) to the glass transition temperature, Tg, was discussed.