It is a great pleasure for me to be asked to write this valedictory message to mark the end of my founding editorship of the European Journal of Applied Mathematics. I am tempted to follow in the discursive footsteps of one of the great founding editors, G. K. Batchelor, of the Journal of Fluid Mechanics fame. However, in accordance with our abiding efforts to keep EJAM crisp and concise, I will simply give you an ‘executive summary’ of my thoughts on what makes an applied mathematics journal successful:

There must be an integration of different styles. Applied mathematics means different things to different people around the world, and it is all too easy for one part of the culture to ignore another on the grounds of being too theoretical, too numerical or too practical. Editors must try to break down these barriers, none more than the board of EJAM, where we have always tried to give equal weight to theory and application. But even (or especially?) within Europe, this balance sometimes appears as hard to achieve as agreement about the euro.

All submissions must be read carefully by at least one editor, in addition to the referees. This is the surest way of minimizing the chances of mistaken rejection (or acceptance) and it is often vital when issues of ‘style’ arise. The reading can be painful for all concerned and I will long remember the following splendid riposte from an anguished author “I see you have eaten the referee's poisoned worm: bon appetit!”.

Along with the personal touch, there must be just the right degree of continuity with which authors can readily identify. Any editorial board striving to promote a particular intellectual policy will invariably have a degree of commonality of interests, and hence a continuity of theme. But this brings the danger of tunnel vision. To balance this, there is a need for a regular and imaginative turnover of board members, and this is an activity with which Cambridge University Press has been most helpful over the years.

Last, but by no means least, is the mandatory requirement that there be an understanding and unfailingly cheerful editorial assistant. This is another respect in which CUP's enlightened attitude has benefited several of their journals, and our authors and editors alike have strong reasons to be thankful to Angela Howard. We are delighted that she will stay on for a few years at least.

We consider periodic solutions which bifurcate from equilibria in simple population models which incorporate a state-dependent time delay of the discrete kind. The delay is a function of the current size of the population. Solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. The stability of the bifurcating solutions depends on the qualitative form of the delay function. This is in contrast to the stability of an equilibrium, which is determined purely by the actual value of this function at the equilibrium.

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

We study the interactions between a nematic liquid crystal disclination and the surface of the half-space which bounds it. When strong anchoring conditions are applied on the boundary, the biaxial core of the disclination affects the repulsive force that tends to drive the disclination away from the surface. If we replace the strong boundary conditions with an anchoring potential, the surface-disclination interaction depends on the surface extrapolation length. In particular, the nematic may expel the disclination if the anchoring strength is below a critical value.

The homogenization problem is considered for the equations of two-phase flow in porous media with a periodic or random small-scale structure of inhomogeneities. The capillary relation between saturation and the drop in pressures at microscales accounts for hysteresis and dynamic memory effects. Homogenized equations are derived, and convergence of solutions to the solution of the homogenized problem is proved. Properties of averaged capillary relation are described in the particular case of a two-component porous medium.

For a pattern-forming system with two unbounded spatial directions that is near the onset to instability, we prove the existence of modulated fronts that connect (i) stable hexagons with the unstable trivial pattern, (ii) stable hexagons with unstable roll solutions, (iii) stable hexagons with unstable hexagons, and (iv) stable roll solutions with unstable hexagons. Our approach is based on spatial dynamics, bifurcation theory, and geometric singular perturbation theory.

The standard scales that are used to non-dimensionalize the temperature- and time-dependent Ginzburg–Landau (TTDGL) model developed by Schmid [27], eliminate temperature- dependent parameters, and thus do not allow for superconducting phenomena due to variations in temperature. In this study, a set of new scales is presented to non-dimensionalize the TTDGL model so that the resulting dimensionless system depends upon a temperature parameter as well. Moreover, some properties of solutions to TTDGL system as a function of temperature are explored. Numerical experiments illustrating the temperature-dependency of vortex nucleation in type-II superconductors as well as the transition to the Meissner state in type-I superconductors are presented.