A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.

Dancing into the second phase of creative industries

As we enter the second phase of creative industries there is a shift away from the early 1990s ideology of the arts as a creative content provider for the wealth generating ‘knowledge’ economy to an expanded rhetoric encompassing ‘cultural capital’ and its symbolic value. A renewed focus on culture is examined through a regional scan of creative industries in which social engineering of the arts occurs through policy imperatives driven by ‘profit oriented conceptualisations of culture’ (Hornidge 2011, p. 263) In the push for artists to become ‘culturpreneurs’ a trend has emerged where demand for ‘embedded creatives’ (Cunningham 2013) sees an exodus from arts-based employment through use of transferable skills into areas outside the arts. For those that stay, within the performing arts in particular, employment remains project-based, sporadic, underpaid, self-initiated and often self-financed, requiring adaptive career paths. Artist entrepreneurs must balance creation and performance of their art with increasing amounts of time spent on branding, compliance, fundraising and the logistical and commercial requirements of operating in a CI paradigm. The artists’ key challenge thus becomes one of aligning core creative and aesthetic values with market and business considerations. There is also the perceived threat posed by the ‘prosumer’ phenomenon (Bruns 2008), in which digital on-line products are created and produced by those formerly seen as consumers of art or audiences for art. Despite negative aspects to this scenario, a recent study (Steiner & Schneider 2013) reveals that artists are happier and more satisfied than other workers within and outside the creative industries. A lively hybridisation of creative practice is occurring through mobile and interactive technologies with dynamic connections to social media. Continued growth in arts festivals attracts participation in international and transdisciplinary collaborations, whilst cross-sectoral partnerships provide artists with opportunities beyond a socio-cultural setting into business, health, science and education. This is occurring alongside a renewed engagement with place through the rise of cultural precincts in ‘creative cities’ (Florida 2008, Landry 2000), providing revitalised spaces for artists to gather and work. Finally, a reconsideration of the specialist attributes and transferable skills that artists bring to the creative industries suggests ways to dance through both the challenges and opportunities occasioned by the current complexities of arts’ practices.