Ourplace : the convergence of locative media and online participatory culture

The trans-locative potential of the Internet has driven the design of many online applications. Online communities largely cluster around topics of interest, which take precedence over participants’ geographical locations. The site of production is often disregarded when creative content appears online. However, for some, a sense of place is a defining aspect of creativity. Yet environments that focus on the display and sharing of regionally situated content have, so far, been largely overlooked. Recent developments in geo-technologies have precipitated the emergence of a new field of interactive media. Entitled locative media, it emphasizes the geographical context of media. This paper argues that we might combine practices of locative media (experiential mapping and geo-spatial annotation) with aspects of online participatory culture (uploading, file-sharing and search categorization) to produce online applications that support geographically ‘located’ communities. It discusses the design considerations and possibilities of this convergence,making reference to an example, OurPlace 3G to 3D, which has to date been developed as a prototype.1 It goes on to discuss the benefits and potential uses of such convergent applications, including the co-production of spatial- emporal narratives of place.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.