An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Motivating domestic energy conservation through comparative, community-based feedback in mobile and social media

The progress of technology has led to the increased adoption of energy monitors among household energy consumers. While the monitors available on the market deliver real-time energy usage feedback to the consumer, the format of this data is usually unengaging and mundane. Moreover, it fails to address consumers with different motivations and needs to save and compare energy. This paper presents a study that seeks to provide initial indications for motivation-specific design of energy-related feedback. We focus on comparative feedback supported by a community of energy consumers. In particular, we examine eco-visualisations, temporal self-comparison, norm comparison, one-on-one comparison and ranking, whereby the last three allow us to explore the potential of socialising energy-related feedback. These feedback types were integrated in EnergyWiz – a mobile application that enables users to compare with their past performance, neighbours, contacts from social networking sites and other EnergyWiz users. The application was evaluated in personal, semi-structured interviews, which provided first insights on how to design motivation-related comparative feedback.

Prioritizing land and sea conservation investments to protect coral reefs

Background: Coral reefs have exceptional biodiversity, support the livelihoods of millions of people, and are threatened by multiple human activities on land (e.g. farming) and in the sea (e.g. overfishing). Most conservation efforts occur at local scales and, when effective, can increase the resilience of coral reefs to global threats such as climate change (e.g. warming water and ocean acidification). Limited resources for conservation require that we efficiently prioritize where and how to best sustain coral reef ecosystems.----- ----- Methodology/Principal Findings: Here we develop the first prioritization approach that can guide regional-scale conservation investments in land-and sea-based conservation actions that cost-effectively mitigate threats to coral reefs, and apply it to the Coral Triangle, an area of significant global attention and funding. Using information on threats to marine ecosystems, effectiveness of management actions at abating threats, and the management and opportunity costs of actions, we calculate the rate of return on investment in two conservation actions in sixteen ecoregions. We discover that marine conservation almost always trumps terrestrial conservation within any ecoregion, but terrestrial conservation in one ecoregion can be a better investment than marine conservation in another. We show how these results could be used to allocate a limited budget for conservation and compare them to priorities based on individual criteria.----- ----- Conclusions/Significance: Previous prioritization approaches do not consider both land and sea-based threats or the socioeconomic costs of conserving coral reefs. A simple and transparent approach like ours is essential to support effective coral reef conservation decisions in a large and diverse region like the Coral Triangle, but can be applied at any scale and to other marine ecosystems.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy