A Fractional Diffusion Model for Dye-Sensitized Solar Cells.

Dye-sensitized solar cells have continued to receive much attention since their introduction by O`Regan and Grätzel in 1991. Modelling charge transfer during the sensitization process is one of several active research areas for the development of dye-sensitized solar cells in order to control and improve their performance and efficiency. Mathematical models for transport of electron density inside nanoporous semiconductors based on diffusion equations have been shown to give good agreement with results observed experimentally. However, the process of charge transfer in dye-sensitized solar cells is complicated and many issues are in need of further investigation, such as the effect of the porous structure of the semiconductor and the recombination of electrons at the interfaces between the semiconductor and electrolyte couple. This paper proposes a new model for electron transport inside the conduction band of a dye-sensitized solar cell comprising of TiO 2 as its nanoporous semiconductor. This model is based on fractional diffusion equations, taking into consideration the random walk network of TiO 2 . Finally, the paper presents numerical solutions of the fractional diffusion model to demonstrate the effect of the fractal geometry of TiO 2 on the fundamental performance parameters of dye-sensitized solar cells, such as the short-circuit current density, open-circuit voltage and efficiency.

Modelling foraging competition between solitarious and gregarious organisms in increasingly heterogeneous environments.

Density dependent phase polyphenism is the exhibiting of two or more distinct phenotypes from a single genotype depending on local population density. The most well known insect to exhibit this phenomenon is the locust, with whom the profound effect on behaviour leads to the classification of the two phases; solitarious, where locusts actively avoid other locusts, and gregarious, where locusts are strongly attracted to other locusts. It has been shown that food distributions at both small and large scales have an effect on the process of gregarisation. While gregarisation offers advantages, such as greater predator avoidance, the relationship between phase polyphenism and potential foraging benefits is still not fully understood. In this paper, we explore the effect of gregarisation on foraging within increasingly heterogeneous environments using a partial differential equation model. We first consider a single two dimensional simulation of a spatially heterogeneous environment to understand the mechanics of gregarious/solitarious foraging. We then look at the steady state foraging advantage (measured as the ratio of per-capita contact with food) in environments ranging from homogeneous to very spatially heterogeneous. Finally, we perform a parameter sensitivity analysis to find which model parameters have the greatest effect on foraging advantage. We find that during the aggregation stage, prior to the onset of marching (which we do not model here), in increasingly heterogeneous food environments it is better to be gregarious than solitarious. In addition, we find that this is intrinsic to the gregarious/solitarious behavioural dynamic as it occurs almost regardless of the model parameters. That is to say, it doesn't matter how fast the organisms disperse or how strong their long range interactions as long as there is the solitarious/gregarious behaviour the gregarious foraging advantage will exist.