Threshold games and cooperation on multiplayer graphs

Objective: The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured - i.e. when a given individual is only competing with a small subset of the entire population. Method: To optimize the focus on multiplayer effects, a class of games were chosen for which the payoff depends nonlinearly on the number of cooperators - this ensures that the game cannot be represented as a sum of pair-wise interactions, and increases the likelihood of observing behaviour different from that seen in two-player games. The chosen class of games are named "threshold games", and are defined by a threshold, $M > 0$, which describes the minimal number of cooperators in a given match required for all the participants to receive a benefit. The model was studied primarily through numerical simulations of large populations of individuals, each with interaction neighbourhoods described by various classes of networks. Results: When comparing the level of cooperation in a structured population to the mean-field model, we find that most types of structure lead to a decrease in cooperation. This is both interesting and novel, simply due to the generality and breadth of relevance of the model - it is likely that any model with similar payoff structure exhibits related behaviour. More importantly, we find that the details of the behaviour depends to a large extent on the size of the immediate neighbourhoods of the individuals, as dictated by the network structure. In effect, the players behave as if they are part of a much smaller, fully mixed, population, which we suggest an expression for.Comment: in PLOS ONE, 4th Feb 201

Fatigue damage evolution in quasi-unidirectional non-crimp fabric based composite materials for wind turbine blades

The fatigue failure of wind turbine blades is controlled by failure mechanisms on multiple scales spanning single fiber fatigue failure at the sub-micron scale, over the fiber bundle structure on the millimeter scale to the quasi-unidirectional non-crimp fabric on the meter scale. At the smaller scales, the 3D x-ray computertomography technique is used non-destructive to observe the fatigue damage evolution on the fiber and bundle scale. Those observations are then linked to the larger scales through mechanical testing of representative volumes of the non-crimp fabric bundle structure. Numerically, those non-crimp fabric bundle structures extracted from the 3D x-ray scans can be used in a multi-scale based finite element models used for understanding the parameters controlling the fatigue damage evolutions. During tensiontension fatigue testing, the damage mechanism is shown to be controlled by local architecture of the socalled backing bundle structure present in the non-crimp fabric. This mechanism is demonstrated to be highly dependent on the presence of curing induced residual stresses. Residual stresses which for an epoxy matrix system can be controlled by the chosen cure profile and thereby the mold time during wind turbine blade manufacture