4,217 research outputs found
A generalized public goods game with coupling of individual ability and project benefit
Facing a heavy task, any single person can only make a limited contribution
and team cooperation is needed. As one enjoys the benefit of the public goods,
the potential benefits of the project are not always maximized and may be
partly wasted. By incorporating individual ability and project benefit into the
original public goods game, we study the coupling effect of the four
parameters, the upper limit of individual contribution, the upper limit of
individual benefit, the needed project cost and the upper limit of project
benefit on the evolution of cooperation. Coevolving with the individual-level
group size preferences, an increase in the upper limit of individual benefit
promotes cooperation while an increase in the upper limit of individual
contribution inhibits cooperation. The coupling of the upper limit of
individual contribution and the needed project cost determines the critical
point of the upper limit of project benefit, where the equilibrium frequency of
cooperators reaches its highest level. Above the critical point, an increase in
the upper limit of project benefit inhibits cooperation. The evolution of
cooperation is closely related to the preferred group-size distribution. A
functional relation between the frequency of cooperators and the dominant group
size is found
Theory of polygonal phases self-assembled from T-shaped liquid crystalline polymers
Extensive experimental studies have shown that numerous ordered phases can be
formed via the self-assembly of T-shaped liquid crystalline polymers (TLCPs)
composed of a rigid backbone, two flexible end chains and a flexible side
chain. However, a comprehensive understanding of the stability and formation
mechanisms of these intricately nano-structured phases remains incomplete. Here
we fill this gap by carrying out a theoretical study of the phase behaviour of
TLCPs. Specifically, we construct phase diagrams of TLCPs by computing the free
energy of different ordered phases of the system. Our results reveal that the
number of polygonal edges increases as the length of side chain or interaction
strength increases, consistent with experimental observations. The theoretical
study not only reproduces the experimentally observed phases and phase
transition sequences, but also systematically analyzes the stability mechanism
of the polygonal phases
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