A characterisation of generically rigid frameworks on surfaces of revolution

A foundational theorem of Laman provides a counting characterisation of the finite simple graphs whose generic bar-joint frameworks in two dimensions are infinitesimally rigid. Recently a Laman-type characterisation was obtained for frameworks in three dimensions whose vertices are constrained to concentric spheres or to concentric cylinders. Noting that the plane and the sphere have 3 independent locally tangential infinitesimal motions while the cylinder has 2, we obtain here a Laman-Henneberg theorem for frameworks on algebraic surfaces with a 1-dimensional space of tangential motions. Such surfaces include the torus, helicoids and surfaces of revolution. The relevant class of graphs are the (2,1)-tight graphs, in contrast to (2,3)-tightness for the plane/sphere and (2,2)-tightness for the cylinder. The proof uses a new characterisation of simple (2,1)-tight graphs and an inductive construction requiring generic rigidity preservation for 5 graph moves, including the two Henneberg moves, an edge joining move and various vertex surgery moves.Comment: 23 pages, 5 figures. Minor revisions - most importantly, the new version has a different titl

More information isn’t always better: the case of voluntary provision of environmental quality

This paper adds to the literature on the voluntary provision of public goods by showing that the warm glow that individuals gain depends on the perceived relative effectiveness of contributions. We use a new survey on pro-environment behaviors, attitudes, and knowledge and find that individuals act in accordance with their beliefs, regardless of whether or not these beliefs are accurate, and engage more frequently in activities that have a higher perceived impact on environmental quality. We find that low provision of the public good is greater among people who believe they cannot do much for the environment and do not consider themselves environmentalists.warm glow; environmental quality; public goods contributions

Identity and environmentalism: the influence of community characteristics

This paper examines the influence of community characteristics on self-proclaimed environmentalism. We find that the composition of a community affects the likelihood that a person claims to be a strong environmentalist, even after controlling for individual characteristics and pro-environment behaviors. Individuals are more likely to definitely agree they are strong environmentalists if they live in areas where a large share of the population has post-graduate degrees and if they live in heavily Democratic areas or heavily Republican areas. These community effects occur only when individuals are predisposed to take on an environmental identity.identity; environmentalism; communicty effects