Density regulation in strictly metric-free swarms

There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition

The Role of Projection in the Control of Bird Flocks

Swarming is a conspicuous behavioural trait observed in bird flocks, fish shoals, insect swarms and mammal herds. It is thought to improve collective awareness and offer protection from predators. Many current models involve the hypothesis that information coordinating motion is exchanged between neighbors. We argue that such local interactions alone are insufficient to explain the organization of large flocks of birds and that the mechanism for the exchange of long-ranged information necessary to control their density remains unknown. We show that large flocks self-organize to the maximum density at which a typical individual is still just able to see out of the flock in many directions. Such flocks are marginally opaque - an external observer can also just still see a substantial fraction of sky through the flock. Although seemingly intuitive we show that this need not be the case; flocks could easily be highly diffuse or entirely opaque. The emergence of marginal opacity strongly constrains how individuals interact with each other within large swarms. It also provides a mechanism for global interactions: An individual can respond to the projection of the flock that it sees. This provides for faster information transfer and hence rapid flock dynamics, another advantage over local models. From a behavioural perspective it optimizes the information available to each bird while maintaining the protection of a dense, coherent flock.Comment: PNAS early edition published online at http://www.pnas.org/cgi/doi/10.1073/pnas.140220211

Roadway Related Tort Liability and Risk Management: 5th Edition

This training material has been prepared to address the tort liability problems faced by the Kentucky Transportation Cabinet and Kentucky local governments. The manual defines the problem by reviewing the national picture of generally growing numbers of suits and escalating financial losses from suits against highway agencies. The manual also sets out solutions, and reviews actions, which can decrease the exposure of highway agencies to these suits. This risk management concept is emphasized throughout the manual

Roadway Related Tort Liability and Risk Management: 3rd Edition

This training material has been prepared to address the tort liability problems faced by the Kentucky Transportation Cabinet and Kentucky local governments. The workbook defines the problem by reviewing the national picture of growing numbers of suits and escalating financial losses from suits against highway agencies. The workbook also sets out solutions, and reviews actions which can decrease the exposure of highway agencies to these suits. This risk management concept is emphasized throughout the workbook

Roadway Related Tort Liability and Risk Management: 4th Edition

This training material has been prepared to address the tort liability problems faced by the Kentucky Transportation Cabinet and Kentucky local governments. The workbook defines the problem by reviewing the national picture of growing numbers of suits and escalating financial losses from suits against highway agencies. The workbook also sets out solutions, and reviews actions which can decrease the exposure of highway agencies to these suits. This risk management concept is emphasized throughout the workbook

Roadway Related Tort Liability and Risk Management: 2nd Edition

This training material has been prepared to address the tort liability problems faced by the Kentucky Transportation Cabinet and Kentucky local governments. The workbook defines the problem by reviewing the national picture of growing numbers of suits and escalating financial losses from suits against highway agencies. The workbook also sets out solutions, and reviews actions which can decrease the exposure of highway agencies to these suits. This risk management concept is emphasized throughout the workbook