Search in Random Media with Lévy Flights

Our work on the subject of search has been motivated by a variety of applications in engineering and technology, and it differs from the physicists’ motivation for such problems, e.g., or the motivation provided by biochemistry, and in theoretical biology . One of our reasons for a more fundamental approach to search comes from the area of traffic routing in wired networks where each end user may send out many search or Smart Packets to seek out paths for the traffic it needs to forward, so that the paths that are used will satisfy useful quality of service (QoS) properties such as minimising delay or packet loss. A similar question arises, with even more acuity, when the networks are ad-hoc and wireless, and the need to reduce uncertainty regarding possible paths is even greater. A distinct but related motivation for our work has been the search for network paths that avoid ongoing Cyberattacks. Another important motivation for our work comes from the field of explosive mine detection and removal on which one of us worked in the past, and in such circumstances it is sensible to see how the natural world deals with such challenges. The related fields of tactical operations, and emergency operations and management also raise many interesting problems related to the search for targets, objects such as landmines, and victims, as part of an organised response to an incident or an emergency. On the other hand, one of us first introduced Lévy flights in diffu-