?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3738%2F&rft.title=River+Networks+and+Optimal+Channel+Networks&rft.creator=Balister%2C+Paul&rft.creator=Balogh%2C+J%C3%B3szef&rft.creator=Bollob%C3%A1s%2C+B%C3%A9la&rft.creator=Caldarelli%2C+Guido&rft.creator=Mastrandrea%2C+Rossana&rft.creator=Morris%2C+Rob&rft.subject=QA+Mathematics&rft.subject=QC+Physics&rft.description=River+networks+represent+a+perfect+example+of+a+physical%0D%0Aphenomenon+that+can+be+described+by+means+of+graph+theory.%0D%0AWater+collected+by+rainfall+flows+from+one+point+to+another%0D%0Aone+(downstream)+in+the+river+basin+creates+a+spanning+(water%0D%0Aflows+uniformly+on+the+terrain+and+therefore+from+every+point%0D%0Aof+the+basin+we+have+water+flow)+tree+(water+cannot+flow+uphill).%0D%0ARivers+on+Earth+and+even+those+that+might+have+been%0D%0Apresent+on+Mars+all+display+similar+statistical+properties%0D%0Athereby+calling+for+a+model+based+on+basic+properties.+%0D%0AA+class+of+models+named+Optimal+Channel+Networks+(OCN)+derive+%0D%0Athe+final+configuration+by+minimising+a+given+cost+function.%0D%0AThe+physical+inspiration+for+the+minimization+problem+traces%0D%0Aback+to+the+ideas+of+Nobel+laureate+Prigogine+on+a+general%0D%0Atheory+of+irreversible+processes+in+open+dissipative+systems.%0D%0AActually%2C+theoretical+results+from+OCN+allowed+to+provide+an%0D%0Aexplanation+to+universal+allometric+behaviour+in+a+variety%0D%0Aof+different+physical+situations+from+species+distribution+to+food+webs+optimisation+alternative+to+the+traditional%0D%0Aapproach.+In+the+specific+case+of+river+networks%2C+the+OCN%0D%0Amodel+postulates+that+the+total+gravitational+energy+loss+in+the%0D%0Asystem+is+minimised.+Empirical+and+theoretical+works+focus%0D%0Agenerally+on+two+dimensional+case%2C+while+recently+(inspired+by%0D%0Avascular+systems)+also+the+three+dimensional+case+has+been%0D%0Aanalysed.%0D%0AHere+we+devise+some+new+analytical+results+that+illustrate%0D%0Athe+role+and+the+properties+of+the+structure+that+minimises%0D%0Athe+cost+function+proposed+in+the+ABM+and+we+also+provide%0D%0Asome+insight+about+the+structure+of+the+absolute+minimum+by+varying+some+of+the+parameters+of+the+model.+In+what+follows+we+will+give+a+theoretical+characterization+of+river+networks+and+provide+a+simple+rule+to+distinguish+spanning+trees+from+natural+river+trees.+Furthermore%2C+we+extend+the+study+of+OCNs+embedded+on+a+lattice+finding+a+lower+and+upper+bound+for+the+energy+of+an+OCN+in+any+dimension+D.&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Balister%2C+Paul+and+Balogh%2C+J%C3%B3szef+and+Bollob%C3%A1s%2C+B%C3%A9la+and+Caldarelli%2C+Guido+and+Mastrandrea%2C+Rossana+and+Morris%2C+Rob++River+Networks+and+Optimal+Channel+Networks.++Working+Paper+++++++(Unpublished)+++