How Nature Works The Science of Self-Organized Critica.ppt

Self-Organized Criticality (自組織臨界現象)一種相變現象 相變與臨界現象是同一種物質在因應不同外在變因，如溫度、壓力等參數的不同，而表現的不同巨觀行為。如水的固、液、汽三相變化，以及導體與陶瓷材料在低溫時所出現的超導現象，都是屬於相變現象的範圍。更廣義的延伸，凡一系統在特定參數條件下有非連續性變化，如蛋自質折疊過程中的二態變化。或是一些非線性系統的自組臨界現象(Self-Organized Criticality)，皆可稱為相變現象。 Self-organized critical phenomena, by contrast, is exhibited by driven systems which reach a critical state by their intrinsic dynamics, independently of the value of any control parameter. The archetype of a self-organized critical system is a sand pile. Sand is slowly dropped onto a surface, forming a pile. As the pile grows, avalanches occur which carry sand from the top to the bottom of the pile. At least in model systems, the slope of the pile becomes independent of the rate at which the system is driven by dropping sand. This is the (self-organized) critical slope. Critical states of a system are signaled by a power-law distribution in some observable. In the case of a solid-liquid transition, one can measure the heat-capacity of the system. In the case of sand-piles, one can measure the distribution of avalanche sizes. In the present case of internet access, curiosity is measured. The analogy with sand piles is clear: a grain dropped onto the pile corresponds to an initial access to the document. The size of an avalanche corresponds to depth of reading of a document. In order to maintain a critical slope in a sand pile in a finite geometry, sand is removed at the edges of the pile. One can think of the sand pile as sitting on a table. Sand falls off as it reaches the edge of the table. The same process could be operating in the case of hypertext access to a document: once readers have achieved a certain depth in the document, they may decide that the document is sufficiently useful to them that they should obtain a hardcopy. At that point, they will stop issuing http requests and then issue a ftp request to retrieve the full document. Self-Organized Criticality /~maslov/soc.htm Self-Organized Criticality (SOC) is a concep