Models of Entanglement
نویسنده
چکیده
There are many ways to pack, and arrange, filaments in space. The packing can be quantified in terms of how much filament length is contained in a typical unit of volume. How something is “arranged” is harder to define, but one can think in terms of systems that are random as opposed to those that have some kinds of regularity. We identify three fundamental regimes of packing (linear, laminar, globular) and illustrate how several different real and virtual filament systems fall into these three regimes. The amount of entanglement in a filament system is an essential property, strongly influencing physical behavior. There are different ways to try to quantify entanglement; we focus here on average crossing number. We present several models of filaments and analyze the typical tangling behavior in the different packing regimes. We conclude with an example comparing the tangling effects of random and orderly packing. Mathematics Subject Classification 2000: Primary 57M25; Secondary 92E10, 53A04, 74K05
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