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Ω is usually referred to as the rate of twist.
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This definition of contact line, which measures the length of curves of intersurface contact in the deformed and twisted goemetries (the vertical line threaded through the center of the double helix) differs from the notion of contact in Ref. 23, which consider the length of curve contacting points when the twisted filaments are unbent into straight configurations. Notably, the line of contact in the twisted configuration decreases with twist, while "unwrapped" line of contact increases with twist.
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m to ln(σ/a ) ≲ -4.5.
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84910082735
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This follows from the fact that to lowest order in Ω, the backbone curves of filaments approximate straight lines, tilted by θ with respect to ẑ.
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In contrast to Refs. 43 and 44 which numerically analyzed vertical cuts of helical tubes, we consider the horizontal cuts, whose shape can be determined analytically.
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55
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84910103517
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note
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Green's theorem is a special case in 2D of Stokes theorem.
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