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Alternatively, for a given bead spacing b, we can dictate the aspect ratio by introducing a scaling factor δ and by using the more general equations r/b=δβ, a /b=4/ { 3 [2ln (2/δ) +1] }, and a/b=2/ { 3 [2ln (2/δ) -1] }. Solutions exist for δ<1.21. This corresponds to the condition that r/b must be less than 0.681. This is a useful result in that for a specified bead number, one can simulate a filament of a given slenderness at an equivalent computational expense.
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Alternatively, for a given bead spacing b, we can dictate the aspect ratio by introducing a scaling factor δ and by using the more general equations r/b=δβ, a /b=4/ { 3 [2ln (2/δ) +1] }, and a/b=2/ { 3 [2ln (2/δ) -1] }. Solutions exist for δ<1.21. This corresponds to the condition that r/b must be less than 0.681. This is a useful result in that for a specified bead number, one can simulate a filament of a given slenderness at an equivalent computational expense.
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We are grateful to Professor A. Nadim for pointing this out to us.
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We are grateful to Professor A. Nadim for pointing this out to us.
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The resultant parametrization is a /b=2/ [3 (-ln2+0.839+0.185/p+0.233/ p2 +1)] and a/b=1/ [3 (-ln2-0.207+0.980/p-0.133/ p2 +1)] with r/b=β, where L/d=p for the parametrization.
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The resultant parametrization is a /b=2/ [3 (-ln2+0.839+0.185/p+0.233/ p2 +1)] and a/b=1/ [3 (-ln2-0.207+0.980/p-0.133/ p2 +1)] with r/b=β, where L/d=p for the parametrization.
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We calculated the parametrization to match slender body theory using the RP tensor to be a /b ≈ 0.559 and a/b ≈ 0.441, with r/b0.437.
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We calculated the parametrization to match slender body theory using the RP tensor to be a /b ≈ 0.559 and a /b ≈ 0.441, with r/b 0.437.
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