Knots in Macromolecules in Constraint Space
We find a power law for the number of knot-monomers with an exponent $0.39 \pm0.13$ in agreement with previous simulations. For the average size of a knot we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present data on the average number of knots given a certain chain length a...
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| creator | Brill, Michael Diesinger, Philipp M Heermann, Dieter W |
| description | We find a power law for the number of knot-monomers with an exponent $0.39
\pm0.13$ in agreement with previous simulations. For the average size of a knot
we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present
data on the average number of knots given a certain chain length and confirm a
power law behaviour for the number of knot-monomers. Furthermore we study the
average crossing number for random and self-avoiding walks as well as for a
model polymer with and without geometric constraints. The data confirms the
$aN\log N + bN$ law in the case of without excluded volume and determines the
constants $a$ and $b$ for various cases. For chains with excluded volume the
data for chains up to N=1500 is consistent with $aN\log N + bN$ rather than the
proposed $N^{4/3}$ law. Nevertheless our fits show that the $N^{4/3}$ law is a
suitable approximation. |
| doi_str_mv | 10.48550/arxiv.cond-mat/0507020 |
| format | Article |
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\pm0.13$ in agreement with previous simulations. For the average size of a knot
we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present
data on the average number of knots given a certain chain length and confirm a
power law behaviour for the number of knot-monomers. Furthermore we study the
average crossing number for random and self-avoiding walks as well as for a
model polymer with and without geometric constraints. The data confirms the
$aN\log N + bN$ law in the case of without excluded volume and determines the
constants $a$ and $b$ for various cases. For chains with excluded volume the
data for chains up to N=1500 is consistent with $aN\log N + bN$ rather than the
proposed $N^{4/3}$ law. Nevertheless our fits show that the $N^{4/3}$ law is a
suitable approximation.</description><identifier>DOI: 10.48550/arxiv.cond-mat/0507020</identifier><language>eng</language><subject>Physics - Soft Condensed Matter ; Physics - Statistical Mechanics</subject><creationdate>2005-07</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/cond-mat/0507020$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.cond-mat/0507020$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Brill, Michael</creatorcontrib><creatorcontrib>Diesinger, Philipp M</creatorcontrib><creatorcontrib>Heermann, Dieter W</creatorcontrib><title>Knots in Macromolecules in Constraint Space</title><description>We find a power law for the number of knot-monomers with an exponent $0.39
\pm0.13$ in agreement with previous simulations. For the average size of a knot
we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present
data on the average number of knots given a certain chain length and confirm a
power law behaviour for the number of knot-monomers. Furthermore we study the
average crossing number for random and self-avoiding walks as well as for a
model polymer with and without geometric constraints. The data confirms the
$aN\log N + bN$ law in the case of without excluded volume and determines the
constants $a$ and $b$ for various cases. For chains with excluded volume the
data for chains up to N=1500 is consistent with $aN\log N + bN$ rather than the
proposed $N^{4/3}$ law. Nevertheless our fits show that the $N^{4/3}$ law is a
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\pm0.13$ in agreement with previous simulations. For the average size of a knot
we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present
data on the average number of knots given a certain chain length and confirm a
power law behaviour for the number of knot-monomers. Furthermore we study the
average crossing number for random and self-avoiding walks as well as for a
model polymer with and without geometric constraints. The data confirms the
$aN\log N + bN$ law in the case of without excluded volume and determines the
constants $a$ and $b$ for various cases. For chains with excluded volume the
data for chains up to N=1500 is consistent with $aN\log N + bN$ rather than the
proposed $N^{4/3}$ law. Nevertheless our fits show that the $N^{4/3}$ law is a
suitable approximation.</abstract><doi>10.48550/arxiv.cond-mat/0507020</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Physics - Soft Condensed Matter Physics - Statistical Mechanics |
| title | Knots in Macromolecules in Constraint Space |
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