Scaling of star polymers: high order results

Schulte-Frohlinde, Verena; Holovatch, Yu.; Ferber, Christian von; Blumen, A.

doi:10.1016/j.physleta.2004.06.063

Cited by 10 publications

(11 citation statements)

References 26 publications

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“…Here, ν RW = 1/2 and ν SAW are the mean square end-to-end distance exponents for the random and self-avoiding walks, correspondingly, and d is space dimension. The exponents η f 1 f 2 have been calculated within field-theoretical renormalization group approach [9,[32][33][34] and are currently know in the fourth order of the ε = 4 − d expansion [35]. Below, we list them together with the ε-expansion for the exponent ν SAW [36] in the corresponding order: Substituting expressions (1.6)-(1.11) into the scaling relations (1.5) one can evaluate loop exponents c i at any value of d. It is well known, however, that ε-expansions of the field theory are asymptotic at best and proper resummation technique is required to get a reliable numerical information on their basis [37,38].…”

Section: -3mentioning

confidence: 99%

DNA thermal denaturation by polymer field theory approach: effects of the environment

Holovatch¹,

Ferber²,

Honchar³

2021

Condens. Matter Phys.

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We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case, the corresponding diverging ε = 4-d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations.

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Section: -3mentioning

confidence: 99%

DNA thermal denaturation by polymer field theory approach: effects of the environment

Holovatch¹,

Ferber²,

Honchar³

2021

Condens. Matter Phys.

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“…Here, ν RW and ν SAW are the mean square end-to-end distance exponents for the random and self-avoiding walks, correspondingly, and d is space dimension. The exponents η f1f2 have been calculated within field-theoretical renormalization group approach [10,21] and are currently know in the fourth order of the ε = 4−d expansion [22]. Below, we list them together with the ε-expansion for the exponent ν SAW [23] in the corresponding order: Where ζ(x) is Riemann zeta-function.…”

Section: Poland-scheraga Model: Scaling Relations and ε-Expansionmentioning

confidence: 99%

DNA thermal denaturation by polymer field theory approach: effects of the environment

Holovatch,

von Ferber,

Honchar

2021

Preprint

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We analyse the effects of the environment (solvent quality, presence of extended structures -crowded environment) that may impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We show that different environments may shift the transition towards or away from the first order regime. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case the corresponding diverging ε = 4 − d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2 the exact values of the exponents are derived from mapping the polymer model onto a two-dimensional random lattice, i.e. in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations.

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“…Therefore the scaling properties of a heterogeneous polymer network made of interacting SAWs and RWs can be reformulated in terms scaling exponents of co-polymer stars made of two interacting sets of SAWs (η S f1f2 ), of RWs (η G f1f2 ) or of a set of SAWs that interacts with RWs (η U f1f2 ) [24]. Field-theoretical renormalization group calculations of the above copolymer star exponents resulted in ε = 4 − d expansions which have been obtained successively within ε 3 [21] and ε 4 [23] accuracy.…”

Section: V1 V1 V3 V3mentioning

confidence: 99%

Variety of Scaling Laws for DNA Thermal Denaturation

Honchar,

von Ferber,

Holovatch

2021

Preprint

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We discuss possible mechanisms that may impact the order of the transition between denaturated and bound DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory approach to calculate entropic exponents associated with the denaturated loop distribution. We discuss in particular variants of this transition that may occur due to the properties of the solution and may affect the self-and mutual interaction of both single and double strands. We find that the effects studied significantly influence the strength of the first order transition. This is manifest in particular by the changes in the scaling laws that govern DNA loop and strand distribution. As a quantitative measure of these changes we present the values of corresponding scaling exponents. For the d = 4 − ε case we get corresponding ε 4 expansions and evaluate the perturbation theory expansions at space dimension d = 3 by means of resummation technique.

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Scaling of star polymers: high order results

Cited by 10 publications

References 26 publications

DNA thermal denaturation by polymer field theory approach: effects of the environment

DNA thermal denaturation by polymer field theory approach: effects of the environment

DNA thermal denaturation by polymer field theory approach: effects of the environment

Variety of Scaling Laws for DNA Thermal Denaturation

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