Correction: Halun et al. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. Entropy 2021, 23, 242

Joanna Halun; Pawel Karbowniczek; Piotr Kuterba; Zoriana Danel

doi:10.3390/e24030413

,

and

¹

Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Cracow, Poland

²

Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland

³

Faculty of Physics, Astronomy and Applied Computer Sciences, Jagiellonian University in Cracow, 30-348 Cracow, Poland

^*

Author to whom correspondence should be addressed.

Entropy2022, 24(3), 413;https://doi.org/10.3390/e24030413

This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics

Version Notes

Order Reprints

The authors wish to make the following correction to this paper []. In our paper [] are a few errors:

On page 8 symbol ‘ $c c$ ’ before $< ρ_{λ}^{(D D)} (\tilde{z}) >$ in the Equation (19) should be removed and looks like:

$\begin{matrix} < ρ_{λ}^{(D D)} (\tilde{z}) > & = \frac{{(2 R_{g})}^{1 / ν}}{L_{0}} \frac{IL \int_{0}^{L} d z G (; z, \tilde{z}) G (; \tilde{z}, z)}{IL \int_{0}^{L} d z G (; z, z)} \\ \approx 2 \frac{{\tilde{z}}^{1 / ν}}{L} (1 + \frac{\sqrt{π}}{2 y} + \frac{π}{4 y^{2}} + \frac{π^{3 / 2}}{8 y^{3}} + O (e^{- 4 y^{2}})) \end{matrix}$

(19)
On page 12 symbol ‘ $c c$ ’ before $< ρ_{λ}^{(D D)} (\tilde{z}) >_{l}$ in the Equation (25) should be removed and looks like:

$\begin{matrix} < ρ_{λ}^{(D D)} (\tilde{z}) >_{l} = B \frac{{\tilde{z}}^{1 / ν}}{L} (1 & + 8 a π \tilde{R} ([e r f c [\frac{a}{\sqrt{2} R_{x}}] - \frac{R_{x}}{a} \sqrt{\frac{2}{π}} e^{- \frac{a^{2}}{2 R_{x}^{2}}}] \\ - 2 [e r f c [\frac{\sqrt{2} a}{R_{x}}] - \frac{R_{x}}{a \sqrt{2 π}} e^{\frac{- 2 a^{2}}{R_{x}^{2}}}])) \end{matrix}$

(25)
On page 16 symbol ‘ $c c$ ’ before $< ρ_{λ}^{(D D)} (\tilde{z}) >_{s t}$ in the Equation (44) should be removed and looks like:

$\begin{matrix} < ρ_{λ}^{(D D)} (\tilde{z}) >_{s t} = B \frac{{\tilde{z}}^{1 / ν}}{L} (1 & - 2 \sqrt{5 π} \tilde{R} a [(\frac{61 R_{x}}{7 a} + \frac{1584}{175} \frac{a}{R_{x}}) e^{- \frac{4 a^{2}}{5 R_{x}^{2}}} \\ - (\frac{155 R_{x}}{7 a} + \frac{10,272}{175} \frac{a}{R_{x}}) e^{- \frac{16 a^{2}}{5 R_{x}^{2}}}]) \end{matrix}$

(44)
On page 21 Appendix B symbol ‘ $c c c c c$ ’ before ${\tilde{G}}_{‖} (p; z, z^{'}; μ_{0}, c_{1_{0}}, c_{2_{0}}, L)$ in the Equation (A5) should be removed and looks like:

$\begin{matrix} {\tilde{G}}_{‖} (p; z, z^{'}; μ_{0}, c_{1_{0}}, c_{2_{0}}, L) & = \frac{1}{2 κ_{0}} ((κ_{0}^{2} + κ_{0} (c_{1_{0}} + c_{2_{0}}) + c_{1_{0}} c_{2_{0}}) e^{κ_{0} L} \\ - (κ_{0}^{2} - κ_{0} (c_{1_{0}} + c_{2_{0}}) + c_{1_{0}} c_{2_{0}}) e^{- κ_{0} L})^{- 1} \\ ((κ_{0}^{2} + κ_{0} (c_{1_{0}} + c_{2_{0}}) + c_{1_{0}} c_{2_{0}}) e^{κ_{0} (L - | z - z^{'} |)} \\ + (κ_{0}^{2} - κ_{0} (c_{1_{0}} + c_{2_{0}}) + c_{1_{0}} c_{2_{0}}) e^{- κ_{0} (L - | z - z^{'} |)} \\ + (κ_{0}^{2} + κ_{0} (c_{2_{0}} - c_{1_{0}}) - c_{1_{0}} c_{2_{0}}) e^{κ_{0} (L - z - z^{'})} \\ + (κ_{0}^{2} - κ_{0} (c_{2_{0}} - c_{1_{0}}) - c_{1_{0}} c_{2_{0}}) e^{- κ_{0} (L - z - z^{'})}) \end{matrix}$

(A5)
On page 22 Appendix C symbol ‘ $c c$ ’ before $< ρ_{λ}^{(D N)} (\tilde{z}) >$ in the Equation (A8) should be removed and looks like:

$\begin{matrix} < ρ_{λ}^{(D N)} (\tilde{z}) > & = \frac{{(2 R_{g})}^{1 / ν}}{L_{0}} \frac{IL \int_{0}^{L} d z G (; z, \tilde{z}) G (; \tilde{z}, z)}{IL \int_{0}^{L} d z G (; z, z)} \\ \approx 2 \frac{{\tilde{z}}^{1 / ν}}{L} + \frac{\tilde{z}}{y^{2}} \frac{(e^{- 4 y^{2}} - e^{- 16 y^{2}})}{(1 - 2 e^{- 4 y^{2}} + 2 e^{- 16 y^{2}})} \end{matrix}$

(A8)

The changes do not influence substantive meaning and the obtained scientific results. The original article has been updated.

Reference

Halun, J.; Karbowniczek, P.; Kuterba, P.; Danel, Z. Investigation of ring and star polymers in confined geometries: Theory and simulations. Entropy 2021, 23, 242. [Google Scholar] [CrossRef] [PubMed]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Correction: Halun et al. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. Entropy 2021, 23, 242

Reference

Article Metrics

Citations

Article Access Statistics