Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis
Models based on self-excluded walks have been widely used to generate random linear chains. In this work, we present an algorithm capable of generating linear strings in two and three dimensions, in a simple and efficient way. The discrete growth process of the chains takes place in a finite time, i...
- Autores:
-
Avellaneda B., David R.
R. González, Ramón E.
Collazos-Morales, Carlos Andrés
Ariza-Colpas, Paola
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2021
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/8819
- Acceso en línea:
- https://hdl.handle.net/11323/8819
https://doi.org/10.1007/978-3-030-86653-2_14
https://repositorio.cuc.edu.co/
- Palabra clave:
- Self-avoiding random walk
Linear chains
Critical exponents
Fractal dimension
Radius of gyration
End-to-end distance
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
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| dc.title.spa.fl_str_mv |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| title |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| spellingShingle |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis Self-avoiding random walk Linear chains Critical exponents Fractal dimension Radius of gyration End-to-end distance |
| title_short |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| title_full |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| title_fullStr |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| title_full_unstemmed |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| title_sort |
Reasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal Analysis |
| dc.creator.fl_str_mv |
Avellaneda B., David R. R. González, Ramón E. Collazos-Morales, Carlos Andrés Ariza-Colpas, Paola |
| dc.contributor.author.spa.fl_str_mv |
Avellaneda B., David R. R. González, Ramón E. Collazos-Morales, Carlos Andrés Ariza-Colpas, Paola |
| dc.subject.spa.fl_str_mv |
Self-avoiding random walk Linear chains Critical exponents Fractal dimension Radius of gyration End-to-end distance |
| topic |
Self-avoiding random walk Linear chains Critical exponents Fractal dimension Radius of gyration End-to-end distance |
| description |
Models based on self-excluded walks have been widely used to generate random linear chains. In this work, we present an algorithm capable of generating linear strings in two and three dimensions, in a simple and efficient way. The discrete growth process of the chains takes place in a finite time, in a network without pre-established boundary conditions and without the need to explore the entire configurational space. The computational processing time and the length of the strings depending on the number of trials N′ . This number is always less than the real number of steps in the chain, N. From the statistical analysis of the characteristic distances, the radius of gyration ( Rg ), and the end-to-end distance ( Ree ), we make a morphological description of the chains and we study the dependence of this quantities on the number of steps, N. The universal critical exponent obtained are in very good agreement with previous values reported in literature. We also study fractal characteristics of the chains using two different methods, Box-Counting Dimension or Capacity Dimension and Correlation Dimension. The studies revealed essential differences between chains of different dimensions, for the two methods used, showing that three-dimensional chains are more correlated than two-dimensional chains. |
| publishDate |
2021 |
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2021-10-29T14:15:50Z |
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2021-10-29T14:15:50Z |
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2021 |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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http://purl.org/coar/resource_type/c_6501 |
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Text |
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https://hdl.handle.net/11323/8819 |
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https://doi.org/10.1007/978-3-030-86653-2_14 |
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Corporación Universidad de la Costa |
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REDICUC - Repositorio CUC |
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https://repositorio.cuc.edu.co/ |
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Corporación Universidad de la Costa REDICUC - Repositorio CUC |
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eng |
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eng |
| dc.relation.references.spa.fl_str_mv |
Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953) Madras, N., Slade, G.: The Self-Avoiding Walk. Birkhauser, Basel (1953) Yamakawa, H.: Modern Theory of Polymer Solutions. Harper and Row, New York (1971) Wilson, K.G., Kogut, J.: The renormalization group and the expansion. Phys. Rep. 12(2), 75–199 (1974) Sokal, A.D.: Molecular Dynamics Simulations in Polymer Sciences. Oxford University Press, New York (1995) Guttmann, A.J., Conway, A.R.: Square lattice self-avoiding walks and polygons. Ann. Comb. 5(3), 319–345 (2001) Jensen, I.: Enumeration of self-avoiding walks on the square lattice. J. Phys. A Math. Gen. 37(21), 5503–5524 (2004) Li, B., Neal, M, Sokal, A.D.: Critical exponent hyper scaling, and universal amplitude ratios for two and three-dimensional self-avoiding walks. J. Stat. Phys. 80(3), 661–754 (1995) Hara, T., Slade, G., Sokal, A.D.: New lower bounds on the self-avoiding walk connective constant. J. Stat. Phys. 72(3), 479–517 (1993) Slade, G.: Self-avoiding walk, spin systems and renormalization. Proc. R. Soc. A 475(2221), 20180549 (2019) Amit, D.J., Parisi, G., Paliti, L.: Asymptotic behavior of the “true” self-avoiding walk. Phys. Rev. B 27(3), 1635–1645 (1983) Rubinstein, M., Colby, R.H.: Polymer Physics. Oxford University Press, New York (2003) Teraoka, I.: Polymer Solutions: An Introduction to Physical Properties. Wiley Inter-science, New York (2002) Bhattarcharjee, S.M., Giacometti, A., Maritan, A.: Flory theory for polymers. J. Phys. Condens. Matter 25, 503101 (2013) Isaacson, J., Lubensky, T.C.: Flory exponent for generalized polymer problems. J. Phys. Lett. 41(19), 469–471 (1980) Mandelbrot, B.B.: The Fractal Geometry of Nature. W. H. Freeman and company, New York (1982) Banerji, A., Ghosh, I.: Fractal symmetry of proteins interior: what have we learned. Cell. Mol. Life Sci. 68(16), 2711–2737 (2011) Dewey, T.G.: Fractals in Molecular Biophysics. Oxford University Press, New York (1997) Maritan, A.: Random walk and the ideal chain problem on self-similar structures. Phys. Rev. Lett. 62(24), 2845–2848 (1989) Kawakatsu, T.: Statistical Physics of Polymers: An Introduction. Springer-Verlag, Heidelberg (2004) Rammal, R., Toulouse, G., Vannimenus, J.: Self-avoiding walks on fractal spaces: exact results and Flory approximation. J. Phys. 45(3), 389–394 (1984) Takayasu, H.: Fractals in the Physical Sciences. Manchester University Press, New York (1990) Feder, J.: Fractals. Physics of Solids and Liquids. Springer-US, New York (1988) Theiler, J.: Estimating fractal dimension. J. Opt. Soc. Am. A 7(6), 1055–1073 (1990) Nayfeh, A., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley Series in Nonlinear Sciences, Germany (2008) Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349 (1983) Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Phys. D Nonlin. Phenom. 9(1), 189–208 (1983) Lhuillier, D.: A simple model for polymeric fractals in a good solvent and an improved version of the Flory approximation. J. Phys. Fr. 49(5), 705–710 (1988) Victor, J.M., Lhuillier, D.: The gyration radius distribution of two-dimensional polymers chains in a good solvent. J. Chem. Phys. 92(2), 1362–1364 (1990) McKenzie, D.S., Moore, M.A.: Shape of self-avoiding walk or polymer chain. J. Phys. A Gen. Phys. 4(5), L82–L85 (1971) des Cloizeaux, J.: Lagrangian theory for self-avoiding random chain. Phys. Rev. A. 10, 1665 (1974) des Cloizeaux, J., Jannink, G.: Polymers in solution: their modelling and structure. Oxford Science Publications. Clarendon Press, Oxford (1990) Caracciolo, S., Causo, M.S., Pelissetto, A.: End-to-end distribution function for dilute polymers. J. Chem. Phys. 112(17), 7693–7710 (2000) Vettorel, T., Besold, G., Kremer, K.: Fluctuating soft-sphere approach to coarse-graining of polymer models. Soft Matter 6, 2282–2292 (2010) Bernal, D.R.: PhD Thesis, http://www.ppgbea.ufrpe.br/sites/www.ppgbea.ufrpe.br/files/documentos/tese_david_roberto_bernal.pdf. Accessed 21 June 2021 |
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Avellaneda B., David R.R. González, Ramón E.Collazos-Morales, Carlos AndrésAriza-Colpas, Paola2021-10-29T14:15:50Z2021-10-29T14:15:50Z2021https://hdl.handle.net/11323/8819https://doi.org/10.1007/978-3-030-86653-2_14Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Models based on self-excluded walks have been widely used to generate random linear chains. In this work, we present an algorithm capable of generating linear strings in two and three dimensions, in a simple and efficient way. The discrete growth process of the chains takes place in a finite time, in a network without pre-established boundary conditions and without the need to explore the entire configurational space. The computational processing time and the length of the strings depending on the number of trials N′ . This number is always less than the real number of steps in the chain, N. From the statistical analysis of the characteristic distances, the radius of gyration ( Rg ), and the end-to-end distance ( Ree ), we make a morphological description of the chains and we study the dependence of this quantities on the number of steps, N. The universal critical exponent obtained are in very good agreement with previous values reported in literature. We also study fractal characteristics of the chains using two different methods, Box-Counting Dimension or Capacity Dimension and Correlation Dimension. The studies revealed essential differences between chains of different dimensions, for the two methods used, showing that three-dimensional chains are more correlated than two-dimensional chains.Avellaneda B., David R.R. González, Ramón E.Collazos-Morales, Carlos AndrésAriza-Colpas, Paolaapplication/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2International Conference on Computational Science and Its Applicationshttps://link.springer.com/chapter/10.1007/978-3-030-86653-2_14Self-avoiding random walkLinear chainsCritical exponentsFractal dimensionRadius of gyrationEnd-to-end distanceReasonable Non-conventional Generator of Random Linear Chains Based on a Simple Self-avoiding Walking Process: A Statistical and Fractal AnalysisArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionFlory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953)Madras, N., Slade, G.: The Self-Avoiding Walk. Birkhauser, Basel (1953)Yamakawa, H.: Modern Theory of Polymer Solutions. Harper and Row, New York (1971)Wilson, K.G., Kogut, J.: The renormalization group and the expansion. Phys. Rep. 12(2), 75–199 (1974)Sokal, A.D.: Molecular Dynamics Simulations in Polymer Sciences. Oxford University Press, New York (1995)Guttmann, A.J., Conway, A.R.: Square lattice self-avoiding walks and polygons. Ann. Comb. 5(3), 319–345 (2001)Jensen, I.: Enumeration of self-avoiding walks on the square lattice. J. Phys. A Math. Gen. 37(21), 5503–5524 (2004)Li, B., Neal, M, Sokal, A.D.: Critical exponent hyper scaling, and universal amplitude ratios for two and three-dimensional self-avoiding walks. J. Stat. Phys. 80(3), 661–754 (1995)Hara, T., Slade, G., Sokal, A.D.: New lower bounds on the self-avoiding walk connective constant. J. Stat. Phys. 72(3), 479–517 (1993)Slade, G.: Self-avoiding walk, spin systems and renormalization. Proc. R. Soc. A 475(2221), 20180549 (2019)Amit, D.J., Parisi, G., Paliti, L.: Asymptotic behavior of the “true” self-avoiding walk. Phys. Rev. B 27(3), 1635–1645 (1983)Rubinstein, M., Colby, R.H.: Polymer Physics. Oxford University Press, New York (2003)Teraoka, I.: Polymer Solutions: An Introduction to Physical Properties. Wiley Inter-science, New York (2002)Bhattarcharjee, S.M., Giacometti, A., Maritan, A.: Flory theory for polymers. J. Phys. Condens. Matter 25, 503101 (2013)Isaacson, J., Lubensky, T.C.: Flory exponent for generalized polymer problems. J. Phys. Lett. 41(19), 469–471 (1980)Mandelbrot, B.B.: The Fractal Geometry of Nature. W. H. Freeman and company, New York (1982)Banerji, A., Ghosh, I.: Fractal symmetry of proteins interior: what have we learned. Cell. Mol. Life Sci. 68(16), 2711–2737 (2011)Dewey, T.G.: Fractals in Molecular Biophysics. Oxford University Press, New York (1997)Maritan, A.: Random walk and the ideal chain problem on self-similar structures. Phys. Rev. Lett. 62(24), 2845–2848 (1989)Kawakatsu, T.: Statistical Physics of Polymers: An Introduction. Springer-Verlag, Heidelberg (2004)Rammal, R., Toulouse, G., Vannimenus, J.: Self-avoiding walks on fractal spaces: exact results and Flory approximation. J. Phys. 45(3), 389–394 (1984)Takayasu, H.: Fractals in the Physical Sciences. Manchester University Press, New York (1990)Feder, J.: Fractals. Physics of Solids and Liquids. Springer-US, New York (1988)Theiler, J.: Estimating fractal dimension. J. Opt. Soc. Am. A 7(6), 1055–1073 (1990)Nayfeh, A., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley Series in Nonlinear Sciences, Germany (2008)Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349 (1983)Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Phys. D Nonlin. Phenom. 9(1), 189–208 (1983)Lhuillier, D.: A simple model for polymeric fractals in a good solvent and an improved version of the Flory approximation. J. Phys. Fr. 49(5), 705–710 (1988)Victor, J.M., Lhuillier, D.: The gyration radius distribution of two-dimensional polymers chains in a good solvent. J. Chem. Phys. 92(2), 1362–1364 (1990)McKenzie, D.S., Moore, M.A.: Shape of self-avoiding walk or polymer chain. J. Phys. A Gen. Phys. 4(5), L82–L85 (1971)des Cloizeaux, J.: Lagrangian theory for self-avoiding random chain. Phys. Rev. A. 10, 1665 (1974)des Cloizeaux, J., Jannink, G.: Polymers in solution: their modelling and structure. Oxford Science Publications. Clarendon Press, Oxford (1990)Caracciolo, S., Causo, M.S., Pelissetto, A.: End-to-end distribution function for dilute polymers. J. Chem. Phys. 112(17), 7693–7710 (2000)Vettorel, T., Besold, G., Kremer, K.: Fluctuating soft-sphere approach to coarse-graining of polymer models. Soft Matter 6, 2282–2292 (2010)Bernal, D.R.: PhD Thesis, http://www.ppgbea.ufrpe.br/sites/www.ppgbea.ufrpe.br/files/documentos/tese_david_roberto_bernal.pdf. 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