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For the Cantor-styled artificial DNA sequence constructed by following the inflation rule A→ABA and B→BBB, using the one-dimensional random walk model and Hurst analysis, we calculate numerically the displacement and its standard deviation, the rescaled range function and the Hurst exponent. The results are compared with those of one-dimensional random binary sequence. We show that Cantor-styled DNA sequence presents correlated behavior, scaling invariability, and self-similarity. In addition, according to the renormalization-group method, we study the charge transfer properties of Cantor-styled DNA sequence, including localization length, charge transmission coefficient and Lyapunov exponent. We find that some resonant peaks can survive in relatively long Cantor-styled DNA sequences, which also implies that there are long-range correlations in Cantor-styled DNA sequences.
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Keywords:
- Cantor-styled DNA sequence /
- correlation property /
- charge transmission coefficient /
- Lyapunov exponent
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[2] Schena M, Shalon D, Davis R W, Brown P O 1995 Science 270 467
[3] Adleman L M 1994 Science 266 1021
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[12] Ma S S, Xu H, Wang H Y, Guo R 2009 Chin. Phys. B 18 3591
[13] Gao J, Xu Z Y 2009 Chin. Phys. B 18 0370
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[19] Hjort M, Stafstrom S 2001 Phys. Rev. Lett. 87 228101
[20] Kasumov A Y, Kociak M, Guéron S,Reulet B, Volkov V T, Klinov D V, Bouchiat H 2001 Science 291 280
[21] Adessi Ch, Walch S, Anantram M P 2003 Phys. Rev. B 67 081405
[22] Yoo K H, Ha D H, Lee J O, Park J W, Kim J, Kim J J, Lee H Y, Kawai T, Choi H Y 2001 Phys. Rev. Lett. 87 198102
[23] Bruinsma R, Grüner G, D'Orsogna M R, Rudnick J 2000 Phys. Rev. Lett. 85 4393
[24] Berlin Y A, Burin A L, Rather M A 2000 J. Phys. Chem. A 104 443
[25] Carpena P, B-Galván P, Ivanov P Ch, Stanley H E 2002 Nature 418 955
[26] Albuquerque E L, Vasconcelos M S, Lyra M L, de Moura F A B F 2005 Phys. Rev. E 71 021910
[27] de Moura F A B F, Lyra M L 1998 Phys. Rev. Lett. 81 3735
[28] Buttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207
[29] Peng C K, Buldyrev S V, Goldberger A L 1992 Nature 356 168
[30] Liu X L, Huang X M, Xu H, Ren Y 2010 Acta Phys. Sin. 59 4202 (in Chinese) [刘小良、黄晓梅、徐 慧、任 意 2010 59 4202]
[31] Farchioni R, Grosso G 1992 Phys. Rev. B 45 6383
[32] Liu X L, Xu H, Deng C S, Ma S S 2007 Physica B 392 107
[33] Anderson P W 1958 Phys. Rev. 109 1492
[34] Liu X L, Ren Y, Xie Q T, Xu H 2010 Phys. Lett. A 374 2163
[35] Sugiyama H, Saito I 1996 J. Am. Chem. Soc. 118 7063
[36] Hurst H E, Black R, Sinaika Y M 1965 Long-Term Storage in Reservior: An Experimental Study (London: Constable)
[37] Guo A M, Xiong S J 2009 Phys. Rev. B 80 035115
[38] Xiong S J, Xiong Y 1999 Phys. Rev. Lett. 83 1407
[39] Maciá E, Domínguez-Adame F, Sáchez A 1994 Phys. Rev. B 49 9503
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[1] Eley D D, Spivey D I 1962 Trans. Faraday Soc. 58 411
[2] Schena M, Shalon D, Davis R W, Brown P O 1995 Science 270 467
[3] Adleman L M 1994 Science 266 1021
[4] Mao C D, Sun W Q, Shen Z Y, Seeman N C 1999 Nature 397 144
[5] Yurke B, Turberfield A J, Mills A P, Simmel F C, Neumann J L 2000 Nature 406 605
[6] Fink H W, Schonenberger C 1999 Nature 398 407
[7] Zhang W, Ulloa S E 2006 Phys. Rev. B 74 115304
[8] Meng X L, Gao X T, Qu Z, Kang D W, Liu D S, Xie S J 2008 Acta Phys. Sin. 57 5316 (in Chinese) [孟宪兰、高绪团、渠 朕、康大伟、刘德胜、解士杰 2008 57 5316]
[9] Liu X L, Xu H, Ma S S, Deng C S Guo A M 2006 Acta Phys. Sin. 55 5562 (in Chinese) [刘小良、徐 慧、马松山、邓超生、郭爱敏 2006 55 5562]
[10] Zhang W, Yang R, Ulloa S E 2009 Phys. Rev. E 80 051901
[11] Stephan R, Dominique B, Enrique M, Kats E 2003 Phys. Rev. Lett. 91 228101
[12] Ma S S, Xu H, Wang H Y, Guo R 2009 Chin. Phys. B 18 3591
[13] Gao J, Xu Z Y 2009 Chin. Phys. B 18 0370
[14] Hartshom R M, Barton J K 1992 J. Am. Chem. Soc. 114 5919
[15] Porath D, Bezryadin A, de Vries S, Dekker C 2000 Nature 403 635
[16] Storm A J, van Noort J, de Vries S, Dekker C 2001 Appl. Phys. Lett. 79 3881
[17] Zhang Y, Austin R H, Kraeft J, Cox E C, Ong N P 2002 Phys. Rev. Lett. 89 198102
[18] Cuniberti G, Craco L, Porath D, Dekker C 2002 Phys. Rev. B 65 241314
[19] Hjort M, Stafstrom S 2001 Phys. Rev. Lett. 87 228101
[20] Kasumov A Y, Kociak M, Guéron S,Reulet B, Volkov V T, Klinov D V, Bouchiat H 2001 Science 291 280
[21] Adessi Ch, Walch S, Anantram M P 2003 Phys. Rev. B 67 081405
[22] Yoo K H, Ha D H, Lee J O, Park J W, Kim J, Kim J J, Lee H Y, Kawai T, Choi H Y 2001 Phys. Rev. Lett. 87 198102
[23] Bruinsma R, Grüner G, D'Orsogna M R, Rudnick J 2000 Phys. Rev. Lett. 85 4393
[24] Berlin Y A, Burin A L, Rather M A 2000 J. Phys. Chem. A 104 443
[25] Carpena P, B-Galván P, Ivanov P Ch, Stanley H E 2002 Nature 418 955
[26] Albuquerque E L, Vasconcelos M S, Lyra M L, de Moura F A B F 2005 Phys. Rev. E 71 021910
[27] de Moura F A B F, Lyra M L 1998 Phys. Rev. Lett. 81 3735
[28] Buttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207
[29] Peng C K, Buldyrev S V, Goldberger A L 1992 Nature 356 168
[30] Liu X L, Huang X M, Xu H, Ren Y 2010 Acta Phys. Sin. 59 4202 (in Chinese) [刘小良、黄晓梅、徐 慧、任 意 2010 59 4202]
[31] Farchioni R, Grosso G 1992 Phys. Rev. B 45 6383
[32] Liu X L, Xu H, Deng C S, Ma S S 2007 Physica B 392 107
[33] Anderson P W 1958 Phys. Rev. 109 1492
[34] Liu X L, Ren Y, Xie Q T, Xu H 2010 Phys. Lett. A 374 2163
[35] Sugiyama H, Saito I 1996 J. Am. Chem. Soc. 118 7063
[36] Hurst H E, Black R, Sinaika Y M 1965 Long-Term Storage in Reservior: An Experimental Study (London: Constable)
[37] Guo A M, Xiong S J 2009 Phys. Rev. B 80 035115
[38] Xiong S J, Xiong Y 1999 Phys. Rev. Lett. 83 1407
[39] Maciá E, Domínguez-Adame F, Sáchez A 1994 Phys. Rev. B 49 9503
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