DNA melting: A phase transition in one dimension

Mathematics and Computers in Simulation

Volumn 40, Issue 3-4, 1996, Pages 305-318

  Peyrard, Michel ^a   Dauxois, Thierry ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DNA; HARMONIC GENERATION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; MELTING; MOLECULAR DYNAMICS; PHASE TRANSITIONS; TRANSFER FUNCTIONS;

ANHARMONIC INTERACTIONS; DNA MELTING; FIRST ORDER TRANSITION; MOLECULAR DYNAMIC SIMULATION; MORSE POTENTIAL; TRANSFER INTEGRAL OPERATOR;

COMPUTER SIMULATION;

EID: 0030123299     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4754(95)00040-2     Document Type: Article

References (35)

1. L. Van Hove, Sur l'intégrale de configuration pour les systèmes de particules à une dimension, Physica XVI 2 (1950) 137.
2. R.B. Griffiths, Peierls proof of spontaneous magnetization in a two-dimensional Ising ferromagnet, Phys. Rev. A 136 (1964) 437.
3. N.D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17 (1966) 1133.
4. J.F. Nagle, The one-dimensional KDP model in statistical mechanics, Amer. J. Phys. 36 (1968) 1114-1117.
5. C. Kittel, Phase transitions of a molecular zipper, Amer. J. Phys. 37 (1969) 917-920.
6. M.Ya. Azbel, Generalized one-dimensional Ising model for polymer thermodynamics, J. Chem. Phys. 62 (1975) 3635.
7. A.M. Kosevich and V.L. Galkin, Phase transition in a double polymer chain in an external field, Soviet Phys. JETP 33 (1971) 444-448; A.M. Kosevich, V.L. Galkin and I.N. Nechiporenko, Effect of concentration of active solution on the melting of a double polymer chain, Soviet Phys. JETP 39 (1974) 124-129.
8. A.M. Kosevich and V.L. Galkin, Phase transition in a double polymer chain in an external field, Soviet Phys. JETP 33 (1971) 444-448; A.M. Kosevich, V.L. Galkin and I.N. Nechiporenko, Effect of concentration of active solution on the melting of a double polymer chain, Soviet Phys. JETP 39 (1974) 124-129.
9. J.A. Krumhansl and R.J. Gooding, Structural phase transitions with little phonon softening and first-order character, Phys. Rev. B 39 (1989) 3047-3053.
10. J.R. Morris and R.J. Gooding, Exactly solvable heterophase fluctuations at a vibrational-entropy-driven first-order phase transition, Phys. Rev. Lett. 65 (1990) 1769-1772.
11. J.R. Morris and R.J. Gooding, Vibrational entropy effects at a diffusionless first-order solid-to-solid transition, Phys. Rev. B 43 (1991) 6057-6067.
12. J.R. Morris and R.J. Gooding, Finite-size scaling study of a first-order temperature-driven symmetry breaking structural phase transition, J. Statist. Phys. 67 (3/4) (1992) 471-506.
13. J.R. Morris and R.J. Gooding, Analytic predictions of the exact thermodynamics of a first-order structural phase transition: A practical second-order self-consistent phonon theory, Phys. Rev. B 46 (1992) 8733-8747.
14. W.C. Kerr and M.J. Rave, Mean-field theory of entropy driven structural phase transitions, Phys. Rev. B 48 (1993) 16234-16245.
15. W. Kerr, A.M. Hawthorne, R.J. Gooding, A.R. Bishop and J.A. Krumhansl, First-order displacive structural phase transitions studied by computer simulations, Phys. Rev. B 45 (1992) 7036-7053.
16. R.J. Gooding and J.R. Morris, Absence of enhanced fluctuations as a first-order transition is approached: An exact transfer-matrix study, Phys. Rev. E 47 (1993) 2934-2937.
17. T. Dauxois, M. Peyrard and A.R. Bishop, Entropy driven DNA denaturation, Phys. Rev. E 47 (1993) R44.
18. R.M. Wartell and A.S. Benight, Thermal denaturation of DNA molecules: A comparison of theory with experiments, Physics Reports 126 (1985) 67.
19. W. Saenger, Principles of Nucleic Acid Structure (Springer, Berlin, 1984).
20. T. Dauxois, M. Peyrard and A.R. Bishop, Dynamics and thermodynamics of a nonlinear model for DNA denaturation, Phys. Rev. E 47 (1993) 684.
21. M. Peyrard and A.Bishop, Statistical Mechanics of a Nonlinear Model for DNA denaturation, Phys. Rev. Lett. 62 (1989) 2755.
22. C. Reiss, Private communication.
23. T. Dauxois, Dynamique non linéaire et mécanique statistique d'un modèle d'ADN, Ph.D. Thesis, Université de Bourgogne, 1993.
24. T. Dauxois and M. Peyrard, Energy localization in nonlinear lattices, Phys. Rev. Lett. 70 (1993) 3935.
25. D.J. Scalapino, M. Sears and R.A. Ferrel, Statistical mechanics of one-dimensional Ginzburgh-Landau fields, Phys. Rev. B 6 (1972) 3409.
26. J.A. Krumhansl and J.R. Schrieffer, Dynamics and statistical mechanics of a one-dimensional model hamiltonian for structural phase transitions, Phys. Rev. B 11 (1975) 3535.
27. J.F. Currie et al., Statistical mechanics of one dimensional solitary-wave-bearing scalar fields: Exact results and ideal gas phenomenology, Phys. Rev. B 22 (1980) 477.
28. S.E. Trullinger and K. Sasaki, Lattice discreteness corrections in the transfer-operator method for kink-bearing chains, Physica D 28 (1988) 181.
29. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1989).
30. 0(t) in the continuum is particularly visible by looking at the figure from the left side, with the eye almost in the plane of the paper.
31. S. Nosé, A molecular dynamics method for simulation in the canonical ensemble, Molecular Phys. 52 (1984) 255.
32. S. Nosé, A unified formulation of the constant-temperature molecular dynamics methods, J. Chem. Phys. 81 (1984) 511.
33. W.G. Hoover, Canonical dynamics: Equilibrium phase-space distribution, Phys. Rev. A 31 (1985) 1695.
34. S. Nosé, Dynamical behavior of a thermostated isotropic harmonic oscillator, Phys. Rev. E 47 (1993) 164.
35. H. Urabe and Y. Tominaga, Low frequency Raman spectra of DNA, J. Phys. Soc. Japan 50 (1981) 3543-3544.