Conference Paper

# Moving Breather Collisions in the Peyrard-Bishop DNA Model.

DOI: 10.1007/978-3-642-02466-5_39 Conference: Complex Sciences, First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009. Revised Papers, Part 1

Source: DBLP

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**ABSTRACT:**We investigate the statistical mechanics of a simple lattice model for the denaturation of the DNA double helix. The model consists of two chains connected by Morse potentials representing the H bonds. We determine the temperature dependence of the interstrand separation and we show that a mechanism involving an energy localization analogous to self-focusing may initiate the denaturation.Physical Review Letters 07/1989; 62(23):2755-2758. · 7.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in time. In some cases, there are exact mobile breather solutions (found numerically), but these solutions have an infinitely extended tail which shows that the breather motion is nonradiative only when it moves (in equilibrium) with a particular phonon field.More generally, at any instability threshold, there is a marginal mode. There are situations where excitations by marginal modes produce new type of behaviors such as the fission of a breather. We may also have fusion. This approach suggests that breathers (which can be viewed as clusters of phonons) may react by themselves or with each other as well as in chemistry with atoms and molecules, or in nuclear physics with nuclei.Physica D Nonlinear Phenomena 01/1998; · 1.67 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Non-propagating localized oscillating solutions are studied in the case of a discrete one-dimensional system with the 2-3 power onsite potential. A multiple-scale asymptotic perturbation expansion is not adequate for describing the large amplitude oscillations we consider. Starting from an exact pulse-like solution in the continuum, we derive an approximate oscillating solution. Our numerical simulations reveal that, whereas the excitations are strongly damped in the strong intersite coupling case, they are long-lived in the discrete cases. An additional modulation phenomenon of the oscillation, seen in the simulation, is explained by combination of the breather oscillations with the zero group velocity phonons modes. Then, applying the Green's functions formalism in analogy with a previous work (S. Takeno et al., Prog. Theor. Phys. Suppl. 94 (1988)), we derive a very accurate expression for the discrete breather with a quasi-infinite lifetime. Lastly, we demonstrate how such excitations can explain why the breathers make the dominant contributions in the dynamics of a simple model of DNA.Physica D Nonlinear Phenomena 01/1992; 57:267-282. · 1.67 Impact Factor

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