dorsal/arxiv
View SchemaEffects of long-range dispersion in nonlinear dynamics of DNA molecules
| Authors | Yuri B. Gaididei, Serge F. Mingaleev, Peter L. Christiansen, Magnus Johansson, Kim O. Rasmussen |
|---|---|
| Categories | |
| ArXiv ID | physics/9906006 |
| URL | https://arxiv.org/abs/physics/9906006 |
Abstract
A discrete nonlinear Schrodinger (NLS) model with long-range dispersive interactions describing the dynamical structure of DNA is proposed. Dispersive interactions of two types: the power dependence $r^{-s}$ and the exponential dependence $e^{-\beta r}$ on the distance, $r$, are studied. For $s$ less than some critical value, $s_{cr}$, and similarly for $\beta \leq \beta_{cr}$ there is an interval of bistability where two stable stationary states: narrow, pinned states and broad, mobile states exist at each value of the total energy. For cubic nonlinearity the bistability of the solitons occurs for dipole-dipole dispersive interaction $(s=3)$, and for the inverse radius of the dispersive interaction $\beta \leq \beta_{cr}=1.67$. For increasing degree of nonlinearity, $\sigma$, the critical values $s_{cr}$ and $\beta_{cr}$ increase. The long-distance behavior of the intrinsically localized states depends on $s$. For $s>3$ their tails are exponential while for $2<s<3$ they are algebraic. A controlled switching between pinned and mobile states is demonstrated applying a spatially symmetric perturbation in the form of a parametric kick. The mechanism could be important for controlling energy storage and transport in DNA molecules.
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"abstract": "A discrete nonlinear Schrodinger (NLS) model with long-range dispersive\ninteractions describing the dynamical structure of DNA is proposed. Dispersive\ninteractions of two types: the power dependence $r^{-s}$ and the exponential\ndependence $e^{-\\beta r}$ on the distance, $r$, are studied. For $s$ less than\nsome critical value, $s_{cr}$, and similarly for $\\beta \\leq \\beta_{cr}$ there\nis an interval of bistability where two stable stationary states: narrow,\npinned states and broad, mobile states exist at each value of the total energy.\nFor cubic nonlinearity the bistability of the solitons occurs for dipole-dipole\ndispersive interaction $(s=3)$, and for the inverse radius of the dispersive\ninteraction $\\beta \\leq \\beta_{cr}=1.67$. For increasing degree of\nnonlinearity, $\\sigma$, the critical values $s_{cr}$ and $\\beta_{cr}$ increase.\nThe long-distance behavior of the intrinsically localized states depends on\n$s$. For $s\u003e3$ their tails are exponential while for $2\u003cs\u003c3$ they are\nalgebraic. A controlled switching between pinned and mobile states is\ndemonstrated applying a spatially symmetric perturbation in the form of a\nparametric kick. The mechanism could be important for controlling energy\nstorage and transport in DNA molecules.",
"arxiv_id": "physics/9906006",
"authors": [
"Yuri B. Gaididei",
"Serge F. Mingaleev",
"Peter L. Christiansen",
"Magnus Johansson",
"Kim O. Rasmussen"
],
"categories": [
"physics.bio-ph",
"q-bio"
],
"title": "Effects of long-range dispersion in nonlinear dynamics of DNA molecules",
"url": "https://arxiv.org/abs/physics/9906006"
},
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