F. R. Romero

Moving breathers in a DNA model with competing short- and long-range dispersive interactions

Abstract Moving breathers is a means of transmitting information in DNA. We study the existence and properties of moving breathers in a DNA model with short-range interaction, due to the stacking of the base pairs, and long-range interaction, due to the finite dipole moment of the bond within each base pair. In our study, we have found that mobile breathers exist for a wide range of the parameter values, and the mobility of these breathers is hindered by the long-range interaction. This fact is manifested by: (a) an increase of the effective mass of the breather with the dipole–dipole coupling parameter; (b) a poor quality of the movement when the dipole–dipole interaction increases; (c) the existence of a threshold value of the dipole–dipole coupling above which the breather is not movable. An analytical formula for the boundaries of the regions where breathers are movable is calculated. Concretely, for each value of the breather frequency, one can obtain the maximum value of the dipole–dipole coupling parameter and the maximum and minimum values of the stacking coupling parameter where breathers are movable. Numerical simulations show that, although the necessary conditions for the mobility are fulfilled, breathers are not always movable. Finally, the value of the dipole–dipole coupling constant is obtained through quantum chemical calculations. They show that the value of the coupling constant is small enough to allow a good mobility of breathers.

Moving discrete breathers in a Klein?Gordon chain with an impurity

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein?Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.

Effect of base-pair inhomogeneities on charge transport along the DNA molecule, mediated by twist and radial polarons

Some recent results for a three-dimensional, semi-classical, tight-binding model for DNA show that there are two types of polarons, namely radial and twist polarons, which can transport charge along the DNA molecule. However, the existence of two types of base pairs in real DNA makes it crucial to find out if charge transport also exists in DNA chains with different base pairs. In this paper, we address this problem in its simple case, a homogeneous chain except for a single different base pair, which we call a base-pair inhomogeneity, and its effect on charge transport. Radial polarons experience either reflection or trapping. However, twist polarons are good candidates for charge transport along real DNA. This transport is also very robust with respect to weak parametric and diagonal disorder.

Moving breathers in a bent DNA model

We study the properties of moving breathers in a bent DNA model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bonds within each base pair. We show that the movement of a breather is hindered by the bending of the chain analogously to a particle in a potential barrier.

THE CALOGERO-BOGOYAVLENSKII-SCHIFF EQUATION IN 2+1 DIMENSIONS

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.

Scattering of atomic dark-bright solitons from narrow impurities

In this work, we examine the collision of an atomic dark?bright soliton, in a two-component Bose?Einstein condensate, with a Gaussian barrier or well. Our study has both an experimental component and a theoretical/computational one. First, we present the results of an experiment, illustrating the classical particle phenomenology (transmission or reflection) in the case of an equal barrier in both components. Then, motivated by the experimental observations, we perform systematic simulations considering not only the case of equal heights of a barrier (or a well), but also the considerably more complex setting, where the potential affects only one of the two components. We systematically classify the ensuing cases within a two-parameter diagram of potential amplitudes in the two components, and provide intuitive explanations for the resulting observations, as well as of their variations as the strength of the potential changes.

Breather trapping and breather transmission in a DNA model with an interface

Abstract. We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.

Dark breathers in Klein-Gordon lattices. Band analysis of their stability properties

Discrete bright breathers are well known phenomena. They are localized excitations that consist of a few excited oscillators in a lattice and the rest of them having very small amplitude or none. In this paper we are interested in the opposite kind of localization, or discrete dark breathers, where most of the oscillators are excited and one or a few units of them have very small amplitude. We investigate, using band analysis, Klein-Gordon lattices at frequencies not close to the linear ones. Dark breathers at low coupling are shown to be stable for Klein-Gordon chains with soft on-site potentials and repulsive dispersive interaction, and with hard on-site potentials and attractive dispersive interactions. At higher coupling dark breathers lose their stability via subharmonic, harmonic or oscillatory bifurcations, depending on the model. However, most of these bifurcations are harmless in the sense that they preserve dark localization. None of these bifurcations disappear when the system is infinite. Dark breathers in dissipative systems are found to be stable for both kinds of dispersive interaction.

Effect of the introduction of impurities on the stability properties of multibreathers at low coupling

Using a theorem dubbed the multibreather stability theorem (Archilla J F R et al 2003 Physica D 180 235) we have obtained the stability properties of multibreathers in systems of coupled oscillators with on-site potentials, and an inhomogeneity. Analytical results are obtained for two-site and three-site breathers, multibreathers, phonobreathers and dark breathers. The inhomogeneity is considered both at the on-site potential and at the coupling terms. All the results have been checked numerically with excellent agreement. The main conclusion is that the introduction of an impurity does not alter the stability properties.

Stability of non-time-reversible phonobreathers

Non-time-reversible phonobreathers are nonlinear waves that can transport energy in coupled oscillator chains by means of a phase torsion mechanism. In this paper, the stability properties of these structures have been considered. An analytical study has been performed for low-coupling solutions based upon the so-called multibreather stability theorem previously developed by some of the authors (Archilla et al 2003 Physica D 180 235). A numerical analysis confirms the analytical predictions and gives a detailed picture of the existence and stability properties for arbitrary frequency and coupling.