Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

Base pair opening in a damped helicoidal Joyeux-Buyukdagli model of DNA in an external force field

Upon the Joyeux-Buyukdagli model of DNA, the helicoidal interactions are introduced, and their effects on the dynamical behaviors of the molecule investigated. A theoretical framework for the analysis is presented in an external force field, taking into account Stokes and hydrodynamics viscous forces. In the semi-discrete approximation, the dynamics of the molecule is found governed by the cubic complex Ginzburg-Landau (CGL) equation. By choosing an appropriate decoupling ansatz, the cubic CGL equation is transformed into a nonlinear differential equation whose analytical solitary wave-like solutions can be explored by means of the direct method, which is more tractable in case where the form of soliton solutions is known. Based on this, a dissipative bright-like soliton solution is obtained. Numerical experiments have been done, and relevant results were brought out, such as the quantitative and qualitative influences of the helical interactions on the parameters of the traveling bubble. The important role-played by these interactions in the DNA biological processes is brought out, showing that depending on the wave number, their effects can increase, decrease, or keep constant the bubble angular frequency, velocity, amplitude, and width, as well as the energy involved by enzymes in the initiation of DNA biological processes. This can prevent some coding or reading errors and resulting genetic damages. Analytical predictions and numerical experiments were in good agreement.

Localization of low-frequency oscillations in single-walled carbon nanotubes

In the framework of the continuum shell theory, we analytically predict a new phenomenon: the weak localization of optical low-frequency oscillations in carbon nanotubes. We clarify the origin of the localization by means of the concept of the limiting phase trajectory and confirm the obtained analytical results by molecular dynamics simulations of simply supported carbon nanotubes. The performed analysis contributes to the new universal approach to the treatment of nonstationary resonant processes.

Multiphase autoresonant excitations in discrete nonlinear Schrödinger systems

Large amplitude, multiphase solutions of periodic discrete nonlinear Schrödinger (NLS) systems are excited and controlled by starting from zero and using a small perturbation. The approach involves successive formation of phases in the solution by driving the system with small amplitude plane wavelike perturbations (drives) with chirped frequencies, slowly passing through a system's resonant frequency. The system is captured into resonance and enters a continuing phase-locking (autoresonance) stage, if the drive's amplitude surpasses a certain sharp threshold value. This phase-locked solution is efficiently controlled by variation of an external parameter (driving frequency). Numerical examples of excitation of multiphase waves and periodic discrete breathers by using this approach for integrable (Ablowitz-Ladik) and nonintegrable NLS discretizations are presented. The excited multiphase waveforms are analyzed via the spectral theory of the inverse scattering method applied to both the integrable and nonintegrable systems. A theory of autoresonant excitation of 0- and 1-phase solutions by passage through resonances is developed. The threshold phenomenon in these cases is analyzed.

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters.

Energy relaxation in nonlinear one-dimensional lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Twisted localized modes

In a number of recent papers the so-called twisted localized mode of the discrete nonlinear Schrödinger equation has been proposed. Herein, we study the existence and stability properties of such modes. We analyze the persistence of quasiperiodic modes and study the domains of existence and numerical stability of the exact form of such solutions. We identify the bifurcations through which they lose their stability and follow the behavior of the intrinsic localized modes and their eigenmodes even in the unstable regime.

Electron-vibron-breather interaction

We study the interaction of breathers in the context of a coupled electron-vibron lattice system. Starting with single-site excitations, it is demonstrated that constellations exist for which the coexistence of electronic and vibronic breathers is assured. The energy exchange between the vibrational and electronic subsystems and its impact on the breather formation are discussed in detail. The coupled electron-vibron dynamics shows a tendency toward energy redistribution into the vibronic degrees of freedom at the expense of the electronic energy content. Attention is paid to the relaxation dynamics in the energy exchange and we discuss the attainment of a steady regime for the coupled electron-vibron dynamics starting from a nonequilibrium state. It is demonstrated that the presence of breathers has a strong impact on the relaxation dynamics. Breathers can assist the relaxation process. With the help of a linear stability analysis, we show why the electronic subsystem acts as an energy donor while the vibron system serves as the energy acceptor. To this end we investigate the existence and stability of localized breathing eigenmodes capable of energy trapping. A frequency analysis reveals that strong exchange also occurs due to a temporal transition from single-frequency breathers to those oscillating with two frequencies and their temporal resonance interaction. Finally, the self-stabilized electron-vibron system relaxes to a combined electron-vibron breather. On increasing the electron-vibron coupling strength, only a vibronic phonobreather of large amplitude survives, whereas the electronic subsystem tends to energy equipartition.

Solitonic energy transfer in a coupled exciton-vibron system

We consider the exciton transfer along a one-dimensional molecular chain. The exciton motion is influenced by longitudinal vibrations evolving in a Toda lattice potential. It is shown how the soliton solutions of the vibron system coupled to the exciton system induce solitonic exciton transfer. To this aim the existence of a regime of suppressed energy exchange between the coupled excitonic and vibrational degrees of freedom is established in the case of which a nonlinear Schrodinger equation for the exciton variable is derived. The nonlinear Schrodinger equation possesses soliton solutions corresponding to coherent transfer of the localized exciton.

Soliton-breather reaction pathways

We use a collective coordinate approach to investigate corpuscular properties of breathers in nonlinear lattice systems. We calculate the breather internal energy and inertial mass and use them to analyze the reaction pathways of breathers with kinks that are preformed in the lattice. We find that there is an effective kink-breather intraction potential that, under some circumstances, is attractive and has a double well shape. Furthermore, we find that in some cases the internal energy of a moving breather can be released during the reaction with the kink and subsequently transformed to kink translational energy. These breather properties seem to be model independent.