Numerical study of breathers in a bent chain of oscillators with long-range interaction

Pterobreathers in a model for a layered crystal with realistic potentials: Exact moving breathers in a moving frame

In this article we perform a thorough analysis of breathers in a one-dimensional model for a layered silicate for which there exists fossil and experimental evidence of moving excitations along the close-packed lines of the K^{+} layers. Some of these excitations are likely breathers with a small energy of about 0.2 eV as the numerically obtained breathers described in the present model. Moving breathers as exact solutions of the dynamical equations are obtained at the price of being generically associated with a plane wave, a wing, with finite amplitude, although this amplitude can be very small. We call them pterobreathers. For some frequencies the wings disappear and the solutions become exact moving breathers with no wings, showing the phenomenon of supertransmission of energy. We perform a theoretical analysis of pterobreathers in systems with substrate potential and show that they are characterized by a single frequency in the moving frame plus the frequency of the wings. We have also studied high-energy stationary breathers which transform into single and double kinks and stable multibreathers with very strong localization.

Energy localization and shape transformations in semiflexible polymer rings

Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape. When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.

Langevin dynamics of conformational transformations induced by the charge-curvature interaction

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular chains may undergo transformation to polygonal shape.

Conformational transformations induced by the charge-curvature interaction: Mean-field approach

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl a molecules is considered.

Rich example of geometrically induced nonlinearity: from rotobreathers and kinks to moving localized modes and resonant energy transfer

We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective "static" features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore "dynamic" features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.

Nonlinearity from geometric interactions: a case example

We propose a ladder model wherein dynamical nonlinearity arises from geometry. It includes two strings of particles which are set along rigid rails of a "railroad" and coupled by linear springs. Physical realizations of the model include dust-particle strings in plasma sheaths and chains of microparticles trapped in a strong optical lattice. The transverse couplings between the strings, along with the motion constraint imposed by the rails, generate nonlinearity. It gives rise to robust solitary waves, which are found analytically in the long-wavelength limit, and are obtained in simulations of the full system.

Bubble generation in a twisted and bent DNA-like model

The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.

Breather statics and dynamics in Klein-Gordon chains with a bend

In this paper, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the bifurcation and stability analysis of the modes that emerge as a function of the strength of the bend angle, but we also examine dynamical effects including the scattering of mobile localized modes (discrete breathers) off of such a geometric structure. The potential outcomes of such numerical experiments (including transmission, trapping within the bend as well as reflection) are highlighted and qualitatively explained. Such models are of interest both theoretically in understanding the interplay of breathers with curvature, but also practically in simple models of photonic crystals or of bent chains of DNA.

Energy funneling in a bent chain of Morse oscillators with long-range coupling

A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions.

Breathers in a system with helicity and dipole interaction

Recent papers that have studied variants of the Peyrard-Bishop model for DNA, have taken into account the long range interaction due to the dipole moments of the hydrogen bonds between base pairs. In these models the helicity of the double strand is not considered. In this paper we have performed an analysis of the influence of the helicity on the properties of static and moving breathers in a Klein-Gordon chain with dipole-dipole interaction. It has been found that the helicity enlarges the range of existence and stability of static breathers, although this effect is small for a typical helical structure of DNA. However, the effect of the orientation of the dipole moments is considerably higher with transcendental consequences for the existence of mobile breathers.

Interplay of nonlinearity and geometry in a DNA-related, Klein-Gordon model with long-range dipole-dipole interaction

Most of the studies on mathematical models of DNA are limited to next neighbor interaction. However, the coupling between base pairs is thought to be caused by dipole interaction, and, when the DNA strand is bent, the distances between base pairs become shorter, therefore the interactions with distant base pairs have to be taken into account. In this paper we analyze the existence and stability of breathers, i.e., localized oscillations in a simple model of bent DNA with long-range dipole interaction. Breathers have been suggested as precursors of the denaturation bubble.