Delocalized nonlinear vibrational modes and discrete breathers in ß-FPUT simple cubic lattice.

The problem of finding various discrete breathers (DBs) in the ß-Fermi-Pasta-Ulam-Tsingou simple cubic lattice is addressed. DBs are obtained by imposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Among 27 DNVMs with the wave vector at the boundary of the first Brillouin zone there are three satisfying this condition. Seven robust DBs of different symmetries are found using this approach.

Discrete breathers in square lattices from delocalized nonlinear vibrational modes.

Standing and moving discrete breathers (or equally, intrinsic localized modes) in a square ß-Fermi-Pasta-Ulam-Tsingou lattice are obtained by applying localizing functions to the delocalized nonlinear vibrational modes (DNVMs) found earlier by Ryabov and Chechin. The initial conditions used in our study do not correspond to exact spatially localized solutions, but make it possible to obtain long-lived quasibreathers. The approach employed in this work can easily be used to search for quasibreathers in three-dimensional crystal lattices, for which DNVMs with frequencies outside the phonon spectrum are known.

Atom deposition and sputtering at normal incidence simulated by the Frenkel-Kontorova chain.

The impact of a molecule of N atoms with a speed of v_{0} on the free end of the Frenkel-Kontorova chain is numerically simulated. Depending on the values of N and v_{0}, different scenarios of the molecule-chain interaction are observed. Molecules with low speed stick to the chain. At somewhat higher speeds, the molecules bounce off the chain. Further increase in v_{0} results in bouncing off a molecule larger than the incident one. At even higher speed, bouncing of the molecule off the chain takes place simultaneously with the formation of a supersonic crowdion (antikink) propagating along the chain. A very high collision velocity leads to the sputtering of atoms from the chain and the formation of single and multiple supersonic crowdions. Interestingly, the sputtering yield Y as the function of v_{0} demonstrates a nonmonotonous dependence. This is explained by the fact that supersonic crowdions can have a discrete set of propagation velocities. When v_{0} is such that supersonic crowdions are effectively excited, the latter transfer energy deep into the chain, and the sputtering is minimal. For some v_{0} ranges, the formation of supersonic crowdions is suppressed. In these cases, the energy transferred from the impact of the molecule to the chain is spent mainly on the sputtering of atoms. The results obtained qualitatively explain the physics of bombardment of a crystal surface by atomic clusters with applications in physical vapor deposition, ion implantation, ion-beam sputtering, and similar experimental techniques.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory.

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. I. Semi-dynamical model.

The analytical expressions for the coherent and diffuse components of the integrated reflection coefficient are considered in the case of asymmetric Bragg diffraction geometry for a single crystal of arbitrary thickness, which contains randomly distributed Coulomb-type defects. The possibility to choose the combinations of diffraction conditions optimal for characterizing defects of several types by accounting for dynamical effects in the integrated coherent and diffuse scattering intensities, i.e. primary extinction and anomalous absorption, has been analysed based on the statistical dynamical theory of X-ray diffraction by imperfect crystals. The measured integrated reflectivity dependencies of the imperfect silicon crystal on azimuthal angle were fitted to determine the diffraction parameters characterizing defects in the sample using the proposed formulas in semi-dynamical and semi-kinematical approaches.

Mass transfer in the Frenkel-Kontorova chain initiated by molecule impact.

The Frenkel-Kontorova chain with a free end is used to study initiation and propagation of crowdions (antikinks) caused by impact of a molecule consisting of K atoms. It is found that molecules with 1

Generalized neighbor-interaction models induced by nonlinear lattices.

It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrödinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

Exact static solutions for discrete phi4 models free of the Peierls-Nabarro barrier: discretized first-integral approach.

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested by Dmitriev [J. Phys. A 38, 7617 (2005)]. We then discuss some discrete phi4 models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently by Cooper [Phys. Rev. E 72, 036605 (2005)] but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schrödinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum phi4 equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.

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.

Two-soliton collisions in a near-integrable lattice system.

We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides) or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.

Fractal structures and multiparticle effects in soliton scattering.

We study in detail the interaction of composite solitary waves and consider, as an example, the breather collisions in a weakly discrete sine-Gordon equation. We reveal a physical mechanism of fractal soliton scattering associated with multiparticle effects, and demonstrate chaotic interaction of two breathers with incommensurable frequencies.

Periodic metastable structures in the discrete straight phi4 model.

For the discrete straight phi(4) model a class of metastable periodic solutions is given in the form of Fourier series. From the symmetry consideration, we eliminate the harmonics with zero amplitudes and thus, reduce the number of degrees of freedom. For the rest of harmonics we establish the hierarchy of their significance. For solutions with a small period we give the exact expression of energy density in terms of amplitudes of harmonics. Conditions of existence and stability of the solutions are discussed. For some limiting cases the approximate solutions of different kinds are given. The analytical results are compared with the results of numerical study. We also discuss a mechanism of transition from a metastable periodic structure into the ground state and apply the results to the lock-in transition in dielectric crystals supporting incommensurate phase.