Aleksey A. Vasiliev

Multi-field continuum theory for medium with microscopic rotations

We derive the multi-field, micropolar-type continuum theory for the two-dimensional model of crystal having finite-size particles. Continuum theories are usually valid for waves with wavelength much larger than the size of primitive cell of crystal. By comparison of the dispersion relations, it is demonstrated that in contrast to the single-field continuum theory constructed in our previous paper the multi-field generalization is valid not only for long but also for short waves. We show that the multi-field model can be used to describe spatially localized short- and long-wavelength distortions. Short-wave external fields of forces and torques can be also naturally taken into account by the multi-field continuum theory.

Effect of discreteness on a sine-Gordon three-soliton solution

Abstract The collision between a kink and high amplitude breather in the Frenkel-Kontorova chain with a small degree of discreteness was studied numerically and the results were compared with an exact three-soliton solution to the sine-Gordon (SG) equation. It was found that there exists a narrow range of parameters of quasiparticles where the collision in the discrete system is strongly inelastic and that the inelastic collision occurs in the vicinity of a separatrix of the SG three-soliton solution.

Inelastic three-soliton collisions in a weakly discrete sine-Gordon system

The three-soliton solutions to the sine-Gordon equation describing the collision of a kink with a breather or with a kink-antikink pair are given and several separatrix three-soliton solutions are extracted from these solutions. The influence of a small perturbation on the three-soliton collisions is studied numerically. As the perturbed system the Frenkel-Kontorova model with a small degree of discreteness is considered. We show that in the three-soliton collisions, in the presence of small perturbation, energy exchange between solitons can take place. The degree of inelasticity of a three-soliton collision is extremely sensitive to the parameters of the collision.

Domain Wall Solutions for EHM Model of Crystal.

For a one-dimensional discrete model of a crystal the solution of the form of a moving domain wall in an odd-periodic commensurate structure was derived in the continuum approximation. The energy of the commensurate odd-periodic structure, the width and the energy of domain wall were expressed in terms of the amplitudes of harmonics of carrying commensurate structure. With the use of the result by Ishibashi, the relation between domain wall solutions in odd-periodic and even-periodic commensurate structures was established. The applicability and the accuracy of the solutions were also discussed. The obtained solutions were found to be more accurate and general than those by other authors.

Domain walls in one-dimensional 3-periodic structure

Abstract The static and dynamic properties of domain walls in the incommensurate phase near the lock-in transition was studied numerically in the frame of the elastically hinged molecule model of crystal which was recently proposed by the present authors. The case of discommen-surations in the 3-periodic commensurate phase was discussed and the analytical expression for the displacements near the domain wall was derived in continum approximation. The interaction of the domain pattern with the external field, processes of collision and breakup of domain walls were investigated.

Dynamics of autowaves in a one-dimensional crystal model

A mechanism of the phase transition between two modulated structures with different wave vectors was proposed and investigated numerically. The phase transition occurs through the mechanism of nucleation and growth of the new phase. The role of the nucleus is played by an unstable domain wall and the domain of a new low energy phase grows due to the motion of autowaves.

Many-field theory for crystals containing particles with rotational degrees of freedom

We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient theory, another is the micropolar type theory and the third one is the many-field theory. The importance of the first two types of theories has already been established, while the theory of the third type still has to be developed. With the use of 1D and 2D examples we show for each of these theories where they can be and should be applied, separately or in a combination.

Topological Soliton Dynamics in Media with Microscopic Rotations

Microscopic rotations can play a very important role in the molecular crystals or in some dielectric crystals where atoms are joined in comparatively rigid clusters and the inter-cluster interactions are comparatively weak. The range of unusual phenomena observed in such materials is fascinating, from incommensurate phase to negative Poisson ratio. Here we focus on the topological soliton dynamics in such materials and describe a number of effects, such as the trigger off and propagation of autowaves, soliton multiplication in the metastable media, soliton collisions and annihilations. All these phenomena are addressed in frame of the elastically hinged mo lecule (EHM) model having microscopic particles with rotational degrees of freedom. For this model we construct various continuum approximations. New important features of the continuum models for media with microscopic rotations are the increase in number of equations of motion due to the increase in number of degrees of freedom and the appearance of the higher gradient terms in the resulting equations. We also construct the multi-field continuum approximation capable of description not only long but also short waves.

Phonon emission from a discrete sine-Gordon breather

Phonon emission from a large-amplitude discrete sine-Gordon breather was studied numerically for a small degree of discreteness. In contrast to the case of highly discrete system investigated by Boesch and Peyrard (Phys. Rev. B 43 (1991) 8491), it was found that the resonance between the breather’s oscillation and the phonons of the lower phonon band edge (ja 0) takes place for a small degree of discreteness. ” 2000 Elsevier Science B.V. All rights reserved.