1. S.V.Dmitriev, T.Shigenari, S.M.Volkova, A.A.Vasiliev and K.Abe, Dynamics of Autowaves in a One-Dimensional Crystal Model. Computational Materials Science 13, 227 (1999).
2. T.Shigenari, S.V.Dmitriev, A.A.Vasiliev and K.Abe, Domain wall solutions for EHM model of crystal. Journal of the Physical Society of Japan 68, 117 (1999).
3. A.A.Vasiliev, A.E.Miroshnichenko, S.V.Dmitriev Modelling of short-wave structures in a hinged chain with interior stress and two-periodic external loadings in nonlinear elastic medium. Modelling of complex systems. Issue 1. Tver State University, 1998. Pp. 7-13. (in Russian, .PS - file, 836Kb).
4. S.V.Dmitriev, T.Kumata, T.Shigenari and K.Abe, Computer simulation for the incommensurate phase near the lock-in transition, J. Korean Phys. Soc. 32, 907 (1998).
5. S.V.Dmitriev, T.Shigenari and K.Abe, Thermally activated motion of domain wall in a crystal with a small degree of discreteness. Computational Materials Science 11, 227 (1998).
6. S.V.Dmitriev, T.Shigenari and K.Abe, Mechanisms of transition between 1q and 2q incommensurate phases in two-dimensional crystal model. Physical Review B58, 2513 (1998).
7. S.V.Dmitriev, T.Shigenari and K.Abe, Mechanism of transition between 1q and 3q incommensurate phases in two-dimensional crystal model. Ferroelectrics 217, 179 (1998).
8. S.V.Dmitriev, T.Shigenari and K.Abe, One-dimensional crystal model for incommensurate phase. II. Compressible molecules. Journal of the Physical Society of Japan 66, 2732 (1997).
9. S.V.Dmitriev, T.Shigenari, A.A.Vasiliev and K.Abe, Dynamics of domain walls in an incommensurate phase near the lock-in transition: One-dimensional crystal model. Physical Review B55, 8155 (1997).
10. T.Shigenari, A.A.Vasiliev, S.V.Dmitriev and K.Abe, Domain walls in one-dimensional 3-periodic structure. Ferroelectrics 203, 335 (1997).
11. S.V. Dmitriev, K.Abe and T.Shigenari, One-dimensional crystal model for incommensurate phase. I. Small Displacements limit. Journal of the Physical Society of Japan 65, 3938 (1996).

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1. S.V.Dmitriev, T.Shigenari, S.M.Volkova, A.A.Vasiliev and K.Abe, Dynamics of Autowaves in a One-Dimensional Crystal Model. Computational Materials Science 13, 227 (1999).

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.

2. T. Shigenari, S.V.Dmitriev, A.A.Vasiliev and K.Abe, Domain wall solutions for EHM model of crystal. Journal of the Physical Society of Japan 68, 117 (1999).

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.

3. A.A.Vasiliev, A.E.Miroshnichenko, S.V.Dmitriev Modelling of short-wave structures in a hinged chain with interior stress and two-periodic external loadings in nonlinear elastic medium. Modelling of complex systems. Issue 1. Tver State University, 1998. Pp. 7-13. (in Russian).

For a hinged chain of finite-size rigid particles in a nonlinear medium, subjected to an interior stress and two-periodic external forces, the two- and four-periodic solutions were obtained and studied. The domains of existents for these solutions in the space of parameters of the system were found with the use of the Catastrophe Theory. Different kinds of transitions between two- and four-periodic solutions were analyzed numerically for some path in the parameter space. In frame of continuum many-field approximation the solution of the form of domain wall between two different two-periodic solutions was found.

4. S.V.Dmitriev, T.Kumata, T.Shigenari and K.Abe, Computer simulation for the incommensurate phase near the lock-in transition, J. Korean Phys. Soc. 32, 907 (1998).
5. S.V.Dmitriev, T. Shigenari and K.Abe, Thermally activated motion of domain wall in a crystal with a small degree of discreteness. Computational Materials Science 11, 227 (1998).

In the frame of the one-dimensional elastically hinged molecule (EHM) model of crystal the thermally activated motion of a rather wide domain wall (DW) was studied by numerical simulation at temperatures much higher than Peierls-Nabarro barrier but much lower than kink-pair nucleation temperature. It was found that DW undergo Brownian-like motion and at some moments the drift velocity of DW can be changed by obtaining (losing) some energy from (to) thermal fluctuations

6. S.V.Dmitriev, T.Shigenari and K.Abe, Mechanisms of transition between 1q and 2q incommensurate phases in two-dimensional crystal model. Physical Review B58, 2513 (1998).

The two-dimensional elastically hinged molecule model of a crystal which contains two anharmonic terms was studied numerically. The results show that the 1 q or 2q incommensurate phase can be stable depending on the parameters of the model. For example, in the sinusoidal incommensurate regime the 1q (2q) phase can be globally stable but in the domain-wall regime the situation can be opposite and the 1q↔2q (1q↔2q) transition can be expected. Another mechanism of the 1q↔2q phase transition stems from the softening of the dispersion surface simultaneously at two points of the Brillouin zone, (к_x, 0) and (0, к_y). In this case the 2q modulated phase can appear as a linear combination of the two 1q modulated phases. Under the assumption that the dispersion surface is slightly perturbed for some reason, the softening first occurs at one of the two points resulting in the 1q phase formation. Further changing of the external parameters leads to the softening at the second point and the 1q↔2q transition can take place. Both these mechanisms of the 1q↔2q phase transition were revealed and studied.

7. S.V.Dmitriev, T.Shigenari and K.Abe, Mechanism of transition between 1q and 3q incommensurate phases in two-dimensional crystal model. Ferroelectrics 217, 179 (1998).

The one-dimensional elastically hinged molecule (EHM) microscopic model of a crystal was generalised to two dimensions on the base of the hexagonal lattices. The two-dimensional model contains two anharmonic terms which allow, depending on parameters of the model, the stability of 1q, 2q or 3q modulated phase. The phase transition between 1q and 3q IC phases characteristic to the hexagonal system was studied numerically by the molecular dynamics technique. The model shows the sequence of phases as it is in quartz on cooling and explains the increase of the 1q IC phase temperature range in quartz under uniaxial stress.

8. S.V.Dmitriev, T.Shigenari and K.Abe, One-dimensional crystal model for incommensurate phase. II. Compressible molecules. Journal of the Physical Society of Japan 66, 2732 (1997).

Influence of the external pressure on the commensurate-incommensurate (IC) phase transition was studied in the frame of the elastically hinged molecule model of crystal which was recently proposed by the present authors. The case of compressible but rather hard molecules was treated.

9. S.V.Dmitriev, T.Shigenari, A.A.Vasiliev and K.Abe, Dynamics of domain walls in an incommensurate phase near the lock-in transition: One-dimensional crystal model. Physical Review B55, 8155 (1997).

A phase transition from a high-symmetry to a low-symmetry commensurate phase through an incommensurate phase was studied in the framework of the one-dimensional elastically hinged molecule model which includes only a fourth-order anharmonic potential. The phase diagram with respect to the harmonic-potential coefficient and the external force was obtained. From the numerical analysis of the equation of motion, it was shown that the incommensurate phase near the lock-in transition contains a periodic system of energetically equivalent domain walls which are mutually repulsive. The properties of the domain walls were studied and the lock-in transition was described as the annihilation process of the walls when the repulsion is changed to attraction.

10. T.Shigenari, A.A.Vasiliev, S.V.Dmitriev and K.Abe, Domain walls in one-dimensional 3-periodic structure. Ferroelectrics 203, 335 (1997).

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 molecules model of crystal which was recently proposed by the present authors. The case of discommensurations in the 3-periodic commensurate phase was discussed and the analytical expression for the displacements near the domain wall was derived in continuum approximation. The interaction of the domain pattern with the external field, processes of collision and breakup of domain walls were investigated.

11. S.V.Dmitriev, K.Abe and T.Shigenari, One-dimensional crystal model for incommensurate phase. I. Small Displacements limit. Journal of the Physical Society of Japan 65, 3938 (1996).

A simple one-dimensional crystal model was proposed in order to study the incommensurate phase formation and its properties were numerically analyzed. In this model each particle (molecule) of the crystal has two degrees of freedom so that a longitudinal sound wave propagation is possible. In the case of small displacements and incompressible molecules the model has the Hamiltonian identical to that for a linear chain with a local fourth order anharmonic potential and the harmonic nearest- and next-nearest-neighbor interactions. Particular emphasis has been placed on the analysis of the incommensurate phases caused by the soft modes with short wavelength which has not been studied in most of the previous investigations.