We consider a discrete two-dimensional model of a crystal with particles having rotational degrees of freedom. We derive the equations of motion and analyze its continuum analog obtained in the long-wave limit. The continuum equations are shown to be the ones of the micropolar elasticity theory. The conditions when the micropolar elasticity equations can be reduced to the equations of conventional elasticity theory are discussed. We show that the rotational degrees of freedom are responsible for the anomalies in the elastic properties of some of the dielectric crystals.

Polarized Raman spectra of the proton ordered phase of ice Ih, i.e., ice XI, were measured above 400 cm(-1) in the range of librational, bending, and stretching vibrations. Vibrational modes in ice XI, of which symmetry is C(2v) (12)(Cmc2(1)), were discussed from the group theoretical point of view. In the librational mode spectra below 1200 cm(-1), several new peaks and clear polarization dependencies were observed. Assignments of the librational modes agree reasonably well with the recent MD calculations by Iwano et al. (J. Phys. Soc. Jpn. 79, 063601 (2010)). In contrast, the spectra for bands above 1200 cm(-1) show no distinct polarization dependencies and the spectra resemble those in ice Ih. In ice XI, however, fine structure composed of several weak peaks appear on the broad bending and the combination band. No direct evidence of the LO-TO splitting of the ν(3) anti-symmetric stretching mode was obtained. It is contrary to the case of the translational modes Abe and Shigenari (J. Chem. Phys. 134, 104506 (2011)). Present results suggest that the influence of the proton ordering in ice XI is weaker than the effect of inter- and intra-molecular couplings in the stretching vibrations of ice Ih.

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.

Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.

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