We present a simple analytical description of transient vibrations of forced anharmonic oscillator in terms of periodic non-smooth functions. Such a description (in chosen variables) is similar to that of a vibro-impact process. The main attention is paid to properties of the limiting phase trajectories (LPTs) describing intensive energy exchange between the oscillator and external force. We show that two dynamical transitions occur in the undamped system under consideration with increasing parameter of nonlinearity. The first transition consists in fast change of slow modulation period and drastic change of amplitude. This transition is characterized by appearance of dynamics resembling vibro-impact behavior in appropriate coordinates (amplitude and phase shift between the oscillator and external force). It corresponds to qualitative transformation of the LPT. The second transition corresponds to annihilation of two stationary points. Numerical study confirms our analytical results.
We carry out a molecular dynamics simulation of the first stages of constrained melting in crystalline polyethylene (PE). When heated, the crystal undergoes two structural phase transitions: from the orthorhombic (O) phase to the monoclinic (M) phase, and then to the columnar (C), quasi-hexagonal, phase. The M phase represents the tendency to the parallel packing of planes of PE zigzags, and the C phase proves to be some kind of oriented melt. We follow both the transitions O→M and M→C in real time and establish that, at their beginning, the crystal tries (and fails) to pass into the partially ordered phases similar to the RI and RII phases of linear alkanes, correspondingly. We discuss the molecular mechanisms and driving forces of the observed transitions, as well as the reasons why the M and C phases in PE crystals substitute for the rotator phases in linear alkanes.
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