The theoretical treatment of self-sustained periodic motion of the explosive crystallization ͑EC͒ front in a thin amorphous film is presented. The main attention is given to the study of nonlinear resonance phenomena occurring due to the presence of a small external periodic perturbation with the frequency being in the vicinity of the ordinary or parametric resonance. Weakly anharmonic oscillations of the EC front velocity are considered with the Van der Pole method, and the expressions for the limit cycle amplitude in the case of free and forced oscillations are derived. Depending on the values of kinetic and thermophysical parameters of the model, different kinds of resonance curves ͑i.e., front oscillation amplitudes versus frequency detuning͒ are obtained and analyzed. Our predictions may be tested experimentally by monitoring the explosive growth rate using the modulation of laser intensity or employing amorphous films with thickness periodicity. It is also shown that inclusion of the results of dynamic stability analysis changes the steady-state EC stability diagram in the (T s ,d) plane ͑T s is the substrate temperature and d the film thickness͒ so that the region of stable EC regimes becomes substantially more limited.
We calculate the eigenfrequencies of a cylindrical cavity with spirals contacting its ends. Explicit expressions are obtained for the case of a long cavity with one spiral contacting both ends and for the case of a cavity with one short spiral contacting one end. Calculations are also performed for the structures without constraints on the length and for a cavity with both spirals having close eigenfrequencies.
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