Resonance-type Behaviour Research Articles

Resonance-type behaviour in a system of nonlinear wave equations

Consider the Cauchy problem for a system of two wave equations in R 3: c 1 2 ∂ t 2 u 1 − Δu 1 = u′ 1 u′ 2 c 2 2 ∂ t 2 − Δu 2 = u′ 1 u′ 2, where prime stands for any partial derivative in space or time variables. If initial data is small in a suitable norm, the following phenomenon occurs: if c 1 ≠ c 2 the system possesses smooth solutions for all t > 0, whereas if c 1 = c 2 the solutions of the system might blowup. The result is proved for a more general form of the above system in the case of a three space dimension; also a similar result is proved for two space dimensions.

Anomalous low-frequency resonance-type behaviour and negative capacitance in doped glasses

It has been found that the dielectric capacitance response of doped silica glasses measured in the frequency range 10-3-105 Hz for temperatures between 500 and 1100K displays anomalous thermally activated resonance-type behaviour. This response is linked to time domain oscillations reported in similar materials. It is shown that negative capacitance can result from these time domain oscillations under certain conditions. One material in which negative capacitance has been seen, a doped boric oxide glass, is also discussed.

Amplitude- and frequency-dependent ultrasonic attenuation in indium-doped tin at 1.3K

The ultrasonic attenuation due to dislocations was studied in the range 3.6-30 MHz in a single crystal of tin doped with 0.0016 at% indium at 1.3K in the normal and superconducting states. The attenuation at various pulse amplitudes shows peaks in both states. The attenuation peaks due to the breakaway of the dislocations from minor pinning points were used to calculate the dislocation resonance frequency. The breakaway stress is found to decrease with increasing frequency in both states. The attenuation shows resonance-type behaviour as a function of frequency. In the superconducting state unpinning starts at a lower pulse amplitude and there is a systematic decrease of the resonance frequency with increasing amplitude. In the normal state there is evidence of unpinning at higher values of pulse amplitude. The nature of the variation of attenuation with amplitude and frequency in both the states has been explained on the basis of Rogers theory (1962).

Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.

Inverse bremsstrahlung absorption in large radiation fields during binary collisions in the Born approximation. III. Inelastic collisions

For pt.II see ibid., vol.9, no.3, p.463 (1976). The simultaneous absorption of radiation and atomic excitation in the course of an electron collision with an atom is described by means of the Born approximation and a generalisation of the usual inelastic cross section formula derived. The asymptotic limits for large fields are investigated. Resonance-type behaviour may occur. The significance of these results in gas breakdown experiments at high fields is discussed. The collisional excitation rate by electrons with a Maxwellian velocity distribution is calculated. At high temperatures the field leads to a reduction in the excitation rate. However, at low temperatures a substantial increase can occur if the field is sufficiently strong.

Frequency shift of acoustic wave in ferromagnet in presence of magnetic field

Frequency shift (or velocity shift) of acoustic wave in ferromagnet at low temperature in presence of matnetic field applied along hard direction has been calculated and a resonance typebehaviour has been found.