Surface Instability of a Vertically Oscillating Granular Layer

In the study of the surface instability of a vertically oscillating granular layer,we obtained experimentally the phase diagram for the surface states of the layer in the driving frequency-acceleration plane,and measured the dispersion relation for the surface waves in a granular layer in comparison to that in viscous fluids.Our experiments show that the onset dimensionless acceleration increases with the driving frequency,and the wavelength of the surface waves increases with the depth of granular layer.These experimental results are in agreement with our theoretical model qualitatively.

Dynamic Casimir Effect in Single Bubble Sonoluminescence

The bubble dynamics for the single bubble sonoluminescence(SBSL)has been coupled with the dynamic Casimir effect due to the quantum vacuum fluctuation.The numerical results show that the power radiated by the Casimir effect is on the order of 10-38 Wand too weak to fit the experimented observation of SBSL although the spectrum of the radiation can be fitted well.It is impossible to take the quantum Casimir effect as a candidate for the origin of SBSL.

Calculation of a Nonuniform and Nonadiabatic Model of Sonoluminescence

A nonuniform and nonadiabatic model has been developed to research the gas dynamics within a bubble of sonoluminescence.The model includes three diffusive effects of gas viscosity,thermal conduction and radiative transport simultaneously,and calculations prove that they have important influences on the characteristics of sonoluminescence.The model has been solved numerically and gives the results of about 104 K peak temperature and l00ps pulse duration which are consistent with recent experiments.

Effect of the Boundary on the Dynamics of Solitary Waves

The effect of the boundary on the dynamics of solitary waves has been studied.The inverse scattering transformation for the solitary wave equation with boundary condition is treated by the reduction group theory.The effective potential of interaction between the solitary wave and the boundary is found to be same as the Morse potential.The physical mechanism of the soliton oscillation could be interpreted by our results.

Effects of Pulse Drive on Single Bubble Sonoluminescence

Single bubble sonoluminescence(SBSL)flashes have been steadily upscaled by a sinusoidal wave with a pulse at each cycle at some suitable phase positions,which proves the prediction of the spiking SBSL suggested by Moss et al.[Phys.Lett.A 211(1996)69].Based on the Rayleigh-Plesset bubble dynamics,the numerical simulation shows a well qualitative agreement with those measured in experiment.

A Dynamical Model for a Thin Layer of Granular Materials

A dynamical model is presented for a thin layer of granular materials similar to that for shallow viscous fluid.We have obtained analytically the expressions for the“thermal expansion”,dispersion relation,and dependence of instability onset on driving frequency and viscosity,which are in agreement with experiments.The numerical calculation for the nonlinear problem reproduces the experimental phenomena for a one-dimensional system.

Internal Subharmonic Resonance in Faraday Experiment

The classical Faraday experiment is a tractable problem in nonlinear physics,and its rich spectrum of nonlinear phenomena has made it a prototype in studying nonlinear wave dynamics in general.Here we report the ob servation of a new type of subharmonic resonances which occurs at some smaller fractional frequencies,such asν/3,ν/4,andν/6,whereνis the forcing frequency.As a result of these resonances,the lower-order surface-wave modes whose eigenfrequencies are close to the fractional frequencies participate into the wave motions.Our theory involving quadratically nonlinear mode couplings shows that an already excited mode itself can act as a parametric source on the lower-order primary modes,thus leading to the cascading subharmonic resonances.

Synchronous Spatiotemporal Oscillation Between Two Parametrically Excited Bound States

The bound state is one of the elemental localized excitations in a parametrically driven systems.In the molecule-like structure,the two identical solitons can interact with each other as a classic“oscillator”.Here the dynamics of two interacting bound states is explored by both experiment and computation.The experiment reveals several important dynamical features,in particular,the polarity ordering rule that determines the stability of a compound structure,and the synchronization in the coupling pairs of opposite polarity which leads to a symmetric and harmonic spatiotemporal oscillation.All these interesting phenomena are numerically simulated with the parametrically driven,damped nonlinear Schröding equation,and their nonlinear dynamics is further concluded as a stability diagram in parameter space.

BIFURCATION IN AIR ACOUSTIC SYSTEMS

In this paper we report the observation and measurement of period-doubling bifurcation in two air acoustic systems, one from the direct radiation of the high power loudspeaker, and the other from the coupling with small cavities situated at its throat.