PACS 43.35.+d -Acoustics: Ultrasonics, quantum acoustics, and physical effects of sound PACS 46.40.-f -Vibrations and mechanical waves PACS 45.50.-j -Dynamics and kinematics of a particle and a system of particles Abstract -It is demonstrated that broad-bandwidth ultrasonic signals containing frequency components in excess of 200 kHz can be created in spherical chains using harmonic excitation at 73 kHz. Multiple reflections created a periodic waveform containing both harmonics and subharmonics of the original forcing frequency, due to non-linear Hertzian contact. These discrete frequencies represented some of the many allowed non-linear normal modes of vibration of the whole chain. Excitation at a single fixed frequency could thus be used to produce wide-bandwidth impulses for different lengths of spherical chains. Experimental results were in good agreement with theoretical predictions.

A narrowband ultrasound source has been used to generate solitary wave impulses in finite-length chains of spheres. Once the input signal is of sufficient amplitude, both harmonics and sub-harmonics of the input frequency can be generated as non-linear normal modes of the system, allowing a train of impulses to be established from a sinusoidal input. The characteristics of the response have been studied as a function of the physical properties of the chain, the input waveform and the level of static pre-compression. The results agree with the predictions of a theoretical model, based on a set of discrete dynamic equations for the spheres for finite-length chains. Impulses are only created for very small pre-compression forces of the order of 0.01N, where strongly non-linear behaviour is expected.

A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory.

The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The discretization of its weak formulation leads to a dense system of linear equations, which is typically solved with an iterative linear method such as GMRES. The application of BEM to simulating wave propagation through large-scale geometries is only feasible when compression and preconditioning techniques reduce the computational footprint. Furthermore, many different boundary integral equations exist that solve the same boundary value problem. The choice of preconditioner and boundary integral formulation is often optimized for a specific configuration, depending on the geometry, material characteristics, and driving frequency. On the one hand, the design flexibility for the BEM can lead to fast and accurate schemes. On the other hand, efficient and robust algorithms are difficult to achieve without expert knowledge of the BEM intricacies. This study surveys the design of boundary integral formulations for acoustics and their acceleration with operator preconditioners. Extensive benchmarks provide valuable information on the computational characteristics of several hundred different models for multiple reflection and transmission of acoustic waves.

In this article, a wave propagation model is presented as the first step in the development of a new type of transluminal procedure for performing elastography. Elastography is a medical imaging modality for mapping the elastic properties of soft tissue. The wave propagation model is based on a Kelvin Voigt Fractional Derivative (KVFD) viscoelastic wave equation, and is numerically solved using a Finite Difference Time Domain (FDTD) method. Fractional rheological models, such as the KVFD, are particularly well suited to model the viscoelastic response of soft tissue in elastography. The transluminal procedure is based on the transmission and detection of shear waves through the luminal wall. Shear waves travelling through the tissue are perturbed after encountering areas of altered elasticity. These perturbations carry information of medical interest that can be extracted by solving the inverse problem. Scattering from prostate tumours is used as an example application to test the model. In silico results demonstrate that shear waves are satisfactorily transmitted through the luminal wall and that echoes, coming from reflected energy at the edges of an area of altered elasticity, which are feasibly detectable by using the transluminal approach. The model here presented provides a useful tool to establish the feasibility of transluminal procedures based on wave propagation and its interaction with the mechanical properties of the tissue outside the lumen.