Multi-Scale Simulation of Nonlinear Thin-Shell Sound with Wave Turbulence

International audienceThin shells — solids that are thin in one dimension compared to the other two — often emit rich nonlinear sounds when struck. Strong excitations can even cause chaotic thin-shell vibrations, producing sounds whose energy spectrum diffuses from low to high frequencies over time — a phenomenon known as wave turbulence. It is all these nonlinearities that grant shells such as cymbals and gongs their characteristic " glinting " sound. Yet, simulation models that efficiently capture these sound effects remain elusive. We propose a physically based, multi-scale reduced simulation method to synthesize nonlinear thin-shell sounds. We first split nonlinear vibrations into two scales, with a small low-frequency part simulated in a fully nonlinear way, and a high-frequency part containing many more modes approximated through time-varying linearization. This allows us to capture interesting nonlinearities in the shells' deformation, tens of times faster than previous approaches. Furthermore, we propose a method that enriches simulated sounds with wave turbulent sound details through a phenomenological diffusion model in the frequency domain, and thereby sidestep the expensive simulation of chaotic high-frequency dynamics. We show several examples of our simulations, illustrating the efficiency and realism of our model

Phase Retrieval by Flattening the Wavefront

Many objects of interest in imaging, such as biological cells or turbulent air, are phase-only objects that are transparent and thus produce little to no contrast in wide-field microscopes. The phase accumulated by this light carries important information about the refractive index and the thickness of the object. We propose a method for retrieving the phase by using a spatial light modulator (slm) to conjugate the phase of the object, flattening the wavefront of light passing through the slm and the object. After we flatten the wavefront, the resulting configuration on the slm is the conjugate of the phase image, which we can easily invert to recover the original phase image. This method retrieves the phase without using any prior knowledge about the object. Our algorithm performs a decomposition of the image into basis functions and searches for the coefficients that yield the flattest output intensity pattern. This algorithm takes advantage of the fact that a relatively small number of basis elements can store the majority of the information in the image. Popular phase retrieval methods such as the Gerchberg¿Saxton algorithm can only converge to the phase image under light that is sufficiently coherent. From our simulations, we find that our method consistently produces correlations of over 99% with the original phase image, using either incoherent or coherent light and only 10% as many basis elements as the number of pixels in the image. We believe this result is a strong indication that this method will be able to reliably retrieve a direct phase image in the laboratory

Patenting and the early-stage high-technology investor:evidence from the field

We discuss the importance of patenting to the venture capital investor in high-technology firms. While literature suggests that patenting will have an impact on the nature and level of investment, the investors themselves are keen to suggest otherwise. We investigate this issue by the use of new primary-source empirical data, gathered by fieldwork methods. Our results help to explain a link between the existence of patenting and the level of investment made. We further support our analysis with illuminating quotes from investors currently active in the field