Shape descriptors for mode-shape recognition and model updating

The most widely used method for comparing mode shapes from finite elements and experimental measurements is the Modal Assurance Criterion (MAC), which returns a single numerical value and carries no explicit information on shape features. New techniques, based on image processing (IP) and pattern recognition (PR) are described in this paper. The Zernike moment descriptor (ZMD), Fourier descriptor (FD), and wavelet descriptor (WD), presented in this article, are the most popular shape descriptors having properties that include efficiency of expression, robustness to noise, invariance to geometric transformation and rotation, separation of local and global shape features and computational efficiency. The comparison of mode shapes is readily achieved by assembling the shape features of each mode shape into multi-dimensional shape feature vectors (SFVs) and determining the distances separating them. © 2009 IOP Publishing Ltd

Microbubble shape oscillations excited through ultrasonic parametric driving\ud

An air bubble driven by ultrasound can become shape-unstable through a parametric instability. We report time-resolved optical observations of shape oscillations (mode n=2 to 6) of micron-sized single air bubbles. The observed mode number n was found to be linearly related to the ambient radius of the bubble. Above the critical driving pressure threshold for shape oscillations, which is minimal at the resonance of the volumetric radial mode, the observed mode number n is independent of the forcing pressure amplitude. The microbubble shape oscillations were also analyzed numerically by introducing a small nonspherical linear perturbation to a Rayleigh-Plesset-type equation, capturing the experimental observations in detail.\ud \u

Shape-preserving diffusion of a high-order mode

The close relation between the processes of paraxial diffraction and coherent diffusion is reflected in the similarity between their shape-preserving solutions, notably the Gaussian modes. Differences between these solutions enter only for high-order modes. Here we experimentally study the behavior of shape-preserving high-order modes of coherent diffusion, known as 'elegant' modes, and contrast them with the non-shape-preserving evolution of the corresponding 'standard' modes of optical diffraction. Diffusion of the light field is obtained by mapping it onto the atomic coherence field of a diffusing vapor in a storage-of-light setup. The growth of the elegant mode fits well the theoretical expectations

Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.Comment: 20 pages, 6 figures, accepted for publication in PLoS On