Jean Pierre Boon | PubMed Health

PubMed2004

Structural and dynamical characterization of Hele-Shaw viscous fingering.

Viscous fingering occurs in the interfacial zone between two fluids confined between two plates with a narrow gap (Hele-Shaw geometry) when a highly viscous fluid is displaced by a fluid with relatively low viscosity. Using a mesoscopic approach--the lattice Boltzmann method--we investigate the dynamics of spatially extended Hele-Shaw flow under conditions corresponding to various experimental systems by tuning the 'surface tension' and the reactivity between the two fluids. We discuss the onset of the fingering instability (dispersion relation), analyse the structural properties (characterization of the interface) and the dynamical properties (growth of the mixing zone) of the Hele-Shaw systems, and show the effect of reactive processes on the structure of the interfacial zone.

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PubMed1995

Dynamical systems theory for music dynamics.

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of temporal dynamics in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the global dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra ( approximately f(-nu)) close to red noise (nu approximately 2) in the low frequency range. (iii) We define an information entropy which provides a measure of the local dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of complexity in the music, but there is no evidence of an analytical relation between local and global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century. (c) 1995 American Institute of Physics.

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