Innovative Wavelet Protocols in Analyzing Elastic Incoherent Neutron Scattering

Wavelet analysis has recently found a wide range of applications in Physics, Mathematics, and signal processing. This is mainly due to its ability to locally resolve a nonstationary signal in terms of functional forms, called mother wavelets, and to firmly locate trend anomalies in the signal. In the present paper, some examples of the application of wavelet analysis to elastic incoherent neutron scattering (EINS) data collected by the IN13 spectrometer at the Institute Laue Langevin (ILL) on water mixtures of the three homologous disaccharides, trehalose, maltose, and sucrose, and on literature data of dry and hydrated lysozyme and myoglobine as a function of temperature and of exchanged wave vector are presented. The experimental findings have been analyzed by means of a wavelet analysis that allows one to characterize the scattered elastic intensity behavior on different scales and to locate the discontinuities and the trend anomalies in the registered signal. This latter procedure is made possible thanks to the multiscale analysis, which allows, by decreasing the scale, one to localize the peculiar trend features. The entire body of the experimental findings reveals different transition temperatures for the three investigated disaccharides together with a stronger temperature dependence of the maltose/H2O and sucrose/H2O systems in comparison with the trehalose/H2O mixture, which signals a stronger character of this latter in comparison with the other two homologous disaccharides. These results justify the better ability of trehalose, with respect to maltose and sucrose, to encapsulate biostructures in a more rigid matrix