Fig. 4: Diffusion and localization fluctuations in encapsulated microbubble-doped gel.
From: Observation of a transition to a localized ultrasonic phase in soft matter
a Pressure P versus time t for an encapsulated microbubble volume fraction ϕ = 1.2% measured in different speckles. The incident wavepacket is based on a Gaussian first derivative, which provides a narrow impulse. The coherent pressure field is observable for 260 μs < t < 268 μs, and is followed by the incoherent field. Inset: measured frequency spectrum of the incident wavepacket. b Incoherent pressure field after time-windowing the data shown in (a). c Normalized transmitted intensity peak envelope I/IO versus t for ϕ = 1.2% after digitally filtering the data in (b) to include the 400–550 kHz range. Here, I/IO is found from averaging over 11 different speckle measurements. Normalization is done so the input pulse peak is unity. The dashed red line is a linear fit to the data. d I/IO versus t for ϕ = 2.7% and for the 340–465 kHz range. Here, I/IO is found from averaging over 11 different speckle measurements. The dashed red line is the result of a linear fit to the data similar to that shown in (c). The solid blue line is a fit to the self-consistent theory (SCT) of localization. Note, the time range in (a, b) is the experiment time while in (c, d) the time range has been shifted so the maximum in I/IO for the incoherent field occurs shortly after t = 0s.
