Zipf's law in photoacoustics, in nature, and in society

Abstract

Regularities in some complex systems can sometimes be expressed in terms of simple laws. A peculiar regularity is identified concerning photoacoustic (optoacoustic) phenomena. In particular, the acoustic signals following phase transitions in liquid irradiated by laser pulses are distributed by magnitude according to the Zjif’s law. This power law distribution describes many man made and naturally occurring phenomena, including city sizes, incomes, word frequencies, and earthquake magnitudes. This law suggests connection with anomalous decay, i.e. it implies that small occurrences are extremely common, whereas large instances are extremely rare. We use this law for signal processing in the course of optoacoustic diagnostics of diluted suspensions. The irradiation of an inhomogeneous liquid sample with a long train of short laser pulses and subsequent recording of a histogram of the magnitudes of the acoustic responses can serve as a diagnostic tool for various applications. The absorption of an incident light by a suspended particle may cause a cavitation event. The random cavitation events also obey the Zipf’s law, this fact being used for detection of individual particles.