Skewed Lorentzian pulses and exponential frequency power spectra

TL;DR

This paper demonstrates that superimposing uncorrelated Lorentzian pulses with random amplitudes results in an exponential frequency spectrum, unaffected by pulse skewness, asymmetry, or amplitude distribution, offering insights into spectra in chaotic fluids and plasmas.

Contribution

It shows that exponential spectra arise from superimposed Lorentzian pulses regardless of skewness or amplitude distribution, advancing understanding of spectral features in chaotic systems.

Findings

Exponential frequency spectrum is independent of pulse overlap and amplitude distribution.

Spectrum remains unaffected by pulse skewness and asymmetry.

Model explains exponential spectra in fluids and magnetized plasmas with chaotic behavior.

Abstract

Frequency power spectra due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes are considered. For pulses with constant duration, there is an exponential frequency spectrum which is independent of the degree of pulse overlap and the pulse amplitude distribution. The spectrum is furthermore shown to be unaffected by skewness of the Lorentzian pulses and even a random distribution of the pulse asymmetry parameter and its correlation with the pulse amplitude. This stochastic model provides new insight to the ubiquitous exponential spectra in fluids and magnetized plasmas exhibiting deterministic chaos, where non-linear advection processes lead to amplitude dependent steepening of smooth pulses.