We demonstrate new powerful methods of statistical analysis of atmospheric aerosols on the example of urban background aerosol in the Brisbane area, Australia. It is shown that even in the absence of notable features on the size distribution, it is still possible to identify distinct particles modes and analyze their mutual interactions and transformations. The obtained unique anti-symmetric correlation patterns between particle modes may serve as fingerprints of particular evolutionary processes in the background aerosols. The obtained results suggest that thermal fragmentation of nano-particles may be one of the major physical mechanisms shaping urban background aerosols. In particular, based on the fragmentation theorem, we demonstrate possible existence of substantially different time scales for fragmentation of atmospheric aerosols. The proposed approaches and obtained results may also be important for the analysis of different types of atmospheric aerosols on local, regional and global scales.