The data of cratering in the penetration of high velocity impact of tungsten,steel,zirconium and titanium ball projectiles against steel and aluminium target plates are given,the corresponding scaling relations are discussed.

The self-similarity in earthquake phenomena has been widely manifested invarious seismological observations such as the magnitude-frequency relation, theaftershock decay rate, and the scaling relation of seismic spectrum.

This paper presents a review on the research progress of the flow behavior of weak negatively buoyant jets injected into homogeneous and linearly stratified ambient fluids by using the dimensional analysis and the scaling analysis,and the validation and quantification of the scaling relations characterizing the flow behavior by using direct numerical method.

The universality proposal and their scale relation in aging phenomena were predicted.

The results conform quite well to the scaling law presented by de-Gennes.

Employing a realistic many-body potentials for a series of simple melts, including Ag, Al, Au, Co, Cu, Mg, Ni, Pb, Pd, Pt, Rh and Si, and using the molecular-dynamics simulation the scaling laws of viscosity with different expressions of the reduction parameters were studied.

The scaling law between the torus doubling bifurcation number p and the forcing frequency ω of the forced logistic map is presented.