  Power law is one of the the simplest forms of the relationship between
different variables of a system. It leads naturally to the introduction of
compound parameters describing physical properties of the system. Often one of
the variables of interest is the object dimension, or time. The prevalence of a
simple power law over the entire range of dimensions or times can be helpfully
interpreted as size or time independence of the corresponding compound physical
parameter of the system. However, it is also often found that a simple power
law only persists for some extreme values, e.g. for very large and/or small
sizes, or very short or long times. Transitions between regimes of different
power law asymptotic behaviour are encountered frequently in the description of
a wide variety of physical systems. While asymptotic power law behaviour may
often be readily predicted, e.g. on dimensional grounds, the evaluation of the
relationship between system parameters in the transition range usually requires
laborious detailed solution. To obviate this difficulty we introduce, on rather
general basis, something we refer to as the merging, or 'knee' function. The
function possesses sufficient flexibility to describe transitions of various
sharpness. To demonstrate its usefuness, the merging function is applied to a
variety of well-known scaling laws in the mechanics and strength of materials
and structures.
