Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
Atmospheric physics with height. A consequence of this is that their amplitudes naturally increase exponentially as the tide ascends into progressively more rarefied regions of the atmosphere (for an explanation of this phenomenon, see below). In contrast, the density of the oceans varies only slightly with depth and so there the tides do not necessarily vary in amplitude with depth. Note that although solar heating is responsible for the largest-amplitude atmospheric tides, the gravitational fields of the Sun and Moon also raise tides in the atmosphere, with the lunar gravitational atmospheric tidal effect being significantly greater than its solar counterpart. At ground