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
Problem of why there is anything at all that the question cannot have a causal explanation (as any cause must itself have a cause) or a contingent explanation (as the factors giving the contingency must pre-exist), and that if there is an answer it must be something that exists necessarily (i.e. something that just exists, rather than is caused). Gottfried Wilhelm Leibniz wrote: ""Why is there something rather than nothing? The sufficient reason [...] is found in a substance which [...] is a necessary being bearing the reason for its existence within itself."" Philosopher of physics Dean Rickles has argued that numbers and mathematics (or their underlying laws)