Spinodal decomposition both complete one cycle per second—but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.) If A(β) is the amplitude of a Fourier component of wavelength λ and wavenumber β = 2π/λ the spatial variation in composition can be expressed by the Fourier integral: in which the coefficients are defined by the inverse relationship: Substituting, we obtain on equating coefficients: This is an ordinary differential equation that has the solution: in which "A(β)" is the initial amplitude of the Fourier component of wave wavenumber β
Vibration theory of olfaction effect in no way argues exclusively for a vibrational theory of olfaction. A study published in 2011 by Franco, Turin, Mershin and Skoulakis shows both that flies can smell deuterium, and that to flies, a carbon-deuterium bond smells like a nitrile, which has a similar vibration. The study reports that drosophila melanogaster (fruit fly), which is ordinarily attracted to acetophenone, spontaneously dislikes deuterated acetophenone. This dislike increases with the number of deuteriums. (Flies genetically altered to lack smell receptors could not tell the difference.) Flies could also be trained by electric shocks either to avoid the deuterated molecule or to