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 fatigue a wind driven turbine), those cycles can not be counted. Multiple time histories can be simulated for a given random process, but such procedure is cumbersome and computationally expensive. Vibration-fatigue methods offer a more effective approach, which estimates fatigue life based on moments of the PSD. This way, a value is estimated, that would otherwise be calculated with the time-domain approach. When dealing with many material nodes, experiencing different responses ("e.g." a model in a FEM package), time-histories need not be simulated. It then becomes viable, with the use of vibration-fatigue methods, to calculate fatigue life in many points on