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
Per-unit system make manual analysis of power systems easier. Although power-system analysis is now done by computer, results are often expressed as per-unit values on a convenient system-wide base. Generally base values of power and voltage are chosen. The base power may be the rating of a single piece of apparatus such as a motor or generator. If a system is being studied, the base power is usually chosen as a convenient round number such as 10 MVA or 100 MVA. The base voltage is chosen as the nominal rated voltage of the system. All other base quantities are derived from these