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
Welfare cost of business cycles output gap. Under this viewpoint, the welfare cost of business cycles is larger, because an economy with cycles not only suffers more variable consumption, but also lower consumption on average. If we consider two consumption paths, each with the same trend and the same initial level of consumption – and as a result same level of consumption per period on average – but with different levels of volatility, then, according to economic theory, the less volatile consumption path will be preferred to the more volatile one. This is due to risk aversion on part of individual agents. One way to