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Theory and implementation

nMOLDYN allows one to calculate the memory function related to the incoherent intermediate scattering function as well. It is defined through the corresponding memory function equation

| (4.164)

The memory function , which depends on q as well as on time, permits the analysis of memory effects on different length scales. As in the previuos cases, the numerical calculation of the memory function equation relevant to the incoherent intermediate scattering function is based on the Autoregressive model, the discrete time signal being here

| (4.165)

See section 4.2.4.11 for more details about auto-regressive process.

In the framework of the Autoregressive model nMOLDYN allows the intermediate coherent scattering function, its Fourier spectrum (the incoherent dynamical structure factor) and its memory function to be computed on a rectangular grid of equidistantly spaced points along the time- and the q-axis, repectively. The user is referred to Section 4.2.4.11 for more theoretical details. The dynamical variable of the correlation function under consideration

| (4.166)

is considered as a discrete "signal", which is modeled by an autoregressive stochastic process of order P. For each q-values the program calculates a set of P complex coefficients for the AR model averaging aver all atoms of the system and over all cartesian components. The correlation functions and their Fourier spectra are then computed according to the algorithm described in Section 4.2.4.11. Starting from the discretized memory function equation, whitch relates the time evolution of the correlation function to its memory function (see Section 4.2.4.11), and using the correlation function calculated by the AR model, the program computes for each q-value the discretized memory function. The program performs the above calculations isotropically.

Next: Parameters Up: Dynamic Incoherent Structure Factor Previous: Dynamic Incoherent Structure Factor Contents