Smearing function

One widely used smearing method was developed by Methfessel and Paxton. Their method uses expressions for the smearing functions that are more complicated than the simple example above but are still characterized by a single parameter, ct (see Further Reading). 

The power-time-pitch representations px (t, z) and py(t, z) are convolved with the frequency-smearing function A, as can be derived from Eq. (1.1), leading to excitation-time-pitch (dB exc, seconds, Bark) representations Ex (t, z) and Ey (t, z) (see Appendices B, C, D of [Beerends and Stemerdink, 1992]). The form of the frequency-smearing function depends on intensity and frequency, and the convolution is carried out in a non-linear way using Eq. (1.2) (see Appendix C of [Beerends and Stemerdink, 1992]) with parameter afreq ... 

Figure 1.7 Overview of the basic transformations which are used in the development of the PAQM (Perceptual Audio Quality Measure). The signals x(t) and y t) are windowed with a window w(t) and then transformed to the frequency domain. The power spectra as function of time and frequency, Px (t, f) and Py(t, /) are transformed to power spectra as function of time and pitch, px(t, z) and py(t, z) which are convolved with the smearing function resulting in the excitations as a function of pitch Ex (/, z) ar 6Ey(t, z). After transformation with the compression function we get the internal representations x(f, z)and ,(, z) from which the average noise disturbance Cn over the audio fragment can be calculated.

Figure 8.5 (a) The DOS for MgO and the smearing function (f( )) used for calculating the state occupancy. (This has a maximum value of 1.) (b) The DOS ofTi02 (rutile). Both calculations used the VASP code with PAW pseudopotentials and the PW91 functional a Gaussian smearing of 0.2eV has been used... 

One of the most often cited criticisms of this method is the assmnption of discontinuous filling of the micropores and the complete filling of a pore at a specific pressure characteristic of its size [9,45,47,50]. This assumption is commonly referred to as the condensation approximation in Hterature. However, other theoretical models for the prediction of adsorption such as Monte Carlo simulations or NL-DFT theory show that this picture is valid only for very small micropores (Z, < 2.0 run) For larger-sized pores, the filling process is shown to be stepwise and proceeds by the formation of an initial monolayer on the pore walls and the subsequent condensation of the sorbate in the inner part of the pore [47]. This aspect of the model often results in the calculated PSD to be more polydisperse than the true distribution and is quite difficult to correct. One of the remedies suggested by Kaminsky et al. [45] could be to consider the calculated PSD to be a convolution of the true PSD. If a smearing function characteristic of the method can be determined, the true distribution can be mathematically deconvoluted from the HK-predicted PSD. 

Furthermore, we showed for the first time the principal possibility of obtaining the correlation induced smearing of the occupation number function from ultra-high resolved Compton spectra and presented the first test experiments on Li. 

I are the thermally smeared Fourier transforms of the basis function pairs summed over all the equivalent unit cell sites,... 

Fast methods for evaluating these integrals for the case of gaussian basis functions are known [12], Also, Hall has described how to get the symmetry operators (B) 1SjB, r, for any crystal space group [13]. The parameters account for thermal smearing of the charge density. In this work I use the form recommended by Stewart [14],... 

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