Fast Fourier transformation of the

The framework we adopted for measuring the scaling behavior from AFM images is the following. The 2-D power spectral density (PSD) of the Fast Fourier Transform of the topography h(x, y) is estimated [541, then averaged over the azimuthal angle

[Pg.413]

Figure 7. High resolution TEM image of a single Au nanoparticle observed inside a stem of alfalfa seedlings grown in gold emiched medium. The inset corresponds to the fast Fourier transform of the crystalline particle. (Reprinted from Ref. [28], 2002, with permission from American Chemical Society)...

Orbitrap The newest of the major mass analyzers, the Orbitrap is a hybrid MS consisting of a LIT mass analyzer, or transmission quadmpoles connected to the high-resolution Orbitrap mass analyzer. The Orbitrap utilizes electrical fields between sections of a roughly egg-shaped outer electrode and an inner (spindle) electrode (Chapter 5). Ions orbit between the inner and outer electrodes and their oscillation is recorded on detector plates (Hardman and Makarov, 2003 Hu et al., 2005). As with the FTICR, fast Fourier transform of the raw data is used to convert the data for mass analysis, making the Orbitrap the second major type of FTMS instrument. The resolving power of the Orbitrap is intermediate... 

Following a fast Fourier transform of the data, the power spectrum shows the power (the Fourier transform squared) as a function of frequency. Random and chaotic data sets fail to demonstrate a dominant frequency. Periodic or quasi-periodic data sets will show one or more dominant frequencies [37]. 

Figure 51 Fast Fourier transform of the potential noise from two nominally identical carbon steel electrodes exposed to 0.2 M HC1 + 0.5 M NaCl + 0.15 M NaN02. (Data courtesy of J. Yuan, M. Inman, T. Lunt, J. Hudson, University of Virginia.)...

The structure factor expression given by Eq. 3 is too computer time intensive for practical purposes. Approximations are usually made in order to make crystallographic refinement feasible. One such approximation consists of computing Fcaicih) by numerical evaluation of the atomic electron density on a finite grid followed by Fast Fourier transformation of the electron density. This speeds up the calculation by at least an order of magnitude [20,21]. Another approximation keeps the first derivatives of Exray constant during the refinement process until any atom has moved by more than a specified small distance relative to the position at which the derivatives were last computed [22]. 

It is usual in laminar mixing simulations to represent the flow using tracer trajectories. The computation of such flow trajectories in a coaxial mixer is more complex than in traditional stirred tank modelling due to the intrinsic unsteady nature of the problem (evolving topology, flow field known at a discrete number of time steps in a Lagrangian frame of reference). Since the flow solution is periodic, a node-by-node interpolation using a fast Fourier transform of the velocity field has been used, which allowed a time continuous representation of the flow to be obtained. In other words, the velocity at node i was approximated... 

The simple treatment of the nearly free ion was based on the use of a fast Fourier transform of the effective potential measured along the helical axis. It is possible, however, to evaluate matrix elements of both the Coulomb interaction and the Morse potential in terms of basis functions that are bound in the x,y-plane and a plane wave along the helical axis. The purpose of this appendix is to outline these evaluations. 

Figure 1. Fast Fourier transform of the function g(t) =

Figure 4. Fluorescence micrograph of a dewetted sample containing 4 wt% of NK85 in polystyrene. The excitation wavelength is 440-480 nm. The inset is the Fast Fourier Transformation of the largest square of the fluorescence image.

Fig. 7.12 TEM images of the fully dense nanosized spinel ceramics produced by sintering at 2 GPa and 795 °C. a and b Different areas revealing that some grain boundaries contain 1-nm amorphous phase regions, c An amorphous triple junction with the inset showing the fast Fourier transform of the main figure, d Image from a region containing nanotwins. Reproduced with permission from [49]. Copyright 2014, Elsevier...

Fig. 3 Transmission electron micrographs of different nanosheets.(A to C) Low resolution TEM images of flakes of BN, M0S2, and WS2, respectively. (D to F) High-resolution TEM images of BN, M0S2, and WS2 monolayers. (Insets) Fast Fourier transforms of the images. (G to I) Butterworth-filtered images of sections of the images in (D) to (F). (Reproduced with permission).

The two-phase flow oscillation frequencies observed can also be analyzed using a non-dimensional approach. Their experimental values are obtained on the basis of the fast Fourier transformation of the pressure drop which evidences frequencies of high energy. The fundamental frequency is the one we deal with here. The oscillation mechanism is based on the two-phase transport along the minicharmel the pressure oscillations are mainly driven by a convective phenomenon. Thus the convective time (r) defined in Eq. (5) is used ... 

The tensile strength and stress of the IPMC are measured in the same manner as those of the IP. The bending stiffness of a fully hydrated IPMC sample is estimated using the free oscillation attenuation method. By bending the sample to the appropriate initial displacement, the free vibration response can be recorded. The natural frequency of the cantilever, is obtained from the fast Fourier transform of the free vibration response curve. The stiffness of the IPMC, Egg, is determined using Eq. 4, which is based on the thin cantilever beam theory of material mechanics ... 

Two-dimensional fast Fourier transform of the fiill 2N X 2N data and filtering... 

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