Gaussian excitations

Figure 7.5 Pulses sequences for ID NOESY and ID relayed NOESY experiments, (a) A ID NOESY sequence with full Gaussian pulses is inferior to the ID NOESY sequence (b) with half-Gaussian excitation, (c) A 90° Gaussian pulse in the pulse sequence of 1D relayed NOESYis appropriate for excitation, since antiphase magnetization is required for the first mixing step. (Reprinted from Mag. Reson. Chem. 29, H. Kessler el al, 527, copyright (1991), with permission from John Wiley and Sons Limited, Baffins Lane, Chichester, Sussex P019 lUD, England.)...

Liu, C., and Kim, D. Y. 2007. Differential imaging in coherent anti-Stokes Raman scattering microscopy with Laguerre-Gaussian excitation beams. Opt. Express 15 10123-34. 

Fig. 4 The upper panel shows the Gaussian excitation pulse with a peak amplitude fulfilling the CDT condition. The resulting current is given in middle panel and its average over three periods of the fast pulse oscillations at the bottom. The onsite energies are equal and centered between the left and the right Fermi energy. (Reproduced from Ref. [38]. Copyright 2004, American Institute of Physics.)...

It is rather tedious to move the spectral window every time we want to select a peak with a shaped pulse, but it is necessary as the center of the Gaussian excitation profile is at... 

The acoustic pulse response of an air filled row of square columns to an incident Gaussian excitation is shown in Figure 5. Here a Gaussian pulse incident from the left has passed a row of square, air filled cavities set in a loss-less elastic fluid. The reflected pulse is seen moving to the left. The air in the cavities is responding to the pulse even though the pulse had already passed the cavity. This is expected as the velocity of sound in air is only 1/5 that in the loss-less fluid considered. 

Here, Qa and Qb account for the different optical properties of the fluo-rophores that distinguish A and B as well as the laser intensity and other instrumental factors. K = kab/kba, and td = w jAD is the characteristic diffusion time for a Gaussian excitation intensity profile with exp(—2) radius w, and S is the area of the laser spot. It is readily shown that for equilibrium systems Gab (t) = Gba (t) due to the fact that kabCB = kbaC [25]. The NESS fluxes can be obtained from the initial slope of the correlation functions. 

The concept of statistical linearization replaces a non-linear dynamical model with a linear model, whose, coefficients are explicitly formulated. However, since these coefficients must be evaluated in terms of statistics that are generated by the non-linear system and, therefore, unknown the usual approach is to evaluate these coefficients based upon assumed statistics. In the gaussian excitation case, the assumed statistics are gaussian. Thus, this lead to a further error in the approximation. 

Thus, for any laboratory model of a structure undergoing wide-band gaussian excitations on a shake table, the statistically equivalent linear model for a given vector of outputs can be obtained directly from data analysis. The question that still remains concerns the quality of the linearized model as compared to the true non- linear model of the structure. We would like to be able to say that because we have shown the statistical linearization coefficients to be the asymptotic maximum likelihood estimates of the coefficients of a linear model, then the linear model is in some sense a projection of the true non-linear model onto linear model space. 

Fig. 5.16 Breaking the diffraction limit in fluorescence microscopy. (A) Relative intensities of a Gaussian excitation pulse (/e(c)// = exp -( r /ro) j, solid curve) and a concentric,...

The excitations ccaisidered in this study have been limited to Gaussian excitations. This however... 

In this study a unitary approach to evaluate the spectral characteristics of the structural response, to perform the reliability assessment, of classically damped linear systems subjected to stationary or nonstationary mono-/multi-correlated zero-mean Gaussian excitations, is described. 

Approximation of the crossing rates by Eq. 3, which assumes a stationary Gaussian excitation and linear, hence also Gaussian response a more elaborate excitation model could involve non-Gaussian excitations and nonlinear structural responses, hence non-Gaussian displacement responses. 

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