Gaussian Field-strength

Fig. 2. A Gaussian shaped PIP with a phase increment A

The absorption curves given by coal macerals approached the horizontal (magnetic field strength) axis more slowly than a Gaussian distribution curve. Shape analysis (16) showed that over much of the curve, the form closely approximated a Lorentzian distribution curve, but both positive and negative deviations were found in the wings of the curves (that is, in various examples, the curves approached the axis either somewhat more or somewhat less rapidly... 

The dimensions of the first-, second-, and third-order susceptibilities in both systems are simply derived from the polarizability power series equation.24 In the Gaussian system, polarization P and electric field strength E have equivalent dimensions [units statV cm 1 = statC cm 2 = (erg cm 3)112] and are related by... 

In the experiment the differentiated absorption curves are obtained. Therefore, we begin with the differentiated form of Equation 8. The differentiation of the field strength H is marked here by a comma. Accordingly, the intensity of the lateral extremes for the differentiated absorption curves is marked (Ii )l/2 and the intensity of the inner extremes (I0 )l/2. The linewidths resulting from the distance of the extremes are marked (Affi)i/2 for the lateral gaussion curves and (AHg)i/2 for the inner curve. In this way the areas under the different gaussian curves defined by Equation 8 are determinable. 

The Jones vectors of a horizontally polarized Gaussian beam E and a vertically polarized Gaussian beam Ey of field strength Eq at the beam waist may be represented as... 

Despite the considerable success of Eq. (7) in consistently rationalizing mobility data in many systems, the Gaussian Disorder Model misses the mark in one major way. The field-strength [E) dependence predicted for a realistic value of d (3.0, approximately the smallest a ever encountered in practice) and various values of E is shown in Figure 39 [63a,b]. Only for strong fields (sometimes only above 10 V cm ) are the results adequately described as linear functions of whereas experimentally this linearity usually extends to the lowest values of E accessible (sometimes as low as lO V cm ) [60b, 63c,d]. It was initially proposed that the... 

Figure 39. Field-strength ( ) dependence of the mobility (p) predicted by the Gaussian Disorder Model. (Reprinted with permission from Ref [63b].)...

Fig. 7b shows representative (u /27rrf field strengths for the 12 ms adiabatic sequences (last points in Fig. 7a) under ideal conditions (solid line), 5% Lorentzian rf inhomogeneity (dashed line), 9.2% Gaussian rf inhomogeneity (dotted line). As mentioned earlier, these rf profiles match the conditions for a typical 4 mm tripleresonance probe. 

Fig.37 FEM calculation of the deformation of a ferrogel block in a uniaxial magnetic field at different field intensities. The magnetic field strength has a Gaussian distribution along the block as shown in the figure. The position of the field maximum is indicated by arrows...

Suppose we now imagine a Gaussian surface in the shape of a box placed in our system as shown in Figure 13.3.4. One end is at the interface. The sides are perpendicular to this end and extend far enough into the solution that the field strength d(f>/dx is essentially zero. The box therefore contains all of the charge in the diffuse layer opposite the portion of the electrode surface adjacent to the end. 

Urn is the energy of fhe mfh state and T is inversely proportional to the lifetime of each sfafe. /(f) is fhe temporal shape of the linearly polarized pulse, taken to have forms such a Gaussian or a sech funcfion. fo is the peak field strength and is the monochromatic frequency. 

Figure 7.18. Traces from the 2D absorption-mode 7-resolved spectrum of menthol 7.1. (a) A region from the ID proton spectrum, (b) the 02 projection of the titled 2D spectrum showing proton-decoupled resonances and (c) the corresponding traces through the/i multiplets in the 2D spectrum. The multiplets for protons 3 and 4 are not fully decoupled for reasons described in the text. The data were acquired with a total acquisition time of 1 s in both t2 and fi using a 60Hz/i window. The selective 180° pulse was a 50 ms Q3 Gaussian cascade, and the gradient strength was 1% of the maximum 53 G cm 0 The broadband 180° pulses were BIPs (720.50.20) applied for 100 Xs at a Bi field strength of 20 kHz.

Fig. 7.1 Snapshots of the dynamics of the sequential ionization model of Ceo- The DFT/B3LYP method with the 3-21G basis set is used. The applied pulse is a Gaussian pulse of Tpg = 30 fs, fpeak = 7.0 X 10 W/cm, and X = 1,800 nm. The polarization direction is the vertical direction. Time = 0 fs is the time of the peak of the laser pulse. The temporal profile of the applied electric field is sketched in the upper left comer of each snapshot of Ceo the open circle in the field profile designates the field strength at the time. In this model, Qo is sequentially ionized from charge = 0 to denoted by charge = 12 under laser irradiation. Qo is elongated along the...

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