Maximum spread factor

Recently, Pasandideh-Fard et al.13661 developed a simple analytical model to predict the maximum spread factor on a flat solid... 

The variance of the instrumental spreading function, i.e. the spreading factor of monodispersed polymer in a SEC column was determined experimentally with narrow MWD polystyrene standard samples by the method of simultaneous calibration. The dependence of the spreading factor on the retention volume deduced from a simple theoretical approach may be expressed by a formula with four physically meaningful and experimentally determinable parameters. The formula fits the experimental data quite well and the conditions for the appearance of a maximum spreading factor are explicable. 

Eg. 9 predicts that a maximum spreading factor exists at a certain particular retention volume. Differ-... 

The spreading factors for the selected models were compared with a set of experiments. Figure 27 shows the maximum spreading factor as a fimrtion of number-averaged molar mass (M ) for the various models and the experimental data. The horizontal error bars with the experimental data represent the polydispersity of used polymers, whereas the vertical error bars show the measurement errors in the diameter. The experimental data was fitted to an exponential decay function and revealed a good correlation (R = 0.92). 

This could be explained by the fact that the model of Park assumes that the droplet has the form of a truncated sphere rather than a cylindrical disk, that is, a droplet on a substrate with a certain (small) contact angle. Only for a value of 23 6 kDa did the calculated maximum spreading factor deviate strongly from the experimental results. 

The variation of the spreading factor with retention volume is shown in Fig. 1. The existence ot a maximum... 

Only a few estimates have been made of the forest fire spread from nuclear detonations. Hill (1961) quotes from earlier US Forest Service studies (not available to the author) minimum forest fire areas of 500, 1000, and 2100 km for 1, 3 and 10 Mt, respectively. These areas correspond to fire occurrence at all points where the radiant heat pulse from nuclear detonations exceeds 15 cal/cm Maximum spread areas which are listed by Hill (1961) are at least a factor of ten higher. 

In this small-scale test method, 460-mm (18-in.) x 150-mm (6-in.) wide and up to 25-mm (1-in.) thick vertical sample is used. The sample is exposed to a temperature of 670 + 4 °C at the top from a 300-mm (18-in.) x 300-mm (12-in.) inclined radiant heater with top of the heater closest to and the bottom farthest away from the sample surface. The sample is ignited at the top and flame spreads in the downward direction. In the test, measurements are made for the arrival time of flame at each of the 75-mm (3-in.) marks on the sample holder and the maximum temperature rise of the stack thermocouples. The test is completed when the flame reaches the full length of the sample or after an exposure time of 15-min, whichever occurs earlier, provided the maximum temperature of the stack thermocouples is reached. Flame spread index (7s) is calculated from the measured data, defined as the product of flame spread factor, F, and the heat evolution factor, Q. 

In the longer term, much will depend on the experimentalists being accurate and expeditious in providing as many as possible reliable experimental data to enlarge the body of actual knowledge, and on the ability of theoreticians to connect the macroscopic fluid behavior with microscopic characteristics and molecular properties of constituent components of the real systems. Of course, the quality of the connection depends at least on different and sometimes opposite factors, such as i) the realism of the developed mechanical models, and ii) a relative simplicity, which is a required condition to warrant maximum spreading. 

FIGURE 16.72 Satellite link losses, spreading factors, maximum nadir angle 0-max, Earth central angle y, and one-way Earth-space time delay vs. satellite altitude, h km. 

In the case of deposition (Figure 26(a)), the maximtun spread factor, defined as f=2RnW < ranges from 1.25 to 5 for different droplet impacts resulting in depositions without a recoil. Scheller and Bousfield proposed the empirical correlation for the maximum spread faaor ... 

Without loss of generality y = y can be assumed. If the dipole moment can be assumed to be a linear function of coordinate within the spread of the frozen Gaussian wave packet, the matrix element (gy,q,p, Pjt(r) Y,q, p ) can be evaluated analytically. Since the integrand in Eq. (201) has distinct maxima usually, we can introduce the linearization approximation around these maxima. Namely, the Taylor expansion with respect to bqp = Qq — Qo and 8po = Po — Po is made, where qj, and pj, represent the maximum positions. The classical action >5qj, p , ( is expanded up to the second order, the final phase-space point (q, p,) to the first order, and the Herman-Kluk preexponential factor Cy pj to the zeroth order. This approximation is the same as the ceUularization procedure used in Ref. [18]. Under the above assumptions, various integrations in U/i(y, q, p ) can be carried out analytically and we have... 

Under general hypotheses, the optimisation of the Bayesian score under the constraints of MaxEnt will require numerical integration of (29), in that no analytical solution exists for the integral. A Taylor expansion of Ao(R) around the maximum of the P(R) function could be used to compute an analytical expression for A and its first and second order derivatives, provided the spread of the A distribution is significantly larger than the one of the P(R) function, as measured by a 2. Unfortunately, for accurate charge density studies this requirement is not always fulfilled for many reflexions the structure factor variance Z2 appearing in Ao is comparable to or even smaller than the experimental error variance o2, because the deformation effects and the associated uncertainty are at the level of the noise. 

This is called a point-spread function, because it describes how what should be a point focus by geometrical optics is spread out by diffraction. The expression in the curly brackets is the one that is of interest. The other terms are phase and overall amplitude terms, as are usual with Fraunhofer diffraction expressions. The function Ji is a Bessel function of the first kind of order one, whose values can be looked up in mathematical tables. 2Ji(x)/x, the function in the curly brackets, is known as jinc(x). It is the axially symmetric equivalent of the more familiar sinc(x) = sin(x)/x (Hecht 2002), the diffraction pattern of a single slit, usually plotted in its squared form to represent intensity. Just as sinc(x) has a large central maximum, and then a series of zeros, so does jinc(x). Ji(x) = 0, but by L Hospital s rule the value of Ji(x)/x is then the ratio of the gradients, and jinc(0) = 1. The next zero in Ji(x) occurs when x = 3.832, and so that gives the first zero in jinc(x). This occurs at r = (3.832/n) x (q/2a)Xo in (3.2), which is the origin of the numerical factor in (3.1). 

Certain simplifications that allow the dynamic response to be reconciled with equivalent static loadings are examined. In earthquake loading the dominant effects are found to occur in the lowest mode for which no cross sectional distortion takes place. In wind loading the dynamic response is spread over several modes. The maximum dynamic tensile stresses at the windward base of the tower can be estimated using simple gust effect factors. 20 refs, cited. 

The optimal current fluctuations are plotted in the left panel of Fig. 3 for different conductors and If. The curves are symmetric owing to the symmetry of the cubic parabola potential. Common features are that they all reach the threshold current at maximum and their time spread is of the order of r. Still, the spread, shape, and most importantly, the integral of the current over time, varies significantly from curve to curve. This proves that the detector in use is dispersive and suffers from the first factor mentioned in the introduction. 

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