Butterfly curves

The buffer-fly curve of FMR fi-equencies vs. applied electric field was observed and shown in Fig. 2 (b), which resembled the widely observed piezoelectric strain vs. electric field butterfly curves for piezoelectric materials and matched the ferroelectric P-E hysteresis loop of PMN-PT single crystal as well. This once again confirmed that the change of FMR fi equency of the FeGaB film results from the ME coupling induced strain in the FeGaB film. 

Figure 7. Butterfly curves of resonance fields vs. electric fields and ferroelectric hysteresis loops of muitiferroic composite Fe304/PZT (a) and FesOVPMN-PT (b).

Figure 4-143 represents a computer-generated plot that demonstrates the effectiveness of eddy current brakes in preventing overspeed of the string. The lower curve assumes the butterfly valve characteristic is linear from 60° open to the closed position. The rate of closure is 3.25 sec. (Butterfly valves are normally used to throttle the expander inlet gas.)... 

Addition of galactomannan to agarose-water systems profoundly alters the optical rotation behavior. Thus, both in the absence and presence of locust-bean gum, there is, below 35°, a sharp shift in optical rotation. However, these shifts are opposite in sign, as shown in Fig. 6. The reheating curves also differ, in that, when locust-bean gum is present, a butterfly-shaped hysteresis curve is obtained.40... 

Figure 1.26 displays the results of the dss coefficient as function of the bias field, the large signal 33 response ( butterfly loop ) as well as constructed x33trev curve of the same pzt... 

The electric field induced intrinsic strain for different crystallographic directions could be calculated from the shift in peak positions (see Figure 7.9). Figure 7.11 shows the result of the measurements for a rhombohedral pzt in [111] and [100] direction. Only one half of each cycle is shown for the sake of a clarity of the plot. The curve for the [100] direction reveals the typical shape of a butterfly loop for the electric field induced strain in ferroelectrics. However in [111] direction, which is parallel to the spontaneous polarization, strain is significantly smaller. From both curves, the so-called unipolar strain can be evaluated as the strain induced at the maximum electric field Emax with a reference to the remanent state (E = 0). The calculation gives strain values in [111] direction of 0.02% and for the [100] direction 0.15%. The observations are in good agreement with theoretical calculations made by Du et al. [22],... 

Draw two graphs. As the independent variable, use the ratio of Viceroy butterflies to Monarch butterflies. As the dependent variables, plot the expected population numbers of each kind of butterfly. Make the curves relative to the maximum population as the ratio varies. Justify why you drew the curves as you did. 

Duration and convexity help explain the change in portfolio value with parallel shifts in the yield curve. However, most yield curve shifts are not parallel, and involve some measure of steepening, flattening, and butterfly shifts, or some combination of the three. 

Turndown devices are most often control valves (not shutoff valves) or dampers. The best valve turndown characteristic is usually accomplished with adjustable port valves or with characterized globe-type valves. Butterfly valves usually have very poor characteristics (not straight-line), but their characteristic curves can sometimes be improved by undersizing or selecting reduced port models. 

Part Three presents the author s insights into trading, based on his experiences working as a gilt-edged market maker and sterling-bond proprietary trader. The topics covered include implied spot and market zero-coupon yields, yield-curve spread trading, and butterfly spreads. 

Currently available HX-MS software provides users with various options to visualize HX results (reviewed in Section 3.3.5). Some common options include deuterium uptake kinetic curves, heat maps [56], and butterfly plots [59]. The latter two present information such as the protein conformational dynamics and the differential deuterium uptake comparisons of full-length proteins in a single graph, making data interpretation more efficient. Anotha- informative way to interpret the HX results is to map the changes of deuterium uptake onto a known X-ray stracture of the antigen [41]. 

The FMR field of the Fe304/PZT and Fe304/PMN-PT muitiferroic composites exhibited the characteristic butterfly shape in their FMR field vs. electric field curves as shown in Fig. 7, which coincided with the ferroelectric hysteresis loops of the PZT and PMN-PT respectively and were similar... 

Fig. 15.19 Backpressure versus mixing performance trade-off curve—butterfly mixer...

The lamellar reflections in small-angle scattering patterns from polymer fibers are often spread onto a curve symmetrical about the fiber axis. These are usually referred to as two-or four-point patterns, the latter sometimes resembling the butterfly pattern frequently found in light scattering. We recently showed that these 2-D patterns could be best analyzed if we describe die intensity distribution in elliptical coordinates because the intensity maxima of the lamellar reflections from oriented polymers fall on an elliptical curve. We now present new analysis to support this assertion. We will also discuss die physical basis for some of the features in the SAXS pattern in terms of misorientation of the lamellar stacks, deformation of the lamellae, and possible correlation between the lamellar spacing and the orientation of the lamellae. 

Figure 7 Installed flow characteristic curve and installed gain curve fora butterfly and a globe control valve. [1] Other factors affecting control valve perfonnafice ...

It is not hard to conclude from numerical experiments, which reveal the manner in which the separatrices converge to the homoclinic butterfly that A must be within the range (0,1). In this case, when a < 0, everything is simple the homoclinic butterfly splits into either two stable periodic orbits (Fig. C.7.8(g)), or just one stable symmetric periodic orbit (Fig. C.7.8(i)). It follows from Sec. 13.6 that when <7 > 0, two bifurcation curves originate from this codimensiomtwo point. They correspond to the saddle-node bifurcation (Fig. C.7.8(d)) and to the double homoclinic loop (Fig. C.7.8(f)). The... 

A fragment of its (r, cr) bifurcation diagram is shown in Fig. C.7.14. Detect the points where the path cr = 10 intersect the curve HB of the homoclinic butterfly and the curve LA on which the one-dimensional separatrices of the saddle tend to the saddle periodic orbits. Find the point on the curve LA above which the Lorenz attractor does not arise upon crossing LA towards larger values of r. The dashed line passing through the T-point in Fig. C.7.14 corresponds to the moment of the creation of the hooks in the two-dimensional Poincare map when the separatrix value varishes A — 0 (see discussion on the Shimizu-Morioka model). ... 

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