Nonlinear characteristic

S. R, Wilson, G. A. Al-Jumaily, and J. R. McNeil. Nonlinear Characteristics of a Stylus Profilometer. Opt. Eng. 26,953, 1987. This describes modeling stylus profilometer response characteristics and explains their shortcomings. 

The nonlinear element here is I => /(eg), eg being the grid voltage. If one introduces the usual approximation of the nonlinear characteristic by a polynomial, it can be shown that the differential equation takes the form... 

Figure 16 shows the experimental arrangement for the measurement of the surface pressure. The trough (200 mm long, 50 mm wide and 10 mm deep) was coated with Teflon. The subphase temperature was controlled within 0.1 C by means of a jacket connected to a thermostated water circulator, and the environmental air temperature was kept at 18 °C. The surface tension was measured with a Wilhelmy plate of platinum(24.5 x 10.0 x 0.15 mm). The surface pressure monitored by an electronic balance was successively stored in a micro- computer, and then Fourier transformed to a frequency domain. The surface area was changed successively in a sinusoidal manner, between 37.5 A2/molecule and 62.5 A2/molecule. We have chosen an unsaturated phospholipid(l,2-dioleoyl-3-sn-phosphatidyI-choline DOPC) as a curious sample to measure the dynamic surface tension with this novel instrument, as the unsaturated lipids play an important role in biomembranes and, moreover, such a "fluid" lipid was expected to exhibit marked dynamic, nonlinear characteristics. The spreading solution was 0.133 mM chloroform solution of DOPC. The chloroform was purified with three consecutive distillations. 

In other words, higher harmonics serve as a useful quantitative measure of the nonlinear characteristics of the thin film. Using the inverse Fourier... 

In conclusion, we have shown that lipid film generally exhibits marked nonlinear characteristics. Nonlinear characteristics become particularly significant under the dynamic and/or nonequilibrium conditions. Further experimental and theoretical studies of nonlinear characteristics of lipid films are desirable. 

Patel et al. °"> successfully operated parametric oscillators in the infrared region (2.5 - 25 pm) using the nonlinear characteristics of tellurium and selenium single crystals. This frequency range is important for the molecular spectroscopy of rotational-vibrational... 

The output from a ruby giant-pulse laser (2 Joule, 30 nsec half-width, = 6943A) passes a KH2PO4 crystal where, due to the nonlinear characteristics of this material, the second harmonic at X = 3471 A is generated with an efficiency of 3 %.The two wavelengths are separated by means of a water filled quartz prism. The ultraviolet light pulse serves as pump pulse. 

Unlike ductile metals, composite laminates containing fiber-reinforced thermosetting polymers do not exhibit gross ductile yielding. However, they do not behave as classic brittle materials, either. Under a static tensile load, many of these laminates show nonlinear characteristics attributed to sequential ply failures. One of the difficulties, then, in designing with laminar composites is to determine whether the failure of the first ply constitutes material failure, termed first-ply failure (FPF), or if ultimate failure of the composite constitutes failure. In many laminar composites, ultimate failure occurs soon after first ply failure, so that an FPF design approach is justified, as illustrated for two common laminar composites in Table 8.9 (see Section 5.4.3 for information on the notations used for laminar composites). In fact, the FPF approach is used for many aerospace and aircraft applications. 

Other important characteristics of the converter are the reflected ripple attenuation and the turn-on characteristics. It is expected that the turn-on characteristics will be difficult to simulate because of the nonlinear characteristics of a saturating core. A nonsaturating core is simply described by Faraday s law, and it can be easily modeled by any of the SPICE simulators. The model used for the EMI filter is shown in Fig. 3.66, and the results of each of the simulators output and the measured impedance plots are shown in Figs. 3.67 to 3.70. 

Example A transformer with a full load current rating of 1000 A is subjected to a load with the following nonlinear characteristics. The transformer has a rated winding eddy current loss density of 10.0% (0.10 pu). Find the transformer derating factor. 

The value of P is on the order of 4000, so at room temperature (298 K), Or = -0.045 for thermistor and 0.0035 for 100-f2 platinum RTD. Compared with RTDs, NTC-type thermistors are advantageous in that the detector dimension can be made small, resistance value is higher (less affected by the resistances of the connecting leads), and it has higher temperature sensitivity and low thermal inertia of the sensor. Disadvantages of thermistors to RTDs include nonlinear characteristics and low measuring temperature range. 

Nonlinear Systems. Nonlinearities play a dominant role in physics and many other disciplines. For example, all material laws have a nonlinear characteristic. In many cases, the usually applied linearization procedures are suitable and well established methods, which might lead to satisfying results. However, nonlinear systems can exhibit a behaviour, which is completely absent in the regime of linear dynamics. Both, the development and the maintenance of such a behaviour seem to be provided by a general mechanism nonlinear dissipation. 

When the differential control is added to the effect of GK translocation, the beta cell acts as a PID controller [36], but with nonlinear characteristics and with saturable signals. This is shown in Fig. 6.5c. The mutual effect of the three parts depends on the actual parameters of the model. Notice that for fast changes (kj =0.005 min-1), the integrator tends to saturate [32]. 

In studying a system by a nonlinear impedance method, use is made of the system s nonlinear characteristics. A variant of the nonlinear impedance method called the amplitude demodulation method was first applied in the electrochemistry of semiconductors, in particular to diamond electrodes, in [83] (see the quoted paper for the theory of the method and the experimental set-up). A perturbing current signal of a high frequency oo, modulated in amplitude at a low frequency 2, is applied to electrochemical cell the demodulated low-frequency voltage signal is to be measured at the frequency 2. In accordance with the theory of the method [83], under the condition of formation of a depletion layer in a semiconductor electrode, the in-phase component of the cell response Re h is inversely proportional to d(C 2)/dE. Hence, for the acceptor concentration in the semiconductor we have [compare Eq. (1)] ... 

One common nonlinear characteristic of control valves is hysteresis, which results in two possible flows at a given valve position, depending on whether the valve is opening or closing. In the steady-state, hysteresis limits resolution in achieving a specific flow with its desired effect on the process. Dynamically, hysteresis also creates pre-stoke deadtime, which contributes to total loop deadtime, thus degrading the performance of the loop. Pre-stroke deadtime is the time that elapses as the controller output slowly traverses across... 

Compared to other methods used to extract the bending force from impact tests, it can be noted that using the present approach several drawbacks existing with the other methodologies are removed a) the increase of fracture time and addition of nonlinearities characteristic of mechanical damping b) the lack of foundation of methods used to numerically smooth the experimental registers c) the additional cost incurred when samples are instrumented. 

The EPA published a follow-up document (1998) that is much more extensive and detailed, and is beyond what can be published as an addendum. U.S. EPA (1998) also has a number of detailed discussions on various features of risk assessment. The importance of scale, the nonlinear characteristics of ecological systems, selection of assessment, and measurement endpoints are all important discussion items. 

Nuclear power reactors inherently have some highly nonlinear characteristics, which means that whatever objective function (there are several possibilities) and constraints are used to define and quantify acceptable LPs, some of these system variables will inevitably be nonlinear functions of the problem s control (decision) variables. Examples of such nonlinearities include the effects of local thermal and hydraulic feedback and the time dependence that results from radiation exposure (an accumulated history effect). Particularly with respect to the latter, the computational expense associated with analyzing a single LP solution can be substantial. When considered within the context of of tens of thousands of solutions, as is often required for the use of modem optimization routines, the CPU run time cost becomes prohibitively expensive. 

The linearized theory would be of interest even if restricted to small changes in concentration since it gives the essential behavior of multicomponent systems. The fact that it may yield accurate results even for large changes in concentration is encouraging, for higher accuracy will require facing the nonlinear characteristics of the differential equations. 

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