Sample quasi-steady

Typical for the spectroscopic character of the measurement is the rapid development of a quasi-steady state stress. In the actual experiment, the sample is at rest (equilibrated) until, at t = 0, oscillatory shear flow is started. The shear stress response may be calculated with the general equation of linear viscoelasticity [10] (introducing Eqs. 4-3 and 4-9 into Eq. 3-2)... 

Under dynamic or quasi-steady-state conditions, a continuously monitored process will reveal changes in the operating conditions. When the process is sampled regularly, at discrete periods of time, then along with the spatial redundancy previously defined, we will have temporal redundancy. If the estimation methods presented in the previous chapters were used, the estimates of the desired process variables calculated for two different times, t and t2, are obtained independently, that is, no previous information is used in the generation of estimates for other times. In other words, temporal redundancy is ignored and past information is discarded. 

As the temperature stimulation is switched off, the static kinetics is governed by equation (4.1.40) with the initial distribution function y(r) from equation (4.2.11). However, all attempts [102] to describe in such a way the experimental tunnelling luminescence decay for F and in KBr (Fig. 4.18) were unsuccessful. Both this observation and the absence of the plateau of 7(f) during the temperature stimulation, characteristic for the quasi-steady states, argue that the tunnelling recombination takes place in correlated pairs. This is in line with the conclusion [107] that for ordinary defect concentrations 1016 cm-3 (X-ray sample excitation for minutes) and the time 105 s the slope is dose-independent but 7(f) oc dose [95]. 

Numerical simulations that combine the details of the thermal-capillary models described previously with the calculation of convection in the melt should be able to predict heat transfer in the CZ system. Sackinger et al. (175) have added the calculation of steady-state, axisymmetric convection in the melt to the thermal-capillary model for quasi steady-state growth of a long cylindrical crystal. The calculations include melt motion driven by buoyancy, surface tension, and crucible and crystal rotation. Figure 24 shows sample calculations for growth of a 3-in. (7.6-cm)-diameter silicon crystal as a function of the depth of the melt in the crucible. 

A sample was heated under nitrogen to 62 C and kept at this temperature (10 hr.) until the stress reached a constant value (8.3 MPa). (On cooling to room temperature, the stress reached 10 MPa) Probably over an infinite period of time, slightly more solvent loss would occur however, in a reasonable time frame, a quasi"-steady state is obtained as illustrated. 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

The calculated water vapor flux f was calculated from the quasi-steady state temperature distribution in the snow sample. Pick s law was used to model the vapor flux. The calculation was performed as follows ... 

Next, the distribution of temperature and temperature gradient of the quasi steady state is depicted in Figure 3. The snow sample was initially kept at -10 °C, and was cooled from the top cooling plate to -65 °C, reaching a quasi steady state in about 6 hours. The temperature distribution showed upward convex curve. Therefore, the temperature gradient was not uniform in the sample. This tendency is same as a typical temperature profile in subarctic snow. In addition, the nonlinearity of the snow temperature distribution resulted from water vapor transport in the snow. ... 

The NMRI technique uses an induction coil surrounding the sample to image nuclear spin density that results from the nuclear spin system rearrangement. An initial magnetic pulsed field orients the nuclear spin system and then it relaxes back toward a random state. Because of the relaxation time and that tomographic reconstruction is needed to extract the 3-D details, there are time limitations (Altobelli et al., 1992) (currently of the order of 10-ms, at best). Consequently, the technique has been used mostly for steady or quasi-steady laminar flows because of the rather low data acquisition rate. However, modifications to allow turbulent and unsteady flows to be investigated have been reported and new... 

Fig. 4.14 Plot of weight percent organic carbon vs. weight percent pyrite sulfur for normal-marine modern sediments. Each plotted point represents the average value of samples in a given core, taken at a sediment depth where contents of organic carbon and pyrite have attained quasi-steady-state values, i.e. where early diagenesis of carbon and sulfur is (essentially) complete. The dashed lines enclose data from a variety of other studies (after Berner and Raiswell 1983). Sediments deposited under anoxic (euxinic) conditions would plot above the trend line, freshwater sediments significantly below.

It is seen that the calibration constant disappears, which assumes that it is constant over the experimental conditions. The calculation is carried out using dedicated software. In some circumstances the crucible used for the sample may have to be different from that used for the calibrant. This means that a correction will be required to take into account the difference between the heat capacity of the two crucibles - readily calculated with sufficient accuracy. Measurements can be made at a series of temperatures but are meaningful only within the quasi-steady-state region of the experiment. The specific heat capacity of sapphire has been listed by ASTM in connection with the standard test method E 1269 (1999) for determining specific heat capacity by differential scanning calorimetry. 

The small delay time requirement is especially important in the case of rapidly changing dynamic samples. It may be waived in the case of some single time point measurements (i.e., while recording quasi-steady samples). In fact, some studies, which target qualitative detection of short-lived species rather than temporal profiles of reactants of intermediates, impose less rigorous requirements for the experimental systems. The following sections provide examples of various TRMS systems emphasizing the role of interfaces. 

Various mass spectrometric techniques facilitate TRMS analyses. Interfaces and ion sources are critical for sample introduction to a mass spectrometer, especially in the case of real-time monitoring of dynamic samples. Temporal resolution of mass analyzers also plays a role when millisecond-timescale processes are recorded over time. However, there exist TRMS methods in which steady or quasi-steady samples are generated. In those cases, the role of MS hardware is diminished while the sample processing steps (e.g., fast quenching, development of product concentration gradients) are of utmost importance. 

From Equation 7.80 it is seen that the vacancy flux always exists at any dependence Ey (r). So, vacancy segregation cannot represent the reason for the stability of a hollow nanoshell. The delay can be connected only with the time of attainment of the quasi-steady state regime. But, evidently, the vacancy segregation in the nanoshell cannot present anything special, since similar segregation must take place in macroscopic samples (for example, at sintering of powder mixtures) and, as far as it is known, it in no way prevents, say, void coalescence. 

Although equilibration during stress-strain measurements was fairly rapid for swollen samples, a period of 2 h was allowed for attainment of equilibrium after each load. However, the question of whether equilibrium was established for bulk specimens is difficult to answer. In our experiments a quasi-steady-state reading was taken after 48 hr. 

The latter equality follows from the quasi-steady-state-assumption. Note that Pi, in a batch reactor is a function of conversion. If other transfer mechanisms are present, the denominator is extended with the corresponding contributions to the initiation process. Whether or not the pp is attached to another pp indeed follows by selecting a random number between 0 and 1 and determining whether the inequality rand(l) < Py is false or true. If connected [true) then the birth conversion of the earlier pp simply follows from the conditional distribution (given that the first sampled pp is created atx = d and grows from an earlier one) ... 

To the extent that K(t) is constant throu out a time interval that is comparable to then the correct time dependent rate expression can be replaced by an approximate quasi steady state analog. Even in the absence of a true steady state, certain features of an average rate coefficient formulation will continue to be applicable (23.25.27,51,32). This conclusion is insensitive to the present assumptions concerning nonreactive scattering. It would be strengthened by the inclusion of a more realistic representation of the energy dependent nonreactive cross section, since a relative reactivity increase would lead to ccmipression of the time and ranges sampled by nonthermal reaction. 

---