Sensitivity, calculation

Field Distribution and Sensitivity Calculation in Microtube Resonators... 

The data for the fluorescence lifetime for this system are plotted against temperature in Figure 11.28, together with its relative temperature sensitivities calculated using Eq. (11.4). It shows that the CrLiSAF fluorescence lifetime decreases monotonically with the temperature increase, although it is rather insensitive to temperature variance around 0°C or below. From about 5°C, the fluorescence lifetime drops more and more sharply with temperature increase. This is seen explicitly from the rapid increase in its... 

X2° = X30 = 0 assumed to be known exactly. The only observed variable is = x. Jennrich and Bright (ref. 31) used the indirect approach to parameter estimation and solved the equations (5.72) numerically in each iteration of a Gauss-Newton type procedure exploiting the linearity of (5.72) only in the sensitivity calculation. They used relative weighting. Although a similar procedure is too time consuming on most personal computers, this does not mean that we are not able to solve the problem. In fact, linear differential equations can be solved by analytical methods, and solutions of most important linear compartmental models are listed in pharmacokinetics textbooks (see e.g., ref. 33). For the three compartment model of Fig. 5.7 the solution is of the form... 

P. Valkd and S. Vajda, An extended ODE solver for sensitivity calculations, Computers and Chemistry, 8 (1984) 255-271. 

The basic scenarios examine some of the important aspects in understanding the calculated environmental impact of aircraft. However, a number of uncertainties remain in the treatment of chemical and physical processes that may influence the effects from aircraft emissions. A series of special sensitivity calculations were therefore designed to investigate the most important of the recognised uncertainties. The subsonic aircraft sensitivity scenarios, as described later, examine uncertainties in the background atmosphere, the treatment of upper tropospheric and lower stratospheric chemical and dynamical processes, and the different analyses of aircraft emissions. 

A general method for assessing the thermal stability of chemical batch reactors by sensitivity calculation based on Lyapunov exponents. Chemical Engineering Science, 49, 2681-8. 

The base case assumptions are shovn in Table III. The methodology used for these sensitivity calculations was as follows ... 

Implementation of the calculation followed in general the scheme of Dougherty et al. [8] The kinetic problem Eq. (1) was solved separately using the BELLCHEM code consisting of a chemical compiler followed by a stiff ODE solver using the method of Gear. [//] Results were stored on disc for subsequent input to the sensitivity calculation. 

It is important to note that in using computer-aided models for batch distillation, the various assumptions of the model can have a significant impact on the accuracy of the results e.g., see the discussion of the effects of holdup above. Uncertainties in the physical and chemical parameters in the models can be addressed most effectively by a combination of sensitivity calculations using simulation tools, along with comparison to data. The mathematical treatment of stiffness in the model equations can also be very important, and there is often a substantial advantage in using simulation tools that take special account of this stiffness. (See the 7th edition of Perry s Chemical Engineers Handbook for a more detailed discussion of this aspect). 

The high mass sensitivity calculated in the previous example justifies the term microbalance in describing the sensing capabilities of the quartz resonator. Equation 3.9 can be used to calculate fr uency shifts for surface accumulations that behave as ideal mass layers. A real film behaves as an ideal mass layer if it is sufficiently thin and rigid so that it moves synchronously with the oscillating device surface. On a TSM resonator, this condition is realized if the acoustic phase shift across the film is small, i.e., ir. The phase shift is... 

If storage is a severe problem, you can save space by reducing the maximum integrator order maxord. Each unit decrease of maxord below the default value of 5 saves Nstvar locations, or Nstvar>i=(Nspar+l) when sensitivity calculations are requested however, the progress is likely to be slower. In any case, maxord must be at least 1 and no greater than 5. 

Set Info(13)= l if E is diagonal but not a unit matrix. Use the — sign if E will be constant between to and the next restart use the - - sign if E will vary with t or u. or with 0 in a sensitivity calculation. Provide the nonzero elements En t,u 6) in a subroutine Esub as described in Section B.5. 

A negative Info (13) signifies that E is constant throughout the problem, or until such time as DDAPLUS may be restarted to change equation forms. In parametric sensitivity calculations this requires that, over the same time interval, E be independent of the sensitivity parameters as well as of t and u. 

Analysis for traces of substances that act as catalysts for reactions can be both highly specific and sensitive. Calculations of the type carried out by Yatsimirskii indicate that, if the rate of a catalytic reaction can be measured spectrophoto-metrically with a change in concentration equivalent to 10 moles/1, and if the catalytic coefficient amounts to 10 cycles/min, the minimum concentration of catalyst that can be measured by following the reaction for 1 min is about 10 moles/1. Such sensitivities can be attained by few other analytical techniques. Tolg considers only mass spectroscopy, electron-probe microanalysis, and neutron-activation analysis methods applied to favorable cases to have better limits of detection than catalytic methods. 

For a long time the main topic of research in the area of sensitivity analysis was to find an accurate and effective method for the calculation of local concentration sensitivities. This question now seems to be settled, and the decoupled direct method (ddm) is generally considered the best numerical method. All the main combustion simulation packages such as CHEMKIN, LSENS, RUNIDL and FACSIMILE calculate sensitivities as well as the simulation results and, therefore, many publications contain sensitivity calculations. However, usually very little information is actually deduced from the sensitivity results. It is surprising that the application of principal component analysis is not widespread, since it is a simple postprocessing method which can be used to extract a lot of information from the sensitivities about the structure of the kinetic mechanism. Also, methods for parameter estimation should always be preceded by the principal component analysis of the concentration sensitivity matrix. 

The first global empirical model for moist CO combustion was created in 1956 [199]. In a more recent article, Yetter et al. [200] compared previous global models for CO oxidation and suggested a procedure for a more systematic generation of global models based on initial concentration sensitivity calculations. 

To determine the effect of uncertainties of the various parameters on the calculated interfacial tension, a set of sensitivity calculations was carried out. It was found that a 1 % uncertainty in the capillary diameter, the capillary depression, or the density of the aluminum, causes a 1.0-1.1% uncertainty in the calculated interfacial tension. The 1% uncertainty in the density of the melt or in the temperature, leads to an uncertainty in the interfacial tension of less than 0.1%. 

Perform slngle-value-best-estlmate analysis. Then acknowledge the uncertainty, perform various sensitivity calculations, and provide a qualitative and/or quantitative discussion of the uncertainty. 

Theoretical sensitivity calculations were carried out for two copolymer systems, poly (chloromethylstyrene-co-2-vinylnaphthalene) (P(CMS-2VN)) and poly(glycidyl methacrylate-co-2-vinyinaphthalene) (P(GMA-2VN)). Polychloromethlstyrene is known as a high sensitivity negative resist ( 7 8 ) (D mw=0.07 C-g /cm2- mole), which shows no postirradiation polymerization. The crosslinking reaction in P(CMS-2VN)... 

So far sensitivity calculations were carried out to estimate DgMw, which is a parameter that characterizes the sensitivity for negative resist materials. Theoretically, gel dose (Dj) can be decreased without limit as molecular weight (Mw) increases. Figure 3 shows predicted sensitivity for P(CMS-2VN) with Mw as a parameter. 

Stewart and Caracotsios produced the code ddasac to perform sensitivity calculations conveniently [3, 2. The following Octave commands show how to use ddasac to solve Example A.2. 

Sensitivity calculated from data given in reference on the basis of compound with mol wt of 100. 

The fact that the sensitivities calculated here are significantly worse than results published before [6], appears to be due mainly to the previous underestimation of the detector background. The sensitivity has also suffered as a result of the inclusion of passive material in this calculation. 

Sensitivity calculations can be utilized equally well for two-, three-, and four-electrode systems. In each case, you must identify the two CC electrodes used for driving an electrical current through the... 

A similar vacuum deposition experiment was carried out using Device 2. In this case, the measured mass sensitivities were 31 cm /g (4.9 Hz-cm /ng) for n - 0 and 65 4 cm /g (10 Hz-cm /ng) for the average of n - 1, 2, and 3. The sensitivity of this device, which Is within a factor of 2 of that for a 97 MHz SAW device (130 cm /g or 13 Hz-cm /ng), Is significantly larger than the sensitivity calculated from Equation 3, This Is probably because plate modes begin to couple with surface modes, enhancing surface particle velocity and thus mass sensitivity, when b/A exceeds approximately five (12). 

The model calculations were performed with CHEMKIN II [117]. A single run calculated the concentrations of all species in dependence of the reaction time for a radial homogeneous plug-flow reactor and for overall isothermal conditions. In addition, sensitivity calculations and flow analysis were performed in order to gain information about important reaction steps. (For details see [128].)... 

Model optimization was done by comparing the experimentally measured concentrations of the main products with the calculated ones, by adjusting the kinetic and thermodynamic parameters and consideration of additional reaction steps [128]. The comparison was done for the experiments at 45 MPa and all temperatures, but the highest and lowest temperature results were weighted most. Because most of the kinetic parameters are usually insensitive to fitting, we used sensitivity calculations to gain information about the most sensitive reactions. 

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