Detectors response models

Detector response models These models are used to predict the response time of a detector device to a fire event, so as to predict how quickly an active intervention will be made by a fire reaction system, such as sprinklers or foam sprayers. Such models use calculated fire heat-release to determine the trigger point of a thermal indicator for example, by calculating the time taken for the local air temperature to reach a trigger value. As such they have very specific inputs and outputs and limited objectives specific to certain devices in contrast to more ambitious categories of models, such as egress or fire endurance models. 

Oxygen Transport. The most widely used methods for measuring oxygen transport are based upon the Ox-Tran instmment (Modem Controls, Inc.). Several models exist, but they all work on the same principle. The most common apphcation is to measure the permeabihty of a film sample. Typically, oxygen is introduced on one side of the film, and nitrogen gas sweeps the other side of the film to a coulometric detector. The detector measures the rate that oxygen comes through the film. The detector response at steady state can easily be converted to At (eq. 1). Simple... 

It has been suggested that a sensitive test of the diffusion model would be found in the evolution of the eh yield (Schwarz, 1969). Early measurements by Hunt and Thomas (1967) and by Thomas and Bensasson (1967) revealed -6% decay within the first 10 ns and 15% decay in 50 ns. The diffusion theory of Schwarz predicts a very substantial decay ( 30%) in the first nanoseconds for instantaneous energy deposition. Schwarz (1969) tried to mitigate the situation by first integrating over pulse duration (-4.2 ns) and then over the detector response time (-1.2 ns). This improved the agreement between theory and experiment somewhat, but a hypothesis of no decay in this time scale would also agree with experiment. Thus, it was decided that a crucial test of the diffusion theory would... 

Recently, Orosz et al. [136] reviewed and critically reevaluated some of the known mechanistic studies. Detailed mathematical expressions for rate constants were presented, and these are used to derive relationships, which can then be used as guidelines in the optimization procedure of the POCL response. A model based on the time-window concept, which assumes that only a fraction of the exponential light emission curve is captured and integrated by the detector, was presented. Existing data were used to simulate the detector response for different reagent concentrations and flow rates. 

To model diffraction intensities, both the detector response and background intensity from thermal diffuse scattering must be included. A general expression for the model intensity including both factors is... 

To deduce a particle size distribution, the detector response must be deconvoluted by means of a simulation calculation. The scattering particles are assumed to be spherical in shape, and the data are subjected to one of three different computational methods. One system uses the unimodal model-dependent method, which begins with the assumption of a model (such as log normal) for the size distribution. The detector response expected for this distribution is simulated, and then the model parameters are optimized by minimizing the sum of squared deviations from the measured and the simulated detector responses. The model parameters are finally used to modify the originally chosen size distribution, and it is this modified distribution that is presented to the analyst as the final result. 

A second approach uses the unimodal model-independent method, which begins with the assumption that the size distribution consists of a finite number of fixed size classes. The detector response expected for this distribution is simulated, and then the weight fractions in each size class are optimized through a minimization of the sum of squared deviations from the measured and simulated detector responses. The third system uses the multimodal model-independent method. For this, diffraction patterns for known size distributions are simulated, random noise is superimposed on the patterns, and then the expected element responses for the detector configuration are calculated. The patterns are inverted by the same minimization algorithm, and these inverted patterns are compared with known distributions to check for qualitative correctness. 

Gel permeation chromatography (gpc) was performed on a Waters GPC-3 with a model 600 solvent delivery system, a 730 data module, a variable wavelength ultraviolet detector (uv), and a refractive index detector (Rl). Calculations were made on the uv detector response with the wavelength set at 325 nm. Three j/Styragel columns of porosities 105, 104, and 103 A were used and calibrated with polystyrene standards. Injection size was 50-125//I of 0.05% solutions with a flow rate of 1.4 ml/min. The solvent was HPLC grade N-methyl pyrrolidone (NMP) obtained from Aldrich Chemical Co. buffered with 0.03 M LiBr and 0.03 M H3P04.(2, 3)... 

Here, the theoretical intensity /Theory convoluted with the detector response function H plus the background B. The detector response is a combination of the pixellated detector and the electron detector response function. The background intensity B, in general, is slowly varying, which can be modeled using a slowly varying function. 

General models of the electron-capture process are based on the kinetic model of Wentworth and co-workers [254,293,295,298,313-315]. The ionization chamber is treated as a homogeneous reactor into which electrons are continuously introduced at a constant rate and electron-capturing solutes are added at a variable rate in a constant flow of carrier gas. The major consumption of electrons is via electron capture and recombination with positive ions. The model can be expanded to allow for the presence of electron-capturing contaminants and the formation of excited state negative ions. The kinetic model provides a reasonable explanation of the influence of pulse sampling conditions and temperature on the detector response, but exactly calculated solutions are rare. Again, this is because the necessary rate constants are usually unavailable, and the identity and relative concentration of all species present in the detector are uncertain. The principal reactions can be summarized as follows ... 

For compounds that capture electrons predominantly by a single reaction pathway some rate constants are negligible and Eq. (3.13) can be simplified. The model can be extended to include stable excited states that are involved in the electron-capture process for a minority of compounds [315]. The detector response is also a function of the cleanliness of the detector represented by the contribution of ki[I] to the electron capture coefficient. 

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