Limit of linearity

Using the fluctuation-dissipation theorem [361, which relates microscopic fluctuations at equilibrium to macroscopic behaviour in the limit of linear responses, the time-dependent shear modulus can be evaluated [371 ... 

The method limit of quantitation and limit of detection must be determined as well as the limit of linearity. The limit of quantitation is defined as the level at which the measurement is quantitatively meaningful the limit of detection is the level at which the measurement is larger than the uncertainty and the limit of linearity is the upper level of the measurement rehabihty (39). These limits are determined by plotting concentration vs response. 

The simplified failure envelopes differ little from the concept of yield surfaces in the theory of plasticity. Both the failure envelopes (or surfaces) and the yield surfaces (or envelopes) represent the end of linear elastic behavior under a multiaxial stress state. The limits of linear elastic... 

First. The problem of a limit of linearity has assumed a certain importance for investigating dynamic properties of filled polymers [4, 5], Even for very small (from the point of view of measuring rheological properties of pure polymer melts) amplitudes of deformation, the values of a modulus depend on the amplitude. 

Figure 16.4. Quantification of A9-tetrahydrocannabinol (9THC) after TFA and 11-nor-9-carboxy-A9-tetrahydrocannabinol (THCCOOH) after PFP in blood using GC-MS/NCI. Drug-free blood was spiked with 9THC (a) and THCCOOH (b) to the concentrations of 0, 5, 10, and 50 or 20ng/mL and with ISs-9THC-D3 and THCCOOH-D3 to 20ng/mL. Monitoring ions were (m/z) 410.3 for 9THC and 572.3 for THCCOOH. The values of validation parameters, expressed in ng/mL, were LOD, 0.25 LOQ, 0.5 limit of linearity, 0.5 to 100 for both analytes [2].

To lowest order, and in the local limit of linear molecules, there are three terms in Eq. (4.113),... 

Schwartz has calculated the approximate confidence limits of linear graphs without elaborate digital computation ( ). 

After the formulation of defect thermodynamics, it is necessary to understand the nature of rate constants and transport coefficients in order to make practical use of irreversible thermodynamics in solid state kinetics. Even the individual jump of a vacancy is a complicated many-body problem involving, in principle, the lattice dynamics of the whole crystal and the coupling with the motion of all other atomic structure elements. Predictions can be made by simulations, but the relevant methods (e.g., molecular dynamics, MD, calculations) can still be applied only in very simple situations. What are the limits of linear transport theory and under what conditions do the (local) rate constants and transport coefficients cease to be functions of state When do they begin to depend not only on local thermodynamic parameters, but on driving forces (potential gradients) as well Various relaxation processes give the answer to these questions and are treated in depth later. 

LOD-Limit of Detection RDL-Reliable Limit of Detection MDL-Method Detection Limit LOQ-Limit of Quantitaion LOL-Limit of Linearity... 

For all practical purposes, the upper limit of quantitation is the point where the calibration curve becomes nonlinear. This point is called the limit of linearity (LOL). These can be seen from the calibration curve presented in Figure 1.3. Analytical methods are expected to have a linear dynamic range (LDR) of at least two orders of magnitude, although shorter ranges are also acceptable. 

The viscoelastic response of polymer melts, that is, Eq. 3.1-19 or 3.1-20, become nonlinear beyond a level of strain y0, specific to their macromolecular structure and the temperature used. Beyond this strain limit of linear viscoelastic response, if, if, and rj become functions of the applied strain. In other words, although the applied deformations are cyclic, large amplitudes take the macromolecular, coiled, and entangled structure far away from equilibrium. In the linear viscoelastic range, on the other hand, the frequency (and temperature) dependence of if, rf, and rj is indicative of the specific macromolecular structure, responding to only small perturbations away from equilibrium. Thus, these dynamic rheological properties, as well as the commonly used dynamic moduli... 

In bioanalysis, extracted samples are usually stored in either autosampler vials or wells in a plate (such as 96-well plate) sealed with pierceable caps or covers. During injection, the autosampler needle has to pierce the caps or covers to load samples. The debris may completely or partially block the autosampler needle, which would result in no sample or variably low sample volumes injected. Accordingly, no or randomly low IS responses are observed. As most autosamplers have a built-in needle flushing mechanism, the debris in the needle might be flushed out later partially or completely. Therefore, the injected volume can be back to normal at a later time without an operator s intervention. Apparently, when a needle will be blocked and when the blocked needle will be cleared by flushing, as well as how it will be blocked (completely or partially) are difficult to predict. Hence, there would be no clear pattern for this type of IS variations. However, the affected injections normally have lowered IS responses (Fig. 9). Despite lowered IS responses, the accuracy of quantitation can usually be maintained except for situations where no or very low amount of samples are injected, resulting in responses outside the limit of linear range or unacceptable S/N. 

The extent of orientation polarization of the point dipole is Mdipoie cos 9 in the direction of the electric field. In the limit of linear response to the electric field, the net average polarization of a freely rotating permanent dipole is... 

For a plastic fat, the yield stress was defined as the stress at the limit of linearity in a small deformation rheological test. Agreement between theory and experiment was found to be good. 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

Most of these assays can be performed using the same automated equipment that is used for plasma, but the assays will need to be validated separately for urine to ensure that the matrix (urine versus plasma) does not interfere with the method and that the enzyme levels present in urine, either endogenously or following injury, are within the limits of linearity. Immunoassays (ELISA) are commercially available for a, tt or i -glutathione-S-transferase in the rat and human (Biotrin International, Dublin). 

Figure 17.22. Experimentally determined ehanges in stress at the limit of linearity (cr ) as a funetion of solids volume fraetion (( )) for blends of milkfat (A), eoeoa butter (B) and modified palm oil (C) with eanola oil erystallized for 24 h at 5°C. Symbols represent the average and standard deviations of 2-6 samples. The line through the data was generated by nonlinear least-squares minimization of the model to the experimental data. Indieated are the estimates of the model parameters. The surfaee free energy term (8) was fixed as a eonstant. (Taken from Marangoni and Rogers 2003).

Minimum detectable amount and upper limit of linearity delimit LR... 

In recent years, many flow systems consisting of several pumps (multipump flow systems) or several injectors (multicommuted flow systems) have been constmcted and exploited. Some of them are dedicated to calibration purposes. For instance, the standard addition method was recently implemented using a multicommuted system with an injection valve and three directive solenoid valves [7]. The system can automatically prepare a series of calibration solutions by successively merging a sample with three standards of different analyte concentrations. The approach is especially suitable for trace analysis because, according to the author s recommendation, it can be used when the analyte concentration in the sample is below the lower limit of linear response of a detector (it allows, in particular, potentiometric... 

One of the first UV detectors suitable for use with packed LC columns was described in 1966 by Horvath and Lipsky [4] and about a year afterward Kirkland [5] described a miniaturized version of the detector in fact, sensor design has changed little since that time. The cell was 10 mm long and 1 mm ID. having a total volume of about 7.5 pi. Kirkland claimed a noise level of 0.0002 absorbance units, and an upper limit of linear dynamic range of 1.2 absorbance units, which was equivalent to a concentration of about 10 g/ml. This gives a... 

Range of calibration, limits of linear detection response, that is where the signal/sample load is within 5%. 

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