Linear experiment

When the type of error cannot be easily identified and quantified from available control data, it may be necessary to use the experhnents employed m method evaluation studies (see Chapter 14). A comparison-of-methods experiment may be used to estimate systematic errors when there is another routme method available for measuring the analyte of interest. Interpretation of the results must consider that the observed differences between two methods could be caused by either method and cannot therefore be assigned to the test method unless the quahty of the comparison method is well documented. Recovery, interference, and linearity experiments may be more specific in estimating systematic errors, including the constant or proportional nature of the systematic errors. 

Most LBAs require some level of sample dilution prior to analysis due to either the assay MRD or high analyte concentrations in the study samples. It is imperative to demonstrate during method development that the analyte, when present in levels above the ULOQ, can be diluted to concentrations within the quantitative range. This may be accomplished by illustrating that the analytical recovery of an ultrahigh matrix spike ( 100 1000 times ULOQ), diluted serially in assay matrix, remains acceptable over a wide concentration range (when corrected for the dilution factor). Dilutional linearity experiments often reveal the presence of a prozone or Hook effect, which is discussed in the next section. 

FIGURE 3.13 Hook effect revealed by dilutional linearity experiment, (a) The analyte when assayed neat resulted in a low measured concentration. When reassayed at multiple dilutions, the measured concentration for several dilutions was greater than the assay ULOQ. (b) The results, when corrected for the dilution factor, showed dilutional linearity at dilutions greater than 400 fold, indicating the presence of a HDHE. 

In the unsteady ID linear experiment with constant flow rate injection, the injection pressure, P, i is expected to increase Unearly with time (see Rg. 9.27) if the flow is ID and fiber tows are filled at the instant the resin arrives there. Since the slope, dPinj/d/ is used to calculate the permeability, K (see Table 9.2), one must carefully check if is almost a first order... 

The main point is that, if there were correlation in the site energies, it would not be possible any more to determine Nc from a linear optical experiment alone because Eq. 2 would contain two unknown quantities. There are indications from non-linear experiments that /o is finite [28]. Another way to estimate is via the ratio of the radiative rates of monomer and aggregate. This ratio is also determined by the number Nc of coherently coupled molecules [7, 29] but is not influenced by correlation effects in the site energies. 

Linearity is the ability to obtain results that are directly or indirectly (by well-defined mathematical transformation) proportional to the concentration of an analyte in a sample within a given range. The range is the interval between the upper and the lower levels of the analytical method that have been demonstrated to obtain acceptable accuracy, linearity, and precision. Hence, the following parameters are typically evaluated during linearity experiments. 

Lower energy photons do not excite electrons into the conduction band, therefore the band-to-band emission will be zero in linear experiments. 

The realized experiments and the obtained results showed that measures by eddy currents present a linear relation between the evolution of the cementation thickness character and the impedance variation. 

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

The experiment was carried out by a continuously working Nd YAG-laser fabricated by NEC. The laser has a maximum output of 1200 W and is controlled by handling facility with a linear axle. A stage index fiber optical waveguide with a diameter of d=1000 pm was used for the control of the beam. The focusing optics consist of a focusing lens (f=l 16 mm) and a collimation lens (f=70 mm). 

The linear dependence of C witii temperahire agrees well with experiment, but the pre-factor can differ by a factor of two or more from the free electron value. The origin of the difference is thought to arise from several factors the electrons are not tndy free, they interact with each other and with the crystal lattice, and the dynamical behaviour the electrons interacting witii the lattice results in an effective mass which differs from the free electron mass. For example, as the electron moves tlirough tiie lattice, the lattice can distort and exert a dragging force. 

The current frontiers for the subject of non-equilibrium thennodynamics are rich and active. Two areas dommate interest non-linear effects and molecular bioenergetics. The linearization step used in the near equilibrium regime is inappropriate far from equilibrium. Progress with a microscopic kinetic theory [38] for non-linear fluctuation phenomena has been made. Carefiil experiments [39] confinn this theory. Non-equilibrium long range correlations play an important role in some of the light scattering effects in fluids in far from equilibrium states [38, 39]. 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

In the next section we discuss linear hydrodynamics and its role in understanding the inelastic light scattering experiments from liquids, by calculating the density-density correlation fiinction,. Spp. 

Figure B1.3.A.9. Diagram depicting the angles used in scattermg experiments employing linearly and circularly polarized light. The subscripts i and s refer to the incident and scattered beam respectively.

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