Effective sample length

The length of the sample kept between the clamps differs from the effective value, for fundamentally two reasons. On the one hand, the section in which the torsion is zero lies within the zone covered by the clamps, so that the clamp separation is smaller than the effective sample length. On the other hand, as stated earlier, the secondary effects of the torsion produce an 

If several frequencies of the vibration are computed as the clamp separation is progressively changed, then from a plot of a versus L the value of AL can be obtained from the intercept of the straight line obtained with the L axis. The linearity of the plot relies on the hypothesis that the modulus does not depend on the frequency as the length of the test sample is varied. In fact, the modulus is frequency-dependent, and a source of error is introduced in the estimation of the sample length by means of this method. When the measurements are carried out in glassy polymers, that error can be avoided by assuming, as a first approximation, a linear dependence of the modulus on frequency, as follows  

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For SFS, fluorescence intensities can be expressed as If = r I where r is the quantum yield at Aex and 4 is the absorbed intensity (Reynolds and Ahmad, 1995b). From Beer s law, 4 = /o(i - exp(-acO), where 4 is the incident intensity, a is the absorption cross section and I is the effective sampling length. For acl l, If 4 r cl. In SFS the excitation wavelength (Aex) and the emission wavelength (Aen ) are scanned synchronously, with a fixed off-set such that aA = (A , - AeJ. The normalized fluorescence intensity can be represented by 4/4 = 4 Te (A )cl, where the qnantum yield and the absorption cross-section are functions of A = (Aem - aA). The intensity distribntion will, therefore, show a pronounced peak when the absorption maximum and the quantum yield maximum overlap. For well defined... 

The total optical path difference between the two arms of the interferometer, for a sample length of about 50 mm, is of the order of 10 mm or less, minimizing the systematic error due to laser frequency fluctuations. To reduce the thermal effects on the interferometer assembly, the interferometer support plate is stabilized to a temperature slightly higher than room temperature and insulated from air currents by a polystyrene foam shield. The temperature variation of the interferometer support is kept below 0.1 K. 

In general Rytov approximation provides better reconstruction than Born approximation [8]. Here, MBLL is approximated locally at each sampling volume and the effective path length is estimated using the Rytov approximation as... 

The following measurements were made on the inner cylinder of a coaxial cylinders viscometer having inner and outer diameters of 24 mm and 26 mm, and an effective cylinder length of 35 mm. Using these data, determine the values of the shear stress, shear rate and apparent viscosity of the sample. 

This method is commonly nsed on spectral data to correct for multiplicative variations between spectra. In spectroscopy, snch variations often originate from nnintended or uncontrolled differences in sample path length (or effective path length, in the case of reflectance spectroscopy), caused by variations in sample physical properties (particle size, thickness), sample preparation, sample presentation, and perhaps even variations in spectrometer optics. Snch variations can be particularly problematic because they are confounded with mnltiplicative effects from changes in component concentrations, which often constitute the signal in qnantitative applications. It is important to note that multiplicative variations cannot be removed by derivatives, mean-centering or variable-wise scaling. 

Petroleum crude and its refinery products have two major component based on distillation. The portion that can be distilled under refinery conditions can be called volatiles and the nondistillables are the nonvolatiles. The volatiles can be analyzed by GC or GC-MS. The crude has both components. The distillate as the names applied, such as naphtha and kerosene contain only volatiles. When GPC is used for analyzing various distillates, the fractions separated by GPC can be characterized by GC or GC-MS. These data can be used to verify the nature of components present in various distillation cuts as a function of GPC elution volume. If the samples such as crude contains both volatiles as well as nonvolatiles, the samples should be separated into volatiles and nonvolatiles. The GPC of both components should be used to calibrate the GPC of the total crude. The parameter that can be obtained from GPC is effective molecular length. It can be used to relate other molecular parameters of interest after calibration. 

In the laboratory experiments, DOC monolith samples (length 7.5 cm, diameter 1.4 cm) with rather thin catalyst layer coating ( 25 pm) were employed to minimize the internal diffusion effects. The samples were placed into a thermostat to suppress the formation of temperature-gradients along the channels. In the course of each experiment, the temperature of the inlet gas and the monolith sample was increased at a constant rate of /min within the range of 300-800 K. The exhaust gases at the inlet of the converter were simulated by synthetic gas mixtures with defined compositions and flow rates (cf. individual figure captions all gas mixtures contained 6% C02 and 6% H20). 

The phase matching condition is Afc L ir, which means that for the generation of CARS the coherence length defined by 7r/ Afc has to exceed the effective interaction length L. The latter is determined by the axial dimension of the nonlinear sample. Thus, the actual extent of Afc acts as a size filter for the scatterer of dimensions for which an efficient CARS signal is generated. When the slab thickness is smaller than the pump wavelength, i.e., L 0, the... 

Let us first be clear about the circumstances in which a single-phase simulation makes sense. The brief and loose answer is when the time (Markov chain length) tea typical of escape from phase a is long compared to the time tsa required for effective sampling of the configuration space of that phase. More fully, and a little more formally when there exists some tsa < tm such that the configuration set q rj defined by Eq. (3) is effectively equivalent to that defined by the condition... 

The effective sampling depth or penetration depth (dp) is representative of the characteristic decay length and represents the distance at which the intensity of the evanescent field has decayed to 1/e with respect to the maximum (at the interface), as defined by ... 

FIGURE 7.29 Microchip CE separation of a sample containing 100 pM of K+, Li+ and Na+ (prepared in the running buffer). The measured plate number for K+ is 43,200 plates/m, with an estimated limit of detection of 18 lM. Running buffer, 10 mM MES/His at pH 6.0 separation conditions, 280 V/cm effective separation length, 3.4 cm contactless conductivity detection at 58 kHz (as optimized in Figure 7.28) [141]. Reprinted with permission from Wiley-VCH Verlag. 

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