Fixed Point Measurement

Besides scanning measurements there are also a few fixed point measurements for paper properties which are assumed to be constant across the web width. For example color measurements are sometimes fixed point measurements as color should not vary across the web width. 

Basis weight is measured in g m and it is the total mass of 1 m of paper, including aU components, Hke fibers, fillers and water. The sensors consist of a radioactive source and a radiation detector on the opposite side of the paper. The absorption of radioactive radiation is a measure of the total mass of the paper. Radioactive sources are usually promethium, krypton or strontium. Promethium provides the signal with the highest sensitivity and can be used for basis weights up to 250 g m. Strontium is used only in very heavy board applications. 

Nowadays detectors are either ion chambers or solid state detectors. Ion chambers are gas filled tubes and require a high voltage to detect electrons. SoHd state detectors use the photovoltaic effect to detect electrons. 

There are also other possible ways to measure basis weight, such as X-ray tubes to generate radiation, or spectroscopic methods, but currently they cannot compete with the sensors based on radioactive radiation. 

The accuracy of a basis weight measurement is typically 0.1 g m. To get a better understanding what this figure really means, it is good to know that the surface of the detector is smaller than 10 cm. Thus, if a sample is fixed between the sensor heads with a size of 10 cm, the weight of this sample is measured with a precision of 0.0001 g. 

---

For the sampling location, fixed-point measurement may be used if the results make it possible to assess exposure of the worker at the workplace. In general, however, personal sampling devices are preferred, which give more representative results of worker exposure. 

The calibration curve of each rosetta strain gauge was so obtained and ftg.5 shows the sum of the principal stresses at the measuring points versus pressure inside the vessel. Further tests were carried out to obtain the calibration factor and to check that it remained constant on the whole scan area of the test surface. This was achieved through additional measurements using the SPATE system on fixed points on the surface located very close to the applied rosetta strain gauges. This procedure gave the following results ... 

Invariant measures correspond to fixed points of P which means that Pp = p iff /r e Ad is invariant. In what follows, we will advocate to discretize the operator P in such a way that its (matrix) approximation has an eigenvector... 

From a mathematical point of view, conformations are special subsets of phase space a) invariant sets of MD systems, which correspond to infinite durations of stay (or relaxation times) and contain all subsets associated with different conformations, b) almost invariant sets, which correspond to finite relaxation times and consist of conformational subsets. In order to characterize the dynamics of a system, these subsets are the interesting objects. As already mentioned above, invariant measures are fixed points of the Frobenius-Perron operator or, equivalently, eigenmodes of the Frobenius-Perron operator associated with eigenvalue exactly 1. In view of this property, almost invariant sets will be understood to be connected with eigenmodes associated with (real) eigenvalues close (but not equal) to 1 - an idea recently developed in [6]. 

An ion beam causes secondary electrons to be ejected from a metal surface. These secondaries can be measured as an electric current directly through a Faraday cup or indirectly after amplification, as with an electron multiplier or a scintillation device. These ion collectors are located at a fixed point in a mass spectrometer, and all ions are focused on that point — hence the name, point ion collector. In all cases, the resultant flow of an electric current is used to drive some form of recorder or is passed to an information storage device (data system). 

Pressure. Standard atmospheric pressure is defined to be the force exerted by a column of mercury 760-mm high at 0°C. This corresponds to 0.101325 MPa (14.695 psi). Reference or fixed points for pressure caUbration exist and are analogous to the temperature standards cited (23). These points are based on phase changes or resistance jumps in selected materials. For the highest pressures, the most rehable technique is the correlation of the wavelength shift, /SX with pressure of the mby, R, fluorescence line and is determined by simultaneous specific volume measurements on cubic metals... 

The KTTS depends upon an absolute 2ero and one fixed point through which a straight line is projected. Because they are not ideally linear, practicable interpolation thermometers require additional fixed points to describe their individual characteristics. Thus a suitable number of fixed points, ie, temperatures at which pure substances in nature can exist in two- or three-phase equiUbrium, together with specification of an interpolation instmment and appropriate algorithms, define a temperature scale. The temperature values of the fixed points are assigned values based on adjustments of data obtained by thermodynamic measurements such as gas thermometry. 

The internal return rate (IRR), a fixed point on the diagram, caimot be viewed as a measure of profitabihty, which should vary with the cost of capital (discount rate). Because the curvature of the total return curve caimot be predicted from the single IRR point, there is no way that the IRR can be correlated with profitabihty at meaningful discount rates. Even both end points, ie, the IRR and the total return at zero discount rate, are not enough to predict the curvature of the total return curve. 

Thermal Methods Level-measuring systems may be based on the difference in thermal characteristics oetween the fluids, such as temperature or thermal conductivity. A fixed-point level sensor based on the difference in thermal conductivity between two fluids consists of an electrically heated thermistor inserted into the vessel. The temperature of the thermistor and consequently its electrical resistance increase as the thermal conductivity of the fluid in which it is immersed decreases. Since the thermal conductivity of liquids is markedly higher than that of vapors, such a device can be used as a point level detector for liquid-vapor interface. 

A comparison of resistivity and electromagnetic techniques (resistance versus specific conductance) shows that resistivity surveys are slower because the technique is necessarily limited to measurements at the fixed electrode points, which must be moved for each new survey. Electromagnetic surveys are not limited by fixed points. Also, certain applications of resistivity methods are best suited for sites where the... 

From the ventilation point of view, the fixed points -38.83 °C (triple-point of mercury), 0.010 °C (triple-point of water), 29.76 °C (melting point of gallium), and 156.60 °C (freezing point of indium) are of relevance. The triple-point of water is relatively simple to achieve and maintain with a triple-point apparatus. Some freezing point cells are covered in standards. In practical temperature calibration of measuring instruments, the lTS-90 fixed points are not used directly. 

Whether you use an audit, a survey, or a combination of both, remember that your results provide a picture of your PSM activities as of a fixed point in time. This creates a useful point of departure for detailed planning, pointing the way toward implementation and establishing a benchmark for future measurement. 

Fest nass, n. solid measure, -punkt, m. fixed point fixed target. 

Since the phase space of a dissipative dynamical system contracts with time, we know that, in the long time limit, t oo, the motion will be confined to some fixed attractor, A. Moreover, becaust of the contraction, the dimension, D, of A, must be lower than that of the actual phase space. While D adds little information in the case of a noiichaotic attractor (we know immediately, and trivially, for example, that all fixed-points have D = 0, limit cycles have D = 1, 2-tori have D = 2, etc.), it is of significant interest for strange attractors, whose dimension is typically non-integer valued. Three of the most common measures of D are the fractal dimension, information dimension and correlation dimension. 

Whatever the representation, whether by fixed point or floating, the number a that appears in the machine may deviate from the number a that is intended, and if a is among the initial data for the problem, the difference a — a will be called the initial error. It may be remarked in passing that errors of measurement may also contribute to the initial error, if a is understood to represent a physical quantity known only approximately as the result of physical measurement. 

The International Temperature Scale — ITS-90 For ITS-90, temperatures of a series of fixed points are measured as accurately as possible with a gas thermometer. A complete description of ITS-90 is given in the literature5 7 and... 

These fixed points are used to calibrate a different kind of thermometer that is easier to use than a gas thermometer. Over the temperature range from 13.8033 to 1234.93 °A (or K), which is the temperature interval most commonly encountered, the thermometer used for ITS-90 is a platinum resistance thermometer. In this thermometer, the resistance of a specially wound coil of platinum wire is measured and related to temperature. More specifically, temperatures are expressed in terms of W(T9o), the ratio of the resistance R(Ttriple point of water R (273.16 K), as given in equation (1.11)... 

Approximately every twenty years, the international temperature scale is updated to incorporate the most recent measurements of the equilibrium thermodynamic temperature of the fixed points, to revise the interpolation equations, or to change the specifications of the interpolating measuring devices. The latest of these scales is the international temperature scale of 1990 (ITS-90). It supersedes the earlier international practical temperature scale of 1968 (IPTS-68), along with an interim scale (EPT-76). These temperature scales replaced earlier versions (ITS-48 and ITS-27). 

The ITS-90 scale is designed to give temperatures T90 that do not differ from the Kelvin Thermodynamic Scale by more than the uncertainties associated with the measurement of the fixed points on the date of adoption of ITS-90 (January 1, 1990), to extend the low-temperature range previously covered by EPT-76, and to replace the high-temperature thermocouple measurements of IPTS-68 with platinum resistance thermometry. The result is a scale that has better agreement with thermodynamic temperatures, and much better continuity, reproducibility, and accuracy than all previous international scales. 

Temperatures on ITS-90, as on earlier scales, are defined in terms of fixed points, interpolating instruments, and equations that relate the measured property of the instrument to temperature. The report on ITS-90 of the Consultative Committee on Thermometry is published in Metrologia and in the Journal of Research of the National Institute of Standards and Technology The description that follows is extracted from those publications.3 Two additional documents by CCT further describe ITS-90 Supplementary Information for the ITS-90, and Techniques for Approximating the ITS-90.4... 

In summary, to obtain 7% from a platinum resistance thermometer, one selects the range of interest, calibrates the thermometer at the fixed points specified for those ranges, and uses the appropriate function to calculate AW(Tw) to be used in equation (A2.5). Companies are available that perform these calibrations and provide tables of W T<)0) versus 790 that can be interpolated to give 7% for a measured W T90). 

The flux ( J ) is a common measure of the rate of mass transport at a fixed point. It is defined as the number of molecules penetrating a unit area of an imaginary plane in a unit of time, and has the units of mol cm 2 s-1. The flux to the electrode is described mathematically by a differential equation, known as the Nemst-Planck equation, given here for one dimension ... 

In turbulent flow there is a complex interconnected series of circulating or eddy currents in the fluid, generally increasing in scale and intensity with increase of distance from any boundary surface. If, for steady-state turbulent flow, the velocity is measured at any fixed point in the fluid, both its magnitude and direction will be found to vary in a random manner with time. This is because a random velocity component, attributable to the circulation of the fluid in the eddies, is superimposed on the steady state mean velocity. No net motion arises from the eddies and therefore their time average in any direction must be zero. The instantaneous magnitude and direction of velocity at any point is therefore the vector sum of the steady and fluctuating components. 

The method of exchange-luminescence [46, 47] is based on the phenomenon of energy transfer from the metastable levels of EEPs to the resonance levels of atoms and molecules of de-exciter. The EEP concentration in this case is evaluated by the intensity of de-exciter luminescence. This technique features sensitivity up to-10 particle/cm, but its application is limited by flow system having a high flow velocity, with which the counterdiffusion phenomenon may be neglected. Moreover, this technique permits EEP concentration to be estimated only at a fixed point of the setup, a factor that interferes much with the survey of heterogeneous processes associated with taking measurements of EEP spatial distribution. 

In general, a thermometer is called primary if a theoretical reliable relation exists between a measured quantity (e.g. p in constant volume gas thermometer) and the temperature T. The realization and use of a primary thermometer are extremely difficult tasks reserved to metrological institutes. These difficulties have led to the definition of a practical temperature scale, mainly based on reference fixed points, which mimics, as well as possible, the thermodynamic temperature scale, but is easier to realize and disseminate. The main characteristics of a practical temperature scale are both a good reproducibility and a deviation from the thermodynamic temperature T which can be represented by a smooth function of T. In fact, if the deviation function is not smooth, the use of the practical scale would produce steps in the measured quantities as function of T, using the practical scale. The latter is based on ... 

The ITS 90 was adopted by the Comite International des Poids et Mesures in September 1989 [14-16], The ITS 90 extends from 0.65 K to the highest temperatures, practicably measurable in terms of the Planck radiation law using monochromatic radiation. The defining fixed points of the ITS 90 are mostly phase transition temperatures of pure substances given in Table 8.2. 

The most interesting liquids for low-temperature thermometry are 3He and 4He, especially for the calibration of resistance thermometers in the range from 0.5 to 4.2 K. Vapour pressure of H2 is also interesting to realize vapour pressure-fixed points included in ITS-90. The measure of He vapour pressure has been carried out with great accuracy [42,43] to establish the ITS-90 (see Section 8.3). There are several experimental precautions to be observed in order to obtain reliable measurements [2],... 

Although not one of the most frequently discussed properties of solids, hardness is an important consideration in many instances, especially in the area of mineralogy. In essence, hardness is a measure of the ability of a solid to resist deformation or scratching. It is a difficult property to measure accurately, and for some materials a range of values is reported. Because of the nature of hardness, it is necessary to have some sort of reference so that comparisons can be made. The hardness scale most often used is that developed by Austrian mineralogist F. Mohs in 1824. The scale is appropriately known as the Mohs scale. Table 7.11 gives the fixed points on which the scale is based. 

A prerequisite for a precise and accurate titration is the reproducible identification of an end point which either coincides with the stoichiometric point of the reaction or bears a fixed and measurable relation to it. An end point may be located either by monitoring a property of the titrand which is removed when the stoichiometric point is passed, or a property which can be readily observed when a small excess of the titrant has been added. The most common processes observed in end-point detection are change of colour change of electrical cell potential change of electrical conductivity precipitation or flocculation. (Electrochemical methods are discussed in Chapter 6 precipitation indicators find only limited use.)... 

---