Fixed-point level

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. 

Sonic Methods A fixed-point level detector based on sonic-propagation characteristics is available for detection of a liquid-vapor interface. This device uses a piezoelectric transmitter and receiver, separated by a short gap. When the gap is filled with liquid, ultrasonic energy is transmitted across the gap, and the receiver actuates a relay. With a vapor filling the gap, the transmission of ultrasonic energy is insufficient to actuate the receiver. 

Fig. 3. Profitabihty diagram for Venture A. (a) Simple diagram. NRR is net return rate IRR, the internal rate of return, is a given fixed point, (b) Three NRR cutoff lines for Venture A where B, C, and D represent NRR values of 15, 10, and 5%/yr, respectively. For example, at a discount rate of 10% per year, the NRR cutoff for Venture A could be as high as 10.74% per year for marginal acceptance (point X). Acceptable levels are to the left of NRR cutoff...

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. 

The point q = p = 0 (or P = Q = 0) is a fixed point of the dynamics in the reactive mode. In the full-dimensional dynamics, it corresponds to all trajectories in which only the motion in the bath modes is excited. These trajectories are characterized by the property that they remain confined to the neighborhood of the saddle point for all time. They correspond to a bound state in the continuum, and thus to the transition state in the sense of Ref. 20. Because it is described by the two independent conditions q = 0 and p = 0, the set of all initial conditions that give rise to trajectories in the transition state forms a manifold of dimension 2/V — 2 in the full 2/V-dimensional phase space. It is called the central manifold of the saddle point. The central manifold is subdivided into level sets of the Hamiltonian in Eq. (5), each of which has dimension 2N — 1. These energy shells are normally hyperbolic invariant manifolds (NHIM) of the dynamical system [88]. Following Ref. 34, we use the term NHIM to refer to these objects. In the special case of the two-dimensional system, every NHIM has dimension one. It reduces to a periodic orbit and reproduces the well-known PODS [20-22]. 

Unlike simple random variables that have no space or time dependence, the statistics of the random velocity field in homogeneous turbulence can be described at many different levels of complexity. For example, a probabilistic theory could be formulated in terms of the set of functions U(x, t) (x, t) e R3 x R However, from a CFD modeling perspective, such a theory would be of little practical use. Thus, we will consider only one-point and two-point formulations that describe a homogeneous turbulent flow by the velocity statistics at one or two fixed points in space and/or time. 

A response surface model of the effects of HA protein concentration (gliadin, the wheat prolamin), HA polyphenol concentration (tannic acid, TA), alcohol, and pH on the amount of haze formed was constructed using a buffer model system (Siebert et al., 1996a). Figure 2.12 shows the effects of protein and polyphenol on haze predicted by the model at fixed levels of pH and alcohol. The model indicates that as protein increases at fixed polyphenol levels, the haze rises to a point and then starts to decline. Similarly, when polyphenol increases at a fixed protein level, the haze increases to a maximum and then declines. 

We believe, nowadays that "a light at the end of the tunnel has appeared and there is a hope for a general approach to the solution of this most urgent kinetic problem, since we have proper "fixed points. Most important is thermodynamics applied to study chemical reactions characterized by complex detailed mechanisms. One should relate thermodynamic and kinetic laws at various levels, supporting kinetics on both micro and macro levels. 

To estimate the uncertainty of a measurement on the scale, the user should consider the uncertainties due to the creation of the scale, and the uncertainty associated with the realization of its fixed points by the RMs. Also, selection of these RMs for realizing the fixed points of a scale depends on the required level of uncertainty of the end use. 

The "pipeline11 structure allows instructions to be processed concurrently in all levels of the pipe in both scalar and vector mode. The eight levels of the MBU-AU pair under optimum conditions can each produce an output every CPU clock cycle (80 nsec). Pipe levels unnecessary to a particular instruction are bypassed. Figure 1 also illustrates how different sections of the arithmetic pipeline are utilized for execution of a particular instruction, i.e., floating-point addition and fixed-point multiplication. 

The intercept of the straight line generated by the two fixed points (that is, the value of t at which V would vanish on that straight line if He could be maintained as an ideal gas down to extremely low temperatures ) is found to be 7b = — 100Vb/( ioo — o) = —273.15°C. This suggests a natural lower limit to temperature, namely, the point where V vanishes. It also suggests a shift of scale whereby the quantity T = lOOL/(Tioo — Vb) is the fundamental entity of interest. Adoption of this method leads an absolute scale for quantifying hotness levels we construct a thermodynamic temperature scale T(K) = r(°C) -I- 273.15, where K stands for kelvins as the temperature unit. This still maintains the desired proportionality between absolute temperature and measured volumes of He at fixed, low pressures. 

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