Hill parameter

Figure 5.4 Laser-doppler anemometer profiles of mean velocity in and above a wind tunnel model study of flow over an isolated sinusoidal two-dimensional ridge covered with a tall canopy. Profiles are located upwind (x = -2L, dot dash line) on the hilltop (solid line) and downwind (x = +2L, dotted line). The hill parameters were H/L = 0.1 hc/H = 1.0. Full details of the experiment can be obtained from the author (Finnigan and Hughes, pers. comm.)...

The influence of experimental conditions on Hill parameter estimation is described by Glende and Reich (1972). According to Reich et al. (1972), a nonlinear regression with a minimum of 15 measuring points should be used for an unbiased determination of parameters. Also, the Hill model has been extended by Adair (1925) to allow for the existence of stable, partly liganded intermediates. 

Table 1. Half Saturation Oxygen Pressure and Hill Parameter of Some Chemically Modified and Mutant Hemoglobins (from Data Collected by Baldwin (1975) and Data of Coleman (1977)). Half Saturation Oxygen Pressure is Given Relative to the Value of the Normal Hemoglobin (HbA).

Fig. 1.3. Correlation between the Hill parameter and partial oxygen pressure at half saturation for chemically modified and mutant hemoglobins from Table 1. hemoglobins modified at a subunits o hemoglobins modified at P subunits. Curves represent calculated values obtained by varying the parameters a (curve a) and the parameter b (curve b), introduced as described in the text. Parameters used in the calculation are four parameters of the AE as given in Fig. 1.1, and five parameters of the GAE S = 0.6...

F, G, H, L, M and N are the Hill parameters, ffij the components of the stress tensor. The strain increment tensor results in... 

Oo is the applied tension or compression stress. With the assumption of isotropic behavior in the 2-3 plane (direction 1 is along the fiber axis), the 6 Hill parameters and the parameter A are determinable with measurements in 3 directions (0°, 45° and 90° fiber orientation), as described by Hyde et al. Afterwards the creep behavior of all other orientations can be calculated and... 

The Hill model was adopted for the compression creep using the 0°, 45 , 90 results at 1473 K, 30 MPa (Figure 6) and a stress exponent of 1.9 which corresponds to the exponent of the 90 orientation. Ideally, the Hill parameters are constant for a material. However, in this case parameters decreased with an increasing creep strain (Figure 6, left). For further calculations, mean Hill parameters were used (Table II). The determination of the average was conducted for strain from 2.4% to 3.2% because of the higher reliability of the measured values. 

Due to averaging no definite solution for the parameter A from equation (6) exists. Hence A (Figure 6, right) was determined by a least square method. The Hill parameters and A were used to calculate creep rates in 15 and 30 fiber orientation as well as for another temperature and stress. In Figure 7 and Figure 8 the results are depicted. 

Figure 6. Determined Hill parameters for compression creep curves at 1473 K and -30MPa Geft) and parameter A hem equation (6) for averag Hill parameters of Table II for a stress exponent of 1.9 (right).

Fig. 4.3. The Jonscher representation of the Dissado-Hills dielectric loss spectrum. So is the static permittivity copH is the principal relaxation rate n and m are the Dissado-Hill parameters. Arrows indicate variations of the loss curve on increasing values of the model parameters.

In order to get an extremely high resolution and a small dead zone" (after the transmitter pulse) single amplifier states must have a bandwidth up to 90 MHz ( ), and a total bandwidth of 35 MHz (-3 dB) can be reached (HILL-SCAN 3010HF). High- and low-pass filters can be combined to band-passes and provide optimal A-scans. All parameters are controlled by software. 

Fig. 5, also an A-scan, shows the possibility of the echo-technique for concrete. The interface and backwall-echo of a 20 cm thick concrete specimen are displayed (RF-display). A HILL-SCAN 3041NF board and a broadband transducer (40mm element 0) are used which enable optimal pulse parameters in a range of 50 to 150 kHz. Remarkable for concrete inspections is the high signal-to-noise ratio of about 18 dB. 

Hential is an exponential-6 potential with just two parameters the mirrimum energy 5 and the well depth e [Hill 1948] ... 

Th ere are sim ilar expression s for sym m etry related in tegrals (sslyy), etc. For direct comparison with CNDO, F is computed as in CNDO. The other INDO parameters, and F, are generally obtained [J. I. Slater, Quantum Theory of Atomic Structure, McGraw-Hill Book Company, Vol. 1, New York, I960.] from fits to experimental atomic energy levels, although other sources for these Slater-Con don parameters are available. The parameter file CINDO.ABP contains the values of G and F (columns 9 and 10) in addition to the CNDO parameters. 

In 1982 a study of the usefulness of DBBF in the production of a blood substitute was reported (99). A single modification achieved the dual goals of reduced oxygen affinity and restricted tetramer—dimer dissociation. This work was confirmed in 1987 (98). The product, called aa-hemoglobin, was formulated in Ringer s lactate. P q under physiologic conditions is 3.7 kPa (28.0 torr). Hill s parameter is 2.2, and the Bohr effect was reduced (100). Plasma retention was increased, and the product appeared to be less heterogeneous than some of the other derivatives under study. Its production was scaled up by Baxter Healthcare Corp., under contract to the U.S. Army. 

Much professional software is devoted to this problem. A diskette for sets of differential and algebraic equations with parameters to be found by this method is by Constantinides Applied Numerical Methods with Personal Computers, McGraw-Hill, 1987). 

Heating, Refrigerating and Air-Conditioning Engineers, New York, 1967. Quinn, Humidity The Neglected Parameter, Test Eng. (July 1968). Treybal, Mass-Ttansfet- Operations, 3d ed. McGraw-Hill, New York, 1980. Wexler, Humidity and Moisture, vol. I, Reinhold, New York, 1965. Zimmerman and Lavine, Psychrometric Charts and Tables, Industrial Research Service, 2d ed., Dover, N.H., 1964. 

Two lists of gas/liquid reactions of industrial importance have been compiled recently. The literature survey by Danckwerts (Gas-Liquid Reactions, McGraw-Hill, 1970) cites 40 different systems. A supplementary list by Doraiswamy and Sharma (Heterogeneous Reactions Fluid-Lluid-Solid Reactions, Wiley, 1984) cites another 50 items, and indicates the most suitable land of reactor to be used for each. Estimates of values of parameters that may be expec ted of some types of gas/liquid reac tors are in Tables 23-9 and 23-10. 

The terms that are linear in the stresses are useful in representing different strengths in tension and compression. The terms that are quadratic in the stresses are the more or less usual terms to represent an ellipsoid in stress space. However, the independent parameter F,2 is new and quite unlike the dependent coefficient 2H = 1/X in the Tsai-Hill failure criterion on the term involving interaction between normal stresses in the 1- and 2-directions. 

This is not to imply that a full-throttle acceleration from rest to that speed is a maneuver frequently executed by the typical driver. The time to 60 mph is rather an easily measured parameter that seiwes as a surrogate for other performance metrics. A car that is slow from 0 to 60 mph will likely have slow response from 40 to 60 mph for freeway merging, or prove lethargic when climbing hills. Reflecting the market preference of the typical new-car buyer, for the average new U.S. passenger car, the acceleration time from 0 to 60 mph has decreased from about 14 seconds in 1975 to fewer than 11 seconds iti 1995. 

Figure 5-12. Power vs. RPM with impeller diameter parameters. Illustration of impeller input power versus speed for a family of Impeller designs, but only of various diameters, showing uniformity of performance. By permission, Oldshue, J. Y, Fluid Mixing Technology, 1983, Chemical Engineering, McGraw-Hill Publications Co. [29].

Where large samples of reactant are used and/or where C02 withdrawal is not rapid or complete, the rates of calcite decomposition can be controlled by the rate of heat transfer [748] or C02 removal [749], Draper [748] has shown that the shapes of a—time curves can be altered by varying the reactant geometry and supply of heat to the reactant mass. Under the conditions used, heat flow, rather than product escape, was identified as rate-limiting. Using large ( 100 g) samples, Hills [749] concluded that the reaction rate was controlled by both the diffusion of heat to the interface and C02 from it. The proposed models were consistent with independently measured values of the transport parameters [750—752] whether these results are transfenable to small samples is questionable. 

Figure 5 shows the joint 95% posterior probability region for the two parameter functions. Shimmer bands are also indicated at the 95% probability level. This analysis confirms the results of Hill et al. that both styrene and acrlyonitrile exhibit a penultimate effect. 

Analysis of the data collected by Hill et al. illustrates how a four parameter problem can be reduced to one involving only two parameters by appropriately formulating the problem. In addition an approach to fitting models directly to triad fraction data is shown. Our analysis confirms the conclusion made by Hill et al. that a penultimate effect does exist for both styrene and acrlyonitrile. 

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