The Campbell model

Campbell [83] proposed a model that uses the syllable as the fundamental unit of duration. In this a syllable duration is predicted from a set of linguistic features after which the individual phone durations within the syllable are then calculated. This approach has the attraction in that it is more modular, where we have one component modelling the prosodic part of the duration and another modelling the phonetic part. 

The prosodic part of the Campbell model uses a neural network to calculate a syllable duration. This is an attractive approach as the neural network, unlike the Klatt or sums-of-products model, can model the interactions between features. A somewhat awkward aspect of the model however is the fact that the syllable duration itself is of course heavily influenced by its phonetic content If left as is, the phonetic variance in model duration may swamp the prosodic variance that the neural network is attempting to predict. To allow for this, Campbell also includes some phonetic features in the model. Campbell maps from syllable to phone durations using a model based on his elasticity hypothesis which states that each phone in a syllable e q)ands or contracts according to a constant factor, normalised by the variance of the phone class. This operates as follows. A mean syllable is created containing the correct phones with their mean durations. This duration is then compared to the predicted duration, and the phones are either expanded or contracted until the two durations match. This expansion/contraction is performed with a constant variance, meaning that if the vowel is expanded by 1.5 standard deviations of its variance, the constant before it will be expanded by 1.5 standard deviations of its variance. 

The problem of the absolute syllable duration can be easily solved by having the neural network predict this z-score instead of an absolute duration, an approach followed by [456]. This then frees the neural network from phonetic factors completely and allows it to use only prosodic features as input. 

In general this model is quite effective as it solves the feature explosion problem by positing a modular approach. One significant weakness however is that the elasticity hypothesis is demonstrably false. If it was true then we would expect the z-scores for all the phones in a syllable to be the same, but this is hardly ever the case depending on context, position and other features the z-scores for phones across a syllable vary widely. This is a problem with only the second component in the model and a more sophisticated model of syllable/phone duration interaction could solve this. In fact, there is no reason why a second neural network could not be used for this problem. 

In general this model is quite eflective since it solves the feature-explosion problem 

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Several solids conveying models were developed by Campbell and his students at Clarkson University [19, 20]. These models will be referred to as either the Clarkson University models or the Campbell models. They proposed that the movement of the screw flight was pushing the polymer bed as the screw turns rather than the frictional force at the barrel moving the polymer pellets down the screw. For these models, they assumed that the solid bed behaved more like an elastic fluid rather than a solid and removed the torque balance constraint. Campbell and Dontula [20] reasoned that because the solid polymer pellets more closely resemble an elastic particulate fluid, no torque balance in the bed would be necessary. They further assumed that the force normal to the pushing flight was due to a combination of the force due to the pressure in the channel and a force proportional to the frictional force exerted at the barrel by the solid bed. The Campbell-Dontula model was first published as ... 

Hyun et al. [21] evaluated both the original model by Darnell and Mol [14] and the model by Campbell and Dontula [19] for accuracy against experimental data, and determined that the Darnell-Mol model was less accurate than that of the Campbell-Dontula model. The incorporation of the lateral stress ratio in the calculations supported their conclusions even more. At the time of the work by Hyun et al, however, the physics for screw rotation was not well appreciated, and the evaluations for the Campbell models [23] were performed with coefficient of friction... 

The viscosity of some polymers at constant temperature is essentially Newtonian over a wide shear rate range. At low enough shear rates all polymers approach a Newtonian response that is, the shear stress is essentially proportional to the shear rate, and the linear slope is the viscosity. Generally, the deviation of the viscosity response to a pseudoplastic is a function of molecular weight, molecular weight distribution, polymer structure, and temperature. A model was developed by Adams and Campbell [18] that predicts the non-Newtonian shear viscosity behavior for linear polymers using four parameters. The Adams-Campbell model is as follows ... 

Figure 3.29 Effect of temperature and shear rate for a GPPS resin with a polydispersity M /M ) of 2.4 and a weight average M ) of 300,000 kg/kg-mole using the Adams-Campbell model [18]...

This is a theoretical equation that was derived from free volume theory. If extruding materials at lower than normal temperatures, the higher sensitivity of the viscosity to temperature is an issue that needs to be considered. The engineering-based viscosity equation developed by Adams and Campbell [18] has been shown to hold for all nominal processing temperatures, from within a few degrees of Tg [26, 27] to conventional extruder melt temperatures. The Adams-Campbell model limiting shear temperature dependence is ... 

Unlike the previous models by Darnell and Mol [14] and Tadmor and Klein [1], which are based upon the assumption of isotropic stress conditions, Campbell s model [20] considered anisotropic stress conditions, as suggested by Schneider [15], but it was assumed to be 1.0 due to the lack of published experimental data on the subject. Variations on the model set forth by Campbell and Dontula [20] include a modification to incorporate the lateral stress ratio [19, 22], and other modifications discussed by Hyun et al. [21, 23]. A modified Campbell-Dontula model with a homogeneous lateral stress is as follows ... 

As stated in Appendix A5, if /jy is redefined in terms of an internal angle, then the following model results and is referred to as the Campbell-Spalding model in the appendix ... 

The modified Campbell-Dontula model was developed using the LDPE resin friction data as applied to an empirical model. The empirical model is shown by Eq. 5.31 for the temperature range of 25 to 110 °C. The coefficients of dynamic friction using Eq. 5.31 is shown in Eig. 5.31. 

The modified Campbell-Dontula model provides an acceptable prediction of the rate at the section exit pressure. For many cases, the coefficients of friction are adjusted until an acceptable performance is obtained. This model and the other models should always be used with caution. As previously discussed, these models use a static force balance to approximate a dynamic process. 

The density of the plug is constant (Campbell model [1] and Yamamuro model [5, 6]). 

Forces for Yamamuro-Penumadu-Campbell Model F, = forwarding force at the barrel wall and centered on surface. p2= force due to pressure and centered on surface. 

Figure A5.6 Force diagram for the Yamamuro-Penumadu-Campbell model...

The ester models, as stated above, were all LC, but two of the ether model compounds, the methoxy- and ethoxy-substituted derivatives, were not, despite the fact that each of these mesogens yielded some liquid-crystallinity in the poly(ether) form. Therefore it seems that the polymers in this system tend to be "more liquid crystalline" than the related small molecules. This hypothesis is supported by the fact that Memeger(H) found liquid crystallinity in allhydrocarbon polymers incorporating the distyrylbenzene mesogen, even in cases where the cis/trans ratio of the unsaturations was as large as 0.3, while Campbell and McDonald (10) noted that iodine isomerization to the all-trans form was essential for the observation of an LC phase in the small-molecule derivatives which they prepared. 

Campbell and co-workers [46] have measured the J-V curves of PPV-based polymers at different temperatures in the range 30-270 K. They were able to fit the trapping model,... 

Fig. 3.19. (a) J-V characteristics of a sample of MEH-PPV with a thickness of 94 nm. The symbols represent the experimental data from Campbell et al. [46] at different temperatures. The solid straight lines are the calculated values using the trapping model in the same order of temperature from 270 to 30 K. (b) The same data re-plotted values of I plotted as a function of 1/ T for V = 10, 2 and 1 V. The figure is taken from [42],... 

Campbell et al. [46] also compared their data with the mobility model. The mobility model showed a very steep rise in the current with voltage at low temperature, which is inconsistent with their data. More recently Berleb et al. [47] and Lupton et al. [48] have also measured the J-V curves of conducting organic semiconductors at different temperatures. Similar discrepancies between theory and their data are found. 

Fig. 3.20. (a) Calculated current density as a function of inverse temperature for V = 10 V for a conducting polymer sample with exponentially distributed traps. The values of the trap distribution parameter Tc are Tc = 2500 K (long dash line), Tc = 1800 K (dash-dot line), Tc = 1500 K (solid line), Tc = 1200 K (dotted line) and Tc = 1000 K (small dash line). The values of the other parameters are Hb = 3 x 1018 cm-3, Nv = 3 - 1020 cm-3, e=2 and /ip = 5 x 10 cm2 V 1 s 1. The inset shows the calculated effective activation energy, Eeb. as a function of the characteristic trap distribution energy ) = kTc. (b) J-V characteristics of a sample of MEH-PPV with a thickness of 94 nm on a log-linear scale. The symbols represent the data of Campbell et al. [46]. The lines represent calculated values using the mobility model. The figure is taken from [42],... 

FIGURE 3.37 The Campbell-Griffiths (1993) plume-driven mantle convection model, (a) the pre-4.0 Ga Earth with descending, depleted cold plumes, and (b) the 2.0-0 Ga Earth with ascending enriched plumes. 

For example, Wu (2000) computed the AUC, AUMC, and MRT for a 1-compartment model and then showed what impact changing the volume of distribution and elimination rate constant by plus or minus their respective standard errors had on these derived parameters. The difference between the actual model outputs and results from the analysis can then be compared directly or expressed as a relative difference. Alternatively, instead of varying the parameters by some fixed percent, a Monte Carlo approach can be used where the model parameters are randomly sampled from some distribution. Obviously this approach is more complex. A more comprehensive approach is to explore the impact of changes in model parameters simultaneously, a much more computationally intensive problem, possibly using Latin hypercube sampling (Iman, Helton, and Campbell, 1981), although this approach is not often seen in pharmacokinetics. 

We thank John Bendler for performing the molecular modeling calculations and for many helpful discussions. Monty Alger and Lorraine Rogers provided some of the permeability data, while John Campbell, Dave Dardaris, Gary Faler, Ed Fewkes, Paul Howson, Rick Joyce, Jerry Lynch and John Maxam contributed to the results described in this report. 

The proposed model can be compared with both the model of Allred ( ) and that of Campbell et al. (8). Allred s model does not have the feature of competing parallel reactions that is essential to the pyrolysis model proposed here. It does, however, have the intermediate product bitumen which reaches a maximum level almost identical to the one in this work. Allred postulates that all kerogen decomposes into bitumen, whereas bitumen in the present work is the remainder of the kerogen after the light hydrocarbon fraction has been stripped off. 

There are some interesting similarities and contrasts between the present model and the Lawrence Livermore Laboratory (LLL) model of Campbell et al.(8) The activation energy of the initial decomposition is similar in both models,... 

During the late 1980s and early 1990s several groups investigated theoretically the low-lying isomers of (H20)e as characterized by model potentials. In particular, Kim et al. [2] used the MCY potential [50] both by itself as well as augmented with 3- and 4-body interactions [51,52], Belford and Campbell [53] used the Campbell-Mezei water model... 

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