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Continuous property modeling

Often the goal of a data analysis problem requites more than simple classification of samples into known categories. It is very often desirable to have a means to detect oudiers and to derive an estimate of the level of confidence in a classification result. These ate things that go beyond sttictiy nonparametric pattern recognition procedures. Also of interest is the abiUty to empirically model each category so that it is possible to make quantitative correlations and predictions with external continuous properties. As a result, a modeling and classification method called SIMCA has been developed to provide these capabihties (29—31). [Pg.425]

Chain stretching is governed by the covalent bonds in the chain and is therefore considered a purely elastic deformation, whereas the intermolecular secondary bonds govern the shear deformation. Hence, the time or frequency dependency of the tensile properties of a polymer fibre can be represented by introducing the time- or frequency-dependent internal shear modulus g(t) or g(v). According to the continuous chain model the fibre modulus is given by the formula... [Pg.20]

The fc-NN approach can also be applied for the prediction of a continuous property v as an alternative to regression methods as described in Chapter 4. The property of an unknown can be simply computed as the average of the properties of k neighbors, or a local regression model can be computed from them. [Pg.231]

Fig. 3.2 Typical applications using chemical multivariate data (schematically shown for 2-dimensional data) cluster analysis (a) separation of categories (b), discrimination by a decision plane and classification of unknowns (c) modelling categories and principal component analysis (d), feature selection (X2 is not relevant for category separation) (eY relationship between a continuous property Y and the features Xi and X2 (f)... Fig. 3.2 Typical applications using chemical multivariate data (schematically shown for 2-dimensional data) cluster analysis (a) separation of categories (b), discrimination by a decision plane and classification of unknowns (c) modelling categories and principal component analysis (d), feature selection (X2 is not relevant for category separation) (eY relationship between a continuous property Y and the features Xi and X2 (f)...
Transport properties (continued.) semiclassical model, 192-193 temperature-dependent resistivity of nanowires, 193-198 Triplet sites on supports, 63-64 Tungsten species, SiC>2-supported, 63 Turnover numbers (TON), nanostructured materials, 6... [Pg.216]

Once the computational model of the molecule is created, it is of most interest to study its properties in the natural environment, in particular, water solvent. Surrounding the molecule with water, allows us to study the solvation process. Like molecules, the solvent may be also described with different levels of accuracy. Beginning with all-atom models of water,48,49 which allow for the studies of solvent structure around solutes but are time consuming and the results are model dependent, to continuous dielectric models,50- 52 which are faster but less accurate and give no knowledge about the solvent itself. Thus, the difference in the level of description for both models is either an advantage or a drawback. These models are commonly known as explicit or implicit solvent models, respectively. [Pg.212]

In the 1990s Northolt and Baltussen developed the so-called continuous chain model, which is able to describe the tensile deformation properties of well-oriented polymer fibres properly. We will not go into detail in describing this outstanding model, but for an exact description of this model the reader is referred to the many publications of these two authors and their co-authors in the years from 1995 to 2005, and in particular to the doctoral thesis (1996) by Baltussen, the 2002 paper by Northolt and Baltussen and the 2005 paper by Northolt et al. on the strength of polymer fibres. [Pg.490]

Constant K and the exponent a of the Mark-Houwink equation, 255 Constitutive properties, 60 Contact angle, 232 Continuous chain model, 489-90 Continuous wave NMR, 365 Contour length, 247, 490 Controllability, 800... [Pg.991]

The persistant model (see Fig. 7d and the figure caption). The continuous persistent model can be obtained by means of some smoothing of the properties of the suitable discrete model at the microscopic level. For this purpose, let us consider the discrete model, which differs from that shown in Fig. 7b only in one respect namely, let us attribute to the spacers some finite stiffness with respect to bending, i.e. for this model... [Pg.85]

The majority of the QSAR strategies aimed at building models are based on regression and classification methods, depending on the problem studied. For continuous properties, like most of the biological activities and physico-chemical properties, the typical QSAR/QSPR model is defined as... [Pg.1252]

In this section, we consider a new approach to building stracture-activity and structure-property models based on the use of continuous functions on space coordinates (called hereinafter continuous molecular fields) to represent molecular... [Pg.433]

Finally, some rather recent devdopments must be noted. Several years ago, Yamakawa and co-workers [25-27] developed the wormlike continuous cylinder model. This approach models the polymer as a continuous cylinder of hydrodynamic diameter d, contour length L, and persistence length q (or Kuhn length / ). The axis of the cylinder conforms to wormlike chain statistics. More recently, Yamakawa and co-workers [28] have developed the helical wormlike chain model. This is a more complicated and detailed model, which requires a total of five chain parameters to be evaluated as compared to only two, q and L, for the wormlike chain model and three for a wormlike cylinder. Conversely, the helical wormlike chain model allows a more rigorous description of properties, and especially of local dynamics of semi-flexible chains. In large part due to the complexity of this model, it has not yet gained widespread use among experimentalists. Yamakawa and co-workers [29-31] have interpreted experimental data for several polymers in terms of this model. [Pg.8]

Develop an unsteady-state model for a stirred batch reactor, using the nonlinear continuous reactor model presented in Example 4.8 as a starting point. For the parameter values given below, compare the dynamics of the linearized models of the batch reactor and the continuous reactor, specifically the time constants of the open-loop transfer function between c a and T c, the concentration of A, and the jacket temperature, respectively. Assume constant physical properties and the following data ... [Pg.450]

The ultimate goal of most multivariate analyses is to develop a model to predict a property of interest. That property may be categorical or continuous. Continuous properties are modeled and predicted by regression methods—Principal Component Regression (PCR) and Partial Least Squares (PLS), in the case of Pirouette. After performing exploratory testing, the next step is to decide... [Pg.354]

Besides predicting categories for samples, MS e-nose instruments can also be used for determining a continuous property of samples. Continuous properties are modeled and predicted by regression methods. Details describing how SPME-MS-MVA has been used for predicting the shelf life of milk are described below (16). [Pg.364]

Mapping Method To introduce this method - the straw man of property modelling - let us remind ourselves about the geometric structure of a map of a faulted surface. Suppose that the faults are normal faults. In such a case each (x, y) point on a horizontal reference plane is mapped into the horizon, or into a fault surface. The boundaries of the fault surfaces are the fault traces which are polygons in the reference plane. The horizon is not itself a continuous surface. However, the union with the fault surfaces repairs the horizon surface to a continuous surface. That this can be done is the main reason for the historical success of mapping software and its main restriction - one cannot describe reverse faults without extensive extra mathematical (and thus software) objects. [Pg.187]

Constant B of Equation 11.54, which describes the effect of temperature, is almost twofold that of pressure (constant C) for the three model parameters (a, Uq, and 5). Such values corroborate the statement that the effect of pressure is lower than that of temperature on hydrocracking of heavy oil. When pressure is changed, some physicochemical properties of the reacting system, such as density, viscosity, etc., change, which in turn affect molecular diffusivity of the gas and liquid. Gas formation is enhanced as the pressure is increased however, its effect on fluid dynamics is partially counterbalanced by the great excess of hydrogen, which dominates the gas phase for the hydrodynamics. Hence, not only purely kinetic aspects are involved in the correlation of the parameters of the continuous kinetic model with pressure and temperature, but thermodynamics and hydrodynamics effects of the liquid-gas mixture are also hidden in these parameters. [Pg.438]


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