Multiple order parameter model

The first step in quantitative description of pure polyamorphic fluid is a selection of the model that can qualitatively describe a possible multiplicity of critical points in wide range of temperatures and pressures. A great many of explanations of multicriticality in monocomponent fluids (perturbation theory models semiempirical models lattice models, two-state models, field theoretic models, two-order-parameter models, and parametric crossover model has been disseminated after the pioneering work by Hemmer and Stell Here we test more extensively the modified van der Waals equation of state (MVDW) proposed in work and refine this model by introducing instead of the classical van der Waals repulsive term a very accurate hard sphere equation of state over the entire stable and metastable regions... 

While the agreement between the experimental data and the theoretical calculation is very satisfying, other types of volume and enthalpy recovery experiments show that the single-ordering parameter model is not sufficiently flexible to rationalize many of the important aspects of the glass transition phenomenon. As a result, more complex models based on multiple ordering parameters are now under development.8... 

M. K. Venkitachalam, L.-Q. Chen, A. G. Khachaturyan, G. L. Messing. A multiple-component order parameter phase field model for anisotropic grain growth. Mater Sci Eng A 238 94, 1997. 

Tanks-in-Series Model Versus Dispersion Model. We have seen that we can apply both of these one-parameter models to tubular reactors using the variance of the RTD. For first-order reactions the two models can be applied with equal ease. However, the tanks-in-series model is mathematically easier to use to obtain the effluent concentration and conversion for reaction orders other than one and for multiple reactions. However, we need to ask what would be the accuracy of using the tanks-in-series model over the dispersion model. These two models are equivalent when the Peclet-Bodenstein number is related to the number of tanks in series, n, by the equation ... 

ABSTRACT This paper is to research an application of the multiplicative seasonal model to forecast the total number of China s coal mine accidents. By the empirical analysis on the data of coal mine accidents from January 2006 to December 2010, an accepted multiplicative seasonal forecasting model ARIMA(4,1,1)(1,1,1) is built up after differing the series to be stationary and estimating the order and parameters of the model. Furthermore, the test of this multiplicative seasonal model shows that it has a desirable fitting effect on the data of coal mine accidents. At last, this model is applied to forecast the number of national coal mine accidents from January 2010 to December 2010, and the forecasted values have a high accuracy when compared to the actual data. 

Abstract Incremental true bond graphs are used for a matrix-based determination of first-order parameter sensitivities of transfer functions, of residuals of analytical redundancy relations, and of the transfer matrix of the inverse model of a linear multiple-input-multiple-output system given that the latter exists. Existing software can be used for this approach for the derivation of equations from a bond graph and from its associated incremental bond graph and for building the necessary matrices in symbolic form. Parameter sensitivities of transfer functions are obtained by multiplication of matrix entries. Symbolic differentiation of transfer functions is not needed. The approach is illustrated by means of hand derivation of results for small well-known examples. 

If the rate of molecular motion in the sample increases, any of these lineshapes will narrow, but the exact shape will depend on the geometry of motion. If the sample is spun at the magic angle, the resonance collapses to a symmetric peak at ct so. If some preferred orientation is induced in the sample, e.g., by mechanical deformation, the resulting spectrum is a convolution of the original powder pattern with the imposed distribution. CSA spectra of oriented materials have been used to derive order parameters and to propose models for the orientation process [23]. Multiple-pulse experiments are needed to observe the CSA of abundant spins, but not of rare... 

For multi-input systems, where there are multiple inputs, the model representation is converted into a matrix form, so that each row represents a different input and the columns represent the parameter specifications. The orders are then stored as the augmented colunm matrix with each column representing the orders of a different row, for example, the B-order would be specified as [ 2, 3 ] for a 2-input system. 

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