Dynamic physical model

In order to create dynamic physical models, it is necessary th.at the following criteria be met ... 

Keywords acausal reasoning, case relations, causal accounts, causal event sequences, causal reasoning, constraint-based reasoning, current electricity, device model, dynamic physical model, dynamic processes. Educational Testing Service, electricity, electrostatics, envisioning, macroscopic models, naive physics, physics, prior knowledge, qualitative arguments, qualitative model, qualitative theory, transient processes... 

Dynamic meteorological models, much like air pollution models, strive to describe the physics and thermodynamics of atmospheric motions as accurately as is feasible. Besides being used in conjunction with air quaHty models, they ate also used for weather forecasting. Like air quaHty models, dynamic meteorological models solve a set of partial differential equations (also called primitive equations). This set of equations, which ate fundamental to the fluid mechanics of the atmosphere, ate referred to as the Navier-Stokes equations, and describe the conservation of mass and momentum. They ate combined with equations describing energy conservation and thermodynamics in a moving fluid (72) ... 

Physical Models versus Empirical Models In developing a dynamic process model, there are two distinct approaches that can be... 

To illustrate the development of a physical model, a simplified treatment of the reactor, shown in Fig. 8-2 is used. It is assumed that the reac tor is operating isothermaUy and that the inlet and exit volumetric flows and densities are the same. There are two components, A and B, in the reactor, and a single first order reaction of A B takes place. The inlet concentration of A, which we shall call Cj, varies with time. A dynamic mass balance for the concentration of A (c ) can be written as follows ... 

As an alternative to deriving Eq. (8-2) from a dynamic mass balance, one could simply postulate a first-order differential equation to be valid (empirical modeling). Then it would be necessary to estimate values for T and K so that the postulated model described the reactor s dynamic response. The advantage of the physical model over the empirical model is that the physical model gives insight into how reactor parameters affec t the v ues of T, and which in turn affects the dynamic response of the reac tor. 

Transfer Functions and Block Diagrams A very convenient and compact method of representing the process dynamics of linear systems involves the use or transfer functions and block diagrams. A transfer func tion can be obtained by starting with a physical model as... 

A key featui-e of MPC is that a dynamic model of the pi ocess is used to pi-edict futui e values of the contmlled outputs. Thei-e is considei--able flexibihty concei-ning the choice of the dynamic model. Fof example, a physical model based on fifst principles (e.g., mass and energy balances) or an empirical model coiild be selected. Also, the empirical model could be a linear model (e.g., transfer function, step response model, or state space model) or a nonhnear model (e.g., neural net model). However, most industrial applications of MPC have relied on linear empirical models, which may include simple nonlinear transformations of process variables. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

It is particularly significant that no evidence is found for localized melting at particle interfaces in the inorganic materials studied. Apparently, effects commonly observed in dynamic compaction of low shock viscosity metals are not obtained in the less viscous materials of the present study. To successfully predict the occurrence of localized melting, it appears necessary to develop a more realistic physical model of energy localization in shock-compressed powders. 

Physical models of commercial fluidized bed equipment provide an important source of design information for process development. A physical model of a commercial fluidized bed processor provides a small-scale simulation of the fluid dynamics of a commercial process. While commercial processes will typically operate at conditions making direct observation of bed fluid dynamics difficult (high temperature, high pressure, corrosive... 

Several theories were proposed in the past to describe the postglitch relaxation of pulsars angular velocity. Each physical model considers the spin-down of the superfluid in a different way. Alpar et al. [3, 4] suggest that the crustal superfluid is responsible for the glitches and postglitch relaxation they describe the dynamical properties of the crust superfluid in terms of a thermal... 

Appendix B consists of a systematic classification and review of conceptual models (physical models) in the context of PBC technology and the three-step model. The overall aim is to present a systematic overview of the complex and the interdisciplinary physical models in the field of PBC. A second objective is to point out the practicability of developing an all-round bed model or CFSD (computational fluid-solid dynamics) code that can simulate thermochemical conversion process of an arbitrary conversion system. The idea of a CFSD code is analogue to the user-friendly CFD (computational fluid dynamics) codes on the market, which are very all-round and successful in simulating different kinds of fluid mechanic processes. A third objective of this appendix is to present interesting research topics in the field of packed-bed combustion in general and thermochemical conversion of biofuels in particular. 

Jaberi, F. A., and S. A. James. 1998. A dynamic similarity model for large eddy simulation of turbulent combustion. J. Physics Fluids 10(7) 1775-77. 

The problem in obtaining a state space model for the dynamics of the CSD from this physical model is that the population balance is a (nonlinear) first-order partial differential equation. Consequently, to obtain a state space model the population balance must be transformed into a set of ordinary differential equations. After this transformation, the state space model is easily obtained by substitution of the algebraic relations and linearization of the ordinary differential equations. 

We use the physical concept of the dynamic melting model proposed by McKenzie (1985) for the situation where the rate of melting and volume porosity are constant and finite while the system of matrix and interstitial fluid is moving. This requires that the melt in excess of porosity be extracted from the matrix at the same rate at which it is formed (the details of the model are shown in Fig. 3 of McKenzie, 1985). 

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