In model verification

The Klauda and Sandler model can be used to predict the uniformly distributed hydrates that form in place on the seafloor with a resulting BSR, rather than those associated with rapid convective fluxes, which tend to be associated with faults, and thus more anecdotal in nature. Klauda and Sandler note that their model can be used to predict 68 of 71 local occurrences where hydrates have been found around the world, and explain the three exceptions. The ability to predict hydrate occurrences is a significant step in model verification. 

Freedman V. L. and Ibaraki M. (2003) Coupled reactive mass transport and fluid flow issues in model verification. Adv. Water Resour. 26, 117-127. 

Hence the high-frequency impedance of a reduced nonconducting polymer and the low-frequency capacitance of an oxidized polymer both depend linearly on layer thickness (via the N factor). The linear dependence of capacitance on thickness is of considerable diagnostic importance in model verification, since we usually expect the total capacitance of a thin film to be inversely proportional to film thickness. We can explain the prediction in Eqn. 438 by noting that low-frequency capacitance is confined to pore walls, which has its major axis orientated at right angles to the electrode surface. Thus the deeper the pore, the more capacitors there are in parallel in the pore wall and consequently the greater the total capacitance. 

Harder, M. 1998. Roughness, age and drift trajectories of sea ice in large-scale simulations and their use in model verifications. Annals of Glaciology 25, in press. 

Model verification. A very important, crucial step in modelling is model verification. This is a cyclic, iterative process which must be repeated with respect to all models at all stages of... 

In the past few years a variety of workshops and symposia have been held on the subjects of model verification, field validation, field testing, etc. of mathematical models for the fate and transport of chemicals in various environmental media. Following a decade of extensive model development in this area, the emphasis has clearly shifted to answering the questions "How good are these models ", "How well do they represent natural systems ", and "Can they be used for management and regulatory decision-making "... 

Verification is the complement of calibration model predictions are compared to field observations that were not used in calibration or fidelity testing. This is usually the second half of split-sample testing procedures, where the universe of data is divided (either in space or time), with a portion of the data used for calibration/fidelity check and the remainder used for verification. In essence, verification is an independent test of how well the model (with its calibrated parameters) is representing the important processes occurring in the natural system. Although field and environmental conditions are often different during the verification step, parameters determined during calibration are not adjusted for verification. 

Sargent, R.G. (1982) Verification and validation of simulation models, in Progress in Modeling and Simulation... 

TA are used to model and analyze dynamic systems with discrete and timed behavior. One of their strengths is the easy modeling in a decomposed fashion as a set of often small and individually acting automata. Time in TA is modeled in a very natural way by a set of clocks that simply measure the time between events. This is a major difference to MIP techniques, where time and dynamic components are described in a rather artificial way by providing variables and inequalities for every point of time within a discretized time horizon. In addition to the advantages in modeling, TA serve as a computational model which can be analyzed by techniques for reachability analysis. These techniques are widely used in the context of verification, in which the objective is to detect possible undesired (bad or forbidden) behaviors [9-11]. The success of these techniques was pushed by the availability and increasing performance of tools for TA, e.g., Uppaal [9, 10, 12, 13]. 

Simplified mathematical models These models typically begin with the basic conservation equations of the first principle models but make simplifying assumptions (typically related to similarity theory) to reduce the problem to the solution of (simultaneous) ordinary differential equations. In the verification process, such models must also address the relevant physical phenomenon as well as be validated for the application being considered. Such models are typically easily solved on a computer with typically less user interaction than required for the solution of PDEs. Simplified mathematical models may also be used as screening tools to identify the most important release scenarios however, other modeling approaches should be considered only if they address and have been validated for the important aspects of the scenario under consideration. 

In the previous section we addressed some of these issues in the context of physical versus empirical models. These issues are also intertwined with the question of model verification what kinds of data are available for determining that the model is a valid description of the process Model building is an iterative process, as shown by the recycling of information in Figure 2.2. 

Model validation requires confirming logic, assumptions, and behavior. These tasks involve comparison with historical input-output data, or data in the literature, comparison with pilot plant performance, and simulation. In general, data used in formulating a model should not be used to validate it if at all possible. Because model evaluation involves multiple criteria, it is helpful to find an expert opinion in the verification of models, that is, what do people think who know about the process being modeled ... 

This revolution will spread to all chemical and petroleum processes that are large enough in scale to justify the investment in model building and experimental verification. Further progress needs better chemical kinetic data. The most deficient area remains in predicting the fluid mechanical and solid flow behaviors in reactors, where progress is sorely needed to round out the science of reaction engineering. 

Experience gained during the past four years has shown that data base improvement programs such as those implemented in Oregon have provided new perspectives into the nature of each airshed s emissions. Subsequent major changes in each community s emission Inventories have Improved dispersion modeling results and provided a level of dispersion model verification Impossible to attain using traditional hl-vol measurements alone. 

Model Verification. There are several ways in which the models described here may be verified ... 

In the current work, we present a comprehensive approach to the problem dynamic mathematical models for simultaneous reactions media, numerical methodology as well as model verification with experimental data. Design and optimization of industrially operating reactors can be based on this approach. 

In general, it appears likely that a fit to the intermediate species profiles should provide the most sensitive means of model verification, even when the result of direct interest is a bulk parameter such as flame speed or rate of energy release. Laser probe methods can be also extremely useful in the absence of full verification, however. Even a semiquantitative measurement of some species in a flame can constitute the clue to the inclusion within the model of an entire subnetwork of chemical reactions. Coupled closely to model predictions, the laser probe results can pinpoint species and reactions which merit special attention, that... 

Abstract. A phase equilibriums in intermetallic compounds hydrides in the area of disordered a-, (3-phase in the framework of the model of non-ideal lattice gas are description. LaNi5 hydride was chosen as the subject for the model verification. Position of the critical point of the P—w.-transition in the LaNi5-hydrogen system was definite. 

The process of research in chemical systems is one of developing and testing different models for process behavior. Whether empirical or mechanistic models are involved, the discipline of statistics provides data-based tools for discrimination between competing possible models, parameter estimation, and model verification for use in this enterprise. In the case where empirical models are used, techniques associated with linear regression (linear least squares) are used, whereas in mechanistic modeling contexts nonlinear regression (nonlinear least squares) techniques most often are needed. In either case, the statistical tools are applied most fruitfully in iterative strategies. 

First principle mathematical models These models solve the basic conservation equations for mass and momentum in their form as partial differential equations (PDEs) along with some method of turbulence closure and appropriate initial and boundary conditions. Such models have become more common with the steady increase in computing power and sophistication of numerical algorithms. However, there are many potential problems that must be addressed. In the verification process, the PDEs being solved must adequately represent the physics of the dispersion process especially for processes such as ground-to-cloud heat transfer, phase changes for condensed phases, and chemical reactions. Also, turbulence closure methods (and associated boundary and initial conditions) must be appropriate for the dis-... 

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