Nonlinear models, computational demands

The design and analysis of realistic power systems increasingly involves the representation of nonlinear models with progressively higher demands on the accuracy of computations. The difficulties of nonlinear problems are well known, and approximation methods, of which perturbation theory is one, are to be welcomed. Of course, perturbation theory has been applied to problems, such as fuel burnup, where the properties are a function of the neutron flux it has been customary, however, to linearize the problem around the unperturbed problem. When the accuracy obtained by this or similar devices is inadequate, there is a case for considering a more general perturbation theory for nonlinear systems. 

A variety of different models have been developed by researchers in order to capture the behavior of SCC beams, based on either concentrated or distributed plasticity. In concentrated plasticity models, all the inelasticity is concentrated at the ends of the member therefore, it deals with material nonlinearity in an approximate but efficient manner. On the contrary, distributed plasticity models simulate the inelastic behavior along the length of the member. This approach is more accurate but at the same time is more computationally demanding. Most of the formulations for both approaches are rather complex and not amenable to generic and routine application in structural engineering design. 

Many systems exhibit nonlinear behavior. This is another systems-level task that is computationally very demanding. Application of bifurcation analysis to simple and complex chemistry hybrid stochastic (KMC)-deterministic (ODE) models has been presented by our group (Raimondeau and Vlachos, 2002b, 2003 Vlachos et al., 1990) for various catalytic surface reactions. Prototype hybrid continuum-stochastic models that exhibit bifurcations were recently explored by Katsoulakis et al. (2004). It was found that mesoscopic... 

A conceptually different and relatively new example of an inferential model, motivated by human performance problems specifically, is nonlinear causal resource analysis (NCRA) [Kondraske, 1988 Vasta and Kondraske, 1994]. Quantitative task demands, in terms of performance variables that characterize the involved subsystems, are inferred from a population data set that includes measures of subsystem performance resource availabilities (e.g., speed, accuracy, etc.) and overall performance on the task in question. This method is based on the following simple concept Consider a sample of 100 people, each with a known amount of cash (e.g., a fairly even distribution from 0 to 10,000). Each person is asked to try to purchase a specific computer, the cost of which is unknown. In the subgroup that was able to make the purchase (some would not have enough cash), the individual who had the least amount of cash provides the key clue. That amount of cash availability provides an estimate of the computer s cost (i.e., the unknown value). Thus, in human performance, demand is inferred from resource availabdities. 

The primary objective in catalyst layer development is to obtain highest possible rates of desired reactions with a minimum amount of the expensive Pt (DOE target for 2010 0.2g Pt per kW). This requires a huge electroche-mically active catalyst area and small barriers to transport and reaction processes. At present, random multiphase composites comply best with these competing demands. Since a number of vital processes interact in a nonlinear way in these structures, they form inhospitable systems for systematic theoretical treatment. Not surprisingly then, most cell and stack models, in particular those employing computational fluid dynamics, treat catalyst layers as infinitesimally thin interfaces without structural resolution. 

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