Problem-solver, role

Assuming that these findings are eventually substantiated by additional research, they find their most obvious application to problem solving in industry, professional practice, and research. Here the procedure could play a role similar to that played by consultants, brainstorming, synectics, and other attempts to augment and "unstick" the problem solver s unsuccessful efforts. A quote from one of our subjects illustrates the possibilities ... 

Globalisation has caused companies to concentrate on core business and critical mass. It has resulted in a restmcture of the chemical industry into two types of focused companies [190] the molecule suppliers (commodities and fine chemicals) and the problem solvers (functional chemicals like additives and pharmaceuticals). Each type has its own characteristics as reflected by the role of the catalyst [418]. 

In addition to their use as stand-alone systems, LPs are often included within larger systems intended for decision support. In this role, the LP solver is usually hidden from the user, who sees only a set of critical problem input parameters and a set of suitably formatted solution reports. Many such systems are available for supply chain management—for example, planning raw material acquisitions and deliveries, production and inventories, and product distribution. In fact, the process industries—oil, chemicals, pharmaceuticals—have been among the earliest users. Almost every refinery in the developed world plans production using linear programming. 

In contrast to our preferred standard mode in this book, we do not develop a Matlab function for the task of numerical integration of the differential equations pertinent to chemical kinetics. While it would be fairly easy to develop basic functions that work reliably and efficiently with most mechanisms, it was decided not to include such functions since Matlab, in its basic edition, supplies a good suite of fully fledged ODE solvers. ODE solvers play a very important role in many applications outside chemistry and thus high level routines are readily available. An important aspect for fast computation is the automatic adjustment of the step-size, depending on the required accuracy. Also, it is important to differentiate between stiff and non-stiff problems. Proper discussion of the difference between the two is clearly outside the scope of this book, however, we indicate the stiffness of problems in a series of examples discussed later. So, instead of developing our own ODE solver in Matlab, we will learn how to use the routines supplied by Matlab. This will be done in a quite extensive series of examples. 

The discussion of modeling and simulation techniques for microreactors shows that the toolbox available at present is quite diverse and goes well beyond the standard capabilities of CFD methods available in commercial solvers. In micro-reactors, special methods needed for the modeling of noncontinuum physics play only a minor role and most of the effects are described by the standard continuum equations. However, even if the laminar nature of the flow somehow reduces the difficulty of simulation problems compared to macroscopic flows, there are a number of problems that are extremely difficult and require very fine computational grids. Among these problems is the numerical study of mixing in liquids that often suffers severely from discretization artefacts. 

The recent development of high-resolution experimental techniques allows for the structural analysis of protein channels with unprecedented detail. However, the fundamental problem of relating the structure of ion channels to their function is a formidable task. This chapter describes some of the most popular simulation approaches used to model channel systems. Particle-based approaches such as Brownian and molecular dynamics will continue to play a major role in the study of protein channels and in validating the results obtained with the extremely fast continuum models. Research in the area of atomistic simulations will focus mainly on the force-field schemes used in the ionic dynamics simulation engines. In particular, polar interactions between the various components of the system need to be computed with algorithms that are more accurate than those currently used. The effects of the local polarization fields need to be accounted for explicitly and, at the same time, efficiently. Continuum models will remain attractive for their efficiency in depicting the electrostatic landscape of protein channels. Both Poisson-Boltzmann and Poisson-Nemst-Plank solvers will continue to be used to... 

At the PNP level, our group has developed an efficient FAS-MG solver for the coupled equations, and we found that the choice of relaxation and interpolation schemes plays a crucial role in stability and efficiency. The Poisson part of the problem is standard and requires no special considerations. The Nernst-Planck part, however, contains strongly varying functions (as discussed above), and this is where focus on the relaxation and interpolation operations is required. 

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