Modeling and the Computer Numerical Analysis vs Simulation

Our spin thus far on the subject of modeling has been primarily complimentary. On the other hand, the advent of powerful computers as a tool for the evaluation of physical problems has not been universally beneficial. As we will describe presently, the establishment of computer-based models is attended by both conceptual and computational difficulties. It is true that the act of creating a numerical incarnation of a given theory requires an unambiguous statement of that theory itself. It is not possible to code up a theory unless the mathematical statement of that theory can be clearly articulated. But these virtues are accompanied by vices as well. Because of the ease with which computational models may be advanced, the act of validation, both conceptual and logical, becomes increasingly uncertain. 

Another difficulty that attends the increasing use of computational models is that of pedagogy. The increasing reliance on simulation suggests that the problems of current interest are so complex that they defy description in proper analytic terms. If it emerges that this scenario is correct (which I expect it is not), then this raises 

Made to Measure by Philip Ball, Princeton University Press, Princeton New Jersey, 1997. This semipopular book examines some of the key materials that are making headlines at the time of this writing. I found the book both enjoyable and very enlightening. 

Molecules by P. W. Atkins, W. H. Freeman and Company, New York New York, 1987. Though the emphasis here is on molecules rather than materials per se, Atkins does a fantastic job of connecting structure and function and illustrates the type of thinking that materials science should emulate in the quest to explicate this connection. 

---