Mathematical scientists and materials scientists are typically educated with and use different technical languages. Time and effort are required to surmount this language barrier. The mathematical scientist should learn enough of the technical language and jargon of the materials scientist to understand what needs to be accomplished in materials science. The materials scientist should focus much of the discussion on mathematical modeling in order to minimize linguistic discord.
Cultural, perceptual, and attitudinal differences between the mathematical and materials communities may lead to unrealistic expectations, with subsequent frustration that causes disillusionment with the collaborative process. This is an obstacle of attitudes that can be circumvented by more effective communication. Materials scientists want to analyze and to understand materials phenomena, whereas mathematical scientists want to develop mathematical theories and computational methods. Goals for any collaboration must be clarified at the outset. Preliminary discussion should help to identify the common interest and to show how each party is likely to benefit from the interaction.
Since there is a significant chance that useful research might never emerge from a collaborative effort, both sides are often reluctant to begin talking with each other. This impediment can be overcome by recognizing that both sides of a potential collaboration need to contribute an initial increment of time to facilitate understanding and useful communication.
Departmental structures in most universities too often discourage mathematical research by materials scientists and materials-oriented research by mathematical scientists by not providing motivating rewards such as tenure, promotion, and salary increases. Overcoming this obstacle requires that such structural disincentives be transformed into incentives that stimulate, encourage, and reward individuals for undertaking cross-disciplinary efforts between the mathematical sciences and materials science.
The last obstacle to collaborative research between materials science and the mathematical sciences is the shortage of funding. This obstacle is particularly important because a great deal of initial investment in time and effort is necessary before a collaboration can be established.
As noted in Chapter 1, the traditional boundaries between disciplines sometimes needlessly constrain the development of unorthodox ideas and new theories. The National Science Foundation recognized this in establishing a number of interdisciplinary science and technology centers, many of which include several institutions and often several disciplines (National Science Foundation, 1993, 1992). In particular, materials science is today a vast