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Mathematical Research in Materials Science: Opportunities and Perspectives 9 RECOMMENDATIONS INTRODUCTION The preceding chapters provide both an overview and some details of recent and current activities in an assortment of materials science areas where mathematical modeling, analysis, and computation play key roles, and they identify areas of mathematical research in which increased activity would accelerate materials research. However, the purpose of this report is not merely to focus in an abstract way on promising directions for collaboration between materials scientists and mathematical scientists, but also to encourage both communities to increase such collaboration for their mutual benefit and for the general benefit of the nation, including the practical benefits to industry and the strengthening of economic competitiveness and national security. Clearly, both the mathematical and materials sciences have much to gain from each other. An increase in collaboration would improve existing materials science models and produce better qualitative and quantitative understanding. In addition to stimulating new mathematical and statistical developments, such collaboration would provide mathematical scientists with new problems whose real-world relevance would bring excitement and practical application. The committee believes that a considerable amount of modern mathematics and statistics would be useful in resolving problems of materials science but is not utilized because materials scientists are unaware of those mathematical and statistical results and mathematical scientists are unaware of the potential applications. Unfortunately, as summarized in Chapter 1, obstacles to collaboration now exist with inhibiting effects that should not be underestimated. To increase awareness of this situation and stimulate thoughtful approaches to improving it, the committee identifies in this chapter what it views as the main obstacles to increased collaboration between the materials science and mathematical sciences communities. The committee's conclusions are based on information gathered in the course of this study, including input from scientists (see appendix) whose work is at the interface between materials science and the mathematical sciences, and the knowledge and experience of the committee's members. This chapter closes with the committee's recommendations to universities, government, industry, and professional societies on how to enhance and further increase collaborative efforts between the two communities and how to attract students and young researchers to such work. Acknowledging Obstacles to Collaboration The committee sees the following as the main obstacles to collaboration: In many cases, successful interaction with materials scientists requires mathematical scientists to learn more physical science. A significant investment of time and effort is required to clear this hurdle.
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Mathematical Research in Materials Science: Opportunities and Perspectives 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. Fostering Increased Collaboration 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
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Mathematical Research in Materials Science: Opportunities and Perspectives and growing body of knowledge based on the physical sciences, engineering, and mathematics but is not obliged to conform to their limits. Despite the obstacles noted above, successful collaboration between materials scientists and mathematical scientists has taken place and is taking place. This collaboration has led to substantial progress in both fields. Much of this progress, mentioned in Chapters 2 to 8, has been possible only through close interaction between members of the two fields. Fruitful collaborative efforts have occasionally sprung up and have involved imaginative and creative researchers on both sides who have had the curiosity and eagerness to expand their horizons. However, as Chapters 2 through 8 also indicate, numerous opportunities exist for new collaborations between members of the two communities, with a concomitantly large potential for benefit both to the research communities themselves and to strategic national interests. Thus ensuring the scientific vigor, technological strength, and economic health of the nation argues in favor of stimulating and facilitating new collaboration between mathematical scientists and materials scientists. RECOMMENDATIONS Universities, government, industry, and professional societies have important roles to play in fostering the kind of interdisciplinary mathematical sciences research and education that will enhance progress in materials science. Since, as was emphasized in Chapter 1, cross-disciplinary collaborations require long-term commitments, all of these communities should strive to provide the means by which long-term collaborative commitments between the mathematical and materials sciences can spring up and thrive. Having taken into consideration input from the contributors listed in the appendix, the committee makes the following recommendations on how to enhance and further increase collaborative efforts between the two communities. Universities The university has perhaps the major role to play, both in encouraging collaboration and in attracting students and young researchers to the mathematical sciences-materials science interdisciplinary area. The committee sees challenges and opportunities at all levels. Seminars led jointly by a mathematical scientist and a materials scientist should be given. Such seminars would both enhance understanding and collaboration and stimulate interest in students and young researchers. Since such joint efforts are very time consuming, recognition of the value and the effort should be reflected in teaching assignments and faculty evaluation. Temporary reassignment, faculty exchanges, and joint appointments in which mathematical scientists would reside in materials science departments and vice versa, should be encouraged. Such reassignment or exchange may sometimes result in a
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Mathematical Research in Materials Science: Opportunities and Perspectives productive, long-term career switch. The visiting scientists should be encouraged to teach courses to students and young researchers in the host department. Such courses would be useful in attracting students to this interdisciplinary area. To be effective, these assignments should be included in accrued credit toward normal sabbatical leaves and regarded favorably in merit and promotion reviews. Young faculty members in the mathematical sciences and in materials science should be encouraged to collaborate in research with colleagues in the other discipline. This approach will require that explicit recognition be given in merit and tenure reviews to the young faculty member as an important contributor to the synergistic effort. In many universities, the pressure to attain tenure inhibits young researchers from entering this cross-disciplinary area at a time when they could have a great impact, and thus it is a major barrier to be overcome. Basic mathematics courses in universities generally do not generate the excitement and awareness of frontier issues in research that are more commonly conveyed in basic physical sciences courses. One consequence is that potential scientists and engineers lose interest in and appreciation for the mathematical sciences, a circumstance that contributes to the communication problems pointed out in this chapter and in Chapter 1. Students in introductory courses should be made aware of cutting-edge mathematical sciences questions that pertain to important materials science research issues. Doing that would also help to raise awareness of the value of quantitative methods in materials science and in general. Federal and State Government Government funding plays a major role in facilitating cross-disciplinary work between the mathematical sciences and materials science, in attracting young researchers to the area, and in enhancing research collaboration at this interface. While federal and state support of individual investigators and small groups should remain the primary approach to funding, some specific actions to enhance collaborative efforts should complement that approach: The most important recommendation is that funding agencies should make special efforts to ensure that interdisciplinary proposals involving mathematical and materials scientists receive careful and appropriate consideration. There is currently a perception that such proposals can "fall through the cracks." The review of an interdisciplinary proposal needs to be coordinated between the agency programs for the different disciplines involved. Reviewers familiar with research issues at the interface should be selected. Also, there should be specific earmarking of funds for joint mathematical-materials proposals and fellowships. The participation of mathematical scientists in programs of government materials research laboratories and materials research groups should be encouraged.
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Mathematical Research in Materials Science: Opportunities and Perspectives Workshops and topical meetings that bring together mathematical and materials scientists from universities, national laboratories, and industry should be supported. Priority should be given to supporting mathematical scientists who are keen on interacting effectively with materials scientists, that is, to those mathematical scientists who have learned or are learning the requisite physical science, and who have penetrated or are in the process of penetrating the jargon barrier in order to conduct a collaborative effort involving the two disciplines. Postdoctoral fellowships that bring mathematical scientists into materials programs should be supported to help attract young researchers to the area. The leveraging effect of interdisciplinary postdoctoral fellowships is large. An on-line glossary of terms used (sometimes in different ways) by different research communities could be made available nationwide as one step toward alleviating the communication problems between the mathematical and physical sciences and engineering communities. Industry Although it does not presume to tell industry how to conduct its business, the committee makes the following recommendations, believing that while the roles that can be played by the various materials industries will differ greatly, there are some common opportunities: Mathematical scientists should be encouraged to take sabbatical leaves and summer employment in industrial materials laboratories; conversely, industrial scientists and managers should be welcomed as adjunct faculty or visitors in university mathematical sciences departments. Industrial firms should employ young mathematical scientists as consultants, making a long-term, several-year commitment (as some firms currently do for young engineering faculty); in doing this, firms should recognize fully that the initial years of employment will involve a substantial investment in educating such consultants in industrial problems. Universities, Government, and Industry Together The recommendations made above would not be complete without the inclusion of joint recommendations to industry, universities, and federal and state governments, all of which stand to benefit from materials science research.
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Mathematical Research in Materials Science: Opportunities and Perspectives A program should be established that offers sabbatical leaves for mathematical scientists to visit industry and government materials science laboratories, and for mathematical scientists from materials science industries or national laboratories to visit universities. A postdoctoral program should be offered to enable young mathematical scientists to work jointly with a materials science industrial company and a university for two years. Both of these programs should be funded jointly through university, industry, and government sources; federal and state governments should initiate the programs. Professional Societies Cognizant of the important role of materials, professional societies in mathematical, engineering, and physical sciences disciplines have given increasing emphasis to materials science and processing at their meetings. These efforts should continue and should be expanded. Professional societies should cooperate in sponsoring and developing programs in materials-related areas; for example, topical meetings and workshops could be jointly sponsored, or a joint national meeting could be organized. Professional societies should encourage the publication of special issues of professional journals and of volumes that focus on advances made possible by collaborative work in the mathematical sciences and materials science. They should strive to ensure that more professional rewards and recognition accrue to contributors to such work.
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