Monday, May 29, 2006

Strength map of carbon nanotube

In theory, carbon nanotubes are 100 times stronger than steel at one-sixth the weight, but in practice, scientists have struggled make nanotubes that live up to those predictions. This is partly because there are still many unanswered questions about how nanotubes break and under what conditions.

Recently, Prof. Boris I. Yakobson at Rice University, his former postdoc Traian Dumitrica (now assistant professor at University of Minnesota), and his doctoral student Ming Hua, have developed a new computer modeling approach to create a “strength map” that plots the likelihood or probability that a carbon nanotube will break—and how it’s likely to break. Four critical variables are considered in the model: load level, load duration, temperature, and chirality. This work was published in the Proceedings of the National Adacemy of Sciences (Apr. 18, 2006 Cover feature). Full text pdf file of this paper is available here .

Saturday, May 27, 2006

1980 Timoshenko Medal Lecture by Paul M. Naghdi

Acceptance Speech upon Receipt of the Timoshenko Medal

Paul M. Naghdi, November 18, 1980, Chicago, Illinois

President Jones, Ladies and Gentlemen:
I would like to express my deep appreciation and gratitude for this honor, which has a very special meaning for me. Even more so, because I have personally known nearly all the previous recipients and I feel deeply honored to be included among them. I have been fortunate over the years to have met a number of distinguished people in our field (some of them are previous recipients of the Timoshenko Medal) who have been very helpful to me. Perhaps this is an appropriate time to mention a few of these people and reminisce a little.

I met Stephen Timoshenko, the first recipient of the Timoshenko Medal, when I was a graduate student at Michigan. In the late 40’s and 50’s the Department of Engineering Mechanics at the University of Michigan, as part of its graduate program, offered extensive, advanced courses in mechanics during summer school. I understood then that this arrangement of offering graduate courses during the summer was initiated by Timoshenko in the early 30’s when he was a professor there. In fact, during the summer of 1949, when I first met Timoshenko, he was a Visiting Professor at Michigan and he taught a course on the theory of plates. As you might expect, the number of people enrolled in the course was quite high – approximately 100. He was a kind person and also I recall that when someone asked him how he would grade, he could not understand how anyone could get less than an A.

I first met Norman Goodier, an early recipient of the Timoshenko Medal, when I was an undergraduate student at Cornell. As a senior in Mechanical Engineering, I took his graduate course on the theory of elasticity (I think it was called applied elasticity). Later when Norman Goodier was a professor at Stanford and I moved to Berkeley, we saw a lot of each other and became good friends. He was one of the warmest people I have ever known. We got together two or three times each year for technical discussions that were both enjoyable and inspiring for me. We had very different ways of thinking about the same subject even though we generally reached the same conclusions.

Another recipient I got to know when I was a graduate student is Sydney Goldstein. I was fortunate to have taken two courses in fluid dynamics from him when he was a visiting professor at Ann Arbor. He was a witty and stimulating teacher in the classroom with a strong sense of commitment toward his subject. He has been an instructive leader in mechanics education and research.

One of the first meetings I attended after receiving my Ph.D. was the first U.S. National Congress of Applied Mechanics in Chicago in June, 1951. I arrived there on a Sunday afternoon at the old Stevens Hotel (I think the current Conrad Hilton is the same hotel). I went to the coffee shop and found myself sitting next to Ray Mindlin. He didn’t know who I was, of course, but I recognized him, introduced myself and took advantage of the situation to ask him some questions on the theory of elasticity. He was delighted and seemed to take an interest in a young person. In fact, our discussion lasted for more than an hour. During that time I learned a great deal and got many hints that kept me busy for several months in connection with a course that I was teaching on elasticity theory.

I met Albert Green, another Timoshenko Medalist, in 1955 when he was on a lecture tour in the U.S. Later, I saw him at several international meetings and we hit it off rather well from the start. When we invited him to come to Berkeley as a visiting professor, he immediately accepted and, from my point of view, that visit led to a very exciting and profitable collaborative effort.
Another person who has been very helpful to me is Dan Drucker. When around 1952 I was first trying to set up an experiment in plasticity, Dan spent a whole day with me sharing his experiences and alerting me to the difficulties that one has to be aware of in conducting any experiment.

Now I should like to make some remarks pertaining to the teaching of mechanics and the impact of teaching on research and that of research on teaching. In the early part of my career I was rather critical of the engineering curricula of the time, including those pertaining to theoretical and applied mechanics. As the years have gone by, I have acquired more understanding. I have developed an increasing sense of admiration and respect for the engineering profession and its standards as compared to numerous other professions with which I am familiar. In recent years, I have revised my thinking about engineering curricula, especially in mechanical engineering, including the part that pertains to undergraduate and graduate instruction in mechanics. I have become highly impressed with the academic discipline and standards of the rather balanced curricula we offer to engineering students, in comparison with somewhat one-sided curricula offered by a number of other professions. Indeed, during the past few years I have often felt that other professions, such as medicine and law, could profit by examining their curricula in the light of those in engineering in general, and mechanical engineering in particular. Of course, despite the high standard and sense of commitment of the engineering profession, there is always room for further growth in striving for excellence.

Applied mechanics is an integral part of engineering but is also more than that. As an interdisciplinary subject, mechanics in its broadest sense serves not only one area but in fact all areas of engineering and a number of other areas in physical sciences as well. As teachers and leaders of mechanics, we have a responsibility to instill a sense of excitement, commitment and urgency within the profession that will set an example for younger people in the field. Quite often nowadays, one does not come away from a technical meeting with a feeling of urgency and commitment. Ideally one should come away from such meetings with a feeling that there are important and exciting problems that must be solved, contributing toward both our understanding of mechanics and the well-being of society.

Since the inception of the Applied Mechanics Division of ASME 53 years ago, the Division and its Journal have contributed much to ASME and the profession by encouraging the pursuit of mechanics and by creating a desirable identity for the field. I hope it is not presumptuous of me to make some comments about our national identity. Most of you probably know that mechanics enjoys high stature comparable to that of other basic disciplines such as physics and chemistry in Western Europe and the USSR – but the same is not true in this country. It is time for us to face the fact that we have a crisis of identity – not so much from our point of view, but from outside the discipline. For example, a large number of universities, including my own, do not have Departments of Mechanics and the visibility of mechanics is absent. Usually, mechanics faculty is a subgroup in a particular department or is diffused in two or more departments. This aspect of a name in the title of a department may not be important to most of us, but the lack of visibility creates a problem from time to time. I was told recently by responsible people in a government agency, which supports a significant portion of mechanics research in this country, that they pattern their organization after universities and in most of our universities mechanics has no visibility. It is perhaps time that the mechanics community, whether in industry or in universities, attempt to effect some changes which would at least add mechanics to the names of the existing departments.

It also seems desirable that the community as a whole be tolerant in accommodating different points of view. In fact, such diversity of viewpoints is likely to create the atmosphere of excitement necessary for vitality of the field. By different viewpoints, I do not mean lowering the standards of our profession or disregarding what we all agree to be good mechanics based on sound physical ideas. On the contrary, I am suggesting that, while maintaining high standards and good taste, different viewpoints and approaches are the essence of scientific progress; and, in fact, such different viewpoints are even more important in engineering and applied sciences than in purely basic sciences. Indeed, the history of science and engineering shows that different approaches to the same topic have led to enlightening results.

Let me mention two examples that illustrate the importance of different perspectives. When I was a graduate student, the only topics that one learned in mechanics consisted of linear elasticity, hydrodynamics and classical rigid body dynamics and the only books to study from, in addition to Timoshenko’s books, were by Love, Lamb and Whittaker. In the nearly 30 years that have elapsed, the whole picture has changed and great progress has been made in the context of nonlinear theories. But often this has not affected the teaching of mechanics at the beginning graduate level. Many of us these days find it much better to first teach finite deformation of elastic solids before embarking on the linear theory of elasticity (and this is an example of different viewpoints).

An important change that has occurred in engineering over the past 20 years is our ability to perform huge calculations by means of the computer. From the point of view of applied mechanics, this is a good thing indeed, since it allows us to deal in a fruitful manner with the rather complicated, realistic constitutive theories which may be necessary to describe some technological processes. I do feel, however, that in emphasizing the use of computers, not enough attention is being paid to the correct formulation of problems, especially when relatively simple analytical solutions are possible. I have had graduate students come to me to ask for help with their problems when all they really wanted was a system of equations that could be put on a computer. This is a serious matter in the case of engineers. If any group should understand the physical basis and the limitations of a theory, it is certainly the engineers. To have taught them that they could go on and use equations without questioning how the equations were acquired is a serious flaw in our recent educational endeavors.

On occasion one hears about the amount of mathematics that should be required in engineering curricula. Not too long ago, I heard a talk in which the question was raised of how much mathematics should one teach in order to ruin a good engineer! Of course, these words were presumably spoken in jest, but I imagine that many people may have come away with the wrong impression. I do not believe the question to ask is how much mathematics should be taught; that is similar to asking how much English should be taught. Each is essential for our profession and the answer is clear. You teach enough of these in a balanced engineering program so that the graduating engineer knows how to read and write English clearly and is able to understand mathematics well enough to function and to communicate.

I indicated earlier my belief that the community should develop more tolerance. Let me elaborate a bit more on this. Suppose I told you that it is possible to develop a theory – essentially an ordinary beam theory of Bernoulli-Euler type – that would be applicable not only to metallic structures as in problems of stability of elastic columns or vibrations of elastic beams, but also to other media such as fluid jets. On the basis of recent experiences, I know that a good many people in solid mechanics (not to mention fluid dynamicists) would be skeptical and would not look kindly on this. However, I recently came across a paper by Weber written nearly 50 years ago about an important stability problem of a viscous jet. If you examine this paper, you will see that Weber was only discussing elementary beam theory that is slightly modified and slightly dressed up. The results, which are quite good, have gained wide acceptance in the fluid dynamics community and have led to the definition of the so-called Weber number. But his method of derivation, which is basically a direct approach to the subject, seems to be largely ignored. Incidentally, this work by Weber is an example of how relatively simple mechanics can successfully serve engineering. Yet, I have not seen the problem mentioned or discussed in any elementary or intermediate level book on fluid dynamics. Imagine how exciting it would be for undergraduates at the sophomore (or junior) level to learn in the same course that the same elementary principles (momentum conservation and continuity equation) can be applied to such different but equally important engineering problems as the stability of an Euler column and the stability of a viscous jet. Here, I should like to borrow from a recent past chairman of the Division, Ronald Rivlin. In his words,

“Forward motion can continue only if the Division maintains its receptivity to new ideas and points of view.”

In conclusion, I would like to express the wish that the sense of community that one feels here tonight could be felt more often and could become the basis for us in the mechanics community to be more supportive of each other in the future.

Thank you for listening.

Saturday, May 20, 2006

1992 Timoshenko Medal Lecture by Jan D. Achenbach

The Wages of Wave Analysis

by Jan D. Achenbach, Northwestern University

The text of the Timoshenko Medal Acceptance Speech delivered at the Applied Mechanics Dinner of the 1992 Winter Annual Meeting of ASME.

Ladies and Gentlemen, Friends and Fellow Members of the Applied Mechanics Division, I am grateful to the Applied Mechanics Division for honoring me with the Timoshenko Medal. When I think of the past recipients of this award, I must, however, stand here with a great deal of humility.

It appears that I am the first member of a next generation, the redoubtable sputnik generation, squeezed in between the elder statesmen and the baby boomers, to receive the medal. Undoubtedly many of my contempo¬raries, who have kept the field of applied mechanics on the move, will follow soon.

Two of my favorite colleagues, Ben Freund and Dan Drucker, participated in tonight's proceedings. Ben, who was one of my first Ph.D. students, has become famous for his work on dynamic fracture. I feel some kind of vicarious pride in his achievements. Ben is a very generous person, as was obvious from his introduction. I am happy Dan Drucker was here to present the medal. I have admired Dan since my graduate student days, not only for his achievements in applied mechanics, for which he received the Timoshenko medal many years ago, but also because he has been a consistent and forceful spokesman for basic and applied research in the high councils, in which he more than anyone else in applied mechanics has taken the time and effort to participate.

Let me tell you of the experience of a colleague who passed away some years ago. He had lived a virtuous life, and he was admitted to Heaven. When he entered the Gate he was briefed by an Angel who explained to him that the pace was relaxed in Heaven. There was plenty of funding for research. Researchers were taking their time, and they studied mechanics problems carefully and in depth. So the Angel said why don't you go to work, and give a seminar a year from now. No problem, our colleague replied, I did some work on the way over here and I can give a seminar tomorrow. The Angel thought for a minute and then said: Fine, but keep one thing in mind, Timoshenko, von Karman and G. I. Taylor will be in the audience. Our colleague decided to take some more time.

In a sense Timoshenko, von Karman and G. I. Taylor, as well as all those other recipients of the medal are in the audience tonight. But then again these luminaries of applied mechanics are in that same sense always in the audience in talks that you and I may give in the AMD sessions that we are attending this week. They have set the standards. Judging from the Sessions I attended we are, however, admirably living up to these standards.

I believe I am the first recipient of the Timoshenko medal who has never seen Timoshenko in person. When I arrived at Stanford as a Graduate Student in 1959, Timoshenko, who was on the faculty, had long since retired. I never saw Timoshenko, but I certainly saw his books. They were used in courses on advanced strength of materials, elasticity, shells, stability, vibrations and dynamics. My exposure to the Timoshenko approach was sandwiched in between a more classical European viewpoint and a more modern American one. Before I came to Stanford I studied in Delft, and took courses from Biezeno and Koiter, both got the Timoshenko medal years ago. The core course in solid mechanics was then and usually still is linear elasticity. Biezeno taught elasticity broadly based on Biezeno and Grammell: "Technische Dynamik", written in German. It was an excellent course but it still was a refreshing experience to be exposed by J.N. Goodier to the Timoshenko approach. After Stanford, I went to Columbia as a Post-Doc, and I decided to listen in on elasticity as taught by Ray Mindlin and I learned a good deal more, particularly since Mindlin included the inertia term. Biezeno, Goodier and Mindlin, all three were incomparable teachers with their own style and particular interests.

If I wanted to stretch the point of connections to Timoshenko, I could tell you that my advisor (C.C. Chao) did his work with Bruno Boley, who worked for Nick Hoff, who was a Ph.D. student of Timoshenko. The genealogy is right. Time marches on.

I have always been happy that, when asked what I do for a living, I can answer I work on waves, particularly when asked by someone outside the field. Waves conjure up thoughts of possibly destructive rapidly moving energies, and visions of sweeping motions propagating towards far horizons, or deep into unknown territories.

My address tonight is entitled "The Wages of Wave Analysis'", as in the "Wages of Sin", i.e., the recompense or return. The wages have indeed been many, certainly for me, but also in an infinitely more important sense for many fields of science and technology. I gave some thought to "Riding the Waves." As you probably know this is a surfer's term which would seem appropriate for a talk in Southern California. Some of you may recall that a num¬ber of years ago there was a movie entitled "The Endless Summer", the story of some surfers who go around the world to search for the perfect wave. My activities in the field of applied mechanics, of almost thirty years, have also been an endless summer looking for the perfect wave.

I received an important exposure to waves in solids in a course taught by J.N. Goodier. The book "Stress Waves in Solids" by Harry Kolsky was the textbook. The book was then already out of print and had not yet been published as a Dover paperback. One copy in a decrepit state was available, xeroxing hardly existed and my fellow students and I copied parts of the book by hand. J believe that was the first time the thought occurred to me that there was a need for another book on waves in solids. My own book Wave Propagation in Elastic Solids was published more than ten years later. I am sure that it has been xeroxed many a time, but pardon the plug, it is still available, in paper-back form.

In this country research on waves in solids was already in bloom when I started, thanks to the work of Harry Kolsky, Julius Miklowitz and Ray Mindlin, all departed from this world, and Werner Goldschmidt and C. C. Chao still very much with us. I learned much from these gentlemen, and also from Joe Keller, as well as from contemporaries such as Y. C. Pao, Subhendu Datta and Ajit Mali. Now there is a good-size group of younger workers in the field. The Wave Propagation Committee of the Applied Mechanics Division is more active than ever before.

Over the years I have tried to advance applied mechanics techniques to analyze wave motion in solids and acoustic media in several areas of science and engineering. There were the obvious applications to impact on structures and rapid crack propagation, but there were also applications that reached further from home base to structural acoustics, seismology and quantitative ultrasonics for nondestructive evaluation. These efforts had their ups and downs. They were least successful in seismology and most successful in nondestructive evaluation. It was hard to contribute to seismology in part because seismologists are very good at wave propagation theory, and they have been initiated in the mysteries of earthquake records. There was, however, a period in the seventies and early eighties when applied mechanicians did significantly contribute to the theory of ground motion and to the understanding of earthquake mechanisms with their recently developed models of rapid crack propagation and the associated radiated wave motion.

When I became interested in non-destructive evaluation in the mid-seventies, the field was dominated by applied physicists and electrical engineers. They had excellent abilities in instrumentation and they were interested in analysis and simulation but did not want to spend a lot of time on it. They welcomed help in the area of wave analysis. The perfect match. By now I have learned something about instru¬mentation and measurement techniques and they have adopted our analytical and numerical approaches. Some of the most knowledgeable men in NDE like Don Thompson, Bruce Thompson and Laszlo Adler are among my best friends, and we happily work together.

In the quest for quality of products, especially large expensive products such as planes, bridges and nuclear reactors, and to insure safety of these products, non-destructive testing will play an important role. It is an essential part of life cycle engineering as are other areas of applied mechanics such as fracture mechanics, or in a more general sense failure mechanics, damage tolerant design philosophy and retirement for cause procedures.

I had the privilege of being introduced by a former student. I have been very fortunate with students. It is a great responsibility to find an interesting, challenging and worthwhile topic for a student to work on, particularly since it generally has to be done within the constraints of available funding for specific projects. The choice has long-range consequences for the student. Ideally advisor and student would follow Wayne Gretsky's example. When Wayne Gretsky, who is often said to best hockey player in the USA, was asked the secret of his success, he replied "I never skate to where the puck is, I skate to where it's going to be." Knowing where to go is a good idea, because as Lewis Carroll wrote: "If you don't know where you are going any road will take you there", I might add including many wrong ones. A well defined objective helps. Let me tell another little story. Two men, say a graduate student and his advisor, were looking for work. They were in a flat country, like Holland, where you can see to the horizon. They arrived at a railroad crossing where a third man happened to be standing. The two men explained that they were looking for work and asked where they could find it. The man who was asked pointed to the horizon and said: "over there where the rails get together, that's where you can find work". The two men started to walk along the track, a long way. Finally one of them, probably the professor, stopped and looked back and said "dammit we passed it".

Once a good topic has been selected, the work's progress may be characterized by different sports metaphors. One would be like a golf game where the student accurately hits a single ball from hole to hole. The role of the research advisor would be that of the caddy who carries the golf clubs, occasionally advises on the selection of an iron or a wood, warns that the terrain may be rougher than it looks, points out some slopes, warns that the edge of the sand trap is closer than it may seem and applauds the good shots. A second would be like a tennis game where student and advisor bound all over the court to hit the ball in all directions until a point is scored. The final result may be better than in the golf game. I actually prefer to play tennis. Of course many of us dream of the quarterback/running back situation where the ball is handed off by the advisor on the one yard line for a single ninety-nine yards run and a touchdown.

A few hundred years ago a wise man said "Much have I learned from my teachers, even more from my colleagues, but most of all from my students." On a more prosaic contemporary level I might add, and much do I owe to the Agencies that have made my learning possible, particularly the Mechanics Division of the Office of Naval Research and the Basic Energy Sciences Division of the Department of Energy.

As you know there are some important signs on the horizon for changes in research funding from basic to applied research. Some of these changes are already halfway here. The National Science Foundation is presently considering its future. There will be less emphasis on basic science and more on education, applied science and technology transfer. There will be a switch from DOD funding to research for civilian applications. These changes will, it seems to me, offer excellent opportunities for us in applied mechanics. Applications of mechanics pervade every area of science and technology.

A recent article in Business Week dealing with the Federal Government's move toward a new science and technology policy that puts more emphasis on "practical research" was entitled "Hey, you in the ivory tower. Come on down". I believe that we in applied mechanics have always been ready to meet on the first floor with our colleagues in industry. Interaction with industry can be very stimulating and in the future many if not all of us will become more involved with mechanics problems for industrial applications. Remember that Timoshenko worked for many years for Westinghouse and Mindlin based some of his most interesting research on the needs of Bell Labs to understand the vibration of crystals.

An effective cooperation requires, however, the participation of someone on the company's payroll. A major problem is that many medium sized and small companies have long since fired their research and development engineers, including the one that worked in applied mechanics, as part of cost-cutting efforts to improve the bottom line or the last quarterly balance sheet or to service the debt from the last hostile takeover. We at universities can contribute in an important way to strengthen R&D efforts for product development and international competitiveness, but we must have colleagues at companies to cooperate with. So hey you out there in the boardrooms and penthouses of corporate America hire some R&D engineers.

An occasion like this tends to generate retrospection. I have tried to keep it to a minimum. I know I have been very lucky. Somehow I have always stumbled into the right places, the right people and pretty much the right problems to work on. Bruno Boley crossed my path twice, the first time at Columbia, the second time at Northwestern. Back in the early sixties Bruno had an idea for post-doctoral positions that had absolutely no strings attached. They were called preceptorships and they paid better than assistant professor jobs, a princely $1000./month. The money was provided by ONR through Hal Liebowitz, who was then the director of ONR's Mechanics Division. I was one of the first beneficiaries. I used the time primarily to round off my education. After 9 months at Columbia I went to Northwestern, and years later Bruno via a detour to Cornell arrived at Northwestern to become Dean. He established an environment conducive to our research work in mechanics. Special thanks go to Bruno. I also want to thank my former and present colleagues at Northwestern for keeping me on my toes. Starting with George Herrmann, and then John Dundurs, Toshio Mura, Leon Keer, Sia Nemat-Nasser, Zdenek Bazant, Ted Belytschko, John Rudnicki and Isaac Daniel, as well as our younger colleagues, Tak Igusa, Brian Moran and Sridhar Krishnaswamy. I thank them all for providing a challenging environment.

The Applied Mechanics Division was founded in 1927 by S. P. Timoshenko. It has a great tradition. In the Sadam Hussein sense the Applied Mechanics Division is the Mother of all Divisions of the ASME. In the regular sense the Applied Mechanics Division is the Mother of several other Divisions to which it has actually given birth over the years, but the Division remains strong and fertile. The changes in the research environment which I mentioned earlier offer great opportunities to our members for a bright future. I have been a proud member of the Division for almost thirty years, and I hope to be an active member for many years to come. Thank you for honoring me with the Timoshenko Medal. Thank you very much.

Wednesday, May 17, 2006

New materials for next generation electronics: Researchers discover stretchable silicon

After the great successes of mechanics in helping to understand failure and performance o microchips about a decade ago, a recent study underlines the importance of mechanics in electronic devices, this time for the next generation microchips that will help to sustain Moore’s law for the years to come.

A team of researchers from the University of Illinois in Urbana-Champaign (UIUC) around John Rogers (Materials Science and Engrg.) and Young Huang (Mechanical and Industrial Engrg.) have created a fully stretchable form of single-crystal silicon with micron-sized, wave-like geometries that can be used to build high-performance electronic devices on rubber substrates.

The key aspect of this new material is that it provides necessary properties to function as electronic device that can be subject to large strains. The researchers believe that this new stretchable silicon offers different capabilities than can be achieved with standard silicon chips. Applications of this material include sensors and drive electronics for integration into artificial muscles or biological tissues, structural monitors wrapped around aircraft wings, conformable skins for integrated robotic sensors, and portable electronics. The snapshot shows the wavy silicon material deposited on an elastic substrate. To create their stretchable silicon, the researchers begin by fabricating devices in the geometry of ultra-thin ribbons on a silicon wafer using procedures similar to those used in conventional electronics. Then they use specialized etching techniques to undercut the devices. The resulting ribbons of silicon are about 100 nanometers thick. In the next step, a flat rubber substrate is stretched and placed on top of the ribbons (Figure upper right). Peeling the rubber away lifts the ribbons off the wafer and leaves them adhered to the rubber surface. Releasing the stress in the rubber causes the silicon ribbons and the rubber to buckle into a series of well-defined waves that resemble an accordion (Figure below)
“The resulting system of wavy integrated device elements on rubber represents a new form of stretchable, high-performance electronics,” said Young Huang, the Shao Lee Soo Professor of Mechanical and Industrial Engineering. “The amplitude and frequency of the waves change, in a physical mechanism similar to an accordion bellows, as the system is stretched or compressed.” A nonlinear continuum mechanics analysis helped to understand these responses of the wavy silicon, for example the dependence of the wavelengths on the silicon properties and thickness, analytically. The mechanics analysis linked the maximum strain in Si ribbon to the applied strain, and therefore provided simple criteria for the development of stretchable silicon such as the maximum stretchability and compressibility.

The scientists have already fabricated wavy diodes and transistors and compared their performance with the traditional devices. Not only did the wavy devices perform as well as the rigid devices, they could be repeatedly stretched and compressed without damage, and without significantly altering their electrical properties.

Besides the unique mechanical characteristics of wavy devices, the coupling of strain to electronic and optical properties might provide opportunities to design device structures that exploit mechanically tunable, periodic variations in strain to achieve unusual responses. In addition to Rogers and Huang, co-authors of the paper were postdoctoral researcher Dahl-Young Khang and research scientist Hanqing Jiang, who will join the Arizona University as an assistant professor. The Defense Advanced Research Projects Agency Department of Energy, and the NSF-funded Nano-CEMMS Center at the University of Illinois funded the work, which was published in January, 2006 “A stretchable form of single crystal silicon for high performance electronics on rubber substrates,” Science, v 311, pp 208-212).

Mechanics of flexible macroelectronics -- an emerging field of research

Flat-panel displays are rapidly replacing cathode-ray tubes as the monitors of choice for computers and televisions, a commercial success that has opened the era of macroelectronics, in which transistors and other micro-components are integrated over large areas. In addition to the flat-panel displays, other macroelectronic products include x-ray imagers, thin-film solar cells, and thin-film antennas.

Like a microelectronic product, a macroelectronic product consists of many thin-film components of small features. While microelectronics advances by miniaturizing features, macroelectronics does so by enlarging systems. Macroelectronic products today are mostly fabricated on substrates of glass or silicon; they are expensive, fragile and not readily portable when their areas are large. To reduce cost and enhance portability, future innovation will come from new choice of materials and of manufacturing processes. For example, thin-film devices on thin polymer substrates lend themselves to roll-to-roll fabrication, resulting in lightweight, rugged and flexible products. These macroelectronic products will have diverse architectures, hybrid materials, and small features. Their mechanical behavior during manufacturing and use poses significant challenges to the creation of the new technologies.

A recent review paper by Suo et al. describes ongoing work in the emerging field of research – mechanics of flexible macroelectronics, with emphasis on the mechanical behavior at the scale of individual features, and over a long time. The following topics have been discussed in the paper:
  • Why many macroelectronic systems will be organic/inorganic hybrid structures, and how they can be made flexible.
  • A way to realize stretchable electronics by using compliant thin-film patterns of stiff materials.
  • How to achieve high ductility of thin metal films on polymer substrates and fatigue of metal films subject to cyclic loads.
  • Cracking in brittle materials such as oxides, nitrides and amorphous silicon on polymer substrates.
  • Issues of interfacial debonding
  • Crawford, G.P. (editor), 2005. Flexible Flat Panel Displays, Wiley, Hoboken, New York.
  • Nathan, A., Chalamala, B.R. (editors), 2005. Special Issues on Flexible Electronics Technology, Proc. IEEE 93, 1235-1510.
  • Z. Suo, J.J. Vlassak and S. Wagner, Micromechanics of macroelectronics. China Particuology 3, 321-328 (2005). (Check out the references of this paper for a comprehensive list of recent literatures in this emerging field of research)

Tuesday, May 16, 2006

The 18th Annual Robert J. Melosh Medal Competition

The 18th Annual Robert J. Melosh Medal Competition for the Best Student Paper in Finite Element Analysis was held on Friday, April 28th, at Duke University. The Competition was inaugurated in 1989 to honor Professor Melosh, a pioneering researcher in finite element methods and former chairman of Civil and Environmental Engineering at Duke University. The event is made possible through generous gifts to Duke University from Elsevier, Sandia National Laboratories, and the extended Melosh family.

The Competition consists of two phases. In the first phase, candidates submit extended abstracts for consideration by the panel of judges. The names and affiliations of the authors are not provided to the judges during this phase. The competition is open to students who are no more than one year beyond the completion of a graduate degree. From the submitted abstracts, six finalists are selected to give oral presentations of their work at the Melosh Symposium. During the past few years, the Symposium has been hosted at UC Berkeley, Rensselaer Polytechnic Institute, and Duke University. The winner and Melosh Medalist is selected on the basis of the combined written and oral scores.

The Melosh finalists represent a young group of researchers with bright futures. Indeed, many of the past finalists have continued on to successful careers in computational mechanics at universities, national laboratories, and industrial research centers. The group of finalists selected for this year's competition are no exception:

  1. Jose Andrade, Stanford University

  2. Roman Arciniega, Texas A&M University

  3. Homayoun Heidari, NC State University

  4. Shanhu Li, Ohio State University

  5. Roger Sauer, UC Berkeley

  6. Haim Waisman, Rensselaer Polytechnic Institute

The judges for this year's Competition were Professor Tom Hughes, UT Austin, Professor JS Chen, UCLA, and Dr. William Scherzinger, from Sandia National Laboratories.

Dr. Homayoun Heidari was selected as the 18th Melosh Medalist for his paper entitled "Novel Subsurface Imaging Algorithms Based on the Finite Element Method." A list of past Melosh Medalists and judges is available at the competition website. A special issue of the journal Finite Elements in Analysis and Design will be assembled to commemorate the event.

Saturday, May 13, 2006

2000 Timoshenko Medal Lecture by Rodney J. Clifton

Applied Mechanics Research and Researchers

2000 Timoshenko Medal Lecture by Rodney J. Clifton

Rod Clifton
November 9, 2000

To begin, I would like to express my appreciation to the members of the Applied Mechanics Division who somehow came to the conclusion that I should be awarded the Timoshenko Medal. I would also like to thank all those who must have written letters or, through other means, provided supportive input that contributed to my being named the recipient of such a prestigious award. I hope that everyone understands that experimental research involves a team effort so that this award should be viewed as being shared by the many excellent graduate students that I have had the privilege of advising. They, along with very supportive technical staff members, are the ones who have done the experiments for the research that is being recognized by this award.

I have been in a state of shock ever since I opened the letter congratulating me on my selection. I was totally surprised. Having assumed the role of Dean of Engineering at Brown two and a half years ago, much of my thinking and energy has been focused on the needs of the Division of Engineering. The possibility of receiving such a high honor from the applied mechanics community was not even on my radar screen. Even before I became pre-occupied with administrative responsibilities, I never thought of myself as a likely choice for the Timoshenko Medal. One look at the list of prior recipients is enough to humble nearly all of us and certainly me. I am deeply grateful --- and want to move on before the Committee decides to reconsider its choice!

The talk given by the Timoshenko Medalist at the Applied Mechanics dinner is one of the few opportunities that we have to come together as a community and reflect on the challenges and opportunities of our discipline. This tradition bears some resemblance to one that I first encountered when I was an undergraduate at the University of Nebraska. I was a member of a social fraternity and at the end of our meetings we had a time for what we called "Remarks for the Good of the Fraternity". Some of the talks were really quite good, a few were very funny --- all were well intentioned. I remember one by a particularly talented English major who gave an impassioned plea for buying pink toilet paper as a way of urging us to put more emphasis on the finer qualities of life and less on such mundane issues as keeping operating costs at a minimum. While most of the talks were less memorable, I still remember the good spirit and the good intentions with which they were delivered.

My talk tonight is offered in this same spirit and can be thought of as 'remarks for the good of the applied mechanics community'. I believe that many members of our community feel that applied mechanics has come to a crossroad. As they look back they see a solid record of achievement. As they look forward they see declining student interest in our discipline, particularly among graduate students and especially among American students. As those of us who are nearing retirement age look back we see a time in the '60s when we had multiple opportunities for good jobs in universities, corporate research centers, and national labs. As some of our younger members look forward they are apprehensive about finding good jobs and those going into academic positions are concerned about obtaining financial support for a research program.

So, what do we make of this? First, we should feel good about the contributions of applied mechanics to the technological society in which we live. During this first year of the new millennium many of the professional societies have identified the outstanding contributions over the past century. On almost any of these lists one can see the supporting hand of applied mechanics. For example, the National Academy of Engineering named 20 of the greatest engineering achievements of the 20th century. Of these, approximately one-third have direct connection to applied mechanics (e.g. the automobile, the airplane, agricultural mechanization, spacecraft, household appliances, and high-performance materials) and even more have an indirect connection through the role of applied mechanics in manufacturing and in ensuring the reliability of the products being made.

Just mentioning these sectors of our economy whose development owes much to applied mechanics does not do justice to the dramatic advances that have occurred in our field over, say, the past forty years --- to choose the time since I first became a graduate student. During this time our field has been transformed by the almost unfathomable increase in computing power and its accessibility to all of us. While we have others to thank for the development of the computers, we have done our part by developing the software that makes it possible for designers to use computers to provide rational, safe, economical designs for airplanes, automobiles, spacecraft, and a wide range of other structural and mechanical systems. On the experimental side we have benefited from advances in lasers and digital electronics, for example, but here too we have developed the techniques that have turned these tools into powerful aids for measuring and understanding the flow of fluids and the deformation and failure of solids ---- from which new and better designs have emerged.

If we are so confident of our contributions in the past, why is there so much hand wringing over our future? Have we gone about as far as we can go? Have the laws of mechanics been repealed? Have they lost their importance? Have other fields become much more important? If so, do those fields not need mechanics? No, we have neither learned all that needs to be known nor have the laws of mechanics become obsolete. Our problem is not with our discipline but with the limitations that we put on it when we decide to stay with what is familiar and comfortable instead of tackling what is unfamiliar and risky. We stand on the threshold of what could be the most exciting time in mechanics since classical mechanics lost some of its luster nearly a century ago with the development of quantum mechanics.

Today we are entering a new age in biology, and a wholly new technology --- called nanotechnology --- appears to be emerging. Both areas call for new understanding from the mechanics community. In biology the greatest excitement is at the level of cells, molecules and genes. Mechanics at this level in biological systems is clearly in its infancy. Members of our community are beginning to look at the mechanics of cell membranes and even the mechanics of individual molecules. Such studies may provide the foundations for understanding how to combat viruses and how to inject drugs and genes where they are needed. While determining the structure of the DNA molecule may have been a problem in electron microscopy, understanding the operation of the DNA molecule is a problem in mechanics --- as is the great unsolved problem of the folding of proteins. Such are the problems I speak of as being unfamiliar and risky --- but possibly holding the key to great payoffs. Furthermore, from my experience in working on the restructuring of our program in biomedical engineering at Brown I believe that the biology community is receptive, even eager, for the participation of those who can make measurements and do computer simulations that will help them understand the processes that occur at the cellular and molecular level.

In the emerging world of nanotechnology we will be working with devices and even machines that are smaller than we can see with our eyes, even with the aid of an optical microscope. Deformations and motions need to be described on the scale of nanometers, i.e. on the scale of 3-4 atomic spacings. What mechanics is required to describe forces and motions at this scale? Who is best equipped to contribute at this scale? Clearly the physicists have much to contribute but so do investigators whose primary background is in applied mechanics. To me one of the exciting results of molecular dynamics and lattice dynamics has been to establish that continuum mechanics descriptions are remarkably good down to surprisingly small scales, say two atomic spacings. Boundary value problems need to be solved and who is better at solving such problems than the mechanics community that developed finite element methods.

What do we need to know to contribute to these high profile areas of opportunity? Certainly we should learn some biology and some quantum mechanics. If we are to understand the literature and interact with the researchers from other disciplines we need to know the language and the central results for the types of problems that we are considering. Progress often occurs at the interfaces between fields and we need to get across those interfaces to gain a perspective from both sides. The last four new faculty members that we have hired in the Solid Mechanics Group at Brown have been educated as physicists. One is educated as a soft matter physicist and has turned his attention to problems in cellular and molecular biology. By now all four appear to be equally comfortable doing ab initio calculations of computational physics or finite strain calculations of computational solid mechanics. To me this is the perspective that we need to see more of in mechanics. Twenty years ago when I was on sabbatical leave at Stanford I sat in on the first year courses in Applied Physics. These were courses in quantum mechanics, electrodynamics, and statistical mechanics --- all courses that I had not had before. All were truly exciting. All now seem indispensable for the challenges that I have been describing as opportunities for an applied mechanics community with a lively, stimulating intellectual curiosity.

If I were to stop here I would be leaving the impression that all of our opportunities lie in biomechanics and nanotechnology. That would be like saying all the sunshine is in Florida. We all have different perspectives on the research needs of our society and of potential contributions that applied mechanics can make. To identify a few from my perspective --- the computational design of alloys, the Holy Grail of materials science, may be achievable as computing power continues to increase and we learn better how to include chemistry and microstructural evolution in our numerical simulations. There are clearly needs and opportunities in the mechanics of thin films and functionally graded materials. Better understanding of self assembly of regular structures is an exciting area of study with great potential for valuable contributions to a number of applications. Greater involvement of mechanics in the development of electrical and optical devices is an attractive direction --- especially when there is strong coupling between the mechanical deformation fields and the electro-optical response as, for example, in the effect of strain on quantum wells. Clearly, the list of new and developing areas of mechanics research is long. Also, I have not attempted to comment on exciting directions for fluid mechanics research. From my work on hydraulic fracturing I know that much more needs to be known about the flows of non-classical fluids --- for example, slurries in which particles that are not neutrally buoyant are carried by fluids that are viscoelastic or may even be foams. From our most recent hire in fluid mechanics, a faculty member who works in microfluidics, I have learned of the challenges of trying to understand flows through micron and sub-micron openings.

I am not trying to give a comprehensive list of future directions for mechanics research. I am also not saying that there are not many attractive research directions within our traditional research areas. Certainly the talks at this meeting, and others like it, continue to provide interesting and valuable new insights. Instead, I am trying to give a few examples to make the point that mechanics has exciting opportunities, but that these opportunities often require us to move into unfamiliar areas and to do our homework so that we can take advantage of the understanding that has been developed in other disciplines.

To say just a few words about my own experiences in seeking opportunities at interfaces with other disciplines I would point to career adjustments that I made in the early ‘70s. In ‘71-’72 I spent a sabbatical leave in the Audiology Department of the Institute for Sound and Vibration Research at Southampton in England. That was my first sabbatical and I was looking for new research directions, but directions that would allow me to continue my interest in waves. At Southampton I worked on a mathematical model for waves in the inner ear. Simultaneously, I had a gas gun built at Brown for studies of the shearing and fracture resistance of materials at very high rates of deformation. The work on the inner ear was satisfying in that the stated wave guide problem was solved and insights were obtained that were interesting from a mechanics perspective. However, the model was ultimately abandoned as it did not give the right scaling laws when I tried to apply it to animals ranging in size from bats to elephants. The gas gun led to new plate impact experiments, designed from the perspective of solid mechanics, but taking advantage of the technology that had been developed by the shock wave physicists for their research on high-pressure equations of state. Essentially overnight, we had reduced the time scale of our experiments by three orders of magnitude --- from microseconds to nanoseconds. We had a grand vision: to extend mechanical testing to loading rates that were two to three orders of magnitude higher than accessible with current methods --- while at the same time simplifying the interpretation of the experiments by using plane wave loading. Those were exciting times, as I believe my former students will attest. We thought of problem after problem to which we could apply our new found capability: plastic flow and fracture of metals; rheology of lubricants; micro-cracking of ceramics; shearing resistance of compacted powders; failure waves in glasses; friction; and martensitic phase transformations. And, we could study these phenomena at the high strain rates that occur in such difficult-to-study applications as ballistic impact, high speed machining, and elastohydrodynamic lubrication.

As it turned out, the initiative on waves in the inner ear did not bear much fruit, but that of new plate impact tests for studying the mechanical behavior of materials has had immeasurable impact on the attention that our research has received. My regret is not that one initiative was not very successful, but that I did not seize more opportunities to broaden the reach of mechanics.

The potential reach of mechanics is surely very broad. Even now, mechanics enables us to understand much of our physical world and to respond to many of the physical needs of the world’s people. Aesthetically, the subject has much appeal in the sense that, when practiced well, it embodies truth, beauty, and usefulness. Mechanics is a discipline that we can be proud to be a part of and eager to share with others. It is a discipline that will remain alive and vital if we do not limit it by allowing our focus to be too narrow.
On this note, I would like to conclude by again thanking the Applied Mechanics Division for this extraordinary honor, and by thanking all of you for the attention that you have given to these remarks.

Wednesday, May 10, 2006

Meshfree CAD Design and Solid Remolding

In the recent issue of Mechanical Engineering (May, 2006), Jean Thilmany, one of the associate editors of the journal, wrote an article, No Mesh, No Fuss, to introduce the next generation of CAD design and solid remodeling ---- the meshfree CAD design.

By throwing away the mesh, the latest meshless CAD design is claimed being faster, more efficient, and representing the future trend. So after all, meshfree methods are thriving in major engineering applications (Read more .... ).

Sunday, May 07, 2006

Wikipedia and Applied Mechanics

AMN: Wikipedia and Applied Mechanics

My first contribution was a new entry for R.D. Mindlin, one of the Timoshenko Medal recipients.

Whence the Force of F=ma?

This is the title of a three-part series published in Physics Today by Frank Wilczek, the Herman Feshbach Professor of Physics at MIT. Prof. Wilczek is considered one of the world's most eminent theoretical physicists, and is the 2004 Nobel laureate in Physics for work he did as a graduate student at Princeton University, when he was only 21 years old.

Prof. Wilczek
contributes regularly to Physics Today and to Nature, explaining topics at the frontiers of physics to wider scientific audiences. The following series of his "musing on mechanics" won the Best American Science Writing in 2005:
Whence the Force of F=ma? 1: Culture Shock
Whence the Force of F=ma? II: Rationalizations
Whence the Force of F= ma ? III: Cultural Diversity

Prof. Wilczek recently published a book named Fantastic Realities, in which 49 inspiring pieces, including the above three, of "mind journeys" are included. This book also includes contribution from his wife Betsy Devine's blog on what winning a Nobel Prize looks like from inside prizewinner's family.
You may also enjoy a recent podcast of Scientific American, in which Prof. Wilczek and his wife talk about their new book

Saturday, May 06, 2006

1997 Timoshenko Medal Lecture by John R. Willis

Mechanics of Research
The text of the Timoshenko Medal Acceptance Speech delivered at the Applied Mechanics Dinner at the 1997 IMECE.
by J. R. Willis, University of Cambridge

The award of the Timoshenko Medal is a singular and unexpected honour. I thank my friends who exaggerated my case so successfully, and promise them that I shall do my best to justify their faith in the future, even if I have not managed it in the past.

I’m not sure if I should say this, but I will. I have attended one Applied Mechanics Division Dinner previously. Bernie Budiansky received the Timoshenko Medal. I was surprised that he spoke for so long! Now I realize why. It was no ordinary after-dinner speech but the Timoshenko Lecture, and its length is prescribed. Therefore, I can only advise now that you settle down and prepare to let your thoughts wander!

A technical exposition is clearly not required, and I sought inspiration, or at least examples of how to proceed, by reading the lectures of a few previous medallists. It seemed to me that I might try to follow, in some approximate way, the path taken by George Batchelor, who was also my boss at a formative time in my career. He was founder and head of the Department of Applied Mathematics and Theoretical Physics in Cambridge.

I was fortunate enough to hold junior posts there, between 1965 and 1972, and perhaps am now even more fortunate to hold a senior post in that department. George is no longer its head but he is there every day, providing an example of dedication to research and scholarship in mechanics.

This, in fact, will be my theme: how does a career develop, in which perhaps the most significant component is research? Naturally, this will relate to applied mathematics and mechanics, because that is all that I know.

The main focus of George’s lecture was how an institution should be organised to stimulate invention and research, and I shall try to address a somewhat similar question.

Yapa Rajapakse asked me the other night what would be the title of my talk. I told him that I hadn’t given one, but perhaps an appropriate title would be “Mechanics of Research”. My concern will be how an individual should position himself or herself, to do fruitful research. So, in particular, what should someone just starting out do, and expect?

To begin, it pays to be good at passing exams. Otherwise, acceptance in a good research school is likely to be difficult. It pays also to have a thesis adviser who has the right sense of what might be important in the future as well as tractable now, with the right amount of effort. This is not always so easy to achieve. Paul Matthews, a physicist of great distinction (I knew him when he was Vice-Chancellor of the University of Bath, where I spent many happy years as a Professor), told me that, when he was a young research student in the Cavendish Laboratory, he one day approached Paul Dirac and asked him if he might be willing to supervise his research. Dirac’s response, utterly sincere and modest, was that he didn’t need any help with his problems at that time.

Few of us have the opportunity to acquire such an anecdote. There is, however, an uncomfortable lesson to be learned by all at this stage. Being clever may be necessary, but it certainly is not sufficient! It is still more important to have commitment and true interest in what you are doing. While a bit of competitive spirit is surely no bad thing (and may be almost essential), the pleasure of achievement against your own standards should be -- probably has to be -- your main reward, since it is certain, whoever you are, that you will see people around you who have more talent, and have done much more significant research than you are ever likely to do yourself. I am reminded here of another story I was once told. I am not sure now whether it was told me by Jock Eshelby, or about him: as a young research student, he went to see a great elder statesman of solid state physics, and asked what were the really significant areas in which an aspiring researcher should concentrate. The reply was, “I don’t know. And if I did, I wouldn’t tell you!”. Or perhaps Jock was the elder statesman: those that knew him can surely imagine him making such a response, mixing humour with truth! The fact is that, unless you are exceptionally lucky, you have to have your own ideas and be satisfied with them.

Having done your first research, and obtained your PhD, the next problem is to find a position which will allow your research to flourish. I wish I could advise here. My own experience is useless, since when I was at that stage, there were more good jobs than there were people to fill them, and I remember with appreciation one of the services my thesis adviser, Maurice Jaswon, rendered at that time. He took sabbatical leave in the USA, and I was able to monitor some of his movements from job offers that I received. I actually took a post-doctoral position at the Courant Institute, New York, and had the benefit of learning from some of the greats of applied mathematics, including Joe Keller, another Timoshenko Medallist. There are two problems now, or so it seems to me.

One is that jobs are scarce. The other is that there is pressure to behave immediately as though you are a great leader, attract research funds and perhaps have more graduate students than is comfortable for you or them. I do believe that foundations have to be laid, by personal study and contemplation. Better to become a motivator and facilitator later! And in any case, you won’t survive long-term as a generator of ideas, unless you are doing quite a bit of research personally. Clearly, these days, some compromise is necessary. I would like to think that talent is recognised not only by amounts of money attracted, or numbers of publications, though it would be quite wrong to infer that independence from these activities as demonstrated by failure to deliver necessarily implies true commitment, or ability, or depth. A positive aspect of the grant culture is that research driven by practical concerns can have fundamental significance and, even when it does not, involvement in such research can provide a perspective from which important generic or fundamental problems may be identified.

Assuming that you keep going successfully, and achieve a senior position either in a University or a Research Department, you surely will acquire wider responsibilities. These are likely to include responsibility for the welfare (and livelihood) of others, and may also involve administration concerning the research infrastructure of your discipline.

I think particularly here of activities relating to publishing. We almost all act as referees (except for those — some very distinguished — who just don’t respond!) and some of us act as journal editors.

I have to admit that I sometimes suspect that people these days write more than they read -- including, in some cases, papers upon which the person’s name appears as author! But enough of that, and back to the functions of an editor. This is not a research activity, but (I do my best to remind myself) it does make an important contribution to the collective scientific endeavour. Furthermore, although you certainly can’t please everyone all the time, it is my experience that the job can make you more friends than enemies. The thing to remember is that you can’t know everything, so you must take the best advice that you can find and then (even when the advice is inadequate, as it can be on occasions!) take a decision in as honest a fashion as you can. Just occasionally, you may have the opportunity to promote some of the first work of someone destined to be a star. This is a real satisfaction. And this reminds me of something else that goes with age and seniority: if you become a head of department -- or similar -- and have the opportunity to make appointments, you must never be afraid of appointing someone you suspect may be better than yourself. I have done this many times. Not only is it essential for the well-being of your unit, but you actually derive credit as well as benefit for your own research.

I realize that I started with the intention of making general comment but have lapsed into personal reminiscence. Now I would like to do this still more explicitly. Certainly the progress of my career has been influenced greatly by various colleagues that I have had. After NYU, I went to Cambridge on the initiative of Rodney Hill.

Of course he is impossible to emulate, but I saw an example towards which to aspire. Also at Cambridge, I interacted with Jock Eshelby, whose papers had already been one of the foundations of my education. I always knew that my main contribution would be mathematical, and I learned important lessons from Gerard Friedlander and Edward Fraenkel in particular.

When I was still relatively young, I moved to the then new University of Bath. Over the next few years, I had the great good fortune to appoint outstanding colleagues, and I learned some more mathematics particularly from John Toland. I also had several excellent students and post-docs. In particular, David Talbot was my student more than 20 years ago. He is still a major collaborator and I am happy to acknowledge my debt to him. One of my best post-docs was Pedro Ponte Castañeda.

Again, we have interacted over the succeeding years to my distinct advantage. When I first returned to Cambridge, I was fortunate to have Pedro as one of my early visitors. Another was Walt Drugan, who was never my student or post-doc but I wish he had been. This is one of the advantages of working in a location that others consider attractive. In the three and a half years I have been back, I have had the benefit of a succession of distinguished long-term visitors including, besides Pedro and Walt, Huajian Gao and Zvi Hashin. I have also, in recent years, done my own share of travelling, and my most frequent single destination has been the laboratory of Sia Nemat-Nasser, where there is always something new and exciting for me to learn.

Travelling and editing a journal do not form an ideal mixture, and would have been much more difficult to combine if I had not had the fortune to have Ben Freund as an outstanding co-editor of JMPS. During periods that I am away, he continues -- I expect -to feed copy to the press, so that short absence is not a problem.

One of the most significant world events of the last few years had impact on me and my research too: the demise of the Soviet Union made available many researchers of great ability, prepared to take more junior positions than objectively they deserved. In my case, I had successively as post-docs Sasha Movchan, Valery Smyshlyaev and Natasha Movchan. I can only liken working with them to driving a powerful car: you touch the accelerator and really move! They all three now have secure positions and do not need me, but still we collaborate, and I get (some of) the credit for their hard work and talent.

This, perhaps, leads me to my final piece of advice: when you get the chance, collaborate with talented younger researchers as much as you can. Few activities can be more rewarding. In my case, this goes a long way towards explaining my presence this evening. Now I would like to conclude, expressing my deep gratitude to all those with whom I have had the good fortune to interact during my career so far, coupled with keen anticipation of more in the future.

Tuesday, May 02, 2006

Song-Ping Zhu Has Found An Exact Solution for the Black-Scholes Equation

Prof. Song-Ping Zhu at University of Wollongong, Austrialia, has recently found another exact solution of celebrated Black-Scholes equation that corresponds to the so-called American option, which has long been regarded as an outstanding problem in finance mathematics modeling, and it has been hailded as a holy grail in mathematics.

The so-called Black-Scholes equation derived by Fischer Black and Myron Scholes in 1973 is the mathematical model for valuation of option. Prior to Zhu's solution, the only existing exact solution of Black-Scholes equation was the solution corrsponding to the so-called European option, which was found by Fischer Black and Myron Scholes in 1970s. This solution has been widely accepted by the financial market as a guide for pricing for the European options. Over time the significance of their discovery was fully recognized, and in 1997 the Nobel Prize for Economics was awarded to Myron Scholes and Robert Merton. (Merton worked in a similar area at about the same time. Black died in 1995 and Nobel Prizes are not awarded posthumously). However, in today’s financial markets worldwide, popularly traded options are of American style. Unlike European options, American options can be exercised at anytime prior to expiry.

Zhu's findings have triggered widespread excitement among his mathematical colleagues who are confident that this long-standing problem has finally been solved. Professor Zhu has now had his journal paper, “An Explicit and Exact Solution of the Value of American Put and its Optimal Exercise Boundary” accepted for publication in the journal, Quantitative Finance.
(See the press release).

Added Notes: Prof. Song Ping Zhu, my childhood friend, is a fluid mechanician, who obtained a PhD degree in applied mechanics in late 1980s from University of Michigan at Ann Arbor. Dr. Zhu is the last PhD student of the late Professor Chia-Shun Yih.