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 .

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.

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

References:

• 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)
  

(via www.macroelectronics.org)

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.

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.

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.