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The drama of a mathematical proof

An article in this week’s New Yorker describes the human drama behind a proof of the Poincare conjecture, one of the seven Millennium Problems. The article is unsparing of several mathematicians of Chinese origin.

Notes added on 27 August.

• Perelman turns down Fields Medal.
  
• Here is an excellent article on the proof in the New York Times.
  
• See the comment posted by Ting Zhu.

Meshfree Methods blog

A blog dedicated to Meshfree Methods has recently been set up by the USACM Specialty Committee on Meshfree Methods. This was inspired in no small part by the work of Professor Zhigang Suo and colleagues on the Applied Mechanics blogs.

Mechanics of Solids and Materials

This graduate level textbook by Robert J. Asaro and Vlado A. Lubarda has recently been published. The website of Cambridge University Press gives some description of the book.

Online Journal Club on Flexible Electronics

In the sidebar of this blog, I've added a link to the Macroelectronics Journal Club, which was started by Teng Li using CiteULike. You may want to read Teng Li's introduction to the Journal Club. You may want to join his club, or create your own club.

e-reader is out

For those who do research on macroelectronics, the e-reader has been a long awaited product. Will it really be as good as a printed book?

Note added on 11 July 2006. See also 5 new design concepts of flexible displays.

Shaky Equilibrium - Phys Rev Focus

The 'crystallization' of shaken sand-like grains matches the process in computer simulations of idealized molecules, implying that the physics of gases and fluids may apply to granular materials.

1990 Timoshenko Medal Lecture by Stephen H. Crandall

The Joy of Applying Mechanics

Stephen H. Crandall, Massachusetts Institute of Technology

Text of Timoshenko Medal acceptance speech delivered at the Applied Mechanics Dinner of the 1990 Winter Annual Meeting of ASME in Dallas, Texas.

Good evening. Thank you Tom and Art for your kind introductions.

Thirty-five years ago I joined the Applied Mechanics Division of ASME. Two years later I was in the audience when the first Timoshenko medal was awarded to Stepan Prokovievich Timoshenko. I wonder how many others here tonight were also in that audience (a show of hands indicated that there were a total of twelve including the speaker). After that first medal, the Division went into high gear. In the next three years, six of the remaining giants of applied mechanics were given Timoshenko medals: Th. von Karman, G. I. Taylor, Arpad Nadai, Sir Richard Southwell, C. B. Biezeno, and Richard Grammel. Then in 1961, the Division settled down to our present steady-state operation of one medal a year. I haven't missed many AMD dinners through the years so I have had the good fortune to see most of the previous 36 awardees receive their medals. Taken together, they form an impressive cavalcade of applied mechanics. I consider it a very great honor to join this team.

I feel proud and humble at the same time. Five years ago when the late Eli Sternberg was accepting the Timoshenko medal he said, in jest, that medals, much like arthritis, were a common symptom of advancing years. I am sure that underneath that jest, deep down in his heart of hearts, Eli was just as proud as I am to receive this award.

In my case I owe a great deal to my mentor the late Jaapie Den Hartog and indirectly to his mentor before that. When I joined the ME department at MIT in 1946 Den Hartog was my first boss. Many of you already know that Den Hartog's first boss, 22 years earlier at Westinghouse, was none other than our Stepan Prokovievich. From this point of view I think you can say that I'm the first third generation Timoshenko medalist.

Many of my predecessors have taken this opportunity to reflect on the state of applied mechanics. Some have been optimistic, others pessimistic. I find myself strongly optimistic. In my time I've seen great changes in mechanics education and great changes in mechanics research. Fifty years ago in the required curriculum for mechanical engineers at MIT there were nine semesters of applied mechanics. Today there are about 2 1/2 semesters in the required curriculum which are devoted to applied mechanics. You could call that the bad news. The good news is that in these same 50 years there has been an enormous growth in the amount of applied mechanics research. The growth rate in the number of mechanics journals over the past 50 years has been substantially greater than the inflation rate in the cost of living. The growth has been in many directions. Some developments have been driven by military and industrial applications. Some developments have been driven by the desire for greater rigor. One direction of development which has flourished during my time has been the treatment of multi-discipline and multi-media problems. Forty years ago I stumbled over the idea that most engineering analysis problems fall into one of three major categories: equilibrium problems, eigenvalue problems, or propagation problems. However, when I wrote Engineering Analysis, all the examples I used were limited to single discipline problems: an elastic structure, or a compressible flow, or a thermal conduction field. The book had hardly been published when I noticed that some of my colleagues were writing about topics like thermoelasticity or electromechanics or magneto-hydrodynamics. I found myself doing research on fluid-structure interactions, on soil-structure interactions, and on random vibration which is the marriage of vibration theory with probability theory.

For the most part, the developments in mechanics are in the applications. The basic theory is pretty much in place. I often tell my dynamics students that the last major break¬through in dynamics was made by a 24-year-old Cambridge University graduate student 325 years ago. His name was Isaac Newton. This is, of course, an exaggeration. Even in classical dynamics there is some growth. We have had a significant advance during the last decade with the development of the theory of chaotic responses to deterministic excitations. I think we can look forward to changes in how mechanics education is organized and to changes in application areas for mechanics research, but I am optimistic that there will continue to be interesting and exciting things to do in mechanics.

My wife Pat has a favorite cookbook called "The Joy of Cooking". What I'd like to do now is to recount to you my views on "The Joy of Applying Mechanics". I have had the good fortune to live through a period when an academic career devoted to applied mechanics could indeed be a joy. The primary reasons for this are the teaching, the research, and the people.

First of all, mechanics is fun to teach. It has its own logical consistency. Almost everything fits, and once you get into it the density of illuminating insights is very great. I sometimes feel sorry for my colleagues in materials and design. Compared to mechanics, those subjects are very difficult to teach well.

Secondly, mechanics is fun to do research in. The thrill of turning up a new insight is an exquisite joy, whatever the discipline, but the richness of insights, at all levels, in mechanics, makes it an especially inviting field. The spectrum of opportunities ranges from abstract analysis, to computational mechanics, to experimental mechanics. One of the spectacular areas of growth that I have witnessed is that of laboratory instrumentation for research in mechanics. For many investigations the latest high-tech instrumentation is indispensable, but mechanics is perhaps unique in providing opportunities for serious work with elementary tools. For example, the most effective technique I found for displaying the salient features of a wide-band random vibration field did not involve laser holography but consisted simply of resurrecting Chladni's 150-year-old technique of sprinkling salt on the vibrating plate.

Finally, mechanics is fun because of the people. The most important people are the students and the national and international brotherhood of fellow researchers in mechanics. Students provide a wonderful stimulus to their teachers. I agree with the statement that the way to stay young is to stop looking in the mirror and to concentrate instead on the faces of the students. A great joy as one grows older is the network of colleagues sharing similar research interests that one meets at national and international meetings. The opportunities for this were greatly expanded for my generation by the invention of the jet plane.

Pat and I enjoy travelling. Our marriage began with a sabbatical year in post-war London and we have subsequently enjoyed sabbaticals in France, Mexico, Israel, and California. We have gone on lecture tours in Australia, the Soviet Union, and China. Over the years we have built up an extended family of applied mechanics friends all around the world. As a spin-off from international travelling I took up the hobby of studying foreign languages. I have enjoyed learning basic conversational skills in several languages but so far I have only reached my goal of being able to give a lecture in the language in French, Spanish, and Russian. At a birthday celebration, not too long ago, I was being "roasted" about this hobby and I would like to share with you one of the jokes they told.

A tiny mouse was running for its life with a big black cat in pursuit. Just in time it popped into its hole and went squeaking with fright to its mother. "Oh mother! There's a terrible big cat outside. It almost killed me." The mother mouse calmed her child down saying, "There, there. You're safe in here." Then she said, "Now I'll teach you a lesson." Where upon mother mouse climbed boldly out of the hole and marched right up to the cat. Looking the cat in the eye she said, "Bow Wow! Arf, Arf!" The cat was so surprised, it turned tail and ran. Mother mouse then turned to her child and said, "Now you see the advantage of having a second language!"

Well, I hope you can see that I've thoroughly enjoyed a career of applying mechanics. To have it all topped off with the Timoshenko Medal is indeed a great delight. My cup runneth over! I shall always be grateful to the Applied Mechanics Division for this heartwarming recognition from my colleagues and friends. Thank you all.

1991 Timoshenko Medal Lecture by Yuan-Cheng Fung

Mechanics of Man

by Yuan-Cheng Fung, University of California, San Diego

The text of the Timoshenko Medal Acceptance Speech delivered at the Applied Mechanics Dinner of the 1991 Winter Annual Meeting of ASME in Atlanta, Georgia.

First of all, let me thank those of you who worked hard to give me this honor. I know how much effort was involved. I want to thank Dr. Saric, Dr. Bogy, and all the Committee members who indulged in me. And thank you all here this evening. To Chia Shun's remarks I am speechless. I love him as a brother. I am proud to be praised by a sibling. He is the Timoshenko Professor at the University of Michigan. With this medal I can catch up with him to honor our hero.

I am very glad to be given this Award, because Timoshenko is my hero. His books on Elasticity, Elastic Stability, and Plates and Shells are the ones I cut my teeth on. Another hero of mine is Theodor von Karman. A third one is Poiseuille, who brought fluid mechanics to medicine. They are my idols, and I am very fortunate to have been given a von Karman medal by ASCE in 1976, a Poiseuille medal by the International Society of Biorheology in 1986, and a Timoshenko medal today. I would like to speak about them. I think they have a common feature in that they developed a mechanics of man, as distinguished from a mechanics of the heaven and earth.

In character, these three men were different. Timoshenko had a father image and is more immitigable. In the first lecture I heard from Timoshenko in 1949, he talked about how brilliant St. Venant was in science and engineering. He questioned why St. Venant was so obscure in French history. He searched for the reasons long and detailed. I felt it was like listening to a tale about a lost uncle on Christmas Eve.

Another good description of Timoshenko I heard from Den Hartog in his Timoshenko Award acceptance speech. Den Hartog said that he was working under Timoshenko at Westinghouse Research Lab when he finished a paper on torsion and hesitated to publish it because he did not know whether it was important enough. Timoshenko told him, "Who do you think you are! One contributes what one can!" One contributes what one can! I like that attitude.

In a von Karman lecture I heard, he opened with a remark about himself. He said that in his youth he missed inventing the radio, in his prime age he missed inventing the airplane, in his senior years he missed inventing the nuclear reactor. In his old age he would miss the exploration of space. So he can only talk about waves, aerodynamics, and aerothermo-dynamics. As a graduate student I did not know what to make of that comment, but I remembered it. It does make sense to me now against his total contributions and ambitions. The story of his inventing the vortex street was this: He was in Gottingen and talked to Herr Hiemenz who had spent years measuring the flow behind a circular cylinder. Hiemenz could not get the flow to be stabilized. The data he obtained was always oscillating. So Karman went to work on it and wrote out the whole theory in one weekend. When he presented it at a meeting in Paris, Henri Benard said that he had photographed the vortices earlier and there were some differences between Karman's theory and the experimental results. Karman made some quick calculations on the back of an envelope, stood up to explain the differences, and suggested that the street should be called "Boulevard de Benard in Paris." Such stories make Karman inimitable.

Poiseuille was born in 1797. He attended Ecole Polytechnique and got his Doctor of Science degree at age 31 with a thesis on the measurement of blood pressure with a small bore mercury manometer. He obtained the first accurate values of blood pressure since Stephen Hales showed the way 119 years earlier (1709). Then, in 1840, at an age of 43, he published his famous paper on water flow in circular cylindrical tubes. He used pipettes of diameter 15 microns to avoid turbulence, a diameter similar to capillary blood vessels. After that he published only one other paper, on the measurement of flow with ether and mercury at the suggestion of the reviewers of his famous paper. His biographers did not know what positions he held in his life until he was 63 years old, when he became an inspector of primary schools in Paris. He died on Dec. 26, 1869 at an age of 72. He exemplifies the case that one paper makes a man.

These three men are not shy in applying mechanics to new areas. They showed that science is developed by man, and man is helped by developments in science. In hard times like this year of budget cuts, it is worth remembering this principle, because society always has a need to improve the lot of people, and engineers are the ones to deliver such improvements. And the society will always provide the needed resources.

I believe in this principle, and did not find too much conflict between personal interest and the necessity for survival. Let me tell you a little bit about myself.

I was born in China in 1919. I grew up in a period when China was very unsure of itself. My memory of my childhood was that the Christmas seasons were the time to seek refuge in the countryside, to get out of the way of the war paths of local war lords fighting for territory. I remember my family crowded in a little boat eating cold chicken. That's probably why I have liked cold chicken all my life. Later, China's problem of survival became even more difficult. In my first junior high school year, Japan took Manchuria (the September 18th event). The next year Japan invaded Shanghai (the January 28th event) and we fled to Peking. At year's end, Japan invaded She-Feng Kou and we fled back to Changchow. Students struck often to protest the government's nonresistance policy. I entered college in 1937 when the Japanese militarists started the last big push to conquer China. I chose to study aeronautics because airplanes were needed most in China's fight for survival.

In 1943, a consortium of American universities offered 20 graduate assistantships to China. The Chinese government held a national examination, selected the candidates, trained them for language, then sent them on their way. I got the position from Caltech. When I arrived in Pasadena and reported to Ernie Sechler on Jan. 6, 1946, Ernie laughed heartily by saying that the assistantship offer had expired by over two years! But he hired me as an RA. I inherited a little wind tunnel built by von Karman and Louis Dunn to study the flutter of the Tacoma Narrows suspension bridge, and was also given the job to study a drawer full of notes and scratch papers written by Tony Biot on theoretical analysis of flutter of that bridge, and to write a report about it. That was how I got into aeroelasticity. Unfortunately, von Karman had retired, Biot had gone to New York, and Dunn had gone to the Jet Propulsion Laboratory. I was left without a supervisor on aeroelasticity. Professor of mathematics Aristotle Michal took me under his wing. He taught me Frechet derivatives, with which I began my thesis on airplane dynamics.

I got my Ph.D. in Aeronautics in 1948, and stayed on the faculty. Ernie Sechler was my mentor. I have an enormous love and respect for him. Whatever I did he could show me a way to make it simpler. He was a wise counselor, and a warm friend. We worked together for 20 years on swept wing design, shell buckling, ICBM base hardening, rocket structure, fuel sloshing, etc.
In 1957, I began my self-study of physiology. I had a sabbatical leave in Gottingen, Germany. I stayed at Prandtl and von Karman's old Institution. I found its work on aeroelasticity rather dull, but the library on physiology next door was excellent. The causal factor for my going to the library was my mother's glaucoma. I translated newly published articles on glaucoma into Chinese and sent them to her in China to give to her surgeon. On returning to Caltech I began working on physiology with Sid Sobin, Wally Frasher, and Ben Zweifach. Together we wrote papers on the capillary blood vessels, red blood cells, the interaction of cells and vessels, and the mechanical properties of living soft tissues. I found continuum mechanics indispensible in clarifying these topics. In 1966, I resigned from Caltech and went to UCSD to devote full time to physiology and bioengineering.

I wanted to demonstrate that physiological problems can be solved with engineering methods. Together with Sid Sobin, I chose to work on the blood circulation in the lung. It was surprising that a thorough search of literature yielded very little reliable basic data on the pulmonary vasculature. The basic information we needed on the anatomy of the lung and biorheological properties of the materials did not exist. We had to obtain them by ourselves. Hence we had to turn ourselves into anatomists and histologists before we could use mathematical tools for physiology. The program was straightforward, but the road was long. For pulmonary circulation, it took us 12 years before we could close the first round. But we had fun on the way, and found many pretty pebbles right and left. The data we collected can be used to solve other problems. The theory worked out can be used clinically. Our patience was pretty good because a master plan existed and we knew the value of every link in the chain. But the importance of longevity became evident.

On approaching retirement, I entered another field: that of the relationship between tissue growth and physical stress. The question began at home. My wife, Luna, has a little high blood pressure which can be controlled with diazyde. But she does not like to take medicine. So she takes diazyde until her blood pressure lowers, then she stops to wait until the blood pressure rises again before taking another pill. This is not what the doctor ordered, and I wanted to know if it was a good idea. So I made a research project out of it. The project turned out to be full of surprises. For example, I found that our blood vessels remodel themselves rather quickly when the blood pressure changes. If the blood pressure was raised as a step function of time, structural change in the blood vessel wall will be detectable in one or two hours. Generally, the inner wall of the blood vessel will thicken first, doubling its thickness in two or three days. Then the outer wall thickens, and can be doubled in about 10 days. Furthermore, the residual stress in the vessel wall changes. Residual stress can be revealed by cutting a vessel segment into a ring, then cutting the ring open radially. The ring opens into a sector. The opening angles of normal arteries vary from place to place in the range of 0 to 90°, but in the aortic arch region it could be about 180°. In the pulmonary trunk it can be 360° or larger, i.e., it has so much residual stress that if it were given a chance to reach zero-stress, the vessel will turn itself inside out! Isn't that amazing! With a stepwise increase of blood pressure, the opening angle will increase first, reach a peak in 2 days, then decrease to an asymptotic value. The up and down swing of opening angle can be as large as 90-100° in some places. Our blood vessels are that alive! Associated with the structural changes, the mechanical properties change also. The constitutive equation changes with time. They are not constitutional laws at all.

These results are published in refereed medical journals such as Circulation Research, Journal of Applied Physiology, American Journal of Physiology, Journal of Biomechanical Engineering, etc., so I am not just telling you stories. You understand the mechanics instantly. I wish the medical people were as easily convinced as you are.

Fortunately, when the blood pressure is returned to normal, the changes are reversible to a large extent. Hence it appears that my wife is right. So she said, "All right. Then why don't you stop here? Why do you still talk about generalization, and more experiments? Why do you have to have a stress-growth law as you call it, sort of a constitutive equation squared?"

I offered Poiseuille as my excuse. I said, "Poiseuille knew that his paper No. 5 is his best. I still think that my next paper will be a better one. I am still experiencing my normal experience. My normal experience is something like this: A problem arises. It looks difficult. It is impossible to crack. I work on it day after day. I draw a blank. Then suddenly it becomes clear. It becomes simpler. Soon it is so simple that it is indeed trivial. I wonder why I did not see it before. So I throw the scratch paper into the waste paper basket. But the experience is pleasant. I call it life's little pleasure. I am still getting these little pleasures. But although the big one has not come, I like the little ones. That's the secret of my life I want to share with you.

Now I will conclude with sincere thanks to the Applied Mechanics Division for this heartwarming recognition from colleagues and friends. Thank you all, I wish you all the best.

1995 Timoshenko Medal Lecture by Daniel D. Joseph

by Daniel D. Joseph , University of Minnesota

In my instructions about the correct behavior of recipients of the Timoshenko Medal at this dinner, Tom Cruse wrote to me that "While I ask that you consider the hour and the length of the evening in selecting the length of your remarks, the time is yours and we are honored to hear from you at that time." This suggests to me that as a Timoshenko Medalist, I can be indulged but that if I really want to be appreciated, I should keep it short.

I understand that when Jerry Ericksen got this award, he said "thank you" and sat down. I would like to follow this courageous path, but I lack the courage and so I will embellish "thank you" just a little.

Of course, I am pleased and honored to get the Timoshenko Medal and I am especially pleased to be introduced by my teacher and dear friend, Phil Hodge. I got my Ph.D. in 1963 at the Illinois Institute of Technology in Chicago. My advisor was L.N. Tao, but I took a graduate course in continuum mechanics with Phil when I was an undergraduate. It was a very demanding and quite unusual course with an emphasis on mathematical rigor at a level at which beginning students in engineering could understand. The course had a very important and permanent influence on my understanding of the mathematics of mechanics which influences me still.

At the University of Minnesota, Phil and I were running buddies. We even ran some marathons together; that is, we started together, then I saw his backside for a few minutes and three or four hours later, I could find him well rested at the finish. I ran 22 marathons; my best time for all of them was 3:42. In that marathon, Phil did it in 3:16 and was No. 1 in his old age group. My marathon running is like my career; not much talent, but very persistent. It is good for me that the Timoshenko Medal is also given to tortoises.

Applied mechanics was very strong at IIT in the early 1960's. The late Peter Chiarulli and Max Frocht were there then, and Eli Sternberg had been there not so much earlier. Another applied mechanician, Walter Jaunzemis, taught us a very thoughtful course on analytical dynamics which I appreciated greatly. He died as a young man. It is so sad to think of these ghosts of my past. My friend, Ronald Rivlin, who thank God is still alive and feisty, told me on the occasion of my 60th birthday that I was too old to die young. This is actually some comfort. It might interest you that Barenblatt and I are editing a collected works of Rivlin which ought to appear next year.

My relations with the people of applied mechanics developed more strongly at IIT than later. Peter Chiarulli arranged for me to present some work I did about Stokes flow over a porous sphere at an ASME meeting in a session chaired by George Carrier. He introduced me as Dr. Joseph. I wasn't a Dr., but George didn't know it. Later, he told me that he always played it safe. A little later, he saved me from later embarrassment by rejecting that paper. Too many mediocre papers were published in the 1960's and 1970's.

Jim Rice noted already in his acceptance speech of last year that the early 1960's was possi¬bly the best time to get a Ph.D. in mechanics ever. Due to Sputnik, there was lots of money for fel¬lowships, new faculty positions and research. I certainly benefited from this; I got a good job eas¬ily at the University of Minnesota in 1963 and my career advanced very fast. One consequence of the atmosphere of the time was to put a bigger than usual emphasis on foundations at the expense of applications. Many engineers in those days had an exaggerated idea of the power of abstract approaches. Mathematicians, and physicists too, have a good sense of the history of their subject. They know their heroes and who to emulate. We have not this sense of history in engineering and it leaves us rudderless and prey to foreign influences like those which, in the 1960's and 70's, led to the unnatural attempt to axiomatize mechanics.

It is probable that in recent times the pendulum has swung too far against abstract approaches based in mathematics in a kind of over-reaction which generally accompanies the correction of abuses.

My career can also be understood in two phases, the first emphasizing mathematics and the second, engineering. Actually, I could point to a third phase—the sociology phase, which came first. Some of you may know that I got a master's degree in sociology from the University of Chicago in 1950. Even though I have a master's degree in this field, I don't get much respect. The problem is that no matter how well educated you may be in sociology, the man on the street has his own opinion. Engineers are much better off because they get the benefit of the doubt.

Probably only a few of you know why I got this medal. Some years ago, when I had no honors and awards but Jerry Ericksen had many, I noticed that to get them, you needed to be certified. I told Jerry that the best kind of certification is that you have already got some honors and awards from elsewhere. Jerry then noted that "every dog knows where other dogs pee."

Joking aside, I owe so much to the string of superb students who have worked with me in these past years: Luigi Preziosi, KangPing Chen, Howard Hu, Pushpendra Singh, Adam Huang, Runyuan Bai, Jimmy Feng, Todd Hesla, Mike Arney, Joe Liu, Geraldo Ribeiro, Chris Christodoulou, Oliver Riccius, Joe Than, P. Huang and many others. These students worked with me on many projects; here, I will mention two: Hyperbolicity and change of type in the flow of viscoelastic fluids and the water-lubricated pipelining of heavy crudes.

In the 1980's, together with Michael Renardy and Jean Claude Saut, I found that the unsteady vorticity equation for many models of viscoelastic fluid is hyperbolic, giving rise to waves of vorticity. In steady flows, the vorticity field can be of one type here and another there, as in transonic flow. The other variables, stresses and velocities, are neither strictly hyperbolic and/or strictly elliptic. To me, it is surprising that with so much mathematical work coming from rational mechanics in the 1960's, 70's and 80's, that the problem of the mathematical classification of type of the governing PDE's was not joined.

The key quantity in the discussion of hyperbolic waves of vorticity is the speed of shear waves. We invented a device in 1986 to measure the speed of these waves. We must have measured these speeds in 200 different fluids by now. There are over 100 values published in my 1990 book on the Fluid Dynamics of Viscoelastic Liquids. You can compute a relaxation time for these speeds, and usually it is an order of magnitude smaller than what other people get by the devices they use. I think that conventional rheometers have a too slow response, most of the signal has decayed by the time those instruments kick in.

Using speeds measured on my device, I have correlated data from our experiments on delayed die swell, the orientational change of falling bodies, the change in the drag law of air bubbles rising in viscoelastic fluids and other anomalous effects that were reported in experiments, which I interpret as a change of type. If you use the speed we measure, you get a good agreement, but not otherwise.

I must confess that the rheology community, though not hostile, seems largely indifferent to these results which I consider to be so important.

Another topic on which we have worked, which I like greatly, is water-lubricated pipelining of heavy oils. It is a gift of nature that if you put water and oil into a pipeline, and the oil is viscous enough, say, greater than 5 poise, the water will go to the walls of the pipe where it lubricates the flow. You can get drag reductions this way of the order of the viscosity ratio. Crude oils with a viscosity of 1,000 poise are not uncommon. They can't be pushed through pipes at that viscosity, but with water there, they go through easily. You've got drag reductions of the order of thousands. This is a technology which has been used and it will be used more and more.

CNN found out about our work on this and did a short video segment on it which I am going to show you. That week, I had a tooth pulled and my face was swollen. Just my luck to have a swollen face on the road to stardom.

I have been asked many times if the lubrication of one fluid by another can be described by a variational principle. Strictly speaking, it cannot; however there is something in the idea of minimum dissipation which is best expressed in anthropomorphic terms. "High viscosity liquids are lazy. Low viscosity liquids are the victims of the laziness of high viscosity liquids because they are easy to push around."

MRS Bulletin features Macroelectronics

The June 2006 issue of MRS Bulletin features Macroelectronics.

The guest editor of this issue include Robert H. Reuss (program manager of DARPA's macroelectronics program), Darrel G. Hopper (principal electronics engineer at US ARFL), and Jae-Geun Park (Materials Center at Samsung Advanced Institute of Technology)

The issue include a theme review article by the guest editors and four theme technical articles covering various topics related to macroelectronics.


(via www.macroelectronics.org)

KEVLAR is a modern material with many applications

1999 Timoshenko Medal Lecture by Anatol Roshko

Small is Good

By Anatol Roshko, California Institute of Technology

The text of the Timoshenko Medal Acceptance Speech delivered at the Applied Mechanics Dinner of the 1999 IMECE in Nashville, TN.

David Belden’s letter announcing the award was really a surprise, almost a shock. At first I wondered whether it was another example of a story which you may have heard and which, I believe, originated in the FSU. Two friends are at a grand reception sipping cocktails when one notices a man with his chest almost completely covered with medals. Says one to the other, “Do you have any idea what those medals are for?” and the other replies, “Well, you see that one at the top left? That one was a mistake; and the others followed automatically.” I humored myself out of that thought but not out of a feeling of guilt. You see, I suddenly felt terrible that I was not a member of the ASME. There had been opportunities but somehow I had let them go by. One reason is that I was concerned about another onslaught of communications, information and other paper that always results and requires attention. Fortunately, ASME lost no time in relieving my guilt. In a few weeks I received a nice invitation and forms to fill out, and now I am Member No.6143358. And sure enough, information has begun to roll in: a beautiful, glossy magazine, notices of various meetings, etc.

I sincerely thank those who put my name forward and the Division of Applied Mechanics for this honor. I want to assure you that, though not a joiner, my destiny has always been in Applied Mechanics, as you will see as my talk progresses.

Other medalists have had some acquaintance or connection with Professor Timoshenko. Mine is mainly through the ending “-ko”. I understand that there are some who think that Tim O’Shenko was an Irishman but, as most of you know, he was Ukrainian. The “-ko” is almost certain identification. So even though I did not have the good fortune to meet Stephen Timoshenko I feel some connection.

Originally, when informed by Dr. Belden about the award and tonight’s dinner, I assumed that it was going to be appropriate to make a few acceptance remarks and that something like what I just said would do it. Not being a member, I was not familiar with the rituals of the Applied Mechanics Division. So when, a few months later, Professor Needleman informed me of the custom, I again had a bit of shock, especially when he told me it should be a NON technical talk; and no blackboard, no overhead projector! And a written copy would be needed for the Newsletter! Well, I have here my illegible hand written notes which I hope to have in printable form before the due date.

What do you want to hear in a non technical talk? Humor? Advice? An appraisal of the field and projections for the future? Views on public policy for Applied Mechanics? I’m not very good at any of that. So I’ve modelled my talk somewhat on that of Professor Willis, the 1997 Medallist, whose acceptance speech I read in the AMD Newsletter and liked very much. Some back copies were kindly provided by Professor Needleman and Mr. Majewski.

The theme is “how to pursue a satisfying career in Applied Mechanics”, and I feel very satisfied with mine. I discovered the generalized formula only at the end of my career, but perhaps someone else can use it. Simply stated it is this: “Be in the right place at the right time.” But there’s an important caveat: the places should be small. I use the term “places” as a generalization for various entities, as you will see. Hence the title of this talk.

My career started in a small high school in a small coal-mining town in the Canadian Rockies. There were 15 in the graduating class. Bellevue High School provided me with an excellent education in the basics, up to introductory calculus. The town was an ethnic pot, it was poor, everyone in it was poor, but the three high school teachers had University degrees! I still don’t know how that worked and why it doesn’t seem to work so well now, but I think one clue may be in the word “small”.

From there I went to the University of Alberta, which at that time had a total enrollment of about 2500. I was in the Civil Engineering class, some 15 in all, but on a special track called Engineering Physics, which allowed me to substitute extra Math and Physics for courses like Concrete Mixing. The Eng. Phys. option was the brainchild of Applied Mechanics professors in the Civil Engineering Department (there was no M.E. Department at that time); they were mainly in Structures and Soil Mechanics. Many of them had gone to the University of Illinois for graduate work. One of them, my good friend George Ford, an Applied Mechaniker at heart, went to Stanford to work with Goodier, the son-in-law of Timoshenko who was still very active then. So I got to know a bit about Timoshenko from George Ford, who went back to Alberta and was instrumental in establishing an M.E. Department there.

From Alberta, after some diversions, I came to Caltech for graduate work in GALCIT. This is, effectively, the department of Aeronautics, but the Division of Engineering and Applied Science does not have Departments. I guess each department would be TOO small. Lucky for me; I got to teach some of the Applied Mechanics courses that George Housner and Don Hudson had established.

In 1946 the enrollment at Caltech was about 1500, half undergrad and half gradate. After half a century it has grown to about 2000, still half and half. Bigness is not big at Caltech. You probably noticed that US News and World Report recently ranked Caltech at the top of Universities in the U.S. (even though it’s not a University!). You may have also heard, at about the same time, another education story from LA County, namely the crisis in the Los Angeles Unified School District. It’s difficult to avoid comparisons—no, not with Caltech but with Bellevue High School. In fact, one of the proposals being suggested is to break up LAUSD into smaller units. About the size of the old Bellevue School District should be about right. (This ends my venture into Public Policy.)

I was fortunate to come into the orbit of Hans Liepmann the first day I arrived at Caltech. Much of my way of seeing and doing things has been influenced by him. Hans was wary of bigness. He liked to keep things lean: big funding brings big baggage with it; you should seek funding for research you want to do, not the other way around; research must be enjoyable to be productive; “smaller” makes it easier to recover from setbacks, even crashes, and so on.

Echoing Professor Willis’ observations, I believe that a productive career in research in Academia is helped by three elements, all related to the fact that research is nurtured by questions and questioning. An ideal mix is the combination of teaching, consulting and research; the elements of this triangle feed each other constructively.
To teach technical material convincingly it is necessary to understand it, and students encourage you to do so. Digging deeply often reveals gaps not only in your own understanding but often in the subject itself. When interacting with students at the research level we teach each other. Liepmann delighted in asserting that even before a PhD thesis is finished the student should know more about his subject than anyone else, including his advisor.

The second element of the triangle which leads to questions and questioning is consulting, using this term in the broad meaning of interaction with the outside world, whether it be industrial companies, government laboratories or other societal entities. My own work was strongly influenced by such activities. Observing engineers solve tough technical problems, with imperfect technologies at their disposal, gave me a healthy respect and admiration for how they get their jobs done, and it often left me with feelings of inadequacy to help. I also realized how inadequate even our best students may be feeling as they stepped out into the real world. This led to the introduction, with Don Coles, of a new course in our curriculum, officially called Technical Fluid Mechanics but unofficially Dirty Fluid Mechanics, the kind you can’t find in textbooks. This enabled us to pass on to our future engineers and researchers some extra help; at the same time it impacted our own research, by the feedback process I’ve mentioned. I suspect that there’s also a place for a course in Dirty Solid Mechanics.

The third corner of the triangle, scientific research, is at the apex. Feynmann called it “the pleasure of finding things out”. Exhilaration may be a better describer. I feel privileged to have experienced it. Professor Oden, in his 1996 acceptance speech, said “I have experienced this phenomenon many times. I am constantly amazed by it, but find it awkward to explain or rationalize”. I had thought to give a few examples here, but there’s no blackboard or overhead projector! But I have promised to write up one of them for Applied Mechanics Reviews.

It seems to me that it is the nature of Applied Mechanics research that it is best carried out by individual investigators or small groups. So it concerns many of us that the trend is toward large consortia of researchers who are supposed to interact with each other and across disciplines. This is inevitably directed research, about which many thoughtful people were concerned when government funding of research accelerated, continuing a process that had begun during World War II. Other thoughtful people point out that this is the only way that societal expenditures on research can continue and even increase, and that anyway there is no net loss to the undirected research that would and will otherwise flourish. Perhaps this trend toward more directed research should be viewed as a contribution to the consulting corner of the triangle which I described and that individuals may still be able to work on their creative ideas under the umbrella of a large consortium. A little moonlighting might be helpful. In fact, life could be very comfortable, except possibly for the Director. But, inevitably, creative people will be left out.

Also troubling is that bigness seems to be crowding out some of the culture that has served Applied Mechanics so well, i.e. the abstraction of well-posed scientific questions from important but messy practical ones (a phrase which I’ve borrowed from Garry Brown). As someone (Prandtl?) remarked, “there is nothing so practical as a sound scientific theory”. It is idealized models, leading to analytical descriptions, that reveal the innermost workings of nature, and they help develop the “intuition” which engineers need to do their “dirty” work. This culture should not diminish; it is already small.

Mr. Chairman, again I thank you and the Division for the honor you have given me, the ASME for signing me up, and you the audience for the opportunity of speaking to you.

A Second-Gradient Theory of Fluid Flow

Recently, Eliot Fried and Mort Gurtin have developed general balance equations and boundary conditions for second-grade materials. Their work is set to appear in the Archive for Rational Mechanics and Analysis and is presently available online (DOI: 10.1007/s00205-006-0015-7). The theory essentially blends classical work by Toupin on elastic materials with couple stresses with a modern, nonstandard principle of virtual power developed by Gurtin. Importantly, the basic formulation is independent of constitutive assumptions, and as such, applicable to both solids and fluids.

Fried and Gurtin consider incompressible fluid flow as one such application. The approach effectively generalizes the Navier-Stokes equations to include higher-order gradients of the velocity field. Through constitutive assumptions, material lengths are naturally introduced in the flow equation and higher-order boundary conditions. Fried and Gurtin refer to the former as the gradient length, L, and the latter as the adherence length, l. This work is of interest because recent simulations suggest that at sufficiently small length scales, the classical Navier-Stokes equations and their boundary conditions fail to accurately describe fluid flow. The new theory provides a mechanism to account for these length scale effects, and being continuum-based, promises to be much more efficient than discrete methods such as molecular dynamics.

In particular, Fried and Gurtin consider the case of plane Poiseuille flow and derive analytical expressions for the velocity profile. If one considers laminar flow through a channel of height h, for example, gradient effects play an increasingly important role on the flow with decreasing ratios h/L of physical to gradient lengths. A plot of the flow profiles predicted by the theory is reproduced here in the Figure to the right. The theory allows for a range of flow profiles from the limiting cases of strong (l approaching infinity) and weak (vanishing l) adherence to the classical results predicted by the Navier Stokes equations.

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 .