Wednesday, June 28, 2006

Nanostructured Metals Reveal Their Secret Strengthening Mechanisms

It is well known that metals are hardened by deformation and soften by annealing. How about nanostructured metals? Can we reply on conventional metal-working lore? In a paper in Science (Huang et al., Science, 312 (2006) 249), Xiaoxu Huang and colleagues at the Riso National Laboratory, Denmark and Osaka University, Japan have found that nanostructured aluminum behaves in contrast to the conventional theories; annealing makes it stronger and tougher whereas deformation (cold working) gains ductility with a trade-off of lowering the strength. The structural scale affects fundamental mechanisms of dislocation-dislocation and dislocation-interface reactions. This finding may stimulate the applied mechanics community to study the fundamental strengthening mechanisms of nanostructured materials from both experimental and theoretical approaches.

Saturday, June 24, 2006

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."

Tuesday, June 20, 2006

IBM, Georgia Tech break silicon speed record

In this week's issue of The Solid State Technology, i.e. on June 20, 2006, IBM and the Georgia Institute of Technology announced that their researchers have demonstrated the first silicon germanium (SiGe) chip capable of operating at ~350GHz at room temperature, and >500GHz at 4.5 Kelvins. (Read more ...)

Sunday, June 18, 2006

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.


Saturday, June 17, 2006

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.

Saturday, June 10, 2006

1962 Timoshenko Medal Lecture by Maurice A. Biot

Timoshenko Lecture: Science and the Engineer

by Maurice A. Biot

As everybody knows, there are two sides to a Medal. The bright side in this case is obviously the encouragement to the recipient. The darker aspect of the other side is something you will have to bear with me. I refer, of course, to the after dinner speech.
First of all, it is a great honor to be associated with the name of Timoshenko, the Teacher, the Scholar, the great Engineer and Scientist. It is widely agreed that the high level of instruction and application of solid-state mechanics in this country is due to his influence and his teaching.

However, to me the name symbolizes much more than the award and the honor. It evokes a brilliant phase and tradition in the practice of science and engineering which unfortunately seems to be on the decline. This is the tradition of clarity, simplicity, intuitive understanding, unpretentious depth, and a shunning of the irrelevant.

There is, of course, no merit in sophistication for its own sake. In the understanding of the physical world, and particularly in the area of technological applications, it is important to perceive what is irrelevant. The level of irrelevance involves a value judgment which usually requires rather subtle habits of thought related to natural endowment and previous experience.

We should not overlook the importance of simplicity combined with depth of understanding, not only for its cultural value, but as a technological tool. It leads to quantitative predictions without laborious and costly calculations; it suggests new inventions and simple solutions of engineering problems. Aside from obvious economic advantages, it also provides an important quality in engineering design, namely reliability. In this respect one cannot help reflect on our dismal record of staggering cost and repeated failures in the field of rocketry.

Deeper physical insight combined with theoretical simplicity provides the short-cuts leading immediately to the core of extremely complex problems and to straightforward solutions. This cannot be achieved by methods which are sophisticated and ponderous even in simple cases. The process of thought which is involved here may be described as "cutting through the scientific red tape" and bypassing the slow grinding mills of formal scientific knowledge. Of course, formal knowledge is essential but, as for everything in life, the truth involves a matter of balance. The instinctive embodiment of this truth is to be found more often in the politician than in the scientist. However, it is essential to the make-up of a competent engineer.

Doubt about the engineer's function in our increasingly complex technological culture has been expressed by the blunt question "Is the engineer obsolete? Should he be replaced by the scientist"? Although such a question is the product of ignorance, the situation is such that, in this country at least, it finds a respectable echo.

What about the physicist? Speaking in general and with due respect for exceptional personalities endowed with outstanding natural ability, I think the physicist has turned away from his own tradition and has tended to become a victim of narrow specialization. Nuclear and particle physics, solid state, spectroscopy, plasma physics, all claim their victims. Many are almost totally ignorant of classical mechanics and are not able to understand the formulation of even simple problems unless it can be reduced to the solution of a Schroedinger equation.

As for the mathematician, a situation has developed which is a complete reversal of what existed in the past. Many of the great names in the history of mathematics of the nineteenth century have been those of distinguished engineers. An outstanding example is Cauchy who graduated as a civil engineer and was engaged in the practice of engineering for many years. These men were of a different breed. They had a deeper grasp of scientific knowledge, a much broader outlook than the professional mathematician of today.

Whatever the cause of this reversal we must face the fact that mathematical science has become dominated by abstract formalism. It is increasingly dehumanized and cut off from its roots in the rich and nourishing soil of physics and engineering, and the other natural sciences. What should be referred to as applied mathematics does not exist on its own, but describes essentially a function and a craft by which the science of mathematics finds its nourishment.

Much of the so-called applied mathematics which is practiced today is almost diametrically opposite to this function. It is permeated with legalistic hair-splitting, shrouded in pretentious language, as if the purpose were to obscure and surround with an aura of mystery and profundity what is very often a simple and even trivial subject.

This trend toward a formalism devoid of humanistic content, this emphasis on form at the expense of substance is found not only in science. It also prevails in our contemporary art and literature and obviously results from deeper, and perhaps self-destructive, undercurrents in our culture.

It constitutes a retrogression toward the abuses of medieval scholasticism and away from that intimate union of craftsmanship and science so characteristic of the Renaissance period. In this connection I recall a quotation from Ortega y Gasset. "Life is not to be lived for the sake of intelligence, science, culture, but the reverse; intelligence, science, culture, have no other reality than that which accrues to them as tools for life. To believe the former is to fall into the intellectualistic folly which, several times in history, has brought about the downfall of intelligence."

Generally speaking, the professional mathematician of today is a specialist in logical systems and rigor. His lack of flexibility makes him unable to exercise one of the very essential functions of mathematics in the natural sciences and engineering, which is to separate the relevant from the irrelevant, to simplify the formulation of complex phenomena, to synthesize and to unify the substance rather than the form. There is not time here to dwell on the details. For contrast let me cite only the brilliant treatment of the Navier-Stokes equations by Prandtl in his famous theory of the boundary layer.

There is, however, a more ominous aspect of this situation which brings up the matter of education of scientists and engineers. We should remember that intuitive ability closely resembles artistic talent. It may be developed or it may be smothered depending on the environment and the training. Rigor and abstract formalism are technical aspects of mathematics which may actually impede invention. They are for the specialist. The engineering student should be exposed to them only as an experience. They should not pervade his thinking nor exceed the point at which the intuitive faculties become inhibited.

In many schools the hard core of mathematical and physical knowledge is submerged in a flood of special courses characterized by abstract-formalistic overtones. There is an emphasis on formal knowledge rather than understanding and the climate is not favorable to creative talent. It should be remembered that one of the important functions of a school is to discover, encourage and develop talent and not only to transmit knowledge. To make the situation worse, we are now witnessing the introduction of the abstract axiomatic approach in high-school mathematics. Such a development involves great dangers to our future scientific and technological standing. It has been said that "Learning is the kind of ignorance distinguishing the studious." I don't want to downgrade studiousness, but I don't think knowledge should be an obstacle to understanding.

While I have dwelt on the more gloomy aspects of this situation, I would like to conclude these few remarks with a more optimistic note.

Let us hope for a revival of humanism and a spirit of synthesis in science. Let us also put new emphasis on engineering as a professional craft, requiring high skill, natural talent, deserving social recognition, and distinctly different from the scientific professions as such. New stirring are appearing in this direction. I am inclined to believe that engineers and engineering schools will play an important part in restoring the unity and central viewpoint in the natural sciences. This is because modern engineering by its very nature must be synthetic. Specialization carried to extremes is a form of death and decay.

One could formulate a principle of degradation of knowledge entirely analogous to the second principle of thermodynamics. It represents a powerful force which can be defeated only by a hard and difficult struggle. The burden of it must be carried, not by teams and organizations, but by a few individuals. In this connection there is much to be said for the smaller schools. They should provide a better environment for unhurried maturing of thought and for the nucleation process by a very small number of qualified people.

It has been customary for the recipient of an award to avail himself of the opportunity to reflect on current problems of professional interest. While I do not pretend to have brought to light any really new ideas, it seems to me that the occasion was most appropriate for their reemphasis in the framework of the Timoshenko tradition.

In this future synthesis and the revival of technological craftsmanship, I think we all agree that in the practice as well as in the teaching, engineers are called upon to play a very fruitful and essential part.

Friday, June 09, 2006

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.

Saturday, June 03, 2006

1974 Timoshenko Medal Lecture by Albert E. Green

Reflections on 40 Years in Mechanics

Albert E. Green, 1974

Thanks to the Society through the President for the presentation of the medal.

Thanks to Dick Shield.

There is one serious disadvantage to receiving the medal – the tradition that the recipient gives an acceptance talk.

Owing to the influence of men like Professor Timoshenko, work in applied mechanics in the U.S. has mostly been centred in engineering schools but sometimes in mathematics, applied mathematics departments or institutes. In Britain theoretical work in applied mechanics has mainly been in departments of mathematics and applied mathematics, but a few departments of engineering have also been concerned with such work. My own experience in Britain has been entirely in departments of mathematics in which there were close links with pure mathematicians. In the United States I have been fortunate to be associated with colleagues at Brown University and at Berkeley, as well as visiting other universities. Although I am in a department of mathematics, both pure and applied, at Oxford, my own title is Sedleian Professor of Natural Philosophy. The Sedleian Chair was founded by Sir William Sedley who by his Will dated October 20, 1618, bequeathed the sum of ₤2,000 to the University, to be laid out in the purchase of lands for its endowment; this bequest took effect in 1621. It is regarded as the oldest of the scientific Chairs even though the Savilian Professorships of Geometry and Astronomy were endowed in 1619, and the first of them actually filled in that year. My immediate predecessors were Professor George Temple, Professor Sydney Chapman and Professor A.E.H. Love, and you will be aware that they dealt with very different aspects of natural philosophy. Professor Love held the Chair for 41 years, from 1899, and his work is well known in the present company. The fourth holder of the Chair who was appointed in 1660 was Thomas Willis. A list of some of the treatises which he wrote makes interesting reading: (1) “Of the accession of the blood”; (2) “Of musculary motion”; (3) “Of urines”; (4) “The anatomy of the brain”; (5) “The description and use of the nerves”. He also wrote about convulsive diseases, scurvy, and the comparative anatomy of some dozen species ranging from the earthworm and lobster to sheep and man. He is regarded as the founder of neurology. In his last writings on rational therapeutics he presented a vast and sometimes horrific pharmacopoeia in which, however, are buried useful descriptions of the anatomy of the blood vessels, the muscular layers of the stomach, and the detailed structure of the lungs. Perhaps we can discern the beginnings of the present fashionable subject of biomechanics in the description of the probang, an ingenious machine for treating a very rare case of a certain man of Oxford who was probably suffering from stricture of the oesophagus.

Willis had as pupils or assistants men who later became well known. They included Robert Hooke, the great inventive physicist and microscopist, John Locke, the physician-philosopher, Edmund King who, with Richard Lower, performed the first blood transfusion, and finally, Thomas Millington and Christopher Wren – who later became Savilian Professor. This set were some of the extraordinarily versatile scientists who, after their “Invisible College” as Robert Boyle termed it, eventually went on from Oxford to found the Royal Society in London – Willis was one of the original Fellows (1663).

At Oxford applied mechanics is studied in the Department of Engineering as well as in Mathematics. In this connection, Sir Richard Southwell, who received the Timoshenko Medal in 1959, held the Chair at Oxford in Engineering.

The term natural philosophy takes me back to early days in Cambridge as some of the papers in the Mathematical Tripos Examination were headed natural philosophy. On looking through the list of those who received the Timoshenko Medal I see four names associated with Cambridge. Professor Lighthill who is there at present, Professor James Goodier who was somewhat before my own time, and I did not know him in those days. Although we corresponded occasionally I only met him in recent years in California. Then there was Professor Sydney Goldstein. I attended many of his lectures both as an undergraduate and as a graduate student and I still have some excellent notes in Electromagnetism and Fluid Dynamics from him. He always packed a tremendous amount into lectures. One habit was to finish a lecture at 10am on one day in the middle of a sentence and then to begin his lecture the next day promptly at 9am continuing the same sentence as he walked in the door! He also disregarded physical disabilities. Occasionally he suffered from gout and would lecture seated on a bench with both feet and legs wrapped in bandages, using the board above as far as he could reach.

The fourth person on the list is Sir Geoffrey Taylor, or more usually known as G.I. I had the good fortune to be one of his research students and am sad to know that he is now incapacitated by illness after a long and very active life in applied mathematics and mechanics. G.I. had a room in the Cavendish Laboratory in Cambridge and he did experiments with the help of a superb technician named Thompson. Many of you will be aware of his classic work on the stability of Couette flow of a viscous fluid between rotating cylinders, which is an excellent combination of theory and experiment. The apparatus which he used for the experiment was still in the laboratory when I was a student. G.I. was an enthusiastic yachtsman and was very interested in developing an anchor which was much lighter than the conventional type and which had more efficient properties. He used to experiment with a model anchor by throwing it into a large box of sand in the laboratory with obvious enjoyment. The anchor was eventually patented and has, I believe, been widely used. Although it may now be surprising to some of my listeners I once did an experiment under his guidance – but not since then!

I recall that when I started with G.I. he suggested an area of work and discussed this with the help of rather illegible scribblings on a sheet of paper. At the end of the discussion I took the treasured paper away in the somewhat vain hope of deciphering some of the main points. Of course, G.I. really knew what answers he expected from an investigation by his somewhat unusual physical insight. I had to seek out appropriate mathematics myself and after about 9 months I was almost in despair as I had made absolutely no progress.

Before I actually started postgraduate study in 1934, G.I. sent me to the International Conference of Applied Mechanics which was held on that occasion in Cambridge. I remember being somewhat overawed by the people at the conference and I understood very little of the technical papers. Of course, being a beginner, I thought that I ought to go to every lecture! I read Professor Eric Reissner’s speech in mechanical engineering which was delivered at this gathering last year and I can endorse his remarks about “the memory of my feelings and impressions of insecurity as an early participant in technical meetings”. At the Cambridge conference I saw – at a distance – some of the well-known workers of that era in mechanics including Timoshenko, von Karman, Prandtl, Beizeno, Burgers and H. Reissner, father of Eric Reissner. For some reason I think I remember correctly that H. Reissner lectured on viscous flow between rotating non-concentric circular cylinders.

The lectures in applied mathematics for both undergraduate and graduate students in Cambridge dealt with a wide variety of subjects. It is interesting to note that many of the things we were taught in Geometry, Algebra, Analysis and Mechanics have now disappeared entirely from syllabuses in most universities! In addition to Sydney Goldstein, I attended lectures by W.R. Dean, L.A. Pars (who was my undergraduate supervisor and a superb mathematician), Eddington, Harold Jeffreys and others. I recall one lecturer who wrote very clear books and papers but was very bad at lecturing. He started with a class of ten. Very soon this was reduced to two – myself and a friend. I then dropped out but my friend persisted only to find that the lecturer did not turn up. My friend went up to the lecturer’s room in one of the colleges to find him still in bed. However, he was then given a good set of notes and went away quite content for the rest of the term.

Later when I had a Fellowship at Jesus College, I got to know people in other disciplines. One interesting person is Sir Arthur Quiller Couch – or Q as he was called – who was Professor of English and a writer of distinction. He compiled the Oxford Book of English verse and wrote many stories about Cornwall, and was once the Mayor of Fowey, a village in Cornwall. In those good old days Q would announce in the University Gazette that he would lecture on Wednesdays in this term (February 14 and March 14) – and then he cancelled one of these and hurried back to Fowey.

Another Fellow, Dr. Brittain, acted as chronicler of Q’s activities. He had two clocks in his room, one at the current time and one at God’s time, which in the summer was not the same.

After leaving Cambridge I spent some years in the Durham Colleges in the University of Durham where the department of mathematics consisted of 3 staff and I was expected to lecture on any topic of the undergraduate course in either pure or applied mathematics – something which I could not do today. If present-day staff were required to do the number of lectures per week that we had to do there would be some sort of sit-down strike or walk-out. It was many years before this situation changed. In Durham I had my first research students. One of these students worked on problems of holes in wooden materials and when he obtained his degree a friend sent him a telegram which aptly read “holes in wood wins scarlet hood”.

From Durham I went to the other, and larger, part of the University, which was at Newcastle upon Tyne (now the University of Newcastle upon Tyne) and first met Professor Shield. In those days he always seemed to be an incredibly young student. I followed two well-known applied mathematicians who had been at Newcastle for many years – Professor Havelock of water wave fame and Professor Goldsbrough who worked on tides and problems concerned with Saturn’s rings. Although they retired when I arrived I had the good fortune to know them for many years. As we know, different languages often cause many problems. I remember Havelock, who was a modest and rather shy man, being very pleased when he received a letter which said “Dear Professor Havelock, the odour of your name pervades the world”. This reminds me of a letter I received after the war from a Japanese colleague saying that he regretted the absence of correspondence owing to the prevailing darkness of the abominable days.

I had a charming pure mathematical colleague, Professor Rogosinski who hated any administrative work. He occasionally had language difficulties and after one meeting in which the future of the University was discussed he emerged and said “well, it is all a dream pipe”.
One of the great advantages of working in a scientific subject is that one gets to know many people from all over the world. I have been very fortunate in being able to work with a number of colleagues which I always find much more satisfactory than working entirely alone. It is interesting to find that similar ideas about a topic in science seem to appear in quite different parts of the world simultaneously. Having said this I am reminded that someone in the United States once remarked that no British Applied Mathematician ever believes anything has been discovered unless he re-discovers it himself!

Years ago, partly because of teaching loads in universities, there was little pressure on staff to engage in research or scholarly activity. Although this sometimes led to very dead departments or individuals, it did mean that work could be undertaken without the continual pressure of the need for publication. After the 1939-45 war interest in research in university departments greatly increased and the pressure on staff, particularly younger members, is tremendous – publish or perish has almost become the watchword. I am afraid that this tends to lead to bad standards. I particularly regret that often due recognition is not given to the type of person in a university who is a true scholar but is not one to produce a large number of papers. Such a person, who often had wide knowledge and understanding, can be invaluable in a department but gets left behind in the promotion stakes. The output of scientific papers in every subject is enormous and in recent years there has been a tremendous increase in the number of journals published. It is practically impossible to keep track of every paper in a particular area of interest, let alone in a variety of topics. As a result some duplication of effort is inevitable. Also I guess that only a small fraction of work is ever read in a thorough way.

In closing I may reflect that in mechanics, as well as in other sciences, there are fashions both in the type of work studied and in the way it is presented – the pendulum tends to swing from one extreme to the other. We all suffer from prejudices in our every day life and it is not surprising that this spills over into science. Some regard highly abstract mathematical presentations of work as being divorced from physics while others regard some aspects of physics as mere hand-waving. I believe that there is something of value in the whole range of scientific thought. Of course, intensive discussion and argument with colleagues is sometimes a very profitable – or at least a very enjoyable exercise. On looking back over the history of science one realizes that most of us can only hope to place one small brick – if that – in the edifice – and even that may get knocked out by following generations. The more one learns over the years the more one realizes how little is really known: This is always the challenge to future generations.