Tuesday, February 28, 2006

George Haller: The recipient of the 2005 AMD Young Investigator Award

Professor George Haller, the recipient of the 2005 AMD Young Investigator Award for Special Achievement in Applied Mechanics, is fascinated by unsolved nonlinear problems in mechanics. He strongly believes that many such problems can be solved by taking a fresh approach: applying nonlinear dynamical systems methods. At the same time, he acknowledges that, more often than not, nonlinear techniques need extension before they apply to real-world mechanics problems. Accordingly, Haller’s research has been a combination of physical modeling and mathematical analysis. He has also been committed to the numerical and experimental verification of his results.

Haller has worked on a broad list of mechanical problems, including resonant energy transfer in molecules, micro-scale chaos in robot control, nonlinear stability of gyroscopic systems, and material transport and mixing in geophysical flows. In solving these problems, he made contributions to mathematical areas including chaos near resonance, infinite-dimensional singular perturbation theory, stability of time-dependent invariant sets, and the theory of invariant and inertial manifolds. Of notable impact is Haller's work on Lagrangian Coherent Structures (LCS), which are hidden material structures governing the mixing of tracers in unsteady fluid flows. Haller's LCS techniques have been used in fluid experiments to visualize the intricate structure of chaotic fluid mixing (Fig. 1), and in designing a scheme to reduce coastal pollution in the ocean. Further unexpected applications include understanding \the motion and feeding of a jellyfish, and predicting apoptosis (cell death) in protein networks; both applications are discussed in a recent SIAM News cover article.

Haller is particularly enthusiastic about his current work on cracking the mystery unsteady flow separation, i.e., the detachment of fluid from a no-slip boundary under time-varying flow conditions. Such detachment is the primary reason for aerodynamic losses in a variety of engineering devices, including airfoils, turbines, pipes, and diffusers. In a groundbreaking 1904 paper, L. Prandtl derived a criterion for separation in steady two-dimensional flows. Recently, Haller’s group at MIT succeeded to extend Prandtl’s criterion to unsteady and 3D fluid flows (Fig. 2). This offers an exciting new tool in the analysis of numerical and experimental flow data, as well as in the monitoring and control of separation on air vehicles.

Ju Li Named 2006 MRS Outstanding Young Investigator

Dr. Ju Li, an assistant professor at the Ohio State University, has been named the 2006 Materials Research Society Outstanding Young Investigator. He is cited for “innovative work on the atomistic and first-principles modeling of nanoindentation and ideal strength in revealing the genesis of materials deformation and fracture.” Professor Li will deliver an award acceptance presentation at the 2006 Materials Research Society Spring Meeting to be held during April 17–21 in San Francisco. See details.

Monday, February 27, 2006

Ronald S. Rivlin (1915-2005)

Professor Ronald S. Rivlin, one of the pioneers in modern theory of finite elastic deformation, passed away in last October at his home in Palo Alto, California. He was 90 years old.

Professor Rivlin was born in England in 1915, and he was educated at Cambridge University. He had taught at both Brown University and Lehigh University in the past five decades. Professor Rivlin was a member of the National Academy of Engineering, and he was awarded ASME Timoshenko medal in 1987. (Read more .....)

Sunday, February 26, 2006

1994 Timoshenko Medal Lecture by James R. Rice

Notes of AMR Administrators. Posted today is the text of the lecture by James R. Rice, the 1994 Timoshenko Medalist, presented on 10 November 1994, in Hyatt Regency Chicago. You can also download a biography of Rice prepared by Tze-Jer Chuang and John W. Rudnicki


Timoshenko Medal Lecture
James R. Rice

It is a great pleasure to be here among so many old friends and colleagues, and to thank you for the recognition symbolized by this award. Especially, it is a pleasure to thank my dear friend Alan Needleman for his kind words of introduction.

Any mechanician must consider it a great honor to receive an award named for Timoshenko. Like for many others here, the sight of his classic black-covered books on elasticity and structural mechanics brings back pleasant memories of my earliest involvement in our field. A while ago my interest in the historical origin of ideas in mechanics developed more purposefully, in response being asked to prepare an article on Solid Mechanics for the Encyclopaedia Britannica. That led ultimately to close study of another Timoshenko book, one that I had known before just by browsing acquaintance, namely, his History of Strength of Materials, with a Brief Account of the History of Theory of Elasticity and Theory of Structures. That was published in 1953, when he was 75 years old. The preface revealed that for 25 years before that time, he had been lecturing to students on the history of concepts and ideas in solid mechanics, and on the careers of those from Galileo to his own mentor, Ludwig Prandtl at Göttingen, who shaped the subject into what was then its modern form. One cannot help but understand that Timoshenko cared in a deep cultural sense about his subject and those who shaped it, and that too adds to the pleasure of receiving this award named for him.

Now, what shall I say to you? I didn't suppose it was appropriate to seek guidance from my Harvard colleagues on that, but some advice came unsolicited from John Hutchinson, as chairperson of the Applied Mechanics Division. A few weeks ago he knocked on my office door, walked in, and announced "Remember, your talk is going to be in the Newsletter and we don't have much room, so keep it short". A little research revealed that he gave the same advice, "keep it short", to our friend Bernie Budiansky, when Bernie spoke on this occasion a few years ago, so perhaps John just feels that he already hears quite enough from the two of us.

This is an occasion on which some reminiscences, at least within John's guideline, could be allowed. I'd like to tell you a little bit about what I've experienced, and to draw some conclusions when I can.

It is difficult to reminisce over my own formative years without sensing the sharp contrast with the far more difficult situation faced by the young generation today. My generation, and especially my own narrow age range within that generation, had things easier, I think, than any group before or after. I entered Lehigh for undergraduate studies one year after Sputnik. It was a time when support for science and engineering was enlarging fast, when opportunities were abundant. There were plenty of graduate fellowships. There were also generous loan programs, fully forgivable for those who went into teaching. I had both at Lehigh, where I also stayed for graduate studies. Getting a postdoc position could be accomplished mainly by a few telephone calls. My first faculty appointment came when, in the midst of a first postdoc year at Brown, our chairperson knocked on the office door and asked if I would like to stay the next year as an Assistant Professor. I said yes and that was that. Promotion and tenure processes were not much more complicated.

But that was then, not now. To quote David Goodstein of Caltech, "We are at the beginnings of the end of the exponential expansion era of science [but we are] still trying to maintain a social structure of science (research, education, funding, institutions, and so on) that is based on the unexamined assumption that the future will be just like the past." I need hardly add that the signs of that exponential expansion of people, not matched by the same growth of resources and opportunities, are everywhere. That makes it incredibly more difficult today for young people, and also for many members of older generations who have had to face job loss or sharply reduced prospects.

I would like to give you some predictions of what more specific difficulties the future will bring, and of how our community should contend with them, but that inclination has to be tempered by another quote, one that I've heard attributed to Neils Bohr: "Prediction is very difficult, especially of the future." So instead I'll return to some reminiscences, although maybe the difficulty of prediction of things other than the future, to which Bohr alluded, makes that an uncertain venture too.

Undergraduate years: Ferdinand Beer at Lehigh had assembled an advanced and challenging program in mechanics for theoretically inclined undergraduates. He had the good sense to know that some independent minded students could be recruited by relaxing the incredibly rigid course requirements common in engineering programs of that day. John Hutchinson had been such a recruit to Ferd's program a couple years before me. Ferd had the help of some talented people, including a cluster of bright young faculty members then beginning their careers: Fazil Erdogan, George Sih, Gerry Smith, and Paul Paris. All of them made their mark in mechanics, and I was fortunate to have them all as teachers. They were good at it and great role models. I was to have a lot of fruitful interaction with Paul Paris, as did John Hutchinson too, in subsequent years in work on nonlinear crack mechanics.

Staying at Lehigh for graduate school was against the advice of my teachers, who knew that the place was hardly on the map in our field at that time (it became a lot more prominent after I left!). But Paris had returned from summers at Boeing with faith that there was something to be done on fracture and fatigue, using the stress analysis of cracks that George Irwin at the Naval Research Laboratory had been pushing, and he had already recruited Sih and Erdogan to the effort. What none of us understood is that we were, essentially, getting on at the ground floor, as this previously neglected area of fracture mechanics began its rapid and, we hope, effective rise towards its modern form.

This has always puzzled me: How do you recognize what topics will grow and blossom, and how do you figure out when, instead, you are committing yourself (and your precious students) to topics on which, at best, only small incremental additions can be made? That latter category inevitably includes most of the presently established, recognized areas within a field. The choice is not so easy at the time as it seems in retrospect. The established, or sanctioned, areas of study always attract lots of bright people, excited by the once-new discoveries that launched the area, and when the star of an area has risen, you do not find it difficult to explain to others why you are joining that area too. I was certainly not sure myself that this new area of fracture mechanics was a star that was going to rise. So while I worked with enthusiasm, even starting as an undergraduate student, on models for interfacial cracks and for plastic effects in fatigue crack growth, that was a hobby. I played it safe as regards what was going to be my Ph. D. thesis topic, and did that in the respectable field of stochastic processes. Well, no one references the work based on my thesis.

Ferdinand Beer pushed me out of Lehigh while I was still quite wet behind the ears. He felt that I had sampled what they had to offer, and called me into his office one day to hint that there would be no impediments to quickly wrapping up my thesis if I could get a postdoc at a place he recommended. His list was short: Brown or Harvard. I said that I had heard great things about Brown from some of my instructors, so I would like to go there, and he worked to see that a postdoctoral fellowship was soon arranged. That was a lot easier then than now, but we should all take Ferd's interest in his students as a model for how we should be looking after our own.

Brown was a great experience. True, when I arrived there in fall of 1964, some distinguished figures were packing their bags to go elsewhere and some were already gone. One was Bill Prager although, happily, he came back to finish his active career there before retiring to Switzerland; another was Eli Sternberg, and I had the pleasure of spending a little time with him on a sabbatical at Caltech in 1988 before his tragic death. But the talent still at Brown was deep. Dan Drucker was my postdoctoral host and mentor, and there was a marvelous group of mechanicians still in residence. Sadly, the last few years have not been kind to that group; of them, death has now claimed my friends Jacques Duffy, Joe Kestin, Harry Kolsky and Jack Pipkin. Also, on arrival in 1964, I found Brown awash with interesting visitors. Rod Clifton was just arriving to the faculty and over the years I was also to enjoy friendships and sometimes collaborations with such newcomers as Pedro Marcal, Ron Armstrong, Ben Freund, Jerry Weiner, Alan Needleman, Constantine Dafermos and Bob Asaro. So Brown managed to renew itself and stay in a leading position despite that exodus, and they certainly survived in good style my own exodus to a neighboring city in 1981, one that Constantine suggested, with a wink, might improve both institutions involved!

I learned much from Dan Drucker. We worked together on how to calculate energy changes of solids due to cracking or removal of material, a problem on which I had some results for the linear elastic case in some notes done at Lehigh. Dan opened my eyes on the importance of generalizing, of figuring out the widest class of materials and circumstances for which some theorem or procedure might be true. That lesson was put to good use in a short time, when the path-independent integral of crack theory was to emerge as I tried to generalize a formula for the energy release rate in crack growth that I had derived for a particular nonlinear elastic material, one whose stress-strain relation mocked ideally plastic response. That integral was discovered independently around the same time by Genady Cherepanov of Moscow, and both of us were soon to learn that, while it had apparently not occurred to him to apply it to cracks, the integral had been developed much earlier by Jock Eshelby of England as a way of calculating forces on heterogeneities and dislocations. We all could have profited, as Jim Knowles and Sternberg later pointed out, by having learned about what Emmy Nöether did in 1919, on associating conservation integrals, like the J integral, with variational principles. Budiansky and I were able to link the new conservation integrals emerging in that way to energy release rates.

Fracture mechanics turned out to be a major catalyst in bringing about the modern union of mechanics with materials science and engineering. The signs of the health of that marriage are evident in several of the AMD sessions I've been to at this conference. I think it must be difficult for modern students to understand the remarkable isolation that existed, at least in the USA, between people in materials, which was mostly called metallurgy then, and people in mechanics. The mainstream opinion in both camps seemed to be that they had nothing to learn from one another. Drucker wanted to change that. I was fortunate to have many contacts also in my early years with Frank McClintock, who was nearby at MIT, and he thought that isolation a scandal. I was happy to sign on as foot soldier to their cause, but the task turned out to be an easy one because, despite mainstream opinion, many willing hands were to be extended from the materials community. My work on elastic-plastic fracture in relation to microscale ductile void growth processes was in furtherance of a program for which McClintock had laid the general outlines, and I had many other fruitful collaborations and contacts with people in materials science and metallurgy. Especially that includes Robb Thomson, and more recently Ali Argon, on atomic and dislocation-scale processes at crack tips, John Knott on microscopic mechanisms of cleavage fracture in steels, Bob Asaro on plastic flow localization, and some others that I'll mention shortly. A lesson I would draw here: We must ask where are there unnatural, unproductive separations between mechanics and other sciences or technologies, and what can be done to close them. Perhaps some current examples can be found.

Joseph Kestin at Brown engaged me, as a willing pupil, on thermodynamics, to which he insisted that all phenomena must march, and that we only had to figure out how to express that fact. That led me to concentrate more fully on some studies I had already begun, on how to relate inelastic deformation in solids to dislocation motion on the microscale. It was soon clear that it was simplest to think of dislocations, and other types of structural rearrangements, as corresponding to a thermodynamicist's internal variables, and that proved a useful route to formulating plastic flow at large strain and identifying general features of viscoplastic constitutive laws. I later worked with Rodney Hill on that area, during a sabbatical at Cambridge in 1971-72. Thermodynamic thinking proved extremely useful as I ventured more into materials science, and helped me address such topics as the embrittlement of material interfaces by solutes and mobile segregants like hydrogen, and diffusive processes of matter transport that are important for high temperature failure of materials. On those topics, I also had collaboration, or at least intense discussion, with some gifted materials scientists, including John Hirth, Mike Ashby, Greg Olson and Tony Evans. Further, the thermodynamic style of approaching problems, especially of making use of what we call reciprocity concepts in elasticity, stood me well in many other studies; they include figuring out the effects of shear faulting on the Earth's inertia tensor and gravity field, formulating what is called weight function theory in elastic crack mechanics, working out dislocation interactions with cracks and with one another, and figuring out ways of calculating J-integrals and energy release rates.

Pedro Marcal opened my eyes to computational mechanics, especially the finite element variety, and we directed students on applications to crack analysis and worried about how to deal with large plastic deformations. Alan Needleman was developing the same expertise as an outgrowth of his thesis work with John Hutchinson at Harvard, and we happily collaborated upon Alan's arrival at Brown, especially on a new class of problems of combined diffusion and plastic creep. Mostly, though, I just sit back and marvel at the computational challenges that Alan and some of his colleagues have mastered in describing flow and fracture phenomena.

Unbelievable as it may seem today, computational mechanics was an area viewed with suspicion, and even some disparagement, by many members of our community. Perhaps our reaction to the new has often been too hesitant. To be sure, we need to be discriminating, and nothing disturbs so much as those who jump on every passing bandwagon. But I think that we can draw a lesson on the importance of recognizing that the things worth doing in mechanics are not embedded in a rigid legacy. A healthy field is organic and fluid, always anxious to examine the new, to nurture it as needed, and absorb what has value.

Now, some words about those who have really done much of the work I've been talking about: I've been blessed when it comes to the gifted young coworkers that I've had as graduate students and postdocs. There was a marvelous group from my years at Brown. They have already made their individual marks, whether on computational methodology, fracture mechanics, materials engineering, rock mechanics, or earthquake processes, and are a great source of pride for me. There is a growing group from the Harvard years who will, I hope, be able to live up to that good example and, indeed, some have done so already. I am extremely happy to see many of them here tonight, and hope it will be alright to ask them to stand so that we can acknowledge them.

For most of the last 20 years I have been dividing my time between such materials themes as I've mentioned and problems on the mechanics of earthquakes. That earthquake interest began rather indirectly, through a collaboration with Andrew Palmer of Cambridge to study landslides in heavily consolidated clay soils, a problem for which it looked like concepts from fracture mechanics could play a role because the slip-rupture surface in such slope failures seems to slowly propagate up-slope like a thin shear crack. We soon were wondering what controlled the speed of propagation and, since soils in such conditions are inevitably water saturated, at least in England where we worked (that too was on sabbatical at Cambridge), interactions between the deforming material and the pressurization and transport of pore fluid was something that naturally came to our attention. Well, at about that same time, geophysicists working on earthquakes had become convinced that interactions between fluids and fault rocks, dilating as they failed, might be important in generating possible precursors to earthquakes. The commonality of the mechanisms under consideration was sufficiently tempting that I was soon heavily into those issues for earthquakes too, and that also was the start of a series of works I did on the mechanics of coupled deformation and diffusion processes in porous solids. Further, that interest in slip surfaces and faults, especially asking from where do they come, was the start of my studies on the localization of deformation into shear zones.

It turned out in light of better data and analysis over the next few years that the idea of dilatancy as a source of earthquake precursors faded. But there is still widespread interest in the interaction of fluids in fault zones, especially in connection with understanding the apparently low strength of some major faults, and that is a major theme in my present work. Here is another thing in which my students and coworkers in that area are now involved: We know that earthquakes are complex events in nearly every sense, including their irregular slip distributions in single events, magnitude distributions, spatial location patterns, and recurrences in time. We want to explain what we can of the origin of this complexity, and to use the statistics of seismicity and recent earthquake history, and crustal deformation measurements where available, together with physical modeling to assign risks of future events. There is now an active controversy over how much of seismic complexity is explainable from nonlinear dynamics acting on a smooth fault, and how much requires the observation that the array of faults on which earthquakes occur forms a complex fractal-like network.

Such issues for seismicity, and also complexity, self-organization and patterning in all manner of mechanical deformation and fracture processes, are topics which have also attracted many people from condensed matter physics in recent years. A definite movement that we see is that solid mechanics is becoming part of the agenda for many people whose field affiliation is physics; we can see signs of that too in some of the sessions at this conference. Such has long been the case for the fluid mechanics side of our house; the APS is a principal sponsor of activity there. Some of that is now happening in solid mechanics under the banner of materials physics in APS, accompanied with wide-ranging, one could even say uninhibited, symposium themes like "Slips, cracks and tears", and "Avalanches, fracture and related instabilities". We thus have an opportunity to make contact with a large theoretical and experimental community. To be sure, their level of education in continuum and fracture mechanics concepts is generally quite limited, so there will be much to learn from us, but so also do they have much to offer, in ways of understanding complexity, in novel theoretical approaches and experimental techniques, and in having a broad and fundamental agenda. So this should be good for all involved.

Well, I've tried to tell you something of my experience and sometimes to draw a lesson. Thank you for your patience in listening, although I must certainly have over-passed the length John wanted. Thank you once again for this honor, it being so much the nicer to receive it in this setting among so many friends and colleagues.

Wednesday, February 22, 2006

The Magic Island Heights: Quantum Size Effect in Thin Films

A group of scientists from France, Japan, and the United States have recently discovered a unique quantum size effect in thin films: the formation of a so-called ``Magic Island'' in the middle of a quasicrystalline substrate, whose growth can be controlled electronically. (Read more .......).

Monday, February 20, 2006

Size Effect on Probability Distribution of Structural Strength

By Zdenék P. Bažant

Recently we have demonstrated the need for a fundamental revision of reliability concepts and design codes for quasibrittle heterogeneous structures, such as concrete structures failing due to concrete fracture or crushing (rather than reinforcement yielding), or large load-bearing fiber-composite structures for ships or aircraft, sea ice plates, etc. While ductile failure occurs simultaneously along the failure surface and is characterized by absence of size effect and Gaussian distribution of structural strength, quasibrittle failures propagates, exhibits a strong size effect and follows at large sizes extreme value statistics of weakest-link model, which leads to Weibull distribution of structural strength (provided that failure occurs at macro-crack initiation). Based on small- and large-size asymptotic properties recently deduced from cohesive crack model and nonlocal Weibull theory, the transition of cumulative probability distribution function (cdf) of structural strength from small to large sizes is modeled by a chain of fiber bundles, in which each fiber with Weibull type tail of strength probability corresponds to one dominant micro-bond within a representative volume element (RVE) in a brittle lower-scale microstructure. The cdf of each fiber (or micro-bond) properties can be deduced from Maxwell-Boltzmann distribution of the atomic thermal energies, which brings about the rescaling of cdf according to temperature, load duration and moisture content. A fascinating by-product of the analysis, with physical implications, is that the Weibull modulus is equal to the number of dominant (simultaneously failing) micro-bonds in an RVE. The structural strength distribution is based on chain-of-bundles model, for which a composite cdf with a Weibull tail grafted on a Gaussian core is proposed. For the smallsize limit, the core is totally Gaussian, and for the large-size limit totally Weibull. In between, the grafting point moves right as the Gaussian core shrinks with increasing size. This causes that the distance from the mean to a point of tolerable failure probability (such as 0.00000001) nearly doubles as the size of quasibrittle structure increases. Consequently, the understrength factor in design codes must be made size dependent. So must the Cornell and Hasofer-Lind reliability indices. Their reformulation (implying replacement of FORM with ‘EVRM’) is proposed. Inseparable from these effects are further problems due to ‘covert’ understrength factors implied in brittle failure provisions of concrete design codes, as well as an irrational hidden size effect implied by excessive load factor for self weight acting alone. To improve design safety and efficiency, experts in statistical reliability and fracture mechanics will need to collaborate to tackle these problems comprehensively. (Read more …)

Tungsten Sulphide Nanotubes Reach Their Theoretical Strength

In general, materials cannot reach their theoretical strength because of the presence of defects. How about defect-free nanotubes? In a paper in PNAS, researchers at the Weizmann Institute of Science, Israel, and the Technical University of Dresden in Germany have performed both tensile and bulking experiments on individual tungsten sulphide nanotubes and found out that the tungsten sulphide nanotubes are as strong as theory predicts for materials without defects. The tubes exhibit a tensile strength close to 16 GPa. This finding may stimulate the applied mechanics community to explore the beauty of nanotubes and other nanomaterials from both experimental and theoretical approaches.

New lithography keeps Moore's law on pace

A new photolithographic technology will create semiconductors with wires thinner than 30 nanometers, one-third the width in today's industry-standard chips, acoording to today's New York Times.

The new technology, known as immersion lithography, replaces the air gap between the optics and the wafer surface with a liquid, increasing resolution and depth of focus. Some of the materials issues have been discussed by scientists at IBM and JSR Micro.

Saturday, February 18, 2006

Large plastic deformation of carbon nanotubes

At temperatures about 2000C, a single-walled carbon nanotube can undergo plastic deformation, becoming 280% longer before breaking, reported by a team of scientists of Boston College, Massachusetts Institute of Technology, and Lawrence Livermore National Laboratory [Nature 439, 281 (2006)]. In situ transmission electron microscope has shown that the large plastic deformation results from motion of kinks in the nanotube.

Thursday, February 16, 2006

A Multiscale Model for Cancer

A team of scientists from Los Alamos National Laboratory, University of Tennessee, and Massachusetts Institute of Technology have proposed a multiscale model to simulate avascular tumor growth. Most previous turmor growth models are based on the reaction-diffusion equations.

Wednesday, February 15, 2006

Breakthrough in Understanding of Heat Dissipation in Carbon Nanotubes

A team at University of Illinois at Urbana-Champaign has made a theoretical breakthrough in understanding how energy dissipates in a nanotube and what causes thermal breakdown in metallic carbon nanotubes [Phy. Rev. Lett., 95, 266803 (2005)]. Their discovery may help move electronic devices made by nanotubes from laboratory to markeplace. Read more.

Tuesday, February 14, 2006

Current Status in Biomaterials Research

If you are interested in learninging what is going on in Biomaterials these days, I highly recommend two articles recently published in the MRS Bulletin. The article by Prof. George Whitesides of Harvard University provided a broad picture on the history and future of Materials and Biomaterials. The main point was that a materials researcher should knock at the doors of the medical doctors and ask for problems (to solve) and collaboration. The other article by Prof. Samuel Stupp et al at Northwestern University was more technical and was oriented towards both Biomedical Materials and Bio-inspired Materials. He listed many natural examples from the Gecko's feet to lotus leaves. What I found most interesting in his research was the peptide amphiphile fibers he has been working on for years. I didn't think it would go any where (in terms of applications) a few years ago, but now it seems to be one of the most successful examples in materials design.

These papers covered the chemistry and biology parts of biomaterials. Mechanics was not inlcuded partly due to their background and partly due to the slow progress in the Mechanics of Biomaterials . But with your spirit in mechanics, I am sure you will sense many mechanics issues there (e.g. how does a hip fracture? how does a bone deform? When replacing a tissue, does the biomaterial need to have the same mechanical properties as the tissue, as many claim?).

References:
1. Expanding Frontiers in Biomaterials, Samuel I. Stupp, Jack J.J.M. Donners, Liang-shi Li, and Alvaro Mata, MRS BULLETIN • VOLUME 30 • NOVEMBER 2005, 864-873.
2. The Intersection of Biology and Materials Science, George M.Whitesides and Amy P.Wong, MRS BULLETIN • VOLUME 31 • JANUARY 2006, 19-27.

2005 Timoshenko Medal Lecture By Grigory I. Barenblatt

Applied Mechanics: an age old science perpetually in rebirth

By Grigory I. Barenblatt

Mr. Chairman, Colleagues, Ladies an Gentlemen:
I want to express my gratitude to the Executive Committee of the Applied Mechanics Division of the American Society of Mechanical Engineers for nominating me for the Timoshenko Medal, and to the Board of Governors for awarding me the Medal on behalf of ASME.

The personality and name of Stepan Prokofievich Timoshenko (Stephen P. Timoshenko as he is called in this country) is very special for me. When I was a beginning student at Moscow High Technical School, where I studied before entering the Mathematics Department at Moscow State University. I purchased his book “The theory of elasticity”: in fact, this was the first technical book in my personal library. The clarity and depth of the presentation of this difficult subject wits then and remains now for me an unsurpassed standard. Something in this book astonished me, and I addressed a question to my maternal grandfather, an eminent Professor of Differential Geometry at Moscow State University. (I was raised by his family after my mother, one of the first virologists, perished preparing a vaccine against encephalitis.) The question wits: the author is definitely a Russian (at that time in our circles nobody noticed the difference between Russians, Byelorussians, and Ukrainians). Why did his book appear in translation from English? Grandfather explained - Timoshenko emigrated after the Revolution (such people were unpopular in the Soviet Union in the late forties) - however, with a kind smile he took from his library and presented me with Timoshenko’s course on elasticity in two volumes, published in Russian in 1914 and 1916 by the Sanct Petersburg Institute of Railways Transportation, and presented to him by the author. SP got the chair at this Institute after some period of unemployment: before that he was Dean at Kiev Polytechnic Institute and was fired by the Minister of Education for substantial exceeding the number of admitted Jewish students allowed by explicitly formulated (this was important) norms. Visiting my family in Moscow last summer after learning about the award, I wanted to bring these volumes to this country, but I was warned that strict rules concerning old books would not allow it. When I already was a young scientist, I was introduced to SP during his visit to Moscow. Also, I was proud when I had seen that SP and James P. Goodier mentioned my work concerning fracture in their book.

Much later when, by the initiative of Joseph B. Keller and Milton D. Van Dyke, Dean Thomas Hughes nominated me for the Timoshenko Professorship at Stanford University I spent many happy hours working in the Timoshenko Room at the Durand Applied Mechanics Building where there is exhibited a remarkable portrait of Stepan Prokofievich. I am deeply grateful to all of them for granting me this unique experience. My collaboration with my eminent colleague and now close friend Alexandre J. Chorin started shortly before that at Berkeley and continues to this day. Alexandre visited me for working together at Stanford; therefore in one of our joint works my affiliation is Stanford University.

Mechanical Engineering and Applied Mechanics, as its part, are among the first and greatest intellectual achievements of mankind. The names of Archimedes and Galileo are known to everybody. I am sad to say that nowadays these disciplines are not popular among bright young people choosing their career. And this tendency is not a new one: it started rather long ago, apparently in the twenties. As you know, G.I. Taylor, one of the first winners of the Timoshenko Medal, worked all his life at Cavendish Physical Laboratory in Cambridge. J .J. Thompson, Lord Ernest Rutherford, Sir Lawrence Bragg, great men of science, all of them Nobel Prize winners, were the Directors of the Cavendish Laboratory during G.I.’s time. According to E.N. da C. Andrade, brilliant physicists at Cavendish who created at these times pioneering works, such as ‘smashing’ the atom, discovering X-ray radiation coming from stars, researching the structure of hemoglobine and mioglobine and, finally founding the double spiral, expressed their astonishment at how such a brilliant person as G.I. Taylor could spend his life dealing with such dull and old stuff as applied mechanics. I want to give a definitive answer. Yes, mechanical engineering and applied mechanics are old art and science. But they are also young because they are eternal art and science. It is very sad that the attitude towards mechanical engineering and applied mechanics as something of secondary interest entered the consciousness of a large and influential part of society, and this attitude cannot leave their children - future students - unaffected.

Allow me another instructive example. Years ago when I had to renew my American visa, I visited the American Consulate in Rome. Strong letters in support of my application preceded my visit to the Consulate, and I was told that the American Consul decided to process my application personally - a rare distinction. So, I was escorted to the Consul immediately and I was shocked: the Consul happened to be a rare beauty in her flourishing age: blue eyes, luxurious black hair, a truly unforgettable impression ... She understood that I was impressed, and she waited a little in asking ordinary questions, and did her job. When only a small, purely technical part of the job remained, she asked her secretary to do it, and said: ”Professor, now we have 5-10 minutes. Could you tell me what you have done in your science to deserve such letters of support?” At that time our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and myself) were working intensively on investigating the scaling laws for turbulent flows in pipes and other shear flows. We came to the conclusion that the fundamental universal logarithmic law which was in use for several decades is not quite correct, and should be abandoned and replaced by a different Reynolds- number-dependent scaling law. I have to admit that many people at that time, and some of them up to now, consider our results as controversial. However, the formulae and all available experiments definitely speak in our favor. I remind you that many similar situations have occurred in the history of science, and not only in science. For instance, when an essay of Maurice Maeterlinck, who won the Nobel Prize for his ‘Blue Bird’, was included in the Index Prohibitorum by the Catholic Church, Maeterlinck wrote “At every crossing the road that leads to the future, each progressive spirit is opposed by a thousand men appointed to guard the past.” In our case, these men can also be understood: if we are right, text-books and lecture courses should be changed and you have to bear in mind that the universal logarithmic law is taught every year in a thousand universities and polytechnic institutes. We continued to defend the truth in our seminars, lectures and publications. I had no choice: my great mentor Andrey Nikolaevich Kolmogorov, whose name is known to everybody in this audience, said: “I have lived being guided by a principle that the truth is a blessing, and our duty is to find it and to guard it.”

I return to the unforgettably charming lady Consul. I decided: obviously the elegant lady who starts and finishes her days by using the flow in pipes should be interested in such work. And I did my best to present our results in the short time given to me. The Beauty - Consul - looked at me (with her wonderful dark blue eyes!) and said: “Professor, of course, what you said is interesting, even exciting. However, frankly speaking, I am astonished. When we have someproblems with pipes, we address a plumber, not a professor with a world-wide reputation!” I was ashamed, and up to now I have a feeling of personal guilt. Indeed, now we know the structure of remote stars better than the strength of a shuttle or a dam and contrary to astronomers and astrophysicists how little we do to explain in particular to younger generations the fundamental depth and beauty of our profession and to popularize it.

Money is not yet wealth. And the leading nations of the XXI century will not necessarily be the countries having more money than others. These will be the nations where great national and global problems will be understood and appreciated by the majority of their populations. The heroes of these nations will be engineers and scientists of great vision and ability to select and explain the problems of primary importance, and to achieve the support, governmental and private, necessary to solve these problems, leading to engineering achievements that bless society.

Such engineers and scientists of great vision and organizing abilities do exist; they are among us. In due time and favorable circumstances they appear and make steps of historic importance. It is enough to remember here John Rockefeller, Thomas Aha Edison, Henry Ford, Robert Oppenheimer, Howard Hughes, and more recently W.R. Hewlett, D. Packard, and William Gates.

A remarkable example, less known, is Leo Szillard, an American physicist of Hungarian origin. It was he who recognized the practical necessity of designing the atomic bomb. He prepared the text of the letter to President Franklin D. Roosevelt, where the crucial importance of immediately starting work on the construction of the atomic bomb was emphasized in strong terms. This text was signed (not very enthusiastically) by Albert Einstein. Roosevelt decided todecline Einstein’s proposal (it is difficult to believe now, but it is possible to understand FDR: the country at that time had to carry the tremendous burden related to supplying the American Army and Allies by ordinary weapons and ammunition). When Szillard learned about the negative decision in preparation, he found a personal friend of FDR, explained to him the problem, its importance and urgency, and persuaded him to interfere. The friend visited FDR, and after dinner asked him only one question: “Frank, do you think, if in 1812 Napoleon had not turned down Fulton, the inventor of the steamer, the world map would be nowadays the same?” And FDR gave the order to start the work. The scale and value of this work - the Manhattan Project - is well known.

However, the common opinion of the layman, even scientific and engineering laymen, is that nowadays there are no such problems of the scale of the Manhattan Project whose importance for the nation and the world is understood by everybody. This is deeply wrong! Such problems do exist, and they can be understood by everybody. First of all, among these problems are large-scale natural disasters, and energy problems. I will present several examples.Tropical hurricanes. The scales of these disasters are huge, and the morale and material losses are formidable. I want to emphasize here that in fact hurricanes present a fascinating problem of applied mechanics. And, in general, Sir James Lighthill, one of the first winners of the Timoshenko Medal, considered natural disasters, in particular, hurricanes, as problems of first importance for applied mathematics and mechanics.

As far as hurricanes are concerned, the situation is as follows. As a preliminary note, I want to mention a simple calculation, by which A.N. Kolmogorov started his course on turbulence at Moscow State. He asked the listeners: What will the velocity be at the surface of the river Volga in Russia (close by its parameters to the Mississippi in this country) if by some miracle it becomes laminar ? The answer was striking: hundreds of thousands of miles per hour! Why then is it kept so slow ? The reason is that the flow is turbulent: it is stuffed with turbulent vortices, and these vortices play the role of brakes, slowing the flows. An analogy: moving along mountain slopes, drivers use chains to cover the wheels - the vortices play the role of such chains.

Sir James Lighthill proposed, on the basis of many observations, a “sandwich model” of hurricanes. According to this model in the ocean during a hurricane there exist three layers: air, sea, and “ocean spray” between them, where “the third fluid” is contained; in fact, air suspension of droplets, sometimes sufficiently large, tens of microns in diameter.

Our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and myself) considered, under some natural assumptions, turbulent flow of ocean spray. The general theory of turbulent flows carrying heavy particles, developed earlier by A.N. Kolmogorov and myself, at that time his graduate student, was used in this consideration. It happened that the droplets reduce turbulence intensity, because turbulent vortices spend a significant part of their energy for suspension of droplets. Returning to the analogy with wheel chains - the chains that are worn out become weaker. The flow accelerates under the same pressure drop. Our calculations showed that this acceleration can be very large, reaching velocities of large tropical hurricanes.

I note that the same mechanism of acceleration of turbulent flows by heavy particles was noticed earlier in the great Chinese rivers Yangtze and the Yellow River, carrying a large amount of sediment, and in dust storms, both terrestrial and Martian. And the basic question arises: is it possible to prevent, or at least reduce the strength of tropical hurricanes? Our answer is affirmative, but it requires the serious large scale work of the mechanical community. The technical problem is to suppress the formation of droplets. In principle it can be done by pouring oil on the surface of the sea. By the way, such practice is known from ancient times when on the decks of vessels several barrels of oil were reliably strengthened, and in critical circumstances the oil was poured overboard. It was noticed that the intensity of the squall was quickly reduced. There exist several attempts to explain this phenomenon, but according to our viewpoint the basic effect is the suppressing of the formation of droplets. By the way, up to now the recommendations for sailors on small boats to pour oil are routinely proposed in the literature. Of course, the oil (or some detergents which also are recommended for using under such circumstances) should be safe. There are several candidates for such materials. And I repeat - a group of enthusiasts headed by young, energetic leaders can solve this problem and do it in real time - the witches like the recent Katrina should never threaten New Orleans andother remarkable cities.

Our paper was published in PNAS a month before Katrina, and it attracted the attention of PR. I was interviewed by TV - after a preliminary make up - and when the lady, senior in the team, was asked by someone who was present, when this interview would be aired, the answer was instructive: “We have to wait for a good hurricane, then more people will pay attention.’’

The problem of forest fires, also very sensitive for the world (remember, e.g., Portugal this summer), bears some similarity to hurricanes. During a forest fire a dark layer is formed above the trees where the debris and soot are moving. They suppress turbulence in the same way as droplets in ocean spray: that is apparently the reason for strong winds and even firestorms.

Another very important matter. I think that an honest analysis, deeply based on scientific consideration of natural and technogenic disasters can be not less but very often more exciting and important than great projects like Manhattan and all these cosmology and particle acceleration enterprises. There is a difference. Money, and even Big Money, cannot prevent such analysis. But Very Big Money plus politics can do it, and in these cases a chain reaction of disasters started. An example: “Titanic”. In 1913 fundamental engineering and scientific analysis of this disaster was not performed; only much later it was understood what had happened there - the temperature was lower than the temperature of the steel embrittlement, and the vessel’s body became brittle. Twenty-seven years later: 24 May 1941 at 5:52 a.m. the HMS battle-cruiser “Hood”, the flagship of the fleet chasing the German battleship “Bismarck” made a first volley. “Bismarck” answered by a shot of a small antiaircraft gun. And at 6:00 a.m. “Hood” sank; fifteen hundred people perished, only four were saved! (The steel was supplied by the same firm as for the “Titanic” .) Thinking about this case I was astonished: 24 May, spring - it should not be cold! But read Volume I11 of Churchill’s “The Second World War” - 24 May was an extremely cold day at the place.. .clearly the temperature of embrittlement again was crossed. And again: no competent engineering and scientific analysis! Only later when the welded “Liberty” ships started to break in two halves in the North Sea (tens of thousands of people perished), such analysis was performed, and Fracture Mechanics was created. George Irwin, later a Timoshenko Medal winner, was the leader. I also participated in this work. Fracture Mechanics is now as a charming lady in her forties: a remarkable past and a lot in the future. A wonderful branch of mechanical engineering and applied mechanics! Each fracture surface can tell you a lot about both the material and the loading: those who are really interested in what happened can achieve it (of course, only if they will be allowed to obtain the fractographs!)!

I want to tell you about one more field, fully deserving the attention of mechanical engineers, and able to create a first class large scale project. Nowadays when the price of gas reliably crossed the $3/gallon line the problems of energy resources is of interest to every layman. The time when I got my Ph.D. degree was difficult for people of my ethnical origin, and after many attempts I got an offer from the Institute of Petroleum of the Academy of Sciences. I was very lucky to get this job, and since that time Petroleum Engineering is also my profession. It is very important practically - this is trivial to say. But I want to emphasize that it is remarkable as an object of applied mechanics. Many ideas which reveal themselves in such fields as gas dynamics, boundary layer theory, etc., as vague models appear in petroleum engineering as exact mathematical formulations - it is an enjoyment to deal with them. What is most important - every new oil and gas deposit presents a new scientific problem, very often leading to good mathematics. The practical problem of highest importance is to enhance oil recovery. Now the legal figure is 30 percent, so it is considered as normal if we leave in the rocks 70 percent of an irrecoverable gift of nature. But take the deposits of Southern California: Lost Hills, Bellridge. The oil there lies in diatomites: rocks of very high porosity, low strength and practically zero permeability. The exploitation of such deposits by ordinary methods, including ordinary hydraulic fracture, leads to huge losses. The oil recovery is low. To find the proper way of development of such deposits means a reliable way to reduce the energy crisis. It cannot be done without the active participation of mechanical engineering and applied mechanics - what I am saying is based on my old and recent experience. The same is true for huge gas deposits inso-called tight sands available in this country - recently I presented a lecture about this subject.

Ladies and gentlemen, colleagues, I come to my conclusion. Sir Winston Churchill, the greatest man of the last century said: “If the human race wishes to have a prolonged and indefinite period of material prosperity, they have only got to behave in a peaceful and helpful way towards one another, and science will do for them all that they wish and more than they can dream. “Nothing is final. Change is unceasing and it is likely that mankind has a lot more to learn before it comes to its journey’s end.. . .” I want to finish my speech by saying that in this future development of mankind our field, mechanical engineering and applied mechanics will play a decisive and governing role. Many fields of science and engineering will appear, become fashionable and disappear, but our branch of activity will always shine because it is eternal and perpetually renewing.

Sunday, February 12, 2006

Fluid droplets could replace plastic lenses in cell-phone cameras

Plastic lens in most camera phones may be replaced with a drop of liquid, such as water, that could be auto-focused by varying the amount of pressure applied to the drop. Such a lens has no moving parts, making it rugged, and it uses only minimal electricity, so it would not drain a cell-phone battery. Additionally, the optical properties of liquids can be better than standard lens material. Read more...

Saturday, February 11, 2006

To discover the sublime in the mundane

L. Mahadevan, the winner of the 2005 Young Investigator Award for Special Achievement in Applied Mechanics, is interested in the mathematical and experimental exploration of the nonlinear and non-equilibrium mechanical behavior of living and nonliving matter in all its forms. For inspiration he looks to the natural world on our scale (with occasional outside forays) to connect everyday experiences of the mundane to quantitative experiments and analysis. He uses a variety of mathematical tools ranging from scaling analyses and geometrical methods to computations, and has a small (but growing) laboratory for tinkering with simple table top experiments.

Specific topics of current interest include the geometry, mechanics and physics of low-dimensional systems such as interfaces, filaments and membranes, and multiscale integrative physiology of biological systems, ranging from macromolecular assemblies through cells and tissues to whole organisms, with a focus on the physical limits and design principles behind biological function viewed comparatively.

A joy of Mahadevan’s work is "to discover the sublime in the mundane". He uncovers explanations of everyday phenomena that are easy to observe, often not so well understood, and are of relevance far beyond what might be first envisaged. His approach to science has been covered by National Public Radio, The New York Times, The Guardian (London), The Daily Telegraph (London), Le Monde (Paris), Die Zeit (Berlin), National Geographic etc. Here is an
article about him in Harvard Gazette.

Friday, February 10, 2006

Swimming in Circles: Motion of Bacteria near Solid Boundaries

Eric Lauga (now at MIT), W. R. Diluzio, G. M. Whitesides, and H. A. Stone of Harvard University published a very interesting paper, in which they demonstrated by using a fluid mechanics model that a bacteria, Esherichia coli, swims in circular trajectories when near solid boundaries,

``Swimming in Circles: Motion of Bacteria near Solid Boundaries,'' By E. Lauga et al, Biophysical Journal, 90:400-412 (2006).

Tuesday, February 07, 2006

Controlling the Thermal Stability of Thin Films by Interfacial Engineering

A research group led by Prof. Tai-Chang Chiang of the University of Illinois at Urbana-Champaign has found a novel technique to effectively control thermal stability of thin films by using different and selective interfactants.

Their research results have been published in a recent issue of Physical Review Letters,

``Controlling the Thermal Stability of Thin Films by Interfacial Engineering,''
by D. A. Ricci, T. Miller, and T.-C. Chiang, Physical Review Letters, 95, 266101, (2005)

This research has attracted a lot of attention in the thin film community. One may find the related news report on lighsources.org.

Saturday, February 04, 2006

Crack Path Prediction in Anisotropic Brittle Materials

Dr. V. Hakim and Dr. A. Karma of Ecole Normale Superieure, Paris, France, worked out a crack path prediction formula by utilizing a generalized energy-momentum tensor whose integral along an arbitrary closed path around crack tip yields all forces acting on the crack, including Eshelby's configurational forces, cohesive forces, and dissipative forces.

Crack Path Prediction in Anisotropic Brittle Materials,
By Vincent Hakim and Alain Karma, Physical Review Letters, 95, 235501, (2005)

They adopted a so-called phase-field approach (Ginzburg-Landau), and the generalized energy-momentun tensor is formulated in a four-dimensional vector field. In a numerical computation, they showed that they can prescisely predict the crack path in an anisotropic brittle material.

Thursday, February 02, 2006

Exact Solution for A Generalized JKR Adhesive Contact Model

Recently, Dr. S. Chen and Prof. H. Gao found an elegant close-form solution for a generalized JKR adhesive conatct model, in which both the normal and the tangential tractions in the contact zone are considered,

Non-slipping adhesive contact of an elastic cylinder on stretched substrates,
By S. Chen and H. Gao, Proceedings of Royal Society of London, 462, 221-228.


The Johnson-Kendall-Roberts (JKR) model is the main adhesive contact model used in applications. A major limitation of the model is its inability to take into account the tangential traction in the contact zone. The newly found solution may help us understand biological adhesion mechanisms such as the hierarchical structures on the foot of Gecko.
(Note: the classical Hertz theory is not exactly an adhesive contact theory, though one can study viscoelastic Hertzian contact.)

Wednesday, February 01, 2006

Researcher Spotlight: Professor Grigory. I. Barenblatt

By Xanthippi Markenscoff


If there is anybody alive who embodies what is mechanics, I would say that he is G.I . Barenblatt. A fluid mechanician just told me that Barenblatt is to mechanics, as Mozart is to music! Natural! Indeed, encompassing solid and fluid mechanics, and their interaction, over a period of fifty years, G.I. Barenblatt has unraveled the structure of physical phenomena of mechanics with unparalleled insight, by probing into the effect of scales. Indeed, he understood the physical processes taking place at each scale, and developed the mathematical concepts and tools to quantify them. He saw how the effect of scales manifests itself in physical phenomena almost in a unified way, and he embarked to harness them! I will try to outline this scaling issue briefly in some of the areas that he developed, but this is by no means comprehensive of his contributions. His contributions are enormous in a wide range of fields, and had profound influence.


In solid mechanics, the Barenblatt crack assumes a finite material cohesive force acting in a small zone at the tip of the crack (``cohesive zone'') which leads to a dissipation of energy so that the faces close smoothly. Barenblatt provided a beautiful mathematical solution in addition to the modeling, and introduced one of the basic characteristics of fracture toughness, the cohesion modulus. The concept of scaling led to similarity laws for fatigue cracks and multiple fracturing, and mathematical models of damage accumulation. The model of the flow in a fully saturated heterogeneous medium with several distinct spatial scales is the Barenblatt double –diffusion model. To model water injected in a rock containing oil (-in order to extract oil-), Barenblatt modeled elegantly a phenomenon called non-equilibrium filtration by introducing the concept of a quasi-steady stabilized zone around the water-oil displacement front, which determines the structure of the transition between injected water and oil. The stabilized zone disappears altogether if the water flow velocity is too high, reversing results of previous models.

Barenblatt not only provided elegant solutions to the aforementioned problems, but, in the context of this work he introduced (with Zeldovich) the new mathematical area of intermediate asymptotics. This arose in the problem of nonlinear filtration, which has a self-similar solution of the second kind, (in which the similarity exponent is found by solving a nonlinear eigenvalue problem rather than by dimensional analysis), and showed that indeed the self-similar solution is an asymptotic representation of the solution of the non-self similar problem.. Indeed, self-similar solutions are always ``intermediate asymptotics'' to the solution of more general problems valid for times and distances that are large enough that the fine details of the boundary / initial conditions disappear, but small enough that the system is not in equilibrium. If the fine details do not disappear, then we have similarity of the second kind, in which the exponents of the power-type scaling depend on the fine details of the pre-self similar state. His books

Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge University Press, 1996, 408 pages.


Scaling, Cambridge University Press, 2003, 171 pages.

are of monumental contribution, in their uniqueness of the topics spanned that exemplify and unify the intermediate asymptotics and renormalization, including flow through porous media, traveling and shock waves, combustion, turbulence and geophysical fluid dynamics.

In his work in fluid mechanics, combustion and geophysical fluid dynamics (interaction of gravity waves, density inhomogeneities and stratified flow), the scaling concepts were further extended to understand the structure of turbulent boundary layers, the scaling of turbulence, and phenomena such as hurricanes. Indeed, the scaling techniques when applied to droplets sandwiched between air and water showed that droplets kicked by the sea waves lubricate the winds and reduce turbulence, hence enhancing the wind speed (up to an order of magnitude). By reducing the size of the droplets (possibly by some chemical additive) the speed of the winds can diminish. This recent work, jointly with Chorin and Prostokishin, unifies theory and application in an Archimedean scope, and carries the contributions of Barenblatt to the 21st century where multiscale analysis presents both theoretical physico-mathematical challenges, as well as challenges of applicability to phenomena of global impact.

Grigory Isaakovich Barenblatt was born in Moscow in 1927 and graduated from the elite Moscow State University, Faculty of Mathematics and Mechanics, in 1950, where he subsequently obtained his Ph.D. and D.Sc. degrees under the guidance of the legendary giant of Soviet science A.N. Kolmogorov. He became Professor in 1962 and remained until 1992 when he was offered the G.I Taylor Chair in Fluid Mechanics at Cambridge University, as its inaugural holder. After his retirement in 1994 as Emeritus G.I. Taylor Professor, he was offered several Visiting Professorships at US Universities, including the Timoshenko Chair Professor at Stanford. Since 1997 he is Professor of Mathematics (in Residence) at UC Berkeley. He is a Foreign Member of the National Academies of Sciences and Engineering of the US, a Foreign Member of the Royal Society of London and has received many prizes, awards, and honorary degrees.

I consider it one of the great fortunes of my life that in 1990 I gave a seminar at the Institute of Problems of Mechanics in Moscow, and that Barenblatt walked in. I did not know who he was but he dominated and electrified the room instantaneously. I happened to be talking on the Sternberg-Koiter wedge paradox (concentrated moment on the apex), a problem that when the wedge becomes a re-entrant corner the solution ``remembers'' the details of the distribution of the moment, an intermediate asymptotics paradigm treated in Barenblatt’s book. In the Russian tradition, the next day he brought me flowers. Knowing Barenblatt gives one the sense of the absolute, in the quest for truth and in the quest for beauty in the world.