# Carlo Cercignani

### Quick Info

Teulada, Sardinia, Italy

Milan, Italy

**Carlo Cercignani**was an Italian mathematician known for his work on the kinetic theory of gases.

### Biography

**Carlo Cercignani**was born to Tuscan parents Luisa Notari and Ario Cercignani in Teulada, a town near the south coast of Sardinia, about 65 km south west of Cagliari. Ario was working there as a provincial veterinary doctor. Carlo's brother, Fausto, who became a renowned essayist, poet and professor of German literature, was born in 1941 also in Sardinia. However the family soon returned to Tuscany and Carlo spent his early years in Pisa, where he attended a Liceo classico, before moving to Milan where he undertook university studies. He studied physics and obtained his laurea in physics in 1961. Continuing to study at Milan, he was awarded a laurea in mathematics in 1963. However, he said [3]:-

Although I certainly have met a number of professors from whom I learned a lot, it was more the way to present an argument rather than to do real research of my own. If it does not seem immodest, I can call myself self-taught. Before the age of eighteen I had learned the basics of analysis through consulting encyclopaedias and by constructing missing proofs on my own (some quite correct, others only fanciful) in the Calculus of Variations, in Rational Mechanics, in Tensor Calculus, and I thoroughly read articles on Einstein's special and general theory of relativity. After the first year of university I studied (in the summer) Pauli's contributions to the theory of relativity, seen by many as very difficult. I graduated first in Physics (advised by Sergio Albertoni) and two years later in Mathematics (advised by Giovanni Ricci). In both cases I did the thesis work completely on my own, although my advisors recommended what I should read. I would say that the study of the works of great scientists have played the most important formative role in my way of doing research.He began publishing papers as soon as he had completed his physics laurea. The papers

*Elementary solutions of the linearized gas-dynamics Boltzmann equation and their application to the slip-flow problem*and

*Solutions of linearized gas-dynamics Boltzmann equation and application to slip-flow problem*appeared in print in 1962 while, in the following year, he published further papers, including two written jointly with his physics advisor Sergio Albertoni, namely

*Numerical Evaluation of the Slip Coefficient*and

*Slip-coefficient expression is derived using an exact analytical solution of the slip flow problem*. However, as well as mathematics and physics, he loved literature. Manozi Franco writes [7]:-

He was also a fan of literature: he had practised learning the Divine Comedy by heart. He loved greatly involving himself in poetry and in translation. Interrupting his work on a difficult theorem, he would suddenly begin to translate Jorge Luis Borges, William Shakespeare, Raymond Queneau, Charles Baudelaire, Stéphane Mallarmé or the Milanese dialect of "La Ninetta del Verzee" by Carlo Porta.Cercignani met Silvana Galdabini, a physics student, while she was studying at Milan. They married in 1966 and had two daughters, Anna and Mara. Anna has a laurea in Germanic philology, while Mara studied telecommunication engineering at the Politecnico of Milan and is now professor of medical physics at the Brighton and Sussex Medical School in England. Returning to Carlo Cercignani's career, he was appointed as a teaching and research assistant at the University of Milan, but over the following few years spent time at a number of foreign institutions, in particular at the Massachusetts Institute of Technology, the University of California, Berkeley, and the Courant Institute of Mathematical Sciences in New York. In 1968 he was appointed as an Associate Professor of Aerodynamics at the Politecnico of Milan. He was promoted to full Professor of Mathematical Physics in 1975. He spent the rest of his career in that position, but he had to battle against severe health problems. For over 30 years he struggled to maintain his active career despite suffering from multiple sclerosis. Giovanni Frosali, at the International Conference on Transport Theory in Portland in September 2011, said:-

The scientific work of Carlo Cercignani was very fruitful. As a mathematician, Cercignani obtained important results in the theory of Partial Differential Equations, Semigroup Theory, Monte-Carlo Methods, Spectral Theory, Riemann-Hilbert Problems, Fourier Analysis, and Functional Analysis. His main research interest was Kinetic Theory. Cercignani devoted a particular attention to the H-theorem, and to the problem of how macroscopic, irreversible evolution equations can follow from microscopic, reversible motion equations. In 1972, he obtained an elegant generalization of the Darrozes-Guiraud formula, and proved an H-theorem for polyatomic gases.Since Cercignani published eight books and over 300 research articles, it is impossible here to give an adequate overview of the range of his contributions. Let us note the diverse fields to which he contributed: to the kinetic theory of rarefied gases, models of turbulence, the transport of neutrons and of semiconductors, the Boltzmann equation and its applications which have proved useful in nanotechnology. However, as Cédric Villani explains in [15], there is a common theme running through the papers concerning very different topics:-

Cercignani has been one of the most active researchers of the Boltzmann equation and related topics. The second half of the last century were very auspicious for kinetic theory and Carlo Cercignani was always among its most important contributors. In 1975 he published his most famous treatise 'The Boltzmann equation and its applications', which collects and unifies numerous results on the Boltzmann equation previously scattered in hundreds of references. During the 1980's, he studied the evaporation-condensation interface between a gas and a liquid, stating an important conjecture for the long-time behaviour of the Boltzmann equation solutions.

Almost all of these show Carlo's passion for the Boltzmann equation, and more generally everything related to Boltzmann. Paradoxically, this focussing comes with an incredible diversity of methods, techniques and points of view. In 45 years of research, the Boltzmann equation led Carlo to work in theoretical mechanics, partial differential equations, numerical analysis, semigroup theory, spectral theory, Riemann-Hilbert problems, Fourier analysis, and many other areas. A few years ago, a collaboration with Sasha Bobylev on self-similar solutions of the Boltzmann equation even led him to a new pretty formula for the inversion of the Laplace transform. In brief, Carlo is at the same time one of the most focussed and one of the most versatile scientists that I know, defying any attempt of classification.Let us look at some of Cercignani's books which he began to write surprisingly early in his career. An early classic was

*Theory and Application of the Boltzmann Equation*(1975). James Glimm writes:-

The Boltzmann equation connects the discrete motion of the individual particles in a gas with the continuous motion of the gas as a whole. It is basic to fluid mechanics and is used in a variety of applications including plasma dynamics, neutron transport, and shock waves. As with many "basic" equations, its Achilles' heel is its complexity. For this reason the author presents, in addition to the general theory, a variety of approximation methods including linearization, asymptotic expansions, and numerical methods. The book is well written and can be used as a text for students learning the subject as well as a reference for workers active in the field.He updated this book thirteen years later, publishing it under the slightly revised title

*The Boltzmann Equation and its Applications*(1988). The publisher (Springer-Verlag) writes:-

This book gives a complete exposition of the present status of the theory of the Boltzmann equation and its applications. The Boltzmann equation, an integro-differential equation established by Boltzmann in 1872 to describe the state of a dilute gas, still forms the basis for the kinetic theory of gases. It has proved fruitful not only for the study of the classical gases Boltzmann had in mind, but also, properly generalized, for electron transport in nuclear reactors, photon transport in superfluids, and radiative transport in planetary and stellar atmospheres. The text presents a unified approach to the problems arising in these different fields, by exploiting similarities whenever they exist and underlining the differences when necessary. But the main exposition is tied to the classical equation established by Boltzmann.Dorfman, reviewing the book, writes [5]:-

I believe that Cercignani has done us all an enormous service by providing books with a high level of clarity such as this one, and I recommend it for anyone interested in the Boltzmann equation.Cercignani moved to writing historical and biographical material in

*Ludwig Boltzmann e la meccanica statistica*(1997). Baracca writes [2]:-

Cercignani's reconstruction of Boltzmann's scientific and personal experience is accurate, lively, and rich in anecdotes that deepen our understanding of his personality and his thought. Moreover, he discusses the physical aspects of Boltzmann's contributions in depth and provides an appraisal of their current interest.

*Ludwig Boltzmann: The Man Who Trusted Atoms*(1998), his English biography of Boltzmann, is his most widely read work enjoyed by specialists and non-specialists alike. Dorfman [6] writes:-

Carlo Cercignani, a well-known mathematical physicist, has written an interesting and thoughtful biography of Ludwig Boltzmann ... This is a valuable and stimulating book that deserves to be read and discussed by people interested in the history of scientific ideas and their role in science today.Rowlinson writes that the first chapters cover Boltzmann's biography and an introduction to the history of physics. Cercignani [12]:-

... then reaches the real point of the book, which is Boltzmann's contribution to equilibrium and, particularly, to non-equilibrium statistical mechanics, and the problem of how the time-irreversible laws of thermodynamics can arise from the reversible laws of micro-mechanics, whether classical, as for Boltzmann, or quantum, for us. This has been the subject of the author's own research and he is well-equipped to give a detailed account of Boltzmann's pioneering contribution and to place it in the context of the state of physics at the very end of the classical era.A review in

*Nature*states:-

Cercignani's beautiful book has the merit, first of all, of bringing Boltzmann fully back to life, as a scientist, a philosopher and a poet, thanks to painstaking research.The

*Journal of Statistical Physics*has a review (in Vol 98, No 5/6, 2000) which notes that the book contains:-

... a thorough analysis of Boltzmann's scientific achievements by an expert on modern kinetic theory, who has also made an effort to read the original papers in "dense German" and has surveyed some of the extensive biographical material. The result is a book that can be highly recommended to all physical scientists and mathematicians, including graduate students.Cercignani received many honours for his wide-ranging contributions to mathematics and physics. He was elected to the Paris Academy of Sciences on 13 March 1995. The citation reads:

The scientific work of Carlo Cercignani in fluid mechanics is dominated by a significant contribution to the kinetic theory of gases and the properties of the Boltzmann equation. He established important theoretical results, including properties of existence and uniqueness of solutions of initial value problems, which are the basis of recent developments in methods for numerical simulation of gas in networks. Carlo Cercignani has contributed much to the international life of the science community, especially during his terms on the Council of the European Society of Mechanics (EUROMECH) and the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM). Great friend of France, he greatly appreciated his visits to universities in Paris, at the École Polytechnique and the Institut des Hautes Études Scientifiques.Among the other honours he received we mention that he was elected to the Istituto Lombardo and the Accademia dei Lincei. He was awarded the Gold Medal of the National Academy of Sciences of Italy (the "Academy of Forty") (1982), the Città di Cagliari Prize for Applied Mathematics (1991), the Humboldt Prize (1994), and the Gold Order of the Italian Order of Merit for Culture and Art (1999).

Finally, we should note that Cercignani's publication list includes many, perhaps surprising, items such as [15]:-

... a collection of poems, a comedy, translations of Homer, and a guide for helping Italians to pronounce Japanese.The poems were published as

*Scherzi in versi*Ⓣ (1999) and the novel is entitled

*La creazione secondo Michele*Ⓣ. Luigi Galgani [9], ends his article with this personal note:-

Just a few days ago, putting some order to my own bookshelves, I found a recent poem of his that somehow had escaped my attention. This poem seems now particularly interesting to me, as it gives an indication of how he lived his last days, when he was almost completely paralyzed. He actually continued to deal with people in his usual way, somehow by joking at first, then perhaps reciting from memory with his beautiful voice a poem suited to the moment, then re-entering into himself and starting thinking about something.

The poem I found has the title "Beethoven in heaven" [This was an Italian translation by Cercignani of a poem Beethoven im Himmel of Ludwig Boltzmann], and is essentially a meditation on pain. Carlo describes how after death he very joyfully goes to heaven. But strangely enough, the chorus of the angels he hears is a little monotonous, and Carlo cannot refrain from telling them. From the style, he recognises it as a piece of Beethoven, but one unknown to him. The angels confirm it, saying Beethoven composed it in heaven. So he asks to meet the composer, which he is allowed to do. Requested by Beethoven to give his opinion about his music, Carlo refrains from speaking, but then, as Beethoven insists, with great humility admits he would have expected some more sublime music. And Beethoven says he completely agrees. "Everything in heaven comes out badly to me. I'm even refraining from composing anymore. You know why? I'm lacking the creative spark, the note that most shines; this note is pain ... Only the one who cries and groans in pain will have humanity, the divine gift ... Did you ever cry together with your wife? The one who doesn't do it is unable to capture true love ... God too, when he was seen among us, was he a king, or wanted to be rich? He was a man's son, full of pain. ..." So Carlo looks at Beethoven ... "How strange - he thinks - is the flowing of the world. A few hours ago I was asking that death should take away the pain in my heart. Now, here, in this high and blessed world, I miss pain. Oh human heart, truly unfathomable and indeed strange."

### References (show)

- S Abbott, Review: Ludwig Boltzmann: The Man Who Trusted Atoms by Carlo Cercignani,
*The Mathematical Gazette***83**(497) (1999), 342. - A Baracca, Review: Ludwig Boltzmann e la mecanica statistica by Carlo Cercignani,
*Isis***90**(2) (1999), 373-374. - C Citrini, Claudio Citrini a colloquio con Carlo Cercignani,
*Lettera Matematica PRISTEM***35**(2000). http://matematica.unibocconi.it/articoli/claudio-citrini-colloquio-con-carlo-cercignani - L Desvillettes, C Mouhot and C Villani, Celebrating Cercignani's conjecture for the Boltzmann equation,
*Kinet. Relat. Models***4**(1) (2011), 277-294. - J R Dorfman, Review: The Boltzmann Equation and its Applications by Carlo Cercignani,
*SIAM Review***31**(2) (1989), 339-340. - J R Dorfman, Review: Ludwig Boltzmann: The Man Who Trusted Atoms by Carlo Cercignani,
*Isis***91**(3) (2000), 595-596. - M Franco, Carlo Cercignani, il matematico che amava scrivere poesie,
*Corriere della Sera*(2010). http://archiviostorico.corriere.it/2010/gennaio/26/Carlo_Cercignani_matematico_che_amava_co_7_100126031.shtml - G Frosali, Carlo Cercignani: In memoriam,
*Nuovo Cimento*C**033**(01) (2011),1-2. - L Galgani, Carlo Cercignani's Interests for the Foundations of Physics,
*Meccanica***47**(2012), 1723-1735. - L Galgani, Carlo Cercignani,
*Dipartomento di Matematica 'Federigo Enriques', Università degli Studi di Milano*. http://www.mat.unimi.it/users/carati/galgani/carlo2.pdf - J Glimm, Review: Theory and Application of the Boltzmann Equation by Carlo Cercignani,
*American Scientist***65**(2) (1977), 242. - J S Rowlinson, Review: Ludwig Boltzmann: The Man Who Trusted Atoms by Carlo Cercignani,
*Notes and Records of the Royal Society of London***53**(3) (1999), 374. - S Schaffer, Heat Death, Ludwig Boltzmann: The Man Who Trusted Atoms by Carlo Cercignani,
*London Review of Books***22**(8) (2000), 33-34. - Y Sone, A Tribute to Carlo Cercignani (1939-2010),
*Phys. Fluids***23**(3) (2011), 1. - C Villani, Introduction for Carlo's special issue,
*J. Stat. Phys.*124 (2-4) (2006), 271-273.

### Additional Resources (show)

Other websites about Carlo Cercignani:

Written by J J O'Connor and E F Robertson

Last Update January 2013

Last Update January 2013