Comptes Rendus Mécanique (CRM)

Giacomo Quaranta

Clara Argerich Martin

Ruben Ibañez

Jean Louis Duval

Elias Cueto

Francisco Chinesta

From linear to nonlinear PGD-based parametric structural dynamics

Editorial board: Académie des sciences, 23, quai de Conti, 75006 Paris, France
Tel.: (+33) (0)1 44 41 45 26.
sec.geopalphy@academie-sciences.fr
http://www.academie-sciences.fr
Objective of the journal: the Comptes rendus Mecanique are open to all scientists, whatever their position or nationality. Through a policy of rapid 
publication of original work, the journal is a highly advantageous means of making advances in fundamental research known to the international 
scientific community. Such communication is achieved in the form of research articles, review articles or articles forming part of a thematic issue.
The journal guarantees a rapid publication and an international diffusion.
Editorial director: Étienne Ghys.
Editor-in-chief: Jean-Baptiste Leblond.
Associate editors: O. Budenkova, J.-M. Coron, F. Chinesta, L. Dormieux, F. Gosselin, G. Ribert, E. Villermaux.
Editorial board:
A. Bensoussan, G. Berry, S. Candel, Y. Choquet-Bruhat, Ph. G. Ciarlet, P. Clavin, M. Combarnous, G. Comte-Bellot, R. Dautray,
P. Deheuvels, G. Duvaut, O. Faugeras, P. Flandrin, R. Glowinski, P. Huerre, G. Huet, G. Iooss, A. Jaumotte, D. Knuth, P. Lax, A. Linan, 
O. Macchi, C.-M. Marle, Y. Meyer, H. Moffatt, R. Moreau, M. Nivat, L. Pandolfi, M. Pélegrin, P. Perrier, H. Petryk, O. Pironneau, 
Y. Pomeau, P.-A. Raviart, J. Salençon, É. Sanchez-Palencia, J. Sifakis, P. Suquet, E. Van der Giessen, M. G. Velarde, A. Zaoui.
Indexation: Current Contents, Inspec, ISI, Pascal, Scopus, Zentralblatt MATH.
© 2019 Académie des sciences. All rights reserved.
Published by Elsevier Masson SAS, Société par actions simplifiée à associé unique, au capital social de 47 275 384 € - RCS Nanterre B 542 037 
031
Office: 65, rue Camille-Desmoulins, 92442 Issy-les-Moulineaux cedex, France.
Shareholder: Elsevier Holding France
Publication information: Comptes Rendus Mecanique (ISSN 1631-0721). For 2019, volume 347 is scheduled for publication. All subscriptions are 
electronic only; prices are available upon request from the Publisher or from the Regional Sales Office nearest you or from this journal’s website 
(http://www.elsevier.com/locate/issn/1631-0721). Further information is available on this journal and other Elsevier products through Elsevier’s 
website: (http://www.elsevier.com). Subscriptions are accepted on a prepaid basis only and are entered on a calendar-year basis.
Desk Editor – Jean-Michel Blengino. Tel.: (+33) (0)1 71 16 54 90 – Fax: (+33) (0)1 71 16 51 84. E-mail: j.blengino@elsevier.com
Subscriptions – Tel.: (+33) (0)1 71 16 55 99 – Fax: (+33) (0)1 71 16 55 77. E-mail: infos@elsevier-masson.fr
Publisher – Giovanni Raneri
President – Daniel Rodriguez
Author enquiries
For enquiries relating to the submission of articles please visit Elsevier’s Authors Home at http://www.elsevier.com/authors. This also provides 
the facility to track accepted articles and set up e-mail alerts to inform you of when an article’s status has changed, as well as detailed artwork 
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Editorial Board

Ridha Ziani

Ahmed Hammami

Fakher Chaari

Ahmed Felkaoui

Mohamed Haddar

Gear fault diagnosis under non-stationary operating mode based on EMD, TKEO, and Shock Detector

Jiangyu Wu

Meimei Feng

Guansheng Han

Benyu Yao

Xiaoyan Ni

Loading rate and confining pressure effect on dilatancy, acoustic emission, and failure characteristics of fissured rock with two pre-existing flaws

Editorial board: Académie des sciences, 23, quai de Conti, 75006 Paris, France
Tel.: (+33) (0)1 44 41 43 61.
fatima.messadi@academie-sciences.fr
http://www.academie-sciences.fr
Objective of the journal: the Comptes rendus Mecanique are open to all scientists, whatever their position or nationality. Through a policy of rapid 
publication of original work, the journal is a highly advantageous means of making advances in fundamental research known to the international 
scientific community. Such communication is achieved in the form of research articles, review articles or articles forming part of a thematic issue.
The journal guarantees a rapid publication and an international diffusion.
Editorial director: Étienne Ghys.
Editor-in-chief: Jean-Baptiste Leblond.
Associate editors: Z. Bažant, F. Chinesta, F. Darve, L. Dormieux, J. Etay, R. Friedrich, F. Gosselin, P. Johnson, E. Mastorakos, J. Rice, H. Stone, 
L. Vervisch, E. Villermaux, J. Willis.
Editorial board:
A. Bensoussan, G. Berry, S. Candel, Y. Choquet-Bruhat, Ph. G. Ciarlet, P. Clavin, M. Combarnous, G. Comte-Bellot, R. Dautray,
P. Deheuvels, G. Duvaut, O. Faugeras, P. Flandrin, R. Glowinski, P. Huerre, G. Huet, G. Iooss, A. Jaumotte, D. Knuth, P. Lax, A. Linan, 
O. Macchi, C.-M. Marle, Y. Meyer, H. Moffatt, R. Moreau, M. Nivat, L. Pandolfi, M. Pélegrin, P. Perrier, H. Petryk, O. Pironneau, 
Y. Pomeau, P.-A. Raviart, J. Salençon, É. Sanchez-Palencia, J. Sifakis, P. Suquet, E. Van der Giessen, M. G. Velarde, A. Zaoui.
Indexation: Current Contents, Inspec, ISI, Pascal, Scopus, Zentralblatt MATH.
© 2019 Académie des sciences. All rights reserved.
Published by Elsevier Masson SAS, Société par actions simplifiée à associé unique, au capital social de 47 275 384 € - RCS Nanterre B 542 037 
031
Office: 65, rue Camille-Desmoulins, 92442 Issy-les-Moulineaux cedex, France.
Shareholder: Elsevier Holding France
Publication information: Comptes Rendus Mecanique (ISSN 1631-0721). For 2019, volume 347 is scheduled for publication. From 2016 all sub-
scription is electronic only, prices are available upon request from the Publisher or from the Regional Sales Office nearest you or from this 
journal’s website (http://www.elsevier.com/locate/issn/1631-0721). Further information is available on this journal and other Elsevier products 
through Elsevier’s website: (http://www.elsevier.com). Subscriptions are accepted on a prepaid basis only and are entered on a calendar year 
basis.
Desk Editor – Jean-Michel Blengino. Tel.: (+33) (0)1 71 16 54 90 – Fax: (+33) (0)1 71 16 51 84. E-mail: j.blengino@elsevier.com
Subscriptions – Tel.: (+33) (0)1 71 16 55 99 – Fax: (+33) (0)1 71 16 55 77. E-mail: infos@elsevier-masson.fr
Publisher – Giovanni Raneri
President – Daniel Rodriguez
Author enquiries
For enquiries relating to the submission of articles please visit Elsevier’s Authors Home at http://www.elsevier.com/authors. This also provides 
the facility to track accepted articles and set up e-mail alerts to inform you of when an article’s status has changed, as well as detailed artwork 
guidelines, copyright information, frequently asked questions and more. Contact details for questions arising after acceptance of an article, 
especially those relating to proofs, are provided after registration of an article for publication.
Imprimé en France par JOUVE Commission paritaire : 0517 T 81774
1, rue du Dr-Sauvé, Mayenne, France Périodicité : 12 numéros par an
Dépôt légal à parution 


Chady Ghnatios

Ré-Mi Hage

Ilige Hage

An efficient Tabu-search optimized regression for data-driven modeling

Francisco J. Montáns

Rafael Gómez-Bombarelli

J. Nathan Kutz

Data-driven modeling and learning in science and engineering

Amjad Al-Hamood

Hazim Jamalia

Amer Imran

Oday Abdullah

Adolfo Senatore

Hakan Kaleli

Modeling and theoretical analysis of a novel ratcheting-type cam-based infinitely variable transmission system

Pierre Collet

Christophe Josserand

Yves Pomeau

Sergio Rica

Emmanuel Villermaux

C. R. Mecanique 347 (2019) 271–272Contents lists available at ScienceDirect
Comptes Rendus Mecanique
www.sciencedirect.com
Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique : hommage à Pierre Coullet
Foreword
This thematic issue of the Comptes rendus Mecanique is dedicated to Pierre Coullet, a definitely original character in the 
scientific landscape. Pierre studied at the University of Nice, where he obtained a Master thesis (so-called thèse de troisième 
cycle at the time) supervised by Enrique Tirapegui on the topic of the renormalization group in field theory. He then got his 
PhD (thèse d’État) under the supervision of Jean Coste. This research led him, in an unexpected way, to exploit the ideas of 
fixed point and functional equation in a domain fully original at the time: whereas the bifurcation of a limit cycle by period 
doubling was well known, the discovery by Pierre and Charles Tresser of an infinite set of period doubling bifurcations 
in a finite range of parameters, together with its properties of universality, was a complete surprise. This research has 
opened a new field in the theory of bifurcations and of dynamical systems with a few degrees of freedom. These wonderful 
theoretical works have given rise to many applications and new experiments. Notably, fluid mechanics experiments directed 
him naturally to the study of chaotic phenomena in spatially extended systems, with many degrees of freedom.
Pierre has an original view as well as a very deep understanding of the underlying physical mechanisms. However, his 
most salient characteristic is, perhaps, the desire to experience novelty in science, in technology and in life, as he made 
innovations since his early scientific age. In the mid 1980’s, he switched from the study of finite-dimensional dynamical 
systems to the understanding of partial differential equations (PDE’s). Very soon he understood that the qualitative behav-
ior of partial differential equations requires intensive numerical simulations. He brought a first pair of Apple McIntosh to 
the “Laboratoire de physique théorique” at Parc Valrose in Nice. His first study concerned the complex Ginzburg–Landau 
equation, a topic on which he received the help of his now former students Lionel Gil and Jocelyne Lega.
He was one of the first to understand that nonlinear optics belonged also to this field. This led him to predict the 
existence of a regime of turbulence mediated by optical vortices, a regime indeed observed afterwards (Fig. 1). In his 
Fig. 1. Curved mirror with concave and convex domains: illustration of the problem of geometric aberration and multiple images (problem posed by Ptolemy 
and solved in the simple case of a spherical concave mirror by Ibn al-Haitham). The photographer’s face appears three times in the image. Once isolated, in 
the middle right and then doubled, in the vicinity of a saddle node bifurcation in the upper part of the picture, slightly to the right of its center. Artwork 
conception by Pierre Coullet, picture by Sergio Rica.https://doi.org/10.1016/j.crme.2019.03.009
1631-0721/© 2019 Published by Elsevier Masson SAS on behalf of Académie des sciences. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
272 Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique : hommage à Pierre Coulletquest for the best, Pierre got a few advanced Sun sparc workstations and he and his team (particularly Kjartan Emilsson) 
developed original interactive numerical simulations, largely recognized as a revolutionary innovation. The main purpose of 
an interactive numerical simulation (instead of simulation running in batch) is that the user can interact with the simulation, 
changing the values of the control parameters during the computation itself for instance, with the routine that simulates a 
physical system governed by elementary rules like in PDE’s. This tool made possible a big step forward in the qualitative 
understanding of the behavior of PDE’s. It is impossible to enumerate the many direct or indirect new ideas generated in 
this way. Today he programs and teaches Swifth (the language for MacOS) always with the same passion as in his early 
days. As a common principle, Pierre always experiences the last technological release or everything he could use to solve a 
problem or express an idea in a better way, a distinct feature of Pierre’s character.
These remarkable achievements earned him a well-deserved scientific recognition nationally and abroad testified by a 
number of awards: Langevin Prize of the French Physical Society (1990), C.S. Freycinet Prize of the French Academy of 
Sciences (1991), Silver medal of the CNRS (1993), Foreign member of the Chilean Academy of Sciences (1999), Humboldt 
Prize (Germany, 2000), Holweck Prize from the SFP and IOP (2001).
Remaining the same very inventive and prolific researcher, Pierre is spending much time and efforts in the training of 
young researchers and in improving the pedagogy of physics at all levels, including to primary and high school teachers, 
to the general public, and within advanced sessions in prestigious institutes and foundations. His passion for the history of 
science has lead him to a reconsider, from a modern point of view, some classical problems in optics and mechanics.
He puts a lot of energy to successfully federate actions for research in his University. Remaining at the forefront of 
worldwide research, with multiple collaborations and a busy activity, he has kept intact the gaiety of his character and his 
friendly and optimistic personality.
We wish you, dear Pierre, to continue with your good mood and to stay on this trajectory of a man and a researcher 
with just as much inventiveness and beautiful discoveries.
Pierre Collet
Centre de physique théorique, CNRS UMR 7644, École polytechnique, 91128 Palaiseau cedex, France
Christophe Josserand, Yves Pomeau
LadHyX, CNRS, École polytechnique, Palaiseau, France
E-mail addresses: christophe.josserand@polytechnique.edu (C. Josserand), yves.pomeau@gmail.com (Y. Pomeau)
Sergio Rica
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile
Physics Center, Universidad Adolfo Ibáñez, Santiago, Chile
E-mail address: sergio.rica@uai.cl
Emmanuel Villermaux ∗
Aix–Marseille Université, CNRS, Centrale Marseille, IRPHE, Marseille, France
E-mail address: emmanuel.villermaux@univ-amu.fr
Available online 1 April 2019* Corresponding author.


Foreword

Nicolas Vandenberghe

A brittle material with tunable elasticity: Crêpe paper

Not a member yet

From linear to nonlinear PGD-based parametric structural dynamics

Editorial Board

Gear fault diagnosis under non-stationary operating mode based on EMD, TKEO, and Shock Detector

Loading rate and confining pressure effect on dilatancy, acoustic emission, and failure characteristics of fissured rock with two pre-existing flaws

Editorial Board

An efficient Tabu-search optimized regression for data-driven modeling

Data-driven modeling and learning in science and engineering

Modeling and theoretical analysis of a novel ratcheting-type cam-based infinitely variable transmission system

Foreword

A brittle material with tunable elasticity: Crêpe paper

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