CV-Bouchet 10-2009

1 Personal data

Name: Freddy BouchetBorn on: June the 17th 1972 in Saint Julien en Genevois (France)Nationality: FrenchCivil status: Marital life. Three children (1998,2000,2005)National service: Professor of mathematics and physics at « Lycée Stendhal » in Milano (Italy)Professional address: Institut Non Linéaire de Nice (INLN). CNRS UMR 6618

1361 route des Lucioles06560 Valbonne - France

Phone / Fax: (33)+4 92 96 73 07 / (33)+4 92 96 73 33E-mail: Freddy.Bouchet@inln.cnrs.frWeb page: http://www.inln.cnrs.fr/rubrique.php3?id_rubrique=79Current position: Researcher position at the CNRS (French National Research Agency)

at INLN, Nice, France

2 Professional experience and educationYear Experience or diploma Places04-.. Researcher position at CNRS INLN-Nice03-04 Agrégé préparateur (post doc) at ENS-Lyon ENS-Lyon France03 Post-Doc directed by Angelo Vulpiani University La Sapienza

Stochastic processes. “Stirring and mixing” Rome - Italy01-02 Post-Doc directed by Stefano Ruffo University of Florence

Statistical mechanics of systems with long range interactions Italy98-01 PHD in physics, Mention Très Honorable (the highest one in UJF) Institut Fourier-Grenoble

supervised by Raoul Robert and Joël Sommeria, untitled Université Joseph FourierStatistical mechanics for geophysical flows (UJF)

96-98 Mathematics and physics teacher Lycée Stendhal - Milan(during the national service, french cooperation) (Italy)

92-96 Student in the Ecole Normale Supérieure de Lyon ENSL95-96 DEA in theoretical physics, option statistical physics. ENSL

Mention Bien (DEA: pre-doctoral course: Master of science)94-95 Agrégation in Mathématics.

(entitles one to teach up to the second year undergraduate, in France)

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3 Publication listPHD-Thesis: (referred as T.)

1. Statistical mechanics of geophysical flows. Université Joseph Fourier - Grenoble

Book I am currently writing a book :

1. F. BOUCHET and J. SOMMERIA Statistical mechanics of geophysical flows Lecture Notes in Physics. WorldScientific.

3.1 Publications in referred international journals (referred as A1, A2, ...)The number CI refers to the number of citations to each article (from ISI Web of science for nonbracketed numbers and from google scholars for bracketed numbers, September 2009). From thisthe H factor is 8 (8 publications cited more than 16 times according ISI). From 2002 to 2008, I havepublished 19 publications in referred international journals. The average number of citations perarticle, for articles that have been published more than three years ago, and less than 6 years ago,is 18.5 (25).

1. F. BOUCHET and J. SOMMERIA 2002 Emergence of intense jets and Jupiter’s Great Red Spot as maximumentropy structures J. Fluid Mech. 464, 165-207. CI : 17 (36)

2. J. BARRE, F. BOUCHET, T. DAUXOIS and S. RUFFO, 2002a Out-of-equilibrium states as statistical equilibriaof an effective mean-field dynamics. Phys. Rev. Lett. 89, 11, 110601. CI : 5 (6)

3. J. BARRE, F. BOUCHET, T. DAUXOIS and S. RUFFO, 2002b Birth and long-time stabilization of out-of-equilibrium coherent structures Eur. Phys. J. B 29, 577-591 CI : 3 (7)

4. F. BOUCHET, F. CECCONI and A. VULPIANI, 2004 A Minimal Stochastic Model for Fermi’s Acceleration,Phys. Rev. Lett., 92, 040601 CI : 6 (4)

5. Y. YAMAGUCHI, J. BARRE, F. BOUCHET, T. DAUXOIS and S. RUFFO, 2004 Stability criteria of the Vlasovequation and quasi-stationary states of the HMF model, Physica A, 337 (1/2) 36-66, CI : 52 (67)

6. F. BOUCHET, 2004 The stochastic process of equilibrium fluctuations, of a system governed by long range inter-actions. Phys. Rev. E, 70, 036113, CI : 17 (27)

7. T. TATEKAWA, F. BOUCHET, T. DAUXOIS and S. RUFFO, 2005 Thermodynamics of the self-gravitating ringmodel, Phys Rev E, 71, 5, 056111-+, CI : 3 (4)

8. P. H. CHAVANIS and F. BOUCHET, 2005 On the coarse-grained evolution of collisionless stellar systems. As-tronomy and Astrophysics, 430, 771-778, CI : 16 (24)

9. P. H. CHAVANIS, F. BOUCHET and J. VATTEVILLE, 2005 Dynamics and thermodynamics of a simple modelsimilar to self-gravitating systems : the HMF model, Eur. Phys. J. B. 46, 61-99, CI : 29 (38)

10. J. BARRE, F. BOUCHET, T. DAUXOIS and S. RUFFO, 2005 Large deviation techniques applied to systems withlong range interactions, J. Stat. Phys., 119 1/2, CI : 24 (29)

11. F. BOUCHET and J. BARRE, 2005 Classification of phase transitions and ensemble inequivalence situations insystems with long range interactions. J. Stat. Phys., 118, 5/6, 1073-1105, CI : 24 (27)

12. F. BOUCHET and T. DAUXOIS, 2005 Prediction of anomalous diffusion and algebraic relaxations for long-rangeinteracting systems, using classical statistical mechanics Phys. Rev. E 72, 045103(R), CI : 19 (31)

13. F. BOUCHET, T. DAUXOIS and S. RUFFO, 2006, Controversy about the applicability of Tsallis statistics to theHMF model, Europhysics News, 37, 2, 9-10, CI : (1)

14. J. BARRE, F. BOUCHET, T. DAUXOIS, S. RUFFO and Y. YAMAGUCHI, 2006, The Vlasov equation and theHamiltonian Mean-Field model, Physica A, 365, 177-183, CI : 6 (7)

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15. Y. Y. YAMAGUCHI, F. BOUCHET, T. DAUXOIS, 2007, Algebraic Correlation Function and Anomalous Diffu-sion in the HMF model. J. Stat. Mech., 1, 20-, CI : 4

16. K. JAIN, F. BOUCHET and D. MUKAMEL, 2007, Relaxation times of unstable states in systems with long rangeinteractions, J. Stat. Mech., 11008

17. F. BOUCHET, T. DAUXOIS, D. MUKAMEL and S. RUFFO, 2008, Phase space gaps and ergodicity breaking insystems with long range interactions, Phys. Rev. E 77, 011125, CI : (1)

18. F. BOUCHET, 2008, Simpler Variational Problem for Statistical Equilibria of the 2D Euler Equation and OtherSystems with Long Range Interactions, Physica D: Nonlinear Phenomena 237, pp. 1976-1981

19. F. BOUCHET and E. SIMONNET, 2009, Random change of flow topology in 2D and geostrophic turbulence,Phys. Rev. Lett., 102, 094504

20. A. VENAILLE and F. BOUCHET, 2009, Ensemble inequivalence, bicritical points, and azeotropy for generalizedFofonoff flows, Phys. Rev. Lett., 102, 104501

21. A. OLIVETTI, J. BARRE, B. MARCOS, F. BOUCHET, F. and R. KAISER, 2009 Breath-ing mode for systems of interacting particles, to be published in Phys. Rev. Lett., eprintarchiv:condmat/0907.4423

22. F. BOUCHET and Y. YAMAGUCHI, 2010, Large time behavior and asymptotic stability of thetwo-dimensional Euler and linearized Euler equations, eprint archiv:condmat/0905.1551

3.2 Other publicationsRefereed conference proceedings. (referred as C1, C2, ...)

1. F. BOUCHET and T. DAUXOIS, 2005 Kinetics of anomalous transport and algebraic correlations in a long rangeinteracting system, Journal of Physics: Conference Series, 7, 34-47, CI : 7

2. F. BOUCHET and J. BARRE, 2006 Statistical mechanics of systems with long range interactions, Journal ofPhysics: Conference Series, 31, 18-26

3. T. TATEKAWA, F. BOUCHET, T.DAUXOIS and S. RUFFO, 2006 Thermodynamics of the self-gravitating ringmodel: Analysis with new iterative method, Journal of Physics: Conference Series, 31, 163-164

4. J. BARRE and F. BOUCHET, 2006, Statistical mechanics and long range interactions Comptes rendus Physique 7- 3-4 (414-)

5. F. BOUCHET, J. BARRE and A. VENAILLE, 2008, Equilibrium and out of equilibrium phase transitions insystems with long range interactions and in 2D flows, in DYNAMICS AND THERMODYNAMICS OF SYSTEMSWITH LONG RANGE INTERACTIONS: Theory and Experiments, AIP Conf. Proc., 970, pp. 117-152

Conference proceedings.

1. J. BARRE and F. BOUCHET, 2002 Mean field justified by large deviation results in long range interacting systems,Acte de conference Dynamics and thermodynamics of systems with long range interactions.

3.3 Most cited papers in Journal of Statistical PhysicsJournal of statistical physics is probably the main reference journal in statistical physics. In the “Stat-Phys” meeting held in Genova in 2007, J. Lebowitz has presented a list of the papers published in2005-2007 that were the most cited. The two first one was my two papers published in JSP in 2005.

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4 Research interests and summary of main achievements

4.1 Main research interestsThe letters and numbers refer to the publication list on the previous page.

1) Statistical mechanics of systems with long range interactions Classification of phase transitions(A11) (please see the publication list below). Equilibrium : large deviation results, and so on (A11, C2, A17, A18). Studyof simple toy models. (A2, A3, A5, A7, A9, A14, A16). Relaxation towards equilibrium (A5, C1, A12, A13). Stochasticprocess of fluctuations. Long range correlations (A6, A9, C1, A12, A15). Ergodicity breaking (A18). Application togeophysical flows (see below) and self-gravitating stars (A7, A8)

2) Statistical mechanics for geophysical flows Equilibrium theory (A17). A model for the Great Red Spotof Jupiter (T, A1). Model of Jupiter’s troposphere (T, A1, S1). Parametrization of small scale geostrophic turbulence (T,S2). Simple ocean models (work in progress)

3) Links between nonlinear dynamics and statistical physics Kinetic theory (A4, A6, A8, C1, A12, A15,A16). Long range correlations, anomalous diffusion, non-Gaussian statistics (A4, C1, A12, A14, A15). Averaging ofrapid variables. Adiabatic dynamics (A2,A3)

4.2 Major achievements1) A model for Jupiter’s Great Red Spot and other vortices

I have explained the emergence and stability of the most important jets and vortices, in the highlyturbulent Jupiter’s atmosphere, by a statistical mechanics of the potential vorticity mixing. I havedevelopped an analytical theory based on an analogy with first order phase transitions in classicalthermodynamics. The vortex shapes then result from a competition between an isoperimetrical prob-lem (length minimization with fixed area) and the effect of the equivalent topography. This providesa very simple analytical model for the Great Red Spot of Jupiter describing all its qualitativefeatures, without the drawback of the previous theories (soliton, ...) and with quantitative agree-ment. I have also modeled all Jovian smaller vortices characters. These results have been obtainedboth for the Quasi-Geostrophic (T, A1, S1) and the Shallow-Water models (P1).

2) Large deviations and classification of phase transitions for systems with long range interac-tions

In many systems, particles or fields have a non integrable interaction potential, for instance self grav-itating stars, 2D vortices, plasma, magnets, and so on. I have proposed a general method to solve theequilibrium statistical mechanics of such systems with long-range interactions, using large deviationtheory (A10). It can be adapted for a large class of simple models ; some of them show inequivalencebetween the microcanical and canonical ensembles of statistical physics (ensemble inequivalence).

Systems with long range interactions are not additive, which can lead to inequivalence betweenthe microcanonical and canonical ensembles. The microcanonical ensemble may show richer behav-ior than the canonical one, including negative heat capacities (the temperature decrease as the energyis increased) and other non-common behaviors like negative temperature jumps at a microcanonicalcritical point, when the energy is increased. I have proposed a generalization of Landau classifi-cation for systems with long range interactions that describes all the possible phase transitions

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associated to situations of ensemble inequivalence (A11). The phenomenology for such phase tran-sitions is richer than the classical one. We have then predicted new ensemble inequivalence situationsthat have never been observed yet and others than have been observed only after our work.

3) Out of equilibrium phase transitions in the 2D Stochastic Navier-Stokes Equation

I have studied the two dimensional Navier Stokes equation with stochastic forces (SNS Eq.). I havepredicted theoretically and observed numerically out of equilibrium phase transitions : theturbulent flow switches randomly from a state with a large scale dipole to a state with a unidi-rectional flow. Similar theoretical considerations lead to the prediction of out of equilibrium phasetransitions in a large class of other geometries, and also for geostrophic, large rotation or 2D magneticflows (S4). One can then infer that such phase transitions exist in possible experimental situations.

4) Equilibrium statistical mechanics of ocean midlatitude jets and vortices

After having successfully modeled Jovian vortices using the potential vorticity statistical mechanics,it was natural to address the interest of this theory in the case of midlatitude oceanic flows. Vorticeslike the Gulf Stream rings are statistical equilibria in Quasi-Geostrophic or Shallow Water models.We have also found strong midbasin eastward jets, similar to the Gulf Stream or the Kuroshio, ascritical points of the mixing entropy, in QG 1-1/2 layers.

Such structures are however not statistical equilibria. In this case, due to the beta effect, thestatistical mechanics predicts equilibria with strong westward jets. This is in accordance with the outof equilibrium nature of the Gulf Stream and Kuroshio.

In baroclinic models, equilibria are dominated by the barotropic component. However the barotropiza-tion is incomplete due to the energy constraint. This is also in accordance with the well known ten-dancy of layered flows toward barotropization.

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5 Conferences, invitations and scientific lectures

5.1 Invited professor1. Waseda University, Tokyo, Japan, group of K.P. Maeda, September 2005.2. Weizmann Institute, Rehovot, Israel, group of D. Mukamel, November 2005.

5.2 Research lectures1. Lecture in Waseda university, Japan, September 2005, “Statistical mechanics of systems with

long range interactions”, (4h.)2. Lecture in Nice university, France, April 2008, “Statistical mechanics of systems with long

range interactions”, (6h.)3. Lecture in the school “Rencontres de Peyresq”, May 2008, “Two dimensional and geophysical

turbulence”, (5h.)

5.3 Talks and conferences in an international contextInvited speaker in international conferences and solicited lectures in schools

1. Conference “Cold Atoms and Long Range Interactions”, Nice, France, September 2004 (invited speaker)

2. The Third 21COE Symposium : Astrophysics as Interdisciplinary Science, Waseda University, Japan, September 2005 (invited speaker)

3. Conference “Dynamics And Thermodynamics Of Systems With Long Range Interactions”, Assisi, Italy, July 2007 (invited speaker)

4. School “Aux rencontres de Peyresq”, Nonlinear physics, Peyresq, France, May 2008 (solicited lecture) (organizing committee)5. Conference “ΣΦ : International conference in statistical physics”, Kolymbari, Crete, Greece, July 2008 (invited speaker)

6. Workshop on “Structures and Waves in Anisotropic Turbulence”, to be held in November 2008, in the framework of the Newton Institute

program : “The Nature of High Reynolds Number Turbulence”. (solicited speaker)7. International Seminar on “Many-body systems far from equilibrium: Fluctuations, slow dynamics and long-range interactions”, to be held in

February 16 - 27, 2009 in Dresden. (invited speaker)

Oral talks in international conferences with competitive selections :8 talks (6 in EGS an EGUmeetings, Conference "Statistical Mechanics of Non-Extensive Systems" Paris, October 2005, Con-ference UPON “Upon Problems on Noise”, Lyon, June 2008)

1. February 1999: EGS congress (European Geophysical Society), Entropy maxima for the Quasi-Geostrophic equations.

2. April 2000: EGS Congress, Entropy maxima for the Quasi-Geostrophic equations, a model for the Great Red Spot of Jupiter.

3. April 2001: EGS Congress, Entropy maxima for the Shallow-Water equations.

4. EGS Congress, April 2002 Model of Jupiter’s troposphere using statistical mechanics.

5. EGS Congress, April 2002 Parametrization of small scale turbulence using a maxing entropy production theory

6. Conference "Statistical Mechanics of Non-Extensive Systems" Paris, October 2005

7. Conference “European Geophysical Union general assembly”, Vienna, April 2007

8. Conference UPON “Upon Problems on Noise”, Lyon, June 2008

5.4 Other talksTalks in international contexts 18 talks in Europe, Japan and the United States, not detailed here.

Talks in national laboratories or in a national context (GDR-Workshops-...)30 talks in Frenchlabs, GDR and workshops

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6 Student direction, teaching, and organization of schools, con-ferences and workshops

6.1 Student and Post-Doc direction

1. Nicolas Sauvage, ENS-Lyon, Master thesis, 04/2005-06/2005

2. Renaud Pochet, ENS-Lyon, License (L3) thesis, 06/2007-07/2007

3. Supervision of 3 students of License (L3) of Nice university. 01/2007-04/2007

4. Antoine Venaille, student at ENS-Lyon, PhD, co-directed by J. Sommeria (LEGI-Grenoble)and myself (Statistical mechanics of the Quasi Geostrophic model). 09/2005-10/2008

5. Hidetoshi Morita, Post-doc, 2D Stochastic Navier Stokes equation, 11/2007-08/2009

6. Marianne Corvellec, student at ENS-Lyon, began a PhD thesis under my supervision, inSeptember 2008. (Out of statistical mechanics of simple ocean models). 09/2008-?

6.2 Teaching

I am “agrégé de mathématiques”, a competitive examination that allow one to teach in High Schoolsand up to the undergraduate level in French “classes préparatoires” or in French universities.

During my military service I have been teacher in a French high school in Italy for 2 years.I have been “moniteur” during my PhD thesis (3 y., 60 h./y.), the first year in mathematics and

the two next years in physics and “Agrégé Préparateur” at ENS-Lyon during one year (192 h./year,mainly in License and for students preparing “Agrégation”).

I have also participated to the Master of physics (M2) of ENS-Lyon (TD in “nonlinear dynamics”,during 2 years).

Basically I have taught mathematics in all classes, with only few exceptions, from “5eme(12 yearsold students)” to the third year of License at university”, and physics from “première (16 years oldstudents)” to the Master degree.

This next list concerns only my most recent teaching, basically from 2005.

1. Examiner for ENS’s applications - “Oral physique, section PC” 2005-2006-2007. 40 h. peryear.

2. Examiner for ENS’s applications - “TIPE, section PC” 2006. 20h.

3. Examiner for ENS’s applications - “Ecrit physique - Composition d’un énoncé + corrections”2007

4. Préparation à l’agrégation de physique ENS-Lyon - Composition d’un sujet de concours + cor-rection. December 2007, January 2008. 30 h.

5. Master M1 Nice. Out of equilibrium statistical physics. 2007-2008. 30 h.

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6.3 Organization of workshops and conferences1. I was the main organizer of an international conference TURBULENCE AND STATISTI-

CAL MECHANICS, held in "Les Houches, France, 2-6 March 2009". Scientific program :fundamental problems in turbulence with an emphasis on its relations with statistical mechan-ics. Scientific committee: E. Bodenschatz, G. Falkovich, U. Frisch, S. Kuksin, S. Nazarenko,R. Pandit, G. Parisi, J.-F.Pinton, I. Procaccia, A. Pumir and A. Vulpiani. Organizing com-mittee: J. Bec, F. Bouchet, F. Gallaire, E. Simonnet, D. Vincenzi. http://www.oca.eu/stat-turbulence/Home.html

2. Since 2007, I am the main organizer of a thematic school on nonlinear dynamics and sta-tistical physics : “Aux Rencontres de Peyresq”. Yearly, one week long school with 30participants. Scientific committee: Y. Pomeau, E. Perez, P. Glorieux, P. Coullet, P. Clavin.http://peyresq.inln.cnrs.fr/

3. Meeting « Physical Oceanography », May 2007, in Nice. Workshop on theoretical problemsrelated to ocean dynamics. 30 participants.

4. Since 2005, I organize (with J. Bec and F. Gallaire) the “Rencontres niçoises de mécaniquedes fluides” . Half day meeting, for fluid mechanician of the Nice area (INLN, Observatoire(OCA), Lab. Dieudonné (mathematics), LPMC, CEMEF). Monthly. http://www.oca.eu/bec/mecaflu/

5. In 2000-2001 (during my PhD thesis), I organized (together with A. Bogdanovic, S. Cohen, ...)in University Joseph Fourier, a cycle of conferences “Midi Sciences”, twice per months, tar-geted to master students, PhD students and researchers from Joseph Fourier university. Averagenumber of participants : 80.

6. Since 2007, I organize together with M. Giudicci (main organizer) the seminars of INLN

7 Collective responsibilities and research management

7.1 Grants1. Fellow of a grant “Lavoisier” (french government - post-doc in Florence), of a Marie Curie

RTN post-doc (Rome). I have been Agrégé préparateur (ENS-Lyon).

2. Leader of the ANR-JC project : STATFLOW, funded in 2006. (ANR is the french researchagency, similar to the NSF in the USA). Scientific project: Out of equilibrium statistical me-chanics (kinetic theory) for 2D and geophysical flows. We study the statistics of the large scaleturbulence, for two dimensional or simple geophysical models. The participants are a specialistof the numerical stability of 2-D and 3-D flows (F. Gallaire, sec. CNRS no 10), by a mathemati-cian of geophysical flows and kinetic theory (F. Rousset, sec. 01) and a specialist of the lowfrequency variability of ocean dynamics (E. Simonnet, sec. 19) and myself (sec. 02), physicistof the statistical mechanics of geophysical flows.

3. Grants for funding “Aux Rencontres de Peyresq” (twice), several fundings for the “RencontresNiçoises de mécanique des fluides” (see above). The conference “Turbulence and StatisticalMechanics” in Les Houches is already partly funded thanks to several funding.

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7.2 Collective responsibilities1. I participate to my lab council

2. I am member of the “commission de spécialistes”, section 29, of Nice university

3. I am referee for most important reviews in my field, including PRL,PRE, JSP, EPJB, EPL, .... Irefer more or less ten articles a year.

4. I have refereed two ANR projects

8 Past mobility and collaborations

8.1 Laboratory changeDuring these four years, I have been post-doc in Roma (with A. Vulpiani), from January 2003 toaugust 2003, agrégé préparateur in ENS-Lyon from September 2003 to September 2004. My CNRSposition began in November 2004. I stayed in ENS-Lyon for a one year period, in order to finishsome ongoing research with T. Dauxois. I am in my new laboratory : INLN, in Nice, since November2005.

8.2 Periods of research abroadI passed two years in Italy during my post-doc. Since I have a fixed research position in CNRS, I havebeen visitor of labs. abroad :

1. I have been invited in the Waseda University, Tokyo, Japan, as invited professor in the physicsdepartment, in the group of K.I. Maeda in September 2005.

2. I have been invited in the Weizmann Institute, Rehovot, Israel, as invited professor in the physicsdepartment, in the group of K.P. Maeda in November 2005.

8.3 CollaborationsI have (or had) regular collaborations with the following persons or group :

1. T. Dauxois. ENS-Lyon

2. D. Mukamel and K. Jane. Weizmann Institute. Israel

3. S. Ruffo. University of Firenze. Italy

4. J. Sommeria and A. Venaille. LEGI (Coriolis). Grenoble (co-direction of A. Venaille PhDthesis).

5. Y. Sota and T. Tatekawa. Waseda University. Tokyo. Japan

6. Y. Yamaguchi. University of Kyoto. Japan

7. F. Gallaire, F. Rousset and J. Barré. Lab. Dieudonné. Nice

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8. P.H. Chavanis. Université Paul Sabatier. Toulouse

9. R. Kaiser. INLN.

10. H. Touchette - London

I plan future collaborations and works with

1. U. Frisch and J. Bec. Observatoire de Nice.

2. A. Majda. NYU -USA

3. T. Schneider. Caltech - USA

4. B. Nadiga and R. Ecke. Los Alamos -USA

5. S. Nazarenko and C. Connaughton. Warwick University - UK

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9 A more detailed description my past research results

My recent research activity is balanced between two main poles. The first one is the study of the sta-tistical mechanics of systems with long range interactions. The second one is the statistical mechanicsof two dimensionnal and geophysical flows.

9.1 Statistical mechanics of systems with long range interactions

IntroductionIn a large number of physical systems, any single particle experiences a force which is dominated

by interactions with far away particles. For instance, in a system with algebraic decay of the inter-particle potential V (r) ∝ 1/rα for large r, when α is less than the spatial dimension of the system, theinteraction is long range (such interactions are sometimes called ”non-integrable”). Such long rangeinteracting systems are not-additive, as the interaction of any macroscopic part of the system with thewhole is not negligible with respect to the internal energy of the given part.

The main physical examples of non-additive, long range interacting systems are : astrophysicalself-gravitating systems, two-dimensional or geophysical fluid dynamics (vortices have a logarithmicinteraction), some of the plasma physics models, models for wave-particle interactions, interactiondue to multiple light scattering in cold atoms, or due to the dipolar force in optics, etc ... Spin systemsand toy models with long range interactions have also been widely studied.

As a consequence of the lack of additivity, peculiar thermodynamic behaviors are likely to beobserved in such Hamiltonian systems. For instance, the usual proof of the validity of the canon-ical ensemble, for a system in contact with a thermostat, or for a part of a bigger isolated system,uses explicitly this additivity property. Hertel and Thirring provided a toy model, mimicking self-gravitating dynamics, which displays inequivalence between canonical and microcanonical solutions,with negative specific heat regions in the microcanonical ensemble. Negative specific heat and en-semble inequivalence, previously known to astrophysicists, were then found in various fields : plasmaphysics and geophysical fluid dynamics. These examples show that new types of phase transitions arefound in long range interacting systems.

Recently, a new light was shed on the equilibrium statistical mechanics of these systems. The firstreason is that a mathematical characterization of ensemble inequivalence [13] and the study of severalsimple models [2] have illustrated different type of inequivalence that might exists between the mi-crocanonical and the canonical ensembles. The second is the appearance of a very useful technique,namely the large deviation theory, to compute the microcanonical number of microstates and thus theassociated microcanonical entropy [1]. The third is a full classification of phase transitions and of en-semble inequivalence in such systems [3]. The last, but not the least reason, is the understanding thatthe broad spectrum of applications should be considered simultaneously since significant advanceswere performed independently in the different domains [12].

The dynamics of all of these systems also share deep analogies between each other. For instance,the analogies between the Vlasov equation and the 2D Euler equation have repeatedly been illustratedin the last forty years. The studies of the equilibrium states linear and nonlinear stabilities, is verysimilar for each of these models (Arnold’s type nonlinear stability theorems) and are deeply relatedto the thermodynamics stability. Recently, we have emphasized the role of Quasi-Stationary-States insuch systems, and explained their long time stability [20].

The out of equilibrium statistical mechanics of systems with long range interactions may be ad-

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dressed in the context of kinetic theory. By analogy with the Boltzmann equation for weak densitygases, the Lennard-Balescu equation (or the Landau equation which is an approximation of the latter)describes the evolution of a quasi-stationary distribution towards a Boltzmann distribution. The name"Lennard Balescu equation" usually refers to plasma physics problems, however a similar approachis also used for self-gravitating systems, or for point vortices in the context of fluid mechanics.

This kinetic theory is a very old subject. There still remain a number of unanswered issues. Themain one is the study of the limit of validity of this approach : whereas it is likely to be valid whenthe quasi-stationary distribution has no "stagnation point", it probably fails in the opposite case. Inthe following, I describe two examples of new results in this context.

We have theoretically explained and predicted, previously observed anomalous diffusion and nonexponential relaxation, in these systems [5, 21]. Both of these works, led in the framework of usualstatistical mechanics, led to a strong controversy with the defenders of Tsallis non extensive statistics(see for instance Bouchet, Dauxois and Ruffo 2006). We have also proved that the relaxation towardsequilibrium of 1D systems with long range interaction is not described by the usual quasi-linearkinetic theory (Lenard-Balescu equation) [5].

An alternative out of equilibrium theory, still not well studied, would be to consider weakly forcedand dissipated systems. This is the spirit of my current research in the context of two dimensionnalflows (section 9.3) and of my research project (section ??).

Several applications of statistical mechanics to systems with long range interactions to astrophys-ical self gravitating systems have been considered [11, 10, 19]. I currently pursue actively this direc-tion of research (see section ??), in collaboration with Y. Sota, T. Takayuki in Tokyo (group of K. I.Maeda, Waseda University). An other field of application concerns the study of the out of equilibriumstatistical mechanics of the 2D Euler (Navier-Stokes) equation as described in the section 9.2 of thisreport. I have also initiated a collaboration with R. Kaiser (Cold atoms, see section ??), in order toinvestigate possible applications of these ideas to their experiment involving cold atoms, with mutuallong range interactions, mediated by multiple scattering of light.

In the following paragraph, I describe in details only the main works done in the thematic ofsystems with long range interactions.

Classification of phase transitions and ensemble inequivalence (Bouchet and Barré 2005, [3])Systems with long range interactions in general are not additive, which can lead to an inequivalence

of the microcanonical and canonical ensembles. The microcanonical ensemble may show richerbehavior than the canonical one, including negative specific heats and other non-common behaviors.

By analogy with the classical Landau classification of phase transitions, valid for systems withshort range interactions ; in this work we proposed a classification of microcanonical phase tran-sitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence, insystems with long range interactions.

This classification is thus an exhaustive list of all possible phase transitions and situations ofensemble inequivalence. We emphasize on impossible situations, due to thermodynamical constraints.

We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensionalfluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet beenobserved in such systems. This opens the quest for observing such phase transitions in real physicalsystems or in models.

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Large deviations and systems with long range interactions (Barré, Bouchet, Dauxois, Ruffo2005, [1])

We have used large deviation estimations for the probability of macrostates in the microcanonicalensemble, in order to solve models with long-range interactions in the microcanonical and canonicalensemble. We show how this can be adapted to obtain the solution of a large class of simple models,which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising,Potts) and continuous (HMF, Free Electron Laser) state variables. We treat both infinite range andslowly decreasing interactions and, in particular, we present the solution of the α−Ising model in one-dimension with 0 ≤α < 1. This extremely simple model already displays ensemble inequivalence.

Large deviation estimations is a very powerful tool that has been then used in a number of otherdomains.

Kinetic theory and nonlinear dynamics in systems with long range interactions (Bouchet, Daux-ois and Yamaguchi 2005-2007, [5, 4, 21])

We have proposed a kinetic description of the Hamiltonian Mean Field model, which is paradig-matic for dynamical systems with long-range interactions, following the classical quasi-linear theory.In this framework, we have shown that generically, the Fokker Planck equation which governs fluc-tuations, has a non exponential relaxation and leads to anomalous behaviors. This mechanism is notlimited to the HMF model.

Studying this Fokker-Planck equation in details, we have predicted algebraic tails for the mo-mentum auto-correlations and anomalous diffusion for the angles. We derive analytically the cor-responding laws in the limit of a large number of particles. We argue that the mechanism for suchan anomalous transport does not depend on some complex structure of the phase space: indeed, thetransport is anomalous for out-of-equilibrium distributions but also for the equilibrium microcanoni-cal distribution.

We have also proved that the relaxation towards equilibrium of 1D systems with long range inter-action is not described by the usual quasi-linear kinetic theory (Lenard-Balescu equation).

Polemic with C. Tsallis group against the “Non extensive statistical mechanics”The classical equilibrium statistical mechanics we use, is based on the classical and natural hypoth-

esis of averaging with respect to a uniform distribution, on an energy shell, of the N particle phasespace (microcanonical distribution). For out of equilibrium problems, our approach deeply rely onthe actual dynamics of the system (kinetic theory).

By contrast, an other school uses maximization of a baseless functional, called “non extensiveentropy”. Then by logically meaningless considerations, but using analogies, they develop a whole“theory” similar to the classical statistical mechanics. This point of view concerning the "Non exten-sive statistical mechanics" may seem extreme, but it is in accordance with the reality, at least as far asI understand it.

Because our works [20, 5] led to contradictions with previous statements of C. Tsallis’ group, thepublication of the latter has been very difficult. This also led to a comment to an article published inEurophysics news (Bouchet, Dauxois and Ruffo, 2006).

Generic ergodicity breaking in systems with long range interactionsWith D. Mukamel, T. Dauxois and S. Ruffo, with have argued that, in systems with long range

interactions, in addition with ensemble inequivalence, we may generically observe “strong ergodicity

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breaking” (the phase space is no more connected). We have exemplified this on very simple models.The redaction of this work is in progress.

Limit of validity of the Vlasov equation [14]With K. Jain and D. Mukamel, we have addressed the validity time for the Vlasov description of a

N-body system with long range interactions. We have proved that the known lower bound t ∝ log(N)(Braun and Hepp, [9]) is actually optimal. We have exemplified this both in systems with continuousstate variables (Hamiltonian dynamics) and discrete systems with Monte Carlo type dynamics

9.2 Equilibrium statistical mechanics of two dimensionnal and geophysicalflows

Model of the Great Red Spot and of Jupiter’s troposphere (Bouchet and Sommeria 2002, Bouchetand Dumont [8, 6]) Atmosphere and oceanic flows have the property to self-organize at large scale.Due to the large difference between typical forcing and inertial time scales, this organization is re-markably stationary in the case of the Jovian planet tropospheres. The comprehension of the stabilityand of the detailed structure of these flows is thus render easier than for any other geophysical flows.Moreover, the excellent quality of the data obtained from spatial probe, make easy a precise compar-ison of predictions with actual flows.

As in the earth atmosphere and in the oceans, these flows are often organized into narrow jets.They can zonally flow around the planet like the eastward jet at 240 latitude in the northern hemisphereof Jupiter (Maxworthy 1984). Jets can alternatively organize into rings, forming vortices, like therings shed by the meandering of the Gulf-Stream in the western Atlantic Ocean. The flow field inJupiter most famous feature, the Great Red Spot, is an oval-shaped jet, rotating in the anticyclonicdirection and surrounding an interior area with a weak mean flow (Dowling and Ingersoll 1989), seefigure 1. Robust cyclonic vortices are also observed with a similar jet structure (Hatzes and al 1981).Smaller features, as the white ovals, have also an oval shape but no more the jet structure.

Such jets and vortices are in a turbulent surrounding, and the persistence of their strength andconcentration in the presence of eddy mixing is intriguing. We explain the emergence and stabilityof the Great Red Spot, in the highly turbulent Jupiter’s atmosphere, by a statistical mechanics ofthe potential vorticity mixing. Using the Quasi-Geostrophic 1-1/2 layer, with topography, when theRossby deformation radius is small, we predict strong jets. These jets can be either zonal, or closedinto a ring structure like the Great Red Spot one. We reproduce the GRS observed velocity field toa very good quantitative accuracy. For smaller vortices, or for stronger topography curvature, wereproduce the characteristics properties of the White Ovals or of the cyclonic Brown Barges. Thelink between their shape, topography and surrounding shear is explicitly described. We obtain verystrong qualitative results for the Jupiter’s vortices. For instance, any of these vortices must be ontopography extrema (in the reference frame moving with the structure), the shear in the active layeris larger than the shear in the deep layer. On a same latitudinal band, the velocity of the vortex isrelated to their latitude. These theoretical predictions are in accordance with the observed propertiesof Jovian vortices.

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R

10 000 km

20 000 km

Figure 1: Upper part: vorticity field and velocity field for the statistical equilibrium modeling theGreat Red Spot. Lower : the observed velocity field, from Dowling and Ingersoll (1988). The actualvalues of the jet maximum velocity, jet width, vortex width and length fit with the observed ones.The strong jet is the interface between two phases, each corresponding to different Potential Vorticitymixing. It obeys a minimal length variational problem, balanced by the effect of the deep layer shear.

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Figure 2: Top: typical vortex shape obtained from the statistical equilibria, for two values of theparameters. Bottom left: the Great Red Spot and one of the White Ovals. Bottom right: one of theBrown Barges of Jupiter’s north atmosphere.

-6 0 6-4

0

4y

x

9.2.1 Ongoing work, not yet published

I briefly describe some of my ongoing works :

1. I am currently writing two articles on the Jovian atmosphere, which are direct extensions of myPhD work on that subject.

2. I am currently writing one article dealing with the equilibrium states of the Quasi-Geostrophicequation, in the limit of small Rossby deformation radius, with strong beta effect. This workis oriented towards ocean application, and linked to the work I have done together with N.Sauvage during its Master thesis and with A. Venaille during his thesis.

3. I am currently writting a book with J. Sommeria on the application of equilibrium statisticalmechanics to geophysical flows.

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9.3 The out of equilibrium statistical mechanics of two dimensional and geo-physical flows

One of the most important problem in turbulence is the prediction of large-scale structures of veryhigh Reynolds’ flows. We consider here the class of two dimensionnal and geostrophic flows relevantfor geophysical applications (ocean and atmosphere). The main physical phenomenon is the self orga-nization of the large scales into jets and vortices. We study the simplest academic problem includingthis type of phenomena : the two-dimensional Navier-Stokes equation with weak stochastic forcesand dissipation.

Two beautiful classical theories deal with two dimensional turbulence. The first one, the cascadetheory is aimed at describing the velocity field statistics for self similar inverse energy cascade ordirect enstrophy cascade. For this first approach, the main hypothesis is self similarity, which isunfortunately broken as soon as large scale structures (vortices and jets) appear. The second theoryis the equilibrium statistical theory that describes the organization of inertial flows [16, 17, 18, 8].However this last approach does not take into account the effect of forces and dissipation.

Most of natural or experimental flows, as far as large scales are concerned, thus do not fall inthe realm of classical theories. This is the motivation to study the two-dimensional Navier-Stokesequation with weak stochastic forcing and dissipation. This is an example of dynamical system forcedby noise, where an out of equilibrium stationary state is reached, without detailed balance. Theexistence of an invariant measure has been mathematically proved recently, together with mixingand ergodic properties [15]. This problem has however never been considered from a physical pointof view. We thus address the following issues: when is the measure concentrated on an inertialequilibrium, how are the large scales selected by the forcing, what is the level of the fluctuations ?

Two dimensional turbulence is an example of physical phenomena where order arises from ran-domness and where fluctuations play a crucial role in selecting the main structures.

9.3.1 Random transitions between large scale flows with different topologies

We study the two dimensional Navier Stokes equation with stochastic forces. The most striking phys-ical result is the existence of out of equilibrium phase transitions : one observes random bifurcationsfrom one topology of large scale flow (dipoles) to another (unidirectional flows). The flow behavessimilarly to a bistable system that switches at random times from one state to the other.

After the theoretical study of a bifurcation diagram for the stationary states of the 2D Euler equa-tion, we have conjectured the existence of these out of equilibrium phase transitions (S4, [7]). Wehave verified their existence using numerical simulations and made a detailed empirical study (S4,[7]). Similar considerations leads to the predictions of out of equilibrium phase transitions in a largeclass of other geometries, and also for geostrophic, large rotation or 2D magnetic flows.

The system roughly behaves as a bistable one. However this analogy is extremely limited. Indeed,in our case no potential landscape exists, that would explain the phenomena. Moreover the turbulentnature of the flow (infinite number of degrees of freedom) renders the phenomena much richer thanin the classical two well problem. Analogies with the Earth magnetic field reversal, and with similarphenomena in experiment of two dimensionnal and geophysical flows will be discussed.

This leads to open issues, as discussed in section 2. The major one is : in this class of phenomenawhere the description by a small number of modes is not valid, can we propose a theory predictingthe selection of large scales flows by the balance between stochastic forces and dissipation ?

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9.3.2 The 2D linearized Euler equations : the stochastic Orr mechanisms and Landau damp-ing

I have obtained theoretical results for the prediction of the velocity and of the vorticity fluctuations,in the context of the Navier Stokes stochastic (NSS) equation, with weak stochastic forcing and dis-sipation. Theoretical arguments and numerical evidences show that flows are then close to equilibriaof the Euler equation. At leading order, fluctuations around such equilibria are then described by thelinearized NSS equation.

I have thus studied theoretically the linearized NS equation with random forces. In the limit ofzero dissipation, as expected no stationary distribution exist for the Gaussian vorticity field. By con-trast, the Gaussian stream function or velocity fields strikingly converge toward a stationary Gaussianprocess. The velocity field thus acts similarly to a dissipative system, when dissipation is no morepresent. An explanation of this seemingly anomalous behavior and its relation to the deterministicLandau damping of plasma physics and Orr mechanism for 2D vortices is given.

From the point of view of turbulence, this work on the 2D linearized Euler and Navier Stokesequations, gives precise estimations on the small scale vorticity field spectra, and determines themechanism of the two dimensional backward energy transfer, and forward enstrophy cascade, forflows dominated by large scale structures.

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Annexe A : Most cited papers in JSP

Figure 3: Document from the Journal of Statistical Physics editorial board.

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References[1] J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo. Large deviation techniques applied to systems with long

range interactions. J. Stat. Phys., 119 1/2, 2005.

[2] Julien Barré, David Mukamel, and Stefano Ruffo. Inequivalence of ensembles in a system with long-rangeinteractions. Phys. Rev. Lett., 87(3):030601, Jun 2001.

[3] F. Bouchet and J. Barré. Classification of phase transitions and ensemble inequivalence, in systems withlong range interactions. J. Stat. Phys., 118 5/6:1073–1105, 2005.

[4] F. Bouchet and T. Dauxois. Kinetics of anomalous transport and algebraic correlations in a long rangeinteracting system. Journal of Physics: Conference Series, 7:34–47, 2005.

[5] F. Bouchet and T. Dauxois. Prediction of anomalous diffusion and algebraic relaxations for long-rangeinteracting systems, using classical statistical mechanics. Phys. Rev. E, 72(4):045103–+, October 2005.

[6] F. Bouchet and T. Dumont. Emergence of the great red spot of jupiter from random initial conditions.cond-mat/0305206, 2003.

[7] F. Bouchet and E. Simonnet. Random changes of flow topology in two dimensional and geophysicalturbulence. ArXiv e-prints, 2008.

[8] F. Bouchet and J. Sommeria. Emergence of intense jets and jupiter’s great red spot as maximum entropystructures. J. Fluid. Mech., 464:165–207, 2002.

[9] W. Braun and K. Hepp. The Vlasov dynamics and its fluctuations in the 1/ N limit of interacting classicalparticles. Commun. Math. Phys., 56:101–113, June 1977.

[10] P. H. Chavanis, J. Vatteville, and F. Bouchet. Dynamics and thermodynamics of a simple model similarto self-gravitating systems: the HMF model. European Physical Journal B, 46:61–99, July 2005.

[11] P.H. Chavanis and F. Bouchet. On the coarse-grained evolution of collisionless stellar systems. Astronomyand Astrophysics, 430:771–778, 2005.

[12] T. Dauxois, S. Ruffo, E. Arimondo, and M. Wilkens. Dynamics and Thermodynamics of Systems withLong-Range Interactions, volume 602 of Lecture Notes in Physics, Berlin Springer Verlag. 2002.

[13] R. S. Ellis, K. Haven, and B. Turkington. Large Deviation Principles and Complete Equivalence andNonequivalence Results for Pure and Mixed Ensembles. J. Stat. Phys., 101:999, 2000.

[14] K. Jain, F. Bouchet, and D. Mukamel. Relaxation times of unstable states in systems with long rangeinteractions. J. Stat. Mech., 2007.

[15] S. B. Kuksin. The eulerian limit for 2D statistical hydrodynamics. J. Stat. Phys., 115:469–492, 2004.

[16] Jonathan Miller. Statistical mechanics of euler equations in two dimensions. Phys. Rev. Lett.,65(17):2137–2140, 1990.

[17] R. Robert. A maximum-entropy principle for two-dimensional perfect fluid dynamics. J. Stat. Phys.,65:531–553, 1991.

[18] J. Sommeria and R. Robert. Statistical equilibrium states for two-dimensional flows. J. Fluid Mech.,229:291–310, August 1991.

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[19] T. Tatekawa, F. Bouchet, T. Dauxois, and S. Ruffo. Thermodynamics of the self-gravitating ring model.Phys. Rev. E, 71(5):056111–+, May 2005.

[20] Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo. Stability criteria of the vlasov equation andquasi-stationary states of the hmf model. Physica A, 337 (1-2):36–66, 2004.

[21] Y. Y. Yamaguchi, F. Bouchet, and T. Dauxois. Algebraic correlation functions and anomalous diffusionin the Hamiltonian mean field model. J. Stat. Mech., 1:20–+, January 2007.

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