**Dr Thierry Dauxois is a theoretical physicist and Director of Research of the Laboratoire de Physique at l’Ecole Normale Supérieure de Lyon. He is also a member of the Editorial Board of Journal of Physics A: Mathematical and Theoretical. He works on a number of topics relating to long-range interacting systems and internal gravity waves, and we talk to him about his career, current research and what it is he finds so appealing about the topics he studies.
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**Could you provide us with a brief summary of your career so far? **

After undergraduate studies in Toulouse and Lyon, I prepared my PhD in Dijon with a long stay at the Los Alamos National Laboratory, USA. I was working on the possibility to use nonlinear waves, more precisely oscillating ones, to understand the dynamics of DNA. We were more specifically interested in localized openings of DNA. Then I did my military service and spent one year in a physics laboratory working on the stability of vortices. Recruited as a CNRS researcher, I continued to work on nonlinear waves, sometimes called solitary waves or solitons, studying their existence, stability and possible applications in condensed matter of fluid mechanics. Then I had the opportunity to spend successively 6 months in Firenze, Italy followed by one year in San Diego, USA. This is where I discovered two new topics for me that have driven my research so far. In Firenze, working with Stefano Ruffo, I discovered the intriguing behavior of long-range interacting systems, while in San Diego, at the Scripps Institution for Oceanography, I discovered thanks to Bill Young the beautiful physics of internal gravity waves that one can find in stratified fluids (oceans, atmosphere, stars etc). In the last 15 years, I pursued both these lines of research, initially purely theoretically, but progressively, I developed a real experimental lab dedicated to internal waves.

**You have done a degree of work on Long-Range Interacting Systems. What other research areas are of interest to you and what led you to this area of research?**

As anticipated above, one of my specialties is nonlinear waves or more precisely solitary waves that are also called solitons. They are exceptionally stable standing waves that have fascinated scientists since they were first observed in 1834. In addition to leading to elegant mathematical theories, they have some widespread theoretical and applied uses in physics. Together with Michel Peyrard, we published a book on it that you might find useful: *Physics of Solitons*. I was also interested in the link between the nonlinear dynamics of these waves and the thermodynamics of the underlying system. In 2000, working with my colleagues Peter Holdsworth and Stefano Ruffo, we discovered an interesting behavior of some waves in a peculiar long-range interacting model. This is how I got interested in long-range interactions: it was well known that they pose serious problems for the formulation of statistical mechanics, and we started to understand how one can circumvent these difficulties. One of the crucial ideas was to study first simple toy models which led us to distinguish the numerous difficulties. This is the usual physicist’s approach that also proved to be very useful here. After 15 years of research in this field, with three Italian colleagues, we have written a book, *Physics of Long-range Interacting Systems*, to make the field easily accessible to newcomers and provide a guide to the vast literature on this topic.

**What kind of problems appeal to you?**

It is a central but difficult question! I would reply that I like to be surprised. Long-range interacting systems have really unexpected behavior if one compares them with the short-range interactions that physicists are more used to deal with. Surprisingly, although gravitation and electromagnetism are central topics, covered in Bachelor’s and Master’s courses in physics, they are not discussed in statistical mechanics classes and in the very large majority of textbooks devoted to this field. I enjoyed discovering the equilibrium and out-of-equilibrium features of these systems, encouraging me to understand more deeply the hypothesis of our commonly used theories.

The second topic that drives my research, Internal gravity waves, is also very intriguing and defies our intuition as physicists.

**What are you currently working on?**

Internal gravity waves propagate in density-stratified fluids owing to the restoring force of buoyancy. They are ubiquitous in the ocean and their amplitude may be large enough for these waves to be observed in satellite images as striking band-like features that travel for thousands of kilometers across the ocean. In terms of global budgets, the most energetic part of the internal wave activity is indeed located in the deep ocean where measurements and associated modeling still lack confidence. This is a key problem for oceanography, as the internal wave field of oceans involves an available amount of energy that can be used for mixing of water, which influences the global circulation and therefore the Earth’s climate. Internal waves are also important for the transport of sediments and plankton, and in the context of astrophysics.

From the physicist’s point of view, internal gravity waves are particularly interesting. They are transverse waves that do not respond to our classical perception of wave phenomena. Their group and phase velocities are perpendicular, their reflection laws are completely different from the usual Snell-Descartes laws, the Huyghens-Fresnel diffraction laws are questionable… All these properties lead to paradoxes that are of high interest from the ‘fundamental physics’ point of view. Moreover part of the above properties, which are consequences of an anisotropic dispersion relation due to gravity, are also encountered for inertial waves (in presence of rotation) or plasma waves (in presence of a magnetic field), and also in astrophysics.

Nonlinearity has unexpected consequences when considering internal waves. A plane wave is solution of the full inviscid nonlinear equation for any amplitude: a quite unusual property. However, this solution is unstable in the nonlinear regime and this instability has been shown to be a central mechanism towards mixing. I am particularly interested in this instability. I am trying to develop an experimental setup – a simplified version of natural systems – in which one would be able to study the cascade toward mixing; it is likely to be a very efficient guide to theoretically understand wave turbulence-like cascade at play in the oceans.

**What do you consider to be the most significant problems to be addressed in your field?**

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Indeed, the continuous energy input to the ocean interior comes from the interaction of global tides with the bottom topography. The subsequent mechanical energy cascade to small-scale internal-wave motion and mixing is a subject of active debate in view of the important role played by abyssal mixing in existing models of ocean dynamics. A question remains: how does energy injected through internal waves at large vertical scales induce the mixing of the fluid.

**What are the challenges facing researchers in mathematics and theoretical physics?**

I am not particularly worried about the future of mathematics and theoretical physics. Why should I be? I am convinced that there are plenty of new discoveries waiting for us. Of course, there is the importance of convincing people about the value of fundamental research, particularly in times when the economy is in a difficult position. However, I am voluntarily optimistic about this issue.

**Where do you think your research will take you next? Are there any other fields you are interested in exploring?**

They are many. You know, I started doing theoretical physics on biophysical related models with the help of computers, while I am doing now fluid mechanics in stratified fluids with the help of experiments. You could easily understand that many problems are interesting to me. To name just one: neurosciences. However, I told you that I like surprises so it is difficult to predict!

**Finally, do you have any advice for young researchers entering the field?**

Take pleasure in discovery, have the curiosity to stay open minded – and a bit of work is also essential.

On behalf of Journal of Physics A I would like to thank Dr Dauxois for talking the time to talk to us.

**Read more:**

- Validity conditions of the hydrostatic approach for self-gravitating systems: a microcanonical analysis
- A stochastic model of long-range interacting particles

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Front image and image 1: copyright Florence Raynal; used with permission. Not covered by CC-BY 3.0.

Categories: Journal of Physics A: Mathematical and Theoretical