Denys DUTYKH's Blog of an applied mathematician

Latest results

In this post I would like to mention a couple of recent submissions that we prepared with my new and old co-authors.

First of all, with my new brazilian friends (Julien Berger and Nathan Mendes) we submitted a manuscript devoted to the understanding of some inverse problems in the heat conduction (yes, I am totally open to new topics). The preprint is already available on HAL server (it contained too many pictures to :

  • J. Berger, D. Dutykh & N. Mendes. On the optimal experimental design for heat and moisture parameter estimation, Submitted, 2016
  • Abstract: In the context of estimating material properties of porous walls based on in-site measurements and identification method, this paper presents the concept of Optimal Experiment Design (OED). It aims at searching the best experimental conditions in terms of quantity and position of sensors and boundary conditions imposed to the material. These optimal conditions ensure to provide the maximum accuracy of the identification method and thus the estimated parameters. The search of the OED is done using the Fisher information matrix and a priori knowledge on the parameters. The methodology is applied for two cases. The first one deals with purely conductive heat transfer, while the second one combines a strong coupling between heat and moisture transfer.

The second preprint is devoted to my more traditional topics, i.e. water wave modelling. Namely, we consider the deep water case and discuss several models, some of them being well-known and some new. The variational derivations and other averaging techniques are equally considered:

  • D. Dutykh, D. Clamond & M. Chhay. Serre-type equations in deep water, Submitted, 2016
  • Abstract: This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling approaches even if new results are presented as well. Namely, we derive the deep water analogue of the celebrated Serre-Green-Naghdi equations which have become the standard model in shallow water environments. The relation to existing models is discussed. Moreover, the multi-symplectic structure of these equations is reported as well. The results of this work can be used to develop various types of robust structure-preserving variational integrators in deep water. The methodology of constructing approximate models presented in this study can be naturally extrapolated to other physical flow regimes as well.

Now I think it is a good time to recharge the batteries… to undertake new research in September :)


French-Spanish workshop


Tomorrow I departure for the next destination - Valladolid (Spain) for a French-Spanish Workshop on Evolution Problems (FSWEP16). This meeting will be hosted by imUVa and Universidad de Valladolid. The Programme can be seen here. I would like to thank the organizers for giving me an opportunity to speak there. My talk will be devoted to the derivation of Galilean invariant and energy-consistent long wave models.

Lectures at Curitiba and internal waves

During these two weeks (1st – 14th of April 2016) I will be in Curitiba, Brazil to deliver some lectures on the Numerical Analysis at a PhD school in PUCPR University. I found on YouTube a short video presenting this University:

The Lecture notes are already available. They will be probably updated in the nearest future to the latest version (including some minor corrections and perhaps some new material):

Otherwise, recently with Didier Clamond we submitted a new mauscript where we report the multi-symplectic structure for the Green-Naghdi-type system describing long internal waves evolution. It seems that this system was derived for the first by E. Barthélémy (1989) in his PhD thesis done at the University of Grenoble. For simplicity, we adopt the rigid lid approximation, but the multi-symplectic structure can be generalized to the free surface case as well. The preprint is already freely available to download:

Any comments and suggestions are welcome!

Singular solitary waves

Phase plane analysis

Finally, yesterday with my collaborators from the University of Nice we submitted our manuscript on the construction of singular solitary wave solutions using the classical Phase Plane Analysis (PPA) and some methods from effective Algebraic Geometry.

This work was presented in many seminars from Japan (Yokohama) to Russia (Novosibirsk) and Austria (Linz). So, now you can find all the details about computations in our preprint available at all popular preprints servers:

Quantum Chaos

Quantum chaos

Recently I had to travel from Bucharest to Lyon (with a connecting flight at Istanbul). Arguably the best thing to do during a flight is to read. So, during my recent flights I read the following interesting article that I am pleased to recommend to you:

The reference is a little bit long, but it includes a lot of interesting historical information. Finally, I can say that after reading it I have an impression to have understood something about Quantum Chaos (QC)! :) In particular, you will learn that QC appears in three different kinds. I also had an impression that this research topic is essentially open. Very little is known about genuine QC.