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 :)