A spectacular property of turbulent flows is their ability to mix components in a very efficient way. The theoretical study of transport and mixing by fluids is expressed naturally by studying the statistical properties of fluid particle trajectories that actually transport the components to mix (the Lagrangian approach). The Lagrangian properties of homogeneous and isotropic turbulence are now relatively well known thanks to investigations of the last 15 years. The case of inhomogeneous flows is much less studied, especially concerning experiments. Most natural or industrial flows are neither homogeneous nor isotropic due to the presence of walls and thus of boundary layers (pipe flows, atmospheric boundary layer…) and/or due to confinement (chemical reactors, combustion chambers). Furthermore, in practical flow configurations, direct numerical simulations of the Navier-Stokes equations with realistic physical parameters are out of reach due to the prohibitive required computation power. In practice, various levels of modeling are introduced to lower to computation power. Generally, only large scales features are simulated and the small-scale motions are modeled in order to only express their impact on the largest scales of the flow. But the small scales and the large scales are strongly coupled in the Navier-Stokes equations. This particularly visible in the case of boundary layers: turbulence is initiated at small scales near the wall and propagates to the large scales at the core of the flow. Thus it is of prime importance to build an efficient model of the small-scale motions in order to simulate satisfactorily the large-scale dynamics. To this end, it is possible to use stochastic models of the fluid particle transport. Models can concern the velocity of particles (models type Thompson-Pope) to simulate the random trajectories of fluid particle by taking into account the local large-scale properties of the flows. Models can be more elaborate by simulating the properties of particle acceleration. This the case of the LES-SSAM model aimed at reproducing the dynamics of acceleration and describe more accurately the statistical of the velocity field. Even if a few models exist, Lagrangian experimental data are scarce concerning inhomogeneous/anisotropic flows. Nevertheless they are essential to validate, to calibrate and to guide the possible improvements of the modeling tools. In this project, we expect: (i) first, to develop Lagrangian measurements in order to investigate the specific properties of confined flows and/or boundary layers. We will use laboratory flows such as a channel flow (boundary layers) and a Von Karman flow (confinement). We will investigate first acceleration of particles in various regions of the flow and the long time dispersion of single particles or pairs of particles. (ii) Second, we will perform direct numerical simulations of the Lagrangian dynamics in the case of a channel flow for which efficient pseudo-spectral methods exist. (iii) Finally we will compare experimental and numerical data to existing dispersion stochastic models for both cases of studied flows. A more elaborate model will be developed in the line of the LES-SSAM model for boundary layer flows. These efforts aim at providing the scientific community a complete database (numeric, experiments, model) in order to contribute to more advanced research on turbulence. It will also provide the industrial community with efficient models to be incorporated in industrial simulation codes.

Turbulent thermal flows in convection cells are inhomogeneous and very complex to predict and to understand due to the variety and the strong coupling of the physical mechanisms at play. These mechanisms change depending on the regime, the flow location and the scale of interest. Thermal boundary layers form near the surfaces, but being buoyancy-unstable, small scale structures called thermal plumes arise from this instability. Their collective motion produce a large scale circulation (LSC), which may suggest that the kinetic energy distributes from smaller to larger scales. Nevertheless, because the LSC itself shears the boundary layers, it may either contribute to turbulent fluctuations (further destabilizing the boundary layer) or impede the rise of the plumes. Heat is transported in the fluid by the thermal plumes, under both their own buoyancy and the advection by the LSC, but also by the turbulent fluctuations. Finally, turbulence in the bulk is nearly homogeneous and may get the kinetic energy to cascade from the large scale to the smaller dissipative scales (and produce heat locally). When the turbulence level is increased, either with higher forcing, or by the introduction of perturbations at the cell surfaces, the flow may experience a spectacular change to a regime of higher heat transfer efficiency. However, there exists a lot of discrepancy between experiments, with huge difference in the observed fluxes. Understanding these conflicting results is critical for areas where such high forcings are expected (e.g. cooling of nuclear power plant, geophysical flows), because the lack of understanding of the physical mechanisms impedes the ability to properly predict realistic heat fluxes. Our goal is to sort among these various mechanisms in order to disentangle the contribution of turbulence and that of the interacting thermal plumes. In order to do so, we wish to use diagnostic tools involving local information such as temperature and velocity correlations, to assess the role of turbulence, and plumes (i.e. statistics about their numbers, their size, their intensity). Such knowledge is key to propose useful physical models because the flow is highly inhomogeneous, and 3D information is pivotal. For example, do the plumes rise evenly over the plate, or only near the edges? How does the spatial distribution of rising plumes change when the forcing is increased? Despite progress made by careful comparison of experimental and numerical simulations studies, key differences remain in the amount and nature of the information provided by each community, making conjoint understanding very difficult. For instance, experimental data is incomplete, but well converged and can reach high forcings. Numerical simulations are fully resolved in space, but reach lower turbulence level and for shorter durations. The tremendous potential capabilities of recent physics-informed deep learning (DL) techniques will help in seamlessly integrating the benefits of each approach into a new modeling and comprehension of turbulent physics. In this project, we will take advantage of both perceptrons or convolutional neural networks frameworks enhanced with physical constraints, in order to mitigate the risks and to speed up and robustify the training phase of the models. More specifically, thanks to DL, we will be able to infer missing data from experiments, and alleviate the cost of expensive numerical simulations by reducing the storage cost. When trained on either experimental or numerical data, DL models will grant fast access to the local temperature and velocity coupling in time and space, to the local instantaneous heat transfer, and to the local temperature field. This will enable to explore the nature of the scalar in highly turbulent thermal convection.

Disentangling multicomponent signals and images into elementary constitutive parts is an important problem because of its ubiquity in many areas of science and technology. This however remains a challenging question for different reasons. On the one hand, there is no unique definition of what « multicomponent » means. On the other hand, we are now overwhelmed by a « deluge » of data and the question of extracting useful information from them has taken new forms. One facet of this proliferation is that getting more data often means facing extended variabilities, with a reduced hope that « universal » methods would be equally efficient in every context. This suggests a move towards more adaptive, ideally data-driven, methods, and it is precisely within this framework that ASTRES is proposed, with the underlying idea that, in a situation where data can now be quantitatively abundant, tailoring methods to individual specificities should add some significant extra value to the result of their processing. More specifically, ASTRES will focus on advanced data-driven signal and image processing techniques aimed at disentangling complicated, nonstationary waveforms and fields into a small number of physically meaningful components. This will be achieved by exploiting local data structure (and in particular phase information) to get improved analysis, synthesis, and processing schemes. Addressing those issues calls for a cooperation of advanced techniques in signal and image processing as well as in applied mathematics, with emphasis on recent optimization methods. This is reflected by the structure of the ASTRES collaboration, which relies on three teams chosen for their acknowledged expertise and complementarity. As for its scientific content, ASTRES is organized around three main techniques of multicomponent signal and image decomposition, namely the « reassignment method » (aimed at providing sharply peaked time-frequency representations), the « synchrosqueezing transform » (which also operates in a transformed domain—time-frequency or time-scale plane—, with a further sake of component reconstruction) and the « Empirical Mode Decomposition » (which directly works in the observation space, but with a similar purpose of component estimation). Those techniques, which share a number of common features—either in their form or in their goals—have attained different levels of maturity. The purpose of ASTRES will be to construct equally sound theoretical frameworks for them, as well as unified frameworks and efficient algorithms. The current status of the methods will be considered as a starting point, paving the way for numerous extensions to more complex settings, in particular multivariate and multidimensional. Finally, one ambition of the ASTRES project is to make the newly developed techniques become an entire part of processing schemes, beyond the sole analysis (or, sometimes, synthesis) tasks for which they have been used so far. In this respect, while ASTRES is mostly a methodological project, it will be both fed by and confronted to specific application areas, in particular in audio, physics and biomedicine.

When strained is applied to Mercury Telluride, a semiconducting gap is opened. When the chemical potential is placed within this gap by an external gate, the electrical conduction takes place at the material surface by charge Dirac carriers (with zero effective mass): this is an excellent (the best) topological insulator with very little residual bulk conduction. In this project, this material will be developed in order to control the energy and properties of the surface states (the Dirac carriers) in order to reach the best electronic transport properties (mobility, interface rugosity etc.). The band structure and the energies and the dispersion of the surface states will be studied by ARPES photoemission at the SOLEIL synchrotron and compared to the theoretical models appropriate to this system. The magneto-transport properties will be studied, with a particular interest on the quantum Hall phases which appear at high magnetic field. Specific experiment will be carried out to understand and characterize the bilayer quantum Hall states, we have recently discovered. At very high magnetic field, we will study an insulating phase which looks like a Hall insulator state (for which the longitudinal resistivity is infinite while the transverse Hall resistivity remains finite). Hg1-xCdxTe is a non centro-symmetric material which gap changes sign and in magnitude by varying x. Between the insulating (CdTe) and topological (HgTe) phases, a semi-metallic phase has been predicted to exist on symmetry arguments which nature is presently unknown. Its theoretical analysis should specify under which circumstances it appears and what experiment will reveal its presence. At the device level, we will design and fabricate hybrid structures where the Dirac carriers are in proximity of a superconductor. These structures will be experimentally studied, and the spectroscopy of the Andreev state measured, with the detection of Majorana fermions which have been predicted in such device as an ultimate objective. Finally we will fabricate simple structures capable of selecting and manipulating the spins of the Dirac carriers in the 2D spin-Hall limit (quantum wells) as well as in the topological insulator (3D) limit.

The dynamical rupture instability studied in this project is the so-called stick-slip instability i. e. the intermittent growth of a crack. Stick-slip rupture instabilities are observed in many different systems, for instance in heterogeneous rubbers used in the automotive tire industry and during the high speed peeling of adhesives in automatic labeling industrial processes, gluing of automotive parts or sealing of electronic housings. Overall, adhesive stick-slip reduces industrial productivity and its hard-to-predict nature hinders the development of new technical applications. From a fundamental perspective, the non-monotonous dependence of fracture energy on crack velocity that triggers stick-slip is still difficult to understand quantitatively due to the complex interplay between the fracture geometry, the strongly non-linear mechanical response of materials in large strain conditions and the existence of heterogeneities either in the material’s microstructure or induced by the rupture mechanism. Furthermore, the various physical parameters influencing the stick-slip instability have rarely been correlated to the actual characteristics of the stick-slip motion (stick and slip velocities, durations and amplitudes). The StickSlip project will develop and/or use various original and custom-designed experimental tools that are able to resolve in time and space the motion of the crack front during stick-slip in two situations: (i) the rupture of an adhesive at the interface between a backing tape and a substrate; (ii) the bulk rupture of an elastomer. The experiments that we propose will shed a new light on stick-slip instabilities in fracture. Measurements of the detailed characteristics of the stick-slip motion will allow us to clarify the key physical parameters controlling the instability (geometry, adhesive or elastomer rheology). The proposed experiments will also be used to test new ideas related to the effect of interfacial or bulk heterogeneities on stick-slip. The collective intermittent motion of the crack front that occurs during adhesive stick-slip might be disturbed by the presence of heterogeneities. A major goal of the project will be to understand whether heterogeneities might, in certain conditions, suppress the stick-slip instability at the macroscopic scale by destroying large scale correlations, and confine the stick-slip dynamics to smaller scales that would be less harmful for industrial applications. Being able to properly control the heterogeneities will be an important challenge of our project. On the one hand, the studies we propose are important for basic science since they will deepen our knowledge of the dependence of the fracture energy on crack velocity and even extend it to the widely unexplored case of materials with interfacial or bulk heterogeneities. Comparisons between adhesive peeling and elastomer tearing will allow us to validate the generality of our analysis. On the other hand, new solutions for controlling the instability (control of rupture geometry, control of polymer rheology, control of heterogeneities) would represent a significant breakthrough for industrial applications. In this context, the technical help offered by Bluestar Silicones is a significant added value to our project.