Equation of state of the neutron star matter, and the nuclear symmetry energy

The nuclear mean-field potentials obtained in the Hartree-Fock method with different choices of the in-medium nucleon-nucleon (NN) interaction have been used to study the equation of state (EOS) of the neutron star (NS) matter. The EOS of the uniform NS core has been calculated for the np$e\mu$ composition in the $\beta$-equilibrium at zero temperature, using version Sly4 of the Skyrme interaction as well as two density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$), and versions D1S and D1N of the Gogny interaction. Although the considered effective NN interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies, they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the \emph{soft} and \emph{stiff} scenarios discussed recently in the literature. Different EOS's of the NS core and the EOS of the NS crust given by the compressible liquid drop model have been used as input of the Tolman-Oppenheimer-Volkov equations to study how the nuclear symmetry energy affects the model prediction of different NS properties, like the cooling process as well as the gravitational mass, radius, and moment of inertia.Comment: To be published in Physical Review

Clustering-based Identification of Precursors of Extreme Events in Chaotic Systems

Abrupt and rapid high-amplitude changes in a dynamical system's states known as extreme event appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic effects, therefore their description and prediction is of great importance. However, because of their chaotic nature, their modelling represents a great challenge up to this day. The applicability of a data-driven modularity-based clustering technique to identify precursors of rare and extreme events in chaotic systems is here explored. The proposed identification framework based on clustering of system states, probability transition matrices and state space tessellation was developed and tested on two different chaotic systems that exhibit extreme events: the Moehliss-Faisst-Eckhardt model of self-sustained turbulence and the 2D Kolmogorov flow. Both exhibit extreme events in the form of bursts in kinetic energy and dissipation. It is shown that the proposed framework provides a way to identify pathways towards extreme events and predict their occurrence from a probabilistic standpoint. The clustering algorithm correctly identifies the precursor states leading to extreme events and allows for a statistical description of the system's states and its precursors to extreme events

Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach

International audienceWe extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the unmeasured state, and (ii) the physical equations of a prototypical chaotic dynamical system. Non-noisy and noisy datasets are considered. First, it is shown that the PI-ESN can accurately reconstruct the unmeasured state. Second, the reconstruction is shown to be robust with respect to noisy data, which means that the PI-ESN acts as a denoiser. This paper opens up new possibilities for leveraging the synergy between physical knowledge and machine learning to enhance the reconstruction and prediction of unmeasured states in chaotic dynamical systems

Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network

The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of nonlinear filtering operations, which are performed by a convolutional autoencoder (CAE). The CAE provides the decomposition in space. Second, we predict the time evolution of the turbulent state in the latent space, which is performed by an echo state network (ESN). The ESN provides the decomposition in time. Third, by assembling the CAE and the ESN, we obtain an autonomous dynamical system: the convolutional autoncoder echo state network (CAE-ESN). This is the reduced-order model of the turbulent flow. We test the CAE-ESN on a two-dimensional flow. We show that, after training, the CAE-ESN (i) finds a latent-space representation of the turbulent flow that has less than 1% of the degrees of freedom than the physical space; (ii) time-accurately and statistically predicts the flow in both quasiperiodic and turbulent regimes; (iii) is robust for different flow regimes (Reynolds numbers); and (iv) takes less than 1% of computational time to predict the turbulent flow than solving the governing equations. This work opens up new possibilities for nonlinear decompositions and reduced-order modelling of turbulent flows from data

Physical Insights of Non-Premixed MILD Combustion using DNS

Moderate or Intense Low-oxygen Dilution (MILD) combustion is a combustion technology that can simultaneously improve the energy efficiency and reduce the pollutant emissions of combustion devices. It is characterised by highly preheated reactants and a small temperature rise during combustion due to the large dilution of the reactant mixture with products of combustion. These conditions are generally achieved using exhaust gas recirculation. However, the physical understanding of MILD combustion remains limited which prevents its more widely spread use. In this thesis, Direct Numerical Simulation (DNS) is used to study turbulence, premixed flames and MILD combustion to obtain these additional physical insights. In a first stage, the scale-locality of the energy cascade is analysed by applying a multiscale analysis methodology, called the bandpass filter method, on DNS of homogeneous isotropic turbulence. Evidence supporting this scale-locality were obtained and the results were found to be similar for Reynolds numbers ranging from 37 to 1131. Using the same method in turbulent premixed flames, the scale-locality of the energy cascade was still observed despite the presence of intense reactions. In addition, it was found that eddies of scales larger than the laminar flame thickness were imparting the most strain on the flame. In a second part, a methodology was developed to conduct the DNS of MILD combustion with mixture fraction variations. This methodology included the effect of mixing of exhaust gases with fuel and oxidiser in unburnt, burnt and reacting states. In addition, a specific chemical mechanism that includes the chemistry of ${\rm OH^*}$ was developed. From these DNS, the role of radicals on the inception of MILD combustion was studied. In particular, due to the reactions initiated by these radicals, the initial temperature rise in MILD combustion was occurring concurrently with an increase in the scalar dissipation rate of mixture fraction which is contrasting to conventional combustion. The reaction zones in MILD combustion were also analysed and extremely convoluted reaction zones were observed with frequent interactions among them. These interactions yielded the appearance of volumetrically distributed reactions. Furthermore, the adequacy of some species to identify these reaction zones was assessed and ${\rm OH}$ showed a poor correlation with regions of heat release. On the other hand, ${\rm OH^*}$, ${\rm HCO}$ or ${\rm OH} \times {\rm CH_2O}$ were found to be well correlated. Through the study of the flame index, the existence of non-premixed and premixed modes of combustion were also highlighted. The premixed mode was observed to be dominant but the contribution of the non-premixed mode to the total heat release was non negligible. Because of the presence of radicals and high reactant temperatures, auto-igniting regions and propagating reaction zones are both observed locally. The balance between these phenomena was investigated and it was found that this was strongly influenced by the typical lengthscale of the mixture fraction field, with a smaller lengthscale favouring sequential autoignition. Finally, using the bandpass filtering method, the effect of heat release rate in MILD combustion on the energy cascade was studied and this showed that the energy cascade was not unduly affected.Qualcomm European Research Studentship Fund in Technolog