Publications

2021

• Enhanced Backscattering of a partially coherent field from an anisotropic random lossy medium
  
  • Garnier Josselin
  • Sølna Knut
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2021, 26 (2), pp.1171-1195. (10.3934/dcdsb.2020158)
  DOI : 10.3934/dcdsb.2020158
• Wave Propagation in Periodic and Random Time-Dependent Media
  
  • Garnier Josselin
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2021, 19 (3), pp.1190-1211. (10.1137/20M1377734)
  DOI : 10.1137/20M1377734
• Long-Time Correlations For A Hard-Sphere Gas At Equilibrium
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  • Simonella Sergio
  Communications on Pure and Applied Mathematics, Wiley, 2021. It has been known since Lanford [22] that the dynamics of a hard sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilibrium. In this paper, we introduce a weak convergence method coupled with a sampling argument to prove that the covariance of the fluctuation field around equilibrium is governed by the linearized Boltzmann equation globally in time (including in diffusive regimes). This method is much more robust and simple than the one devised in [4] which was specific to the 2D case. (10.48550/arXiv.2012.03813)
  DOI : 10.48550/arXiv.2012.03813
• COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting
  
  • Hansen Nikolaus
  • Auger Anne
  • Ros Raymond
  • Mersmann Olaf
  • Tušar Tea
  • Brockhoff Dimo
  Optimization Methods and Software, Taylor & Francis, 2021, 36 (1), pp.114-144. We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. The platform and the underlying methodology allow to benchmark in the same framework deterministic and stochastic solvers for both single and multiobjective optimization. We present the rationales behind the (decade-long) development of the platform as a general proposition for guidelines towards better benchmarking. We detail underlying fundamental concepts of COCO such as the definition of a problem as a function instance, the underlying idea of instances, the use of target values, and runtime defined by the number of function calls as the central performance measure. Finally, we give a quick overview of the basic code structure and the currently available test suites. (10.1080/10556788.2020.1808977)
  DOI : 10.1080/10556788.2020.1808977
• Finite state N-agent and mean field control problems
  
  • Cecchin Alekos
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2021, 27, pp.31. We examine mean field control problems on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the mean field control problem as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. In absence of any convexity assumption, we exploit this characterization to prove convergence, as N grows, of the value functions of the centralized N-agent optimal control problem to the limit mean field control problem value function, with a convergence rate of order . Then, assuming convexity, we show that the limit value function is smooth and establish propagation of chaos, i.e. convergence of the N-agent optimal trajectories to the unique limiting optimal trajectory, with an explicit rate. (10.1051/cocv/2021032)
  DOI : 10.1051/cocv/2021032
• Coherent Soliton States Hidden in Phase Space and Stabilized by Gravitational Incoherent Structures
  
  • Garnier Josselin
  • Baudin Kilian
  • Fusaro Adrien
  • Picozzi Antonio
  Physical Review Letters, American Physical Society, 2021, 127 (1), pp.014101. We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for gravitational interactions. We unveil a previously unrecognized regime: By increasing the nonlinearity, the system self-organizes into an incoherent localized structure that contains “hidden” coherent soliton states. The solitons are hidden in the sense that they are fully immersed in random wave fluctuations: The radius of the soliton is much larger than the correlation radius of the incoherent fluctuations, while its peak amplitude is of the same order of such fluctuations. Accordingly, the solitons can hardly be identified in the usual spatial or spectral domains, while their existence is clearly unveiled in the phase-space representation. Our multiscale theory based on coupled coherent-incoherent wave turbulence formalisms reveals that the hidden solitons are stabilized and trapped by the incoherent localized structure. Furthermore, hidden binary soliton systems are identified numerically and described theoretically. The regime of hidden solitons is of potential interest for self-gravitating Boson models of “fuzzy" dark matter. It also sheds new light on the quantum-to-classical correspondence with gravitational interactions. The hidden solitons can be observed in nonlocal nonlinear optics experiments through the measurement of the spatial spectrogram. (10.1103/PhysRevLett.127.014101)
  DOI : 10.1103/PhysRevLett.127.014101
• Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates
  
  • Goldman Michael
  • Merlet Benoît
  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore, 2021, 22 (3), pp.1473--1509. We study a family of non-convex functionals {E} on the space of measurable functions u : Ω 1 × Ω 2 ⊂ R n 1 × R n 2 → R. These functionals vanish on the non-convex subset S(Ω 1 × Ω 2) formed by functions of the form u(x 1 , x 2) = u 1 (x 1) or u(x 1 , x 2) = u 2 (x 2). We investigate under which conditions the converse implication "E(u) = 0 ⇒ u ∈ S(Ω 1 × Ω 2)" holds. In particular, we show that the answer depends strongly on the smoothness of u. We also obtain quantitative versions of this implication by proving that (at least for some parameters) E(u) controls in a strong sense the distance of u to S(Ω 1 × Ω 2). (10.2422/2036-2145.201906_006)
  DOI : 10.2422/2036-2145.201906_006
• Importance of mass and enthalpy conservation in the modeling of titania nanoparticles flame synthesis
  
  • Orlac'Ch Jean-Maxime
  • Darabiha Nasser
  • Giovangigli Vincent
  • Franzelli Benedetta
  Combustion Theory and Modelling, Taylor & Francis, 2021, 25, pp.389-412. In most simulations of fine particles in reacting flows, including sooting flames, en-thalpy exchanges between gas and particle phases and differential diffusion between the two phases are most often neglected, since the particle mass fraction is generally very small. However, when the nanoparticles mass fraction is very large representing up to 50 % of the mixture mass, the conservation of the total enthalpy and/or the total mass becomes critical. In the present paper, we investigate the impact of mass and enthalpy conservation in the modeling of titania nanoparticles synthesis in flames, classically characterized by a high conversation rate and consequently a high nanoparticles concentration. It is shown that when the nanoparticles concentration is high, neglecting the enthalpy of the particle phase may lead to almost 70 % relative error on the temperature profile and to relative errors on the main titania species mass fractions and combustion products ranging from 20 % to 100 %. It is also established that neglecting the differential diffusion of the gas phase with respect to the particle phase is also significant, with almost 15 % relative error on the TiO2 mole fraction, although the effect on combustion products is minor. (10.1080/13647830.2021.1886330)
  DOI : 10.1080/13647830.2021.1886330
• Spontaneous Periodic Orbits in the Navier–Stokes Flow
  
  • van den Berg Jan Bouwe
  • Breden Maxime
  • Lessard Jean-Philippe
  • van Veen Lennaert
  Journal of Nonlinear Science, Springer Verlag, 2021, 31 (2), pp.41. In this paper, a general method to obtain constructive proofs of existence of periodicorbits in the forced autonomous Navier–Stokes equations on the three-torus isproposed. After introducing a zero finding problem posed on a Banach space of geometricallydecaying Fourier coefficients, a Newton–Kantorovich theorem is applied toobtain the (computer-assisted) proofs of existence. The required analytic estimates toverify the contractibility of the operator are presented in full generality and symmetriesfrom themodel are used to reduce the size of the problem to be solved. As applications,we present proofs of existence of spontaneous periodic orbits in the Navier–Stokesequations with Taylor–Green forcing. (10.1007/s00332-021-09695-4)
  DOI : 10.1007/s00332-021-09695-4
• Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations
  
  • Cancès Clément
  • Nabet Flore
  • Vohralík Martin
  Mathematics of Computation, American Mathematical Society, 2021, 90 (328), pp.517-563. We propose a finite element scheme for numerical approximation of degenerate parabolic problems in the form of a nonlinear anisotropic Fokker-Planck equation. The scheme is energy-stable, only involves physically motivated quantities in its definition, and is able to handle general unstructured grids. Its convergence is rigorously proven thanks to compactness arguments, under very general assumptions. Although the scheme is based on Lagrange finite elements of degree 1, it is locally conservative after a local postprocess giving rise to an equilibrated flux. This also allows to derive a guaranteed a posteriori error estimate for the approximate solution. Numerical experiments are presented in order to give evidence of a very good behavior of the proposed scheme in various situations involving strong anisotropy and drift terms. (10.1090/mcom/3577)
  DOI : 10.1090/mcom/3577