Publications

2021

• A Non-Nested Infilling Strategy for Multi-Fidelity based Efficient Global Optimization
  
  • Sacher Matthieu
  • Le Maitre Olivier
  • Duvigneau Régis
  • Hauville Frédéric
  • Durand Mathieu
  • Lothode C.
  International Journal for Uncertainty Quantification, Begell House Publishers, 2021, 11 (1), pp.1-30. Efficient Global Optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multi-fidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multi-fidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multi-fidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multi-fidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements. (10.1615/Int.J.UncertaintyQuantification.2020032982)
  DOI : 10.1615/Int.J.UncertaintyQuantification.2020032982
• Log-Sobolev Inequality for the Continuum Sine-Gordon Model
  
  • Bauerschmidt Roland
  • Bodineau Thierry
  Commun.Pure Appl.Math., 2021, 74 (10), pp.2064-2113. We derive a multiscale generalisation of the Bakry-Émery criterion for a measure to satisfy a log-Sobolev inequality. Our criterion relies on the control of an associated PDE well-known in renormalisation theory: the Polchinski equation. It implies the usual Bakry-Émery criterion, but we show that it remains effective for measures that are far from log-concave. Indeed, using our criterion, we prove that the massive continuum sine-Gordon model with β < 6π satisfies asymptotically optimal log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. (10.1002/cpa.21926)
  DOI : 10.1002/cpa.21926
• Concurrent shape optimization of the part and scanning path for additive manufacturing
  
  • Boissier Mathilde
  • Allaire Grégoire
  • Tournier Christophe
  , 2021.
• A weak solution theory for stochastic Volterra equations of convolution type
  
  • Jaber Eduardo Abi
  • Cuchiero Christa
  • Larsson Martin
  • Pulido Sergio
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2021, 31 (6), pp.2924-2952. We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence in $L^p$ spaces. The main tools are new a priori estimates on Sobolev--Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit of classical martingale problem theory. We also prove uniqueness and path regularity of solutions under additional hypotheses. To illustrate the applicability of our results, we consider scaling limits of nonlinear Hawkes processes and approximations of stochastic Volterra processes by Markovian semimartingales.
• Transmission eigenvalues for multipoint scatterers
  
  • Grinevich Piotr
  • Novikov Roman
  Eurasian Journal of Mathematical and Computer Applications, Eurasian National University, Kazakhstan (Nur-Sultan), 2021, 9 (4), pp.17–25. We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed. (10.32523/2306-6172-2021-9-4-17-25)
  DOI : 10.32523/2306-6172-2021-9-4-17-25
• Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure
  
  • Boutin Benjamin
  • Coquel Frédéric
  • Lefloch Philippe G.
  Networks and Heterogeneous Media, American Institute of Mathematical Sciences, 2021, 16 (2), pp.283-315. In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish the existence of self-similar solutions to the coupled Riemann problem. We continue here this analysis in the restricted case of one-dimensional scalar equations and investigate the internal structure of the interface in order to derive a selection criterion associated with the underlying regularization mechanism and, in turn, to characterize the nonconservative interface layer. In addition, we identify a new criterion that selects double-waved solutions that are also continuous at the interface. We conclude by providing some evidence that such solutions can be non-unique when dealing with non-convex flux-functions. (10.3934/nhm.2021007)
  DOI : 10.3934/nhm.2021007
• A Bayesian Approach for Quantile Optimization Problems with High-Dimensional Uncertainty Sources
  
  • Sabater Christian
  • Le Maitre Olivier
  • Congedo Pietro Marco
  • Görtz Stefan
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2021, 376, pp.113632. Robust optimization strategies typically aim at minimizing some statistics of the uncertain objective function and can be expensive to solve when the statistic is costly to estimate at each design point. Surrogate models of the uncertain objective function can be used to reduce this computational cost. However, such surrogate approaches classically require a low-dimensional parametrization of the uncertainties, limiting their applicability. This work concentrates on the minimization of the quantile and the direct construction of a quantile regression model over the design space, from a limited number of training samples. A Bayesian quantile regression procedure is employed to construct the full posterior distribution of the quantile model. Sampling this distribution, we can assess the estimation error and adjust the complexity of the regression model to the available data. The Bayesian regression is embedded in a Bayesian optimization procedure, which generates sequentially new samples to improve the determination of the minimum of the quantile. Specifically, the sample infill strategy uses optimal points of a sample set of the quantile estimator. The optimization method is tested on simple analytical functions to demonstrate its convergence to the global optimum. The robust design of an airfoil’s shock control bump under high-dimensional geometrical and operational uncertainties serves to demonstrate the capability of the method to handle problems with industrial relevance. Finally, we provide recommendations for future developments and improvements of the method. (10.1016/j.cma.2020.113632)
  DOI : 10.1016/j.cma.2020.113632
• Flag-approximability of convex bodies and volume growth of Hilbert geometries
  
  • Vernicos Constantin
  • Walsh Cormac
  Annales Scientifiques de l'École Normale Supérieure, Gauthier-Villars ; Société mathématique de France, 2021, 54, pp.1297-1315. We show that the volume entropy of a Hilbert geometry on a convex body is exactly twice the flag-approximability of the body. We then show that both of these quantities are maximized in the case of the Euclidean ball. We also compute explicitly the asymptotic volume of a convex polytope, which allows us to prove that simplices have the least asymptotic volume, as was conjectured by the first author. (10.24033/asens.2482)
  DOI : 10.24033/asens.2482
• VARIATIONAL APPROXIMATION OF INTERFACE ENERGIES AND APPLICATIONS
  
  • Amstutz Samuel
  • Gourion Daniel
  • Zabiba Mohammed
  Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, European Mathematical Society, 2021, 23 (23), pp.59-102. Minimal partition problems consist in finding a partition of a domain into a given number of components in order to minimize a geometric criterion. In applicative fields such as image processing or continuum mechanics, it is standard to incorporate in this objective an interface energy that accounts for the lengths of the interfaces between components. The present work is focused on the theoretical and numerical treatment of minimal partition problems with such interface energies. The considered approach is based on a Γ-convergence approximation combined with convex analysis techniques. (10.4171/IFB/450)
  DOI : 10.4171/IFB/450
• Reciprocal association between participation to a national election and the epidemic spread of COVID-19 in France: nationwide observational and dynamic modeling study.
  
  • Zeitoun Jean-David
  • Faron Matthieu
  • Manternach Sylvain
  • Fourquet Jerome
  • Lavielle Marc
  • Lefevre Jeremie
  European Journal of Public Health, Oxford University Press (OUP): Policy B - Oxford Open Option D, 2021. Objective: To investigate possible reciprocal associations between the intensity of the COVID-19 epidemic in France and the level of participation at national elections. Design: Observational study and dynamic modelling using a sigmoidal mixed effects model. Setting: All hospitals where patients were admitted for COVID-19. Participants: All admitted patients from March 18, 2020 to April 17, 2020. Main outcome measures: Abstention and admission rate for COVID-19. Results: Mean abstention rate in 2020 among departments was 52.5%+/-6.4 and had increased by a mean of 18.8% as compared with the 2014 election. There was a high degree of similarity of abstention between the two elections among the departments (p<0.001). Among departments with a high outbreak intensity before the election, those with a higher participation were not affected by a significantly higher number of COVID-19 admissions after the elections. The sigmoidal model fitted the data from the different departments with a high degree of consistency. The covariate analysis showed that a significant association between participation and number of admitted patients was observed for both elections (2020: B=-5.36, p<1e-9 and 2014: B=-3.15, p<1e-6) contradicting a direct specific causation of the 2020 election. Participation was not associated with the position of the inflexion point suggesting no effect in the speed of spread. Conclusions: Our results suggest that the surrounding intensity of the COVID-19 epidemic in France did not have any local impact on citizens participation to a national election. The level of participation to the 2020 election had no impact on the spread of the pandemic. (10.1101/2020.05.14.20090100)
  DOI : 10.1101/2020.05.14.20090100
• Approximating the Total Variation with Finite Differences or Finite Elements
  
  • Chambolle Antonin
  • Pock Thomas
  , 2021, 22, pp.383--417. We present and compare various types of discretizations which have been proposed to approximate the total variation (mostly, of a grey-level image in two dimensions). We discuss the properties of finite differences and finite elements based approach and compare their merits, in particular in terms of error estimates and quality of the reconstruction. (10.1016/bs.hna.2020.10.005)
  DOI : 10.1016/bs.hna.2020.10.005
• Qualitative indicator functions for imaging crack networks using acoustic waves
  
  • Audibert Lorenzo
  • Chesnel Lucas
  • Haddar Houssem
  • Napal Kevish
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2021. We consider the problem of imaging a crack network embedded in some homogeneous background from measured multi-static far field data generated by acoustic plane waves. We propose two novel approaches that can be seen as extensions of linear sampling-type methods and that provide indicator functions which are sensitive to local cracks densities. The first approach uses multiple frequencies data to compute spectral signatures associated with artificially embedded localized obstacles. The second approach also exploits the idea of incorporating an artificial background but uses data for a single frequency. The indicator function is built using a similar concept as for differential sampling methods: compare the solution of the interior transmission problem for healthy inclusion with the one with embedded cracks. The performance of the methods is tested and discussed on synthetic examples and the numerical results are compared with the ones obtained using the classical factorization method. (10.1137/20M134650X)
  DOI : 10.1137/20M134650X
• Fast Incremental Expectation Maximization for finite-sum optimization: nonasymptotic convergence
  
  • Fort Gersende
  • Gach Pierre
  • Moulines Eric
  Statistics and Computing, Springer Verlag (Germany), 2021, 31 (48). Fast Incremental Expectation Maximization (FIEM) is a version of the EM framework for large datasets. In this paper, we first recast FIEM and other incremental EM type algorithms in the {\em Stochastic Approximation within EM} framework. Then, we provide nonasymptotic bounds for the convergence in expectation as a function of the number of examples $n$ and of the maximal number of iterations $\kmax$. We propose two strategies for achieving an $\epsilon$-approximate stationary point, respectively with $\kmax = O(n^{2/3}/\epsilon)$ and $\kmax = O(\sqrt{n}/\epsilon^{3/2})$, both strategies relying on a random termination rule before $\kmax$ and on a constant step size in the Stochastic Approximation step. Our bounds provide some improvements on the literature. First, they allow $\kmax$ to scale as $\sqrt{n}$ which is better than $n^{2/3}$ which was the best rate obtained so far; it is at the cost of a larger dependence upon the tolerance $\epsilon$, thus making this control relevant for small to medium accuracy with respect to the number of examples $n$. Second, for the $n^{2/3}$-rate, the numerical illustrations show that thanks to an optimized choice of the step size and of the bounds in terms of quantities characterizing the optimization problem at hand, our results desig a less conservative choice of the step size and provide a better control of the convergence in expectation. (10.1007/s11222-021-10023-9)
  DOI : 10.1007/s11222-021-10023-9
• Phase-field approximation for a class of cohesive fracture energies with an activation threshold
  
  • Chambolle Antonin
  • Crismale Vito
  Advances in Calculus of Variation, Walter de Gruyter GmbH, 2021, 14 (4), pp.475-497. We study the Γ-limit of Ambrosio-Tortorelli-type functionals Dε(u, v), whose dependence on the symmetrised gradient e(u) is different in Au and in e(u) − Au, for a C-elliptic symmetric operator A, in terms of the prefactor depending on the phase-field variable v. The limit energy depends both on the opening and on the surface of the crack, and is intermediate between the Griffith brittle fracture energy and the one considered by Focardi and Iurlano in [43]. In particular we prove that G(S)BD functions with bounded A-variation are (S)BD. (10.1515/acv-2019-0018)
  DOI : 10.1515/acv-2019-0018
• Detecting seed bank influence on plant metapopulation dynamics
  
  • Louvet Apolline
  • Machon Nathalie
  • Mihoub Jean‐baptiste
  • Robert Alexandre
  Methods in Ecology and Evolution, 2021, 12 (4), pp.655-664. Seed banks are known to play a key role in plant metapopulations. However, detecting seed banks remains challenging and requires intense monitoring efforts. Assessing the genuine effect of seed banks on plant metapopulation dynamics (rather than their presence) may offer a much easier while still biologically relevant way to overcome this issue. In this study, we developed a new metric: the seed bank characteristic event (SBCE) probability. Instead of detecting seed bank directly, the SBCE probability measures seed bank contribution to the observed metapopulation dynamics. Exploring seed bank parameters (colonization, germination and seed bank death probabilities, initial proportion of patches containing a seed bank), a wide range of monitoring durations (from 3 to 10 years) and number of patches in the metapopulation (from 10 to 1,000 patches), we examined the conditions under which the SBCE probability is correctly estimated. To test the robustness of our approach, we further introduced false negatives, false positives or parameter heterogeneity between patches. Finally, we applied the SBCE probability method to the monitoring of tree bases plant species in Paris, France, to assess the applicability of the method to real‐world datasets and increase the understanding of plant metapopulation dynamics within an urban environment. Our results indicate that the SBCE probability is well‐estimated when enough monitoring years or number of patches are considered, and for probabilities of false negatives or false positives of up to 0.1. However, the SBCE probability estimation is not robust to colonization probability heterogeneity between patches. When we applied the SBCE probability method to the real monitoring dataset, we found a contrasted contribution of the seed bank to the observed metapopulation dynamics from one street and one species to another. The study suggests that the measurement of seed bank contribution is less data‐demanding than assessment of seed bank presence. Applying the estimation method to the monitoring of tree bases plant species highlights a significant contribution of the seed bank to plant metapopulation dynamics in an urban environment, and illustrates how the method can be applied on real‐world datasets. (10.1111/2041-210x.13547)
  DOI : 10.1111/2041-210x.13547
• Abnormal acoustic transmission in a waveguide with perforated screens
  
  • Chesnel Lucas
  • Nazarov Sergei
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2021. We consider the propagation of the piston mode in an acoustic waveguide obstructed by two screens with small holes. In general, due to the features of the geometry, almost no energy of the incident wave is transmitted through the structure. The goal of this article is to show that tuning carefully the distance between the two screens, which form a resonator, one can get almost complete transmission. We obtain an explicit criterion, not so obvious to intuit, for this phenomenon to happen. Numerical experiments illustrate the analysis. (10.5802/crmeca.70)
  DOI : 10.5802/crmeca.70
• ELASTOPLASTIC TOPOLOGY OPTIMIZATION AND CYCLICALLY LOADED STRUCTURES VIA DIRECT METHODS FOR SHAKEDOWN
  
  • Boissier Mathilde
  • Deaton Joshua
  • Beran Philip
  • Vermaak Natasha
  Structural and Multidisciplinary Optimization, Springer Verlag, 2021, 64 (1), pp.189-217. For the first time, the lower bound shakedown theorem is integrated into a level set based topol-ogy optimization framework to identify lightweight elastoplastic designs. Shakedown is a cyclic elastoplastic behavior in which, upon cycling beyond the elastic limit, the accumulation of plastic strain arrests and purely elastic behavior is recovered. In contrast to most elastoplastic toplogy optimization, the use of a lower bound shakedown limit allows elastoplastic shakedown limits to be rigorously estimated using only the elastic solution. Under small deformations assumptions, this amounts to solving one simple partial differential equation, avoiding the non-linearity associated with plasticity, and thus simplifying the resolution process. Numerical results are provided for several benchmark examples. The results highlight the design performance enhancements attributed to allowing elastoplastic shakedown to occur instead of designing to first yield. In particular, up to 10% reduction in weight is found for the simple structures considered. (10.1007/s00158-021-02875-6)
  DOI : 10.1007/s00158-021-02875-6
• Duality and approximation of stochastic optimal control problems under expectation constraints
  
  • Pfeiffer Laurent
  • Tan Xiaolu
  • Zhou Yulong
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2021, 59 (5), pp.3231–3260. We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is in duality with an optimization problem involving the Lagrange multiplier associated with the constraints. Then by convex analysis techniques, we provide a general existence result and some a priori estimation of the dual optimizers. We further provide a necessary and sufficient optimality condition for the initial constrained control problem. The same results are also obtained for a discrete time constrained control problem. Moreover, under additional regularity conditions, it is proved that the discrete time control problem converges to the continuous time problem, possibly with a convergence rate. This convergence result can be used to obtain numerical algorithms to approximate the continuous time control problem, which we illustrate by two simple numerical examples. (10.1137/20M1349886)
  DOI : 10.1137/20M1349886
• Stochastic Preconditioning of Domain Decomposition Methods for Elliptic Equations with Random Coefficients
  
  • Reis Joao Felício Dos
  • Le Maître Olivier P
  • Congedo Pietro M
  • Mycek Paul
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2021, 381, pp.113845. This paper aims at developing an efficient preconditioned iterative domain decomposition (DD) method for the sampling of linear stochastic elliptic equations. To this end, we consider a non-overlapping DD method resulting in a Symmetric Positive Definite (SPD) Schur system for almost every sampled problem. To accelerate the iterative solution of the Schur system, we propose a new stochastic preconditioning strategy that produces a preconditioner adapted to each sampled problem and converges toward the ideal preconditioner (i.e., the Schur operator itself) when the numerical parameters increase. The construction of the stochastic preconditioner is trivially parallel and takes place in an off-line stage, while the evaluation of the sample's preconditioner during the sampling stage has a low and fixed cost. One key feature of the proposed construction is a factorized form combined with Polynomial Chaos expansions of local operators. The factorized form guaranties the SPD character of the sampled preconditioners while the local character of the PC expansions ensures a low computational complexity. The stochastic preconditioner is tested on a model problem in 2 space dimensions. In these tests, the preconditioner is very robust and significantly more efficient than the deterministic median-based preconditioner, requiring, on average, up to 7 times fewer iterations to converge. Complexity analysis suggests the scalability of the preconditioner with the number of subdomains. (10.1016/j.cma.2021.113845)
  DOI : 10.1016/j.cma.2021.113845
• State-constrained control-affine parabolic problems II: second order sufficient optimality conditions
  
  • Aronna Maria Soledad
  • Frédéric Bonnans Joseph
  • Kröner Axel
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2021. In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform. (10.1137/19M1286906)
  DOI : 10.1137/19M1286906
• A semi-supervised method for the characterization of degradation of nuclear power plants steam generators
  
  • Pinciroli Luca
  • Baraldi Piero
  • Shokry Ahmed
  • Zio Enrico
  • Seraoui Redouane
  • Mai Carole
  Progress in Nuclear Energy, Elsevier, 2021, 131, pp.103580. (10.1016/j.pnucene.2020.103580)
  DOI : 10.1016/j.pnucene.2020.103580
• Size matters for OTC market makers: General results and dimensionality reduction techniques
  
  • Bergault Philippe
  • Guéant Olivier
  Mathematical Finance, Wiley, 2021, 31 (1), pp.279-322. (10.1111/mafi.12286)
  DOI : 10.1111/mafi.12286
• Quantifying the closeness to a set of random curves via the mean marginal likelihood
  
  • Rommel Cédric
  • Bonnans Joseph-Frédéric
  • Gregorutti Baptiste
  • Martinon Pierre
  ESAIM: Probability and Statistics, EDP Sciences, 2021, 25, pp.1-30. In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories. (10.1051/ps/2020028)
  DOI : 10.1051/ps/2020028
• Propagation for KPP bulk-surface systems in a general cylindrical domain
  
  • Bogosel Beniamin
  • Giletti Thomas
  • Tellini Andrea
  Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2021, 213, pp.42. In this paper, we investigate propagation phenomena for KPP bulk-surface systems in a cylindrical domain with general section and heterogeneous coefficients. As for the scalar KPP equation, we show that the asymptotic spreading speed of solutions can be computed in terms of the principal eigenvalues of a family of self-adjoint elliptic operators. Using this characterization, we analyze the dependence of the spreading speed on various parameters, including diffusion rates and the size and shape of the section of the domain. In particular, we provide new theoretical results on several asymptotic regimes like small and high diffusion rates and sections with small and large sizes. These results generalize earlier ones which were available in the radial homogeneous case. Finally, we numerically investigate the issue of shape optimization of the spreading speed. By computing its shape derivative, we observe, in the case of homogeneous coefficients, that a disk either maximizes or minimizes the speed, depending on the parameters of the problem, both with or without constraints. We also show the results of numerical shape optimization with non homogeneous coefficients, when the disk is no longer an optimizer. (10.1016/j.na.2021.112528)
  DOI : 10.1016/j.na.2021.112528
• Dissipation-enhanced collapse singularity of a nonlocal fluid of light in a hot atomic vapor
  
  • Azam Pierre
  • Fusaro Adrien
  • Fontaine Quentin
  • Garnier Josselin
  • Bramati Alberto
  • Picozzi Antonio
  • Kaiser Robin
  • Glorieux Quentin
  • Bienaimé Tom
  Physical Review A, American Physical Society, 2021, 104 (1), pp.013515. We study the out-of-equilibrium dynamics of a two-dimensional paraxial fluid of light using a near-resonant laser propagating through a hot atomic vapor. We observe a double shock-collapse instability: a shock (gradient catastrophe) for the velocity, as well as an annular (ring-shaped) collapse singularity for the density. We find experimental evidence that this instability results from the combined effect of the nonlocal photon-photon interaction and the linear photon losses. The theoretical analysis based on the method of characteristics reveals the main result that dissipation (photon losses) is responsible for an unexpected enhancement of the collapse instability. Detailed analytical modeling makes it possible to evaluate the nonlocality range of the interaction. The nonlocality is controlled by adjusting the atomic vapor temperature and is seen to increase dramatically when the atomic density becomes much larger than one atom per cubic wavelength. Interestingly, such a large range of the nonlocal photon-photon interaction has not been observed in an atomic vapor so far and its microscopic origin is currently unknown. (10.1103/PhysRevA.104.013515)
  DOI : 10.1103/PhysRevA.104.013515