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Dynamics of inclined carbon nanotube (CNT) reinforced composite beams under a moving mass with influence of CNT agglomeration is studied. The beams compose of a homogeneous core and two composite face layers with effective properties being estimated by Eshelby–Mori–Tanaka approach. A novel finite element formulation is formulated and used to establish the equation of motion. Dynamic response is computed for a simply supported beam by Newmark method. The result reveals the important role of the CNT agglomeration on the dynamic response. The effects of the mass velocity, inclined angle and agglomeration parameters on the dynamic behavior are investigated in detail.

We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [1]. We focus here on test cases of physical interest where the dynamics of the system is modelled by the Langevin equation and is simulated using the molecular dynamics software LAMMPS. In this work, the parareal algorithm uses a family of machine-learning spectral neighbor analysis potentials (SNAP) as fine, reference, potentials and embedded-atom method potentials (EAM) as coarse potentials. We consider a self-interstitial atom in a tungsten lattice and compute the average residence time of the system in metastable states. Our numerical results demonstrate significant computational gains using the adaptive parareal algorithm in comparison to a sequential integration of the Langevin dynamics. We also identify a large regime of numerical parameters for which statistical accuracy is reached without being a consequence of trajectorial accuracy.

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearities of the equation, within a splitting approach. The approximation relies on mixed low order finite element methods with regularization techniques. In order to account for data singularities in non-smooth cases, we introduce an adaptive mesh refinement technique. The error indicator is based an independent formulation of the Monge–Ampère equation under divergence form, which allows to explicit a residual term. We show that the error is bounded from above by an a posteriori error indicator plus an extra term that remains to be estimated. This indicator is then used within the existing least-squares framework. The results of numerical experiments support the convergence of our relaxation method to a convex classical solution, if such a solution exists. Otherwise they support convergence to a generalized solution in a least-squares sense. Adaptive mesh refinement proves to be efficient, robust, and accurate to tackle test cases with singularities.

This article presents the scientific work of Ismaël Boulliau who was, at the same time and in turn, mathematician, astronomer, astrologer, meteorologist, but above all a scientific intermediary who exchanged an important correspondence with the greatest scholars and intellectuals of his time. It is mainly based on the thesis of the Dutch Henricus Johannes Maria Nellen translated 14 years later into French, on the occasion of the $3^{\rm rd}$ centenary of the death of Ismaël Boulliau.

Since ancient times, natural phenomena have been observed and described, the first stage in the development of knowledge, often involving supposedly supernatural forces. It was in Europe in the 17th century that a scientific approach was developed, which became meteorology in the 19th century. A scientific approach required instruments, and it was in Florence in 1608 that the first thermometer was manufactured. Fifty years later, Ismaël Boulliau, the first French scientist to receive a thermometer from Florence, followed an approach based on observation and recording. This article sets out to show how, over the course of two centuries, a truly scientific meteorology emerged at the dawn of the twentieth century.

An attempt to improve the accuracy of resolvent-based predictions by including velocity correlations in the linear model is developed here. Closure assumptions for unresolved nonlinearities are thus pushed back to a higher order. Turbulent channel flow is considered as a test case: response and forcing modes obtained from singular value decomposition of the new resolvent model are compared to Spectral Proper Orthogonal Decomposition (SPOD) modes extracted from a Direct Numerical Simulation (DNS) database. The performance of the approach is also measured against previous resolvent-based models. The new model does not yield significant global improvement, but does improve predictions in some regions. Further work on the method should target the linear modeling of the velocity-pressure gradient correlation tensor.

A stable scheme is proposed in this paper in order to obtain approximate solutions of second-moment turbulent models for incompressible flows with or without thermal transport equation. The analysis of the convective terms, which includes the solution of the associated Riemann problem, enables to propose a standard projection scheme, and to get rid of spurious oscillations.

This study proposes a theoretical contribution to the problem of the various distortions affecting axisymmetric capillary bridges, due to gravity or to bending effects linked to the Gaussian curvature. We deduce a clear hierarchization of effects between various reference configurations and put in a prominent position an exact first integral for the Young–Laplace equations, classical or generalized. These relationships are taken advantage of to obtain the theoretical expression of the varying inter-particle force, quantified effects of flexural strength. Finally, we establish a generalization of the classical “gorge method” to calculate accurately the capillary force of a profile subjected to distorsion due to bending when the gravity effects are negligible or not taken into account.

The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges. The common thread is to be able to calculate accurately in any situation the bending stress over the free surface, represented mathematically by the integral of the Gaussian curvature over the surface (called the total curvature) involved in the generalized Young–Laplace equation. We prove in particular that the resultant of the bending energy is directly linked to the wetting angles at the contact line.

Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. These methods, such as the Proper Orthogonal Decomposition (POD) or Reduced Basis (RB) methods, are very effective when the family of solutions has fast-decaying Karhunen–Loève eigenvalues or Kolmogorov widths, reflecting the approximability by finite-dimensional linear spaces. On the other hand, they become ineffective when these quantities have a slow decay, in particular for families of solutions to hyperbolic transport equations with parameter-dependent shock positions. The objective of this work is to explore the ability of nonlinear model reduction to circumvent this particular situation. To this end, we first describe particular notions of nonlinear widths that have a substantially faster decay for the aforementioned families. Then, we discuss a systematic approach for achieving better performance via a nonlinear reconstruction from the first coordinates of a linear reduced model approximation, thus allowing us to stay in the same “classical” framework of projection-based model reduction. We analyze the approach and report on its performance for a simple and yet instructive univariate test case.

In order to trace the footsteps of Ismaël Boulliau (also known as Bullialdus) in the dust of history, we adopt a quantitative approach based on an analysis of the extensive literature which has been digitized and which is therefore open to the application of computerized bibliometric techniques to detect patterns and trends over time. In particular, we use the Google Books database which contains millions of digitized books, manuscripts, reports, etc. in several languages. We apply the Google Ngram software to analyze the rate of referencing Boulliau’s work in the literature, in timeseries form. We also search Google Scholar which is an academic bibliographic database and search engine and is in many cases the most comprehensive source. The results show clear evidence that Boulliau was a man who escaped the limitations of old paradigms of thought and influenced the advancement of European science long after his death.

This article deals with the life of Ismaël Boulliau, french astronomer.

The wind has always been a major concern for Gustave Eiffel due to its effects on the large metal constructions he made. “The wind, my enemy”, he said. Eiffel expresses through his speeches his desire to put science at the service of technology. Meteorology must help the aviator, the peasant or the sailor. It is for men that Gustave works. He therefore recommends simplifying practices so that the results are accessible to all. So the meteorology must give usable information immediately.

Ismaël Boulliau spent the first third of his life in Loudun, where he was born five years before the assassination of Henri IV at the end of September 1605. When he left for Paris in the early 1630s, Louis XIII, seconded by Richelieu, reigns supreme. Loudun has changed a lot. He was born in a prosperous and active city, he leaves a bruised city. During his years in Loudun, the young Ismaël Boulliau witnessed the transformations that this article sets out to describe.

Since Galileo, the universality of the free fall of bodies has questioned physicists: the fall in the vacuum is independent of mass and composition. With the theory of general relativity, Enstein revolutionized the understanding of gravitation. The principle of Equivalence is then posed by Einstein as the founding principle of general relativity with the first consequence: the universality of free fall. This principle, tested more and more accurately since Galileo, has just taken a new step thanks to the MICROSCOPE space mission, which has improved the precision of the test by two orders of magnitude to $2.7\times 10^{-15}$.

Adaptive optics (AO), now installed on all the astronomical ground-based telescopes, make it possible to overcome the angular resolution limitations imposed by atmospheric turbulence. This article presents the state-of-the-art in the field of astronomical applications, and shows how adaptive optics has revolutionized ground-based astronomical observation over the last twenty years, overcoming countless scientific and technical challenges. Finally, we present how the concept will be applied, by 2030, on future giant telescopes to answer some of astronomy’s most fundamental questions concerning the birth of the universe or the existence of life outside the solar system.

Canadian astrophysicist Hubert Reeves (April 2011) considers Audouin Dollfus to be one of the greatest contemporary French astronomers. In particular, he discovered Saturn’s satellite Janus, determined the composition of the soil on Mars, detected atmospheric residue on Mercury and helped choose the landing site for the Apollo 11 mission, which enabled Neil Armstrong to set foot on the Moon for the first time. He was also a high-flying aeronaut, as he still holds the world record for the highest manned flight in a balloon equipped with an astronomical telescope.

This paper presents a method derived from Whitham’s variational formulation of the problem of interfacial capillary–gravity short-crested waves. It is developed for the resolution of the problem of waves generated by obliquely reflecting interfacial waves from a vertical wall. In essence, Whitham’s method is not changed, but computations are performed and arranged to produce a method that has been applied to a number of cases demonstrating the effectiveness and the flexibility of the approach. The performance of the method is illustrated in several examples including the case of harmonic resonance.

Mass transfer from particles is encountered in many biomedical applications. In operating conditions, particles are subjected to flows whose effect on solute transport is still not well understood. In this article we consider mass transfer from core-shell capsules and fibers subjected to various flow conditions. The combined effects of the flow and the shell permeability on the mass transfer efficiency are analyzed and quantified by correlations for the Sherwood number (the dimensionless mass transfer coefficient). The permeability is found to significantly affect the mass transfer efficiency, but it is a hardly measurable quantity. A new characterization method is proposed and validated using experimental data. All the obtained results can be applied to heat transfer from or to particles subjected to flow.

We review different models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists of minimizing a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin finite elements. The discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are used to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the variety of shapes achievable with these models.

Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable discretization space, and next perform a Galerkin approximation of the problem on that space. We investigate here how these approaches can be implemented in a non-intrusive way, in order to facilitate their dissemination within industrial codes or non-academic environments. We develop an abstract framework that covers a wide variety of MsFEMs for linear second-order partial differential equations. Non-intrusive MsFEM approaches are developed within the full generality of this framework, which may moreover be beneficial to steering software development and improving the theoretical understanding and analysis of MsFEMs.

A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the optimal value function obtained from a family of universal approximators. The cost functional for the training of an approximate optimal feedback law incorporates two main features. First, it contains the average over the objective functional values of the parametrized feedback control for an ensemble of initial values. Second, it is adapted to exploit the relationship between the maximum principle and dynamic programming. Based on universal approximation properties, existence, convergence and first order optimality conditions for optimal neural network feedback controllers are proved.

In-situ (tomography) experiments are generally based on scans reconstructed from a large number of projections acquired under constant deformation of samples. Standard digital volume correlation (DVC) methods are based on a limited number of scans due to acquisition duration. They thus prevent analyses of time-dependent phenomena. In this paper, a modal procedure is proposed that allows time-dependent occurrences to be analyzed. It estimates spacetime displacement fields during the whole loading history. The spatial modes are based on standard DVC, which is subsequently enriched using projection-based digital volume correlation (P-DVC) to measure the temporal amplitudes. The method is applied to two cases, namely, a virtual experiment mimicking wedge splitting and an actual shear test on a pantographic metamaterial inducing large motions. With the proposed method, the temporal amplitude in the real test was measured for each projection leading to a temporal resolution of one tenth of a second and the analysis of 16,400 time steps. For the proposed algorithm, the sensitivity to the acquisition angle of the sample was investigated and measurement uncertainties were assessed.

A variational solution to the transient heat flow measure above a closed conductive region of arbitrary perimeter aspect, held at constant temperature, and which is embedded in an otherwise insulating boundary plane, is presented. Upon developing the general variational formulation, a full range solution for the circular disk conductor is considered as an example when implementing a two term trial function that comprises a general form based on known physical solutions to the problem at long and short times. The particular combination of the Lagrange density for the total transient diffusive flux and of the form of the trial functions are evidently effective in dealing with the difficulties often experienced when dealing with mixed boundary value heat transfer problems of the parabolic type which have a non-periodic time variable.

This paper concerns numerical simulations of time-dependent problems in computational solid mechanics. A perturbation method, with the time as perturbation parameter, is proposed to solve two classical problems: an elastic bar excited by an end force and the dynamic buckling of a cylindrical panel. Specific quadratic recast of the equations is proposed to solve the nonlinear problems. Numerical results show that asymptotic time expansions is robust, efficient and gives more accurate solutions than the ones obtained with classical time-integration schemes (implicit or explicit), even when the considered meshes are coarse.

This paper revisits the different arts of engineering. The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. Then, the art of simulation concerns the ability of solving these complex mathematical objects expected to describe the physical reality as accurately as possible (accuracy with respect to the exact solution of the models) and as fast as possible. Finally, the art of decision making needs to ensure accurate and fast predictions for efficient diagnosis and prognosis. For that purpose physics-informed digital twins (also known as Hybrid Twins) will be employed, allying real-time physics (where complex models are solved by using advanced model order reduction techniques) and physics-informed data-driven models for filling the gap between the reality and the physics-based model predictions. The use of physics-aware data-driven models in tandem with physics-based reduced order models allows us to predict very fast without compromising accuracy. This is compulsory for diagnosis and prognosis purposes.

The present work is a continuation of a paper presented by the two first authors in the proceedings of the “Computational Science for the $21^{\rm st}$ century” conference held in Tours in 1997 honouring the $60^{\rm th}$ birthday of Roland Glowinski. It is devoted to the solution of 1D convection-diffusion equations in dominant convection regime situations. In that paper, an “a posteriori” VMS filtering technique was introduced. We present an extension of this technique to nonlinear convection-diffusion equations (a traffic model), providing an efficient method for the resolution of shocks from just the Galerkin solution at targeted times. We also present a residual-based “a posteriori” VMS filtering, that provides quite accurate stable solutions, can be extended to multi-dimensional problems, and can be applied locally. We finally present some numerical tests exhibiting the high accuracy of the obtained solutions.

This article is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and $\tt {T}$-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our $\tt {T}$-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model.

We review the class of implicit algebraic constitutive relations for fluids which includes in its ambit those whose material properties depend on the invariants of the stress, the symmetric part of the velocity gradient, as well as their mixed invariants. Such constitutive relations can describe the response of complex fluids whose material properties depend on the mechanical pressure, shear rate, etc. The class of models under consideration can describe the non-monotone relationship between the shear stress and the shear rate observed in experiments on colloids, as well as other novel response characteristics of non-Newtonian fluids. Constitutive relations for power-law fluids, generalized Stokesian fluids and Piezo-viscous fluids are special sub-classes of the class of fluids considered herein.

The simulation of the cyclone separation efficiency can rapidly become very expensive in time of calculation, which is not suitable for industrial application. The prediction of the complex turbulent gas flow inside a cyclone is necessary to estimate its pressure drop, its characteristics and finally its separation efficiency. Even though classic models such as RSM and LES can effectively predict such type of flow, the quality of the results and the computation cost can be discussed. In this work, Partially Averaged Navier–Stokes (PANS) method is proposed to simulate the fluid flow inside a gas cyclone. Compared to experimental and numerical results of a literature review, this model predicts reasonably the time-averaged tangential and axial velocity fields, and more accurately the pressure drop across the cyclone in shorter CPU times. The sensitivity of the PANS approach to the unresolved to total kinetic energy ratio $f_{k}$ was also evaluated with two different definitions. The first one was the standard definition developed by Girimaji et al. [1] and the second one was based on a statistical equivalence between the DES and PITM. The proposed model offers a better cost to quality ratio compared to the classic RANS approach.

In this paper, we study the Dirichlet problem for a semilinear pseudo-parabolic equation. By using the energy estimates and ordinary differential inequalities, we studied the upper and lower bounds of blow-up time of the solutions. The results of this paper extend and complete the results on this model.

Finer strategies of spacecraft fire mitigation require more experimental data related to fire detection. Fire detection systems developed on Earth rely massively on the optical detection of soot particles, which are present in the smoke. To detect the fire correctly, it is thus important to know how the optical properties of these particles are affected in reduced gravity. With different transport processes and increased residence time, soot in reduced gravity can be different from those produced at normal gravity. As their optical properties are related to their morphological properties, a better understanding about the evolution of soot particle morphology in flames under microgravity conditions is required. Within this context, a novel technique of soot sampling using electric field is applied to a spreading non-premixed flame at normal and micro-gravity. The soot particles sampled are observed subsequently under Transmission Electron Microscopy (TEM). Density, soot particle projected area, radius of gyration, fractal dimension, and primary particle size are extracted and the influence of gravity is investigated with the evolution of these morphological properties within the flame. Though the present study cannot be conclusive in itself, the similarity between the evolution of the optical density measured throughout the flame just before the electric perturbation required by the sampling technique and the evolution of the amount of soot deposited due to the electric perturbation along the sampling plates supports the future works that need to be devoted to further assess the consistency of the technique.

In this study, structure – property relationships (SPR) have been investigated using machine learning methods (ML). The research objective was to create a ML model that can predict the stress – strain response of materials at different temperatures from a given microstructure with industrially acceptable accuracy and high computational efficiency. Automated microstructure generation techniques and numerical simulations were developed to create a dataset for the ML model. Two – phase 3D representative volume elements (RVEs) were analyzed using finite element analysis (FEA) to obtain the stress – strain responses of the RVEs. The phase arrangement of the RVEs, the temperature, and the stress – strain responses were used to train the ML model. The microstructure arrangement and the temperature – dependent mechanical properties of each phase were known parameters, while the output parameter was the stress – strain response of the two – phase RVE. The ML model has shown excellent prediction accuracy in the temperature range from 20 °C to 250 °C. In addition, the model showed very high computational efficiency compared to FEA, allowing much faster prediction of the stress – strain curves at specific temperatures.

This work proposes a new method aiming at the direct identification of viscoelastic properties of materials with a Laplace formalism implemented in the Virtual Fields Method and named L-VFM. Using a single test, this formalism allows for a direct extraction of the different viscoelastic properties without any parametric description of their time dependency. The Laplace transform enables the use of theory of elasticity in the Laplace domain. The constitutive equations are expressed in the plane stress framework with the 2D plane stress stiffness coefficients. The conversion from the 2D plane stress stiffness coefficients to the bulk and shear moduli as well as Poisson’s ratio and Young’s modulus is realised in the Laplace domain. The inverse Laplace transform is then applied to these functions in order to obtain the temporal evolution of the material properties. The L-VFM changes the viscoelastic identification from a non-linear to a linear process.

We study the existence of a weak solution to a regularized, moving boundary, fluid-structure interaction problem with multi-layered poroelastic media consisting of a reticular plate located at the interface between the free flow of an incompressible, viscous fluid modeled by the 2D Navier–Stokes equations, and a poroelastic medium modeled by the 2D Biot equations. The existence result holds for both the elastic and viscoelastic Biot model. The free fluid flow and the poroelastic medium are coupled via the moving interface (the reticular plate) through the kinematic and dynamic coupling conditions. The reticular plate is “transparent” to fluid flow. The nonlinear coupling over the moving interface presents a major difficulty since both the fluid domain and the poroelastic medium domain are functions of time, and the finite energy spaces do not provide sufficient regularity for the corresponding weak formulation to be well-defined. This is why in this manuscript we consider a regularized problem by employing convolution with a smooth kernel only where needed. The resulting problem is still very challenging due to the nonlinear coupling and the motion of the fluid and Biot domains. We provide a constructive existence proof for this regularized fluid-poroelastic structure interaction problem. This regularized problem is consistent with the original, nonregularized problem in the sense that the weak solutions constructed here, converge, as the regularization parameter tends to zero, to a classical solution of the original, nonregularized problem when such a classical solution exists, assuming viscoelasticity in the Biot poroelastic matrix [1]. Furthermore, the existence result presented in this manuscript, is a crucial stepping stone for the singular limit problem in which the thickness of the reticular plate tends to zero. Namely, in [1] we will show that, in the case of a Biot poroviscoelastic matrix, the moving boundary problem obtained in the singular limit as the thickness of the plate tends to zero, has a weak solution.

The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. The numerical tests indicate that considerable cost reduction (a factor of 50 to 1000) can be achieved while preserving engineering accuracy.

The Cahn–Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues, following the theory of mixtures. We are interested in quantifying the pressure jump at the interface between phases in the case of incompressible flows. To do so, we depart from the spherically symmetric dynamical compressible model and include an external force. We prove existence of stationary states as limits of the parabolic problems. Then we prove the incompressible limit and characterize compactly supported stationary solutions. This allows us to compute the pressure jump in the small dispersion regime and in particular the force dependent curvature effect.

The paper describes a study of wet foams in microgravity whose bubble size distribution evolves due to diffusive gas exchange. We focus on the comparison between the size of bubbles determined from images of the foam surface and the size of bubbles in the bulk foam, determined from Diffuse Transmission Spectroscopy (DTS). Extracting the bubble size distribution from images of a foam surface is difficult so we have used three different procedures: manual analysis, automatic analysis with a customized Python script and machine learning analysis. Once various pitfalls were identified and taken into account, all the three procedures yield identical results within error bars. DTS only allows the determination of an average bubble radius which is proportional to the photon transport mean free path $\ell ^*$. The relation between the measured diffuse transmitted light intensity and $\ell ^*$ previously derived for slab-shaped samples of infinite lateral extent does not apply to the cuboid geometry of the cells used in the microgravity experiment. A new more general expression of the diffuse intensity transmitted with specific optical boundary conditions has been derived and applied to determine the average bubble radius. The temporal evolution of the average bubble radii deduced from DTS and of the same average radii of the bubbles measured at the sample surface is the same (to a factor probably close to one) throughout the coarsening. Finally, ground experiments were performed to compare bubble size distributions in a bulk wet foam and at its surface at times so short that diffusive gas exchange is insignificant. They were found to be similar, confirming that bubbles seen at the surface are representative of the bulk foam bubbles.

The initial mechanism of cellular instabilities on the flame surface was investigated experimentally. Firstly, mono-dispersed ethanol droplets were created via the Wilson cloud principle in a spherical combustion chamber, and aerosol ethanol/air flame propagation was tracked under microgravity conditions. Schlieren images revealed that at the beginning of the cellular structure formation, dark spots formed linking to the signal loss in a density gradient. This phenomenon is assumed to be local extinction and quenching on the flame front due to either liquid droplets’ presence or evaporation. To further investigate the observed phenomenon, stagnation flame experiments were performed for rich propane/air gaseous flames with isolated ethanol droplet injection. The evidence for the local extinction on the flame surface due to droplet passage was found via the Chemiluminescence method. The intrinsic instabilities were found to be triggered by the droplets in cases where the flame cannot recover its initial state.

This article traces the main lines of the evolution of the ideas that have prevailed and the choices that have been made in modelling the fracture of materials for a century. In particular, the emphasis is on the creation and development of damage mechanics with its primary ambition to remedy the shortcomings of Griffith’s fracture theory. We underline the successes of this enterprise and the advances it has allowed by insisting on the key role played by the variational approach, but we also show its limits.

Roland Glowinski published 8 books and more than 300 articles. He was also an editor of many very well cited proceedings. Hence this attempt to summarize his scientific work is not likely to do justice to his work. Nevertheless, we will try to extract his major contributions, such as the augmented Lagrangian algorithm, various domain decomposition and fictitious methods and their performance on the Navier–Stokes equations in a moving domain. Roland has created a school of applied mathematicians remarkable by their rigor and efficiency for industrial applications. He marked his time and his books will be authorities as long as computer architectures are similar to their present structures.

We introduce two finite element formulations to approximate magneto-static problems with discontinuous electric potential based respectively on the electrical scalar potential and the magnetic field. This work is motivated by our interest in Liquid Metal Batteries (LMBs), a promising technology for storing intermittent renewable sources of energy in large scale energy storage devices. LMBs consist of three liquid layers stably stratified and immiscible, with a light liquid metal on top (negative electrode), a molten salt in the middle (electrolyte) and a heavier liquid metal on bottom (positive electrode). Energy is stored in electrical potential differences that can be modeled as jumps at each electrode-electrolyte interface. This paper focuses on introducing new finite element methods for computing current and potential distributions, which account for internal voltage jumps in liquid metal batteries. Two different formulations that use as primary unknowns the electrical potential and magnetic field, respectively, are presented. We validate them using various manufactured test cases, and discuss their applications for simulating the current distribution during the discharge phase in a liquid metal battery.

This paper is devoted to recall several contributions to the numerical control of PDE’s that have origin in Glowinski’s work. I will consider null controllability problems for linear and nonlinear heat equations and some free-boundary systems. We will also deal with some bi-objective optimal control problems. Additionally, some new methods and results will be announced.

In this paper Piola transformations are found that relate the Eulerian and Lagrangian external loads which third gradient continua can sustain. As shown by Gabrio Piola and Paul Germain, the most effective postulation scheme in mechanics is based on the principle of virtual work and therefore continuum mechanics must be mathematically founded based on the theory of distributions and on differential geometry. Using the principle of virtual work, the set of admissible external loads sustainable by third gradient continua is seen to include: i) volume force density, ii) surface density of contact force, iii) surface density of contact double force, iv) surface density of contact triple force, v) line density of edge contact forces, vi) line density of contact edge double forces and vii) contact forces concentrated on wedge points. Following the nomenclature introduced by Paul Germain, forces are dual in virtual work of virtual displacements, surface and line double forces are dual of the derivatives of virtual displacements in the normal direction(s) of the surfaces and edges constituting the boundary of the continuum, and surface triple forces are dual of the second normal derivatives of virtual displacements. Volume and surface forces transform as in first gradient Cauchy continua. Moreover we find that: a) the virtual work expended by Eulerian surface triple force, when transformed into the Lagrangian description, must be represented as the work expended by all the kinds of external Lagrangian loads listed in i)-vii); b) Eulerian surface double force transforms into Lagrangian surface double force, surface contact force and edge contact line force; c) Eulerian edge contact line double force transforms into Lagrangian edge contact line double forces, edge line forces and point concentrated wedge forces; d) Eulerian edge and wedge contact line forces transforms into their Lagrangian counterpart only. The Piola transformation formulas deduced in this paper depend on the first, second and third gradients of placement. The presented results allow for the formulation of well-posed boundary condition problems for third gradient continua in the Lagrangian description, and are relevant in computational mechanics. In view of the obtained Piola transformation formulas, the concept of dead loads needs to be modified. We believe to have given an example of how the Mechanics in the French Style, as developed on the ideas by D’Alembert and Lagrange, is still a fertile tool of invention.

We discuss the role and impact of lattice fluid dynamics, namely Lattice Gas Cellular Automata and lattice Boltzmann, on the general framework of Computational Fluid Dynamics.

Core-shell configurations are ubiquitous in nature such as in the form of bacterial and cells. Inspired by this, microcapsules are designed with actives as the cores surrounded by thin shells. They not only play an increasing role as artificial models for understanding dynamic behaviors of biological cells in flows, but are also becoming a fundamental class of artificial vehicles at the heart of drug delivery and release in applications. The mechanical properties of the shells are of great importance in this context. Here, we review recent experimental and theoretical characterizations of microcapsules, focusing on the soft and deformable particles with liquid cores. We begin by exploring the concept and fabrication of artificial microcapsules, followed by a discussion of different methods on the mechanical characterization of the shell.

In the future, higher plant cultivation will be a key component of Bioregenerative Life-Support Systems. This will require a deep understanding of phenomena that play an important role at the core of plant metabolism and of their interaction with the environment. Plants are complex organisms that must be studied with the use of leaf replicas. This enables the study of physical phenomena at the leaf surface, without biochemical or biological interactions nor genetic variability. To assess the influence of gravity, it is a necessary step to develop precise mechanistic models of plant behaviour in space. This review article presents the state-of-the-art of leaf replicas and concomitant phenomena, with a space gaze.

Flame spread over an insulated electrical wire is a major source of fire scenario in a space vehicle. In this work, an engineering model that predicts the creeping flame spread over cylindrical wires in microgravity is developed. The model is applied to interpret experimental data obtained in parabolic flights for wires composed by a 0.25 mm radius nickel-chromium (NiCr) metallic core coated by low-density polyethylene (LDPE) of different thicknesses ranging from 0.15 mm to 0.4 mm. The model relies on the assumption that, in the pyrolysis region, the NiCr and the LDPE are in thermal equilibrium. This assumption is supported by more detailed numerical simulations and the model reduces then to solving the heat transfer equations for both NiCr and LDPE in the pyrolysis region and in the region ahead of the flame front along with a simple degradation model for LDPE, an Oseen approximation of opposed oxidizer flow and an infinitely fast gas-phase chemistry. The flame spread rate (FSR) is controlled by two model parameters, which are measurable from intrinsic material and ambient gas properties: the convective flame heat flux transferred to the solid ahead from the flame front and the gaseous thermal heat length near the flame front. These parameters are then calibrated from experimental data for a given wire geometry and the calibrated model is validated against experimental data for other wire geometries and ambient conditions. The heat transfer mechanisms ahead of the pyrolysis front are investigated with a special emphasis on the LDPE thickness and the conductivity of the metallic core. In addition to NiCr, metallic cores of lower and higher conductivities are considered. The polymer is shown to be thermally thick for all tested wire geometries and core conductivities. The flame heat flux is found to dominate the heat transfer in the preheat zone where it applies. The core has nevertheless a significant impact in the heating of the LDPE with its contribution increasing with the core conductivity and when decreasing the LDPE thickness.