Publications

2019

• Avis en réponse à la saisine HCB - dossier 2018-151. Paris, le 10 janvier 2019
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2019.
• Existence of strong solutions to the Dirichlet problem for the Griffith energy
  
  • Chambolle Antonin
  • Crismale Vito
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2019, 58 (136). In this paper we continue the study of the Griffith brittle fracture energy minimisation under Dirichlet boundary conditions, suggested by Francfort and Marigo in 1998. In a recent paper, we proved the existence of weak minimisers of the problem. Now we show that these minimisers are indeed strong solutions, namely their jump set is closed and they are smooth away from the jump set and continuous up to the Dirichlet boundary. This is obtained by extending up to the boundary the recent regularity results of Conti, Focardi, Iurlano, and of Chambolle, Conti, Iurlano. (10.1007/s00526-019-1571-7)
  DOI : 10.1007/s00526-019-1571-7
• Incomplete graphical model inference via latent tree aggregation
  
  • Robin Geneviève
  • Ambroise Christophe
  • Robin Stephane S.
  Statistical Modelling, SAGE Publications, 2019, 19 (5), pp.545-568. Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical cases, not all variables involved in the network have been observed, and the samples are actually drawn from a distribution where some variables have been marginalized out. This challenges the sparsity assumption commonly made in graphical model inference, since marginalization yields locally dense structures, even when the original network is sparse. We present a procedure for inferring Gaussian graphical models when some variables are unobserved, that accounts both for the influence of missing variables and the low density of the original network. Our model is based on the aggregation of spanning trees, and the estimation procedure on the Expectation-Maximization algorithm. We treat the graph structure and the unobserved nodes as missing variables and compute posterior probabilities of edge appearance. To provide a complete methodology, we also propose several model selection criteria to estimate the number of missing nodes. A simulation study and an illustration flow cytometry data reveal that our method has favorable edge detection properties compared to existing graph inference techniques. The methods are implemented in an R package. (10.1177/1471082X18786289)
  DOI : 10.1177/1471082X18786289
• Longest increasing paths with gaps
  
  • Basdevant Anne-Laure
  • Gerin Lucas
  ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....], 2019, 16 (2), pp.1141--1163. We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal gaps between abscissae and ordinates of successive points of the path. For both cases (continuous and discrete) our approach rely on couplings with well-studied models: respectively the classical Ulam-Hammersley problem and last-passage percolation with geometric weights. Thanks to these couplings we obtain explicit limiting shapes in both settings. We also establish that, as in the classical Ulam-Hammersley problem, the fluctuations around the mean are given by the Tracy-Widom distribution.
• Statistical estimation in a randomly structured branching population
  
  • Hoffmann Marc
  • Marguet Aline
  Stochastic Processes and their Applications, Elsevier, 2019, 129 (12), pp.5236-5277. We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the observation of the trait at birth of the first n generations of the process, we construct nonparametric estimator of the transition of the associated bifurcating chain and study the parametric estimation of the branching rate. In the limit $n → ∞$, we obtain asymptotic efficiency in the parametric case and minimax optimality in the nonparametric case. (10.1016/j.spa.2019.02.015)
  DOI : 10.1016/j.spa.2019.02.015
• The asymptotic geometry of the Teichmüller metric
  
  • Walsh Cormac
  Geometriae Dedicata, Springer Verlag, 2019, 200 (1), pp.115-152. We determine the asymptotic behaviour of extremal length along arbitrary Teichmüller rays. This allows us to calculate the endpoint in the Gardiner-Masur boundary of any Teichmüller ray. We give a proof that this compactification is the same as the horofunction compactification. An important subset of the latter is the set of Busemann points. We show that the Busemann points are exactly the limits of the Teichmüller rays, and we give a necessary and sufficient condition for a sequence of Busemann points to converge to a Busemann point. Finally, we determine the detour metric on the boundary. (10.1007/s10711-018-0364-z)
  DOI : 10.1007/s10711-018-0364-z
• A stochastic data-based traffic model applied to vehicles energy consumption estimation
  
  • Le Rhun Arthur
  • Bonnans Frédéric
  • de Nunzio Giovanni
  • Leroy Thomas
  • Martinon Pierre
  IEEE Transactions on Intelligent Transportation Systems, IEEE, 2019. A new approach to estimate traffic energy consumption via traffic data aggregation in (speed,acceleration) probability distributions is proposed. The aggregation is done on each segment composing the road network. In order to reduce data occupancy, clustering techniques are used to obtain meaningful classes of traffic conditions. Different times of the day with similar speed patterns and traffic behavior are thus grouped together in a single cluster. Different energy consumption models based on the aggregated data are proposed to estimate the energy consumption of the vehicles in the road network. For validation purposes, a microscopic traffic simulator is used to generate the data and compare the estimated energy consumption to the reference one. A thorough sensitivity analysis with respect to the parameters of the proposed method (i.e. number of clusters, size of the distributions support, etc.) is also conducted in simulation. Finally, a real-life scenario using floating car data is analyzed to evaluate the applicability and the robustness of the proposed method. (10.1109/TITS.2019.2923292)
  DOI : 10.1109/TITS.2019.2923292
• A Scaling Analysis of a Star Network with Logarithmic Weights
  
  • Robert Philippe
  • Véber Amandine
  Stochastic Processes and their Applications, Elsevier, 2019. The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has L requests to transmit and is idle, it tries to access the channel at a rate proportional to log(1+L). A stochastic model of such an algorithm is investigated in the case of the star network, in which J nodes can transmit simultaneously, but interfere with a central node 0 in such a way that node 0 cannot transmit while one of the other nodes does. One studies the impact of the log policy on these J+1 interacting communication nodes. A fluid scaling analysis of the network is derived with the scaling parameter N being the norm of the initial state. It is shown that the asymptotic fluid behavior of the system is a consequence of the evolution of the state of the network on a specific time scale $(N t , t∈(0, 1))$. The main result is that, on this time scale and under appropriate conditions, the state of a node with index $j≥1$ is of the order of $N^{a_j(t)}$ , with $0≤a_j(t)<1$, where $t →a_j(t)$ is a piecewise linear function. Convergence results on the fluid time scale and a stability property are derived as a consequence of this study. (10.1016/j.spa.2018.06.002)
  DOI : 10.1016/j.spa.2018.06.002
• Imputation of mixed data with multilevel singular value decomposition
  
  • Husson François
  • Josse Julie
  • Narasimhan Balasubramanian
  • Robin Geneviève
  Journal of Computational and Graphical Statistics, Taylor & Francis, 2019, 28 (3), pp.552-566. Statistical analysis of large data sets offers new opportunities to better understand many processes. Yet, data accumulation often implies relaxing acquisition procedures or compounding diverse sources. As a consequence, such data sets often contain mixed data, i.e. both quantitative and qualitative and many missing values. Furthermore, aggregated data present a natural \textit{multilevel} structure, where individuals or samples are nested within different sites, such as countries or hospitals. Imputation of multilevel data has therefore drawn some attention recently, but current solutions are not designed to handle mixed data, and suffer from important drawbacks such as their computational cost. In this article, we propose a single imputation method for multilevel data, which can be used to complete either quantitative, categorical or mixed data. The method is based on multilevel singular value decomposition (SVD), which consists in decomposing the variability of the data into two components, the between and within groups variability, and performing SVD on both parts. We show on a simulation study that in comparison to competitors, the method has the great advantages of handling data sets of various size, and being computationally faster. Furthermore, it is the first so far to handle mixed data. We apply the method to impute a medical data set resulting from the aggregation of several data sets coming from different hospitals. This application falls in the framework of a larger project on Trauma patients. To overcome obstacles associated to the aggregation of medical data, we turn to distributed computation. The method is implemented in an R package. (10.1080/10618600.2019.1585261)
  DOI : 10.1080/10618600.2019.1585261
• Quantifying uncertainties in signal position in non-resolved object images: application to space object observation
  
  • Sanson Francois
  • Frueh Carolin
  Advances in Space Research, Elsevier, 2019. Charged Coupled Devices (CCDs) and subsequently Complementary metal-oxide-semiconductor (CMOS) detectors revolutionized scientific imaging. On both the CCD and CMOS detector, the generated images are degraded by inevitable noise. In many applications, such as in astronomy or for satellite tracking , only unresolved object images are available. Strategies to estimate the center of the non-resolved image their results are affected by the detector noise. The uncertainty in the center is classically estimated by running prohibitively costly Monte Carlo simulations, but in this paper, we propose analytic uncertainty estimates of the center position. The expressions that depend on the pixel size, the signal to noise ratio and the extension of the object signal relative to the pixel size are validated against rigorous Monte Carlo simulations with very satisfying results. Numerical tests show that our analytic expression is an efficient substitute to the Monte Carlo simulation thereby reducing computational cost. (10.1016/j.asr.2018.12.040)
  DOI : 10.1016/j.asr.2018.12.040
• New preconditioners for Laplace and Helmholtz integral equations on open curves
  
  • Alouges François
  • Averseng Martin
  , 2019. The numerical resolution of wave scattering problems by open curves leads to ill-conditioned linear systems which are difficult to precondition due to the geometrical singularities at the edges. We introduce two new preconditioners to tackle this problem respectively for Dirichlet or Neu-mann boundary data, that take the form of square roots of local operators. We describe an adapted analytical setting to analyze them and demonstrate the efficiency of this method on several numerical examples. A complete new pseudo-differential calculus suited to the study of such operators is postponed to the second part of this work.
• C-mix: a high dimensional mixture model for censored durations, with applications to genetic data
  
  • Bussy Simon
  • Guilloux Agathe
  • Gaïffas Stéphane
  • Jannot Anne-Sophie
  Statistical Methods in Medical Research, SAGE Publications, 2019, 28 (5), pp.1523--1539. We introduce a supervised learning mixture model for censored durations (C-mix) to simultaneously detect subgroups of patients with different prognosis and order them based on their risk. Our method is applicable in a high-dimensional setting, i.e. with a large number of biomedical covariates. Indeed, we penalize the negative log-likelihood by the Elastic-Net, which leads to a sparse parameterization of the model and automatically pinpoints the relevant covariates for the survival prediction. Inference is achieved using an efficient Quasi-Newton Expectation Maximization (QNEM) algorithm, for which we provide convergence properties. The statistical performance of the method is examined on an extensive Monte Carlo simulation study, and finally illustrated on three publicly available genetic cancer datasets with high-dimensional co-variates. We show that our approach outperforms the state-of-the-art survival models in this context, namely both the CURE and Cox proportional hazards models penalized by the Elastic-Net, in terms of C-index, AUC(t) and survival prediction. Thus, we propose a powerfull tool for personalized medicine in cancerology. (10.1177/0962280218766389)
  DOI : 10.1177/0962280218766389
• Topological derivative for the nonlinear magnetostatic problem
  
  • Amstutz Samuel
  • Gangl Peter
  Electronic Transactions on Numerical Analysis, Kent State University Library, 2019, 51, pp.169-218. (10.1553/etna_vol51s169)
  DOI : 10.1553/etna_vol51s169
• Initiation of a validation strategy of reduced-order two-fluid flow models using direct numerical simulations in the context of jet atomization
  
  • Cordesse Pierre
  • Murrone A.
  • Ménard T.
  • Massot Marc
  NASA Technical Memorandum, National Aeronautics and Space Administration, 2019, pp.1-11. In industrial applications, developing predictive tools relying on numerical simulations using reduced-order models nourish the need of building a validation strategy. In the context of cryogenic atomization, we propose to build a hierarchy of direct numerical simulation test cases to assess qualitatively and quantitatively diffuse interface models. The present work proposes an initiation of the validation strategy with an air-assisted water atomization using a coaxial injector.
• Avis en réponse à la saisine HCB - EFSA-GMO-ES-2018-154. Paris, le 5 avril 2019
  
  • Du Haut Conseil Des Biotechnologies Comité Scientifique
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2019.
• Avis en réponse à la saisine HCB - dossier EFSA-GMO-RX-013. Paris, le 30 janvier 2019
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2019.
• On a Wasserstein-type distance between solutions to stochastic differential equations
  
  • Bion-Nadal Jocelyne
  • Talay Denis
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2019, 29 (3), pp.1609-1639. In this paper, we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic differential equations. This new distance is defined by restricting the set of possible coupling measures. We prove that it may also be defined by means of the value function of a stochastic control problem whose Hamilton–Jacobi–Bellman equation has a smooth solution, which allows one to deduce a priori estimates or to obtain numerical evaluations. We exhibit an optimal coupling measure and characterize it as a weak solution to an explicit stochastic differential equation, and we finally describe procedures to approximate this optimal coupling measure. A notable application concerns the following modeling issue: given an exact diffusion model, how to select a simplified diffusion model within a class of admissible models under the constraint that the probability distribution of the exact model is preserved as much as possible? (10.1214/18-AAP1423)
  DOI : 10.1214/18-AAP1423
• Derivation of a two-phase flow model with two-scale kinematics, geometric variables and surface tension using variational calculus
  
  • Cordesse Pierre
  • Kokh Samuel
  • Di Battista Ruben
  • Drui Florence
  • Massot Marc
  NASA Technical Memorandum, National Aeronautics and Space Administration, 2019. The present paper proposes a two-phase flow model that is able to account for two-scale kinematics and two-scale surface tension effects based on geometric variables at small scale. At large scale, the flow and the full geometry of the interface may be retrieved thanks to the bulk variables, while at small scale the interface is accurately described by volume fraction, interfacial area density and mean curvature, called the geometric variables. Our work mainly relies on the Least Action Principle. The resulting system is an extension of a previous work modeling small scale pulsation in which surface tension was not taken into account at large or small scale. Whereas the original derivation assumes a cloud of monodispersed spherical bubbles, the present context allows for polydispersed, non-spherical bubbles. The resulting system of equations solely involves small scale geometric variables, thus contributing in the construction of a unified model describing both large and small scales.
• On the stability of matrix-valued Riccati diffusions
  
  • Bishop Adrian N
  • del Moral Pierre
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2019, 24. The stability properties of matrix-valued Riccati diffusions are investigated. The matrix-valued Riccati diffusion processes considered in this work are of interest in their own right, as a rather prototypical model of a matrix-valued quadratic stochastic process. Under rather natural observability and controllability conditions, we derive time-uniform moment and fluctuation estimates and exponential contraction inequalities. Our approach combines spectral theory with nonlinear semigroup methods and stochastic matrix calculus. This analysis seem to be the first of its kind for this class of matrix-valued stochastic differential equation. This class of stochastic models arise in signal processing and data assimilation, and more particularly in ensemble Kalman-Bucy filtering theory. In this context, the Riccati diffusion represents the flow of the sample covariance matrices associated with McKean-Vlasov-type interacting Kalman-Bucy filters. The analysis developed here applies to filtering problems with unstable signals. (10.1214/19-EJP342)
  DOI : 10.1214/19-EJP342
• Avis en réponse à la saisine HCB - habilitation agents 2019. Paris, le 4 juillet 2019
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2019, pp.2 p..
• Uniform sampling in a structured branching population
  
  • Marguet Aline
  Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2019, 25 (4A), pp.2649-2695. We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of the descendants at birth depends on the trait of the mother and on the number of descendants. In this article, we explicitly describe the penalized Markov process, named auxiliary process, corresponding to the dynamic of the trait along the spine by giving its associated infinitesimal generator. We prove a Many-to-One formula and a Many-to-One formula for forks. Furthermore, we prove that this auxiliary process characterizes exactly the process of the trait of a uniformly sampled individual in the large population approximation. We detail three examples of growth-fragmentation models: the linear growth model, the exponential growth model and the parasite infection model. (10.3150/18-BEJ1066)
  DOI : 10.3150/18-BEJ1066
• Morphological organization of point-to-point transport in complex networks
  
  • Kang Min-Yeong
  • Berthelot Geoffroy C.B.
  • Nicolaides Christos
  • Colonna Jean-François
  • Sapoval Bernard
  • Grebenkov Denis S
  • Tupikina Liubov
  Scientific Reports, Nature Publishing Group, 2019, 9, pp.8322. We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. the random choice of two nodes, a source and a drain, to which a potential difference is applied, selects two tree-like structures, one emerging from the source and the other converging to the drain. these trees merge into a large cluster of the remaining nodes that is found to be quasi-equipotential and thus presents almost no resistance to transport. such a global "tree-cluster-tree" structure is universal and leads to a power law decay of the currents distribution. Its exponent, −2, is determined by the multiplicative decrease of currents at successive branching points of a tree and is found to be independent of the network connectivity degree and resistance distribution. (10.1038/s41598-019-44701-6)
  DOI : 10.1038/s41598-019-44701-6
• Approximating the Volume of Tropical Polytopes is Difficult
  
  • Gaubert Stéphane
  • Maccaig Marie
  International Journal of Algebra and Computation, World Scientific Publishing, 2019, 29 (02), pp.357--389. We investigate the complexity of counting the number of integer points in tropical polytopes, and the complexity of calculating their volume. We study the tropical analogue of the outer parallel body and establish bounds for its volume. We deduce that there is no approximation algorithm of factor $\alpha=2^{\text{poly}(m,n)}$ for the volume of a tropical polytope given by $n$ vertices in a space of dimension $m$, unless P$=$NP. Neither is there such an approximation algorithm for counting the number of integer points in tropical polytopes described by vertices. If follows that approximating these values for tropical polytopes is more difficult than for classical polytopes. Our proofs use a reduction from the problem of calculating the tropical rank. For tropical polytopes described by inequalities we prove that counting the number of integer points and calculating the volume are $\#$P-hard. (10.1142/S0218196718500686)
  DOI : 10.1142/S0218196718500686
• Spreading and vanishing for a monostable reaction-diffusion equation with forced speed
  
  • Bouhours Juliette
  • Giletti Thomas
  Journal of Dynamics and Differential Equations, Springer Verlag, 2019, 35, pp.92 - 117. Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the subdomain where the reaction term is positive is shifting/contracting at a given speed c. This problem arises in particular in the modelling of the impact of climate change on population dynamics. By placing ourselves in the appropriate moving frame, this leads us to consider a reaction-diffusion-advection equation with a heterogeneous in space reaction term, in dimension N ≥ 1. We investigate the behaviour of the solution u depending on the value of the advection constant c, which typically stands for the velocity of climate change. We find that, when the initial datum is compactly supported, there exists precisely three ranges for c leading to drastically different situations. In the lower speed range the solution always spreads, while in the upper range it always vanishes. More surprisingly, we find that that both spreading and vanishing may occur in an intermediate speed range. The threshold between those two outcomes is always sharp, both with respect to c and to the initial condition. We also briefly consider the case of an exponentially decreasing initial condition, where we relate the decreasing rate of the initial condition with the range of values of c such that spreading occurs. (10.1007/s10884-018-9643-5)
  DOI : 10.1007/s10884-018-9643-5
• A kinetic model of reactive crystal surfaces A Kinetic Model of Reactive Crystal Surfaces
  
  • Aoki Kazuo
  • Giovangigli Vincent
  AIP Conference Proceedings, American Institute of Physics, 2019, 2132. A kinetic model describing chemical reactions on a crystal surface is introduced. The Boltzmann equations involve particles interacting with potentials generated by fixed crystal particles and interacting with a phonon gas describing the fluctuating part of the potentials. Chemical reactions between gas/physisorbed, chemisorbed and crystal species are taken into account. The phonons are assumed to be at equilibrium for the sake of simplicity. A modified kinetic entropy is introduced for the coupled system and the H theorem is established. Using a fluid scaling and the Chapman-Enskog asymptotic method, species fluid boundary conditions involving heterogeneous reactions are recovered at the surface. (10.1063/1.5119623)
  DOI : 10.1063/1.5119623