Fatma Abdelhedi

Landry Ntsama
email: landry.ntsama@ut-capitole.fr

Gilles Zurfluh

Modélisation d'un entrepôt de documents XML

Le format XML est aujourd'hui omniprésent dans les organisations et sur le Web. Il facilite le transport et l'échange de données complexes et hétérogènes représentant une information précieuse très peu, voire pas du tout exploitée. Les technologies OLAP et les systèmes d'entrepôts de données actuels permettent l'analyse et le stockage des données transactionnelles issues des bases données relationnelles. Cependant, ces outils ne sont pas adaptés à l'analyse des documents XML du fait de leur structure hiérarchique, ou de leur contenu étant souvent textuel. Nous proposons dans cet article une approche permettant de construire un entrepôt de document XML « centré document » dont le schéma conceptuel est modélisé en utilisant le formalisme UML ; nous présentons aussi une architecture pour l'intégration physique de ces documents dans un environnement XML natif.

Introduction

Le format XML facilite la description et l'échange des données complexes provenant de sources hétérogènes. De plus sa structure balisée et auto-descriptive [START_REF] Fankhauser | Xml for data warehousing changes and challenges[END_REF] permet une représentation aisée de différents types de données (structurés et semistructurés). C'est aujourd'hui un standard de communication tant au sein des organisations que sur le Web. Les systèmes OLAP et les entrepôts de données permettent respectivement l'analyse multidimensionnelle et le stockage orienté sujet des données transactionnelles. Les données stockées sont décrites par un schéma multidimensionnel [START_REF] Golfarelli | The dimensional fact model: a conceptual model for data warehouses[END_REF], qui permet à un décideur de réaliser des analyses OLAP sur les cubes de données définis dans l'entrepôt. Les systèmes OLAP permettent ainsi une analyse interactive en représentant les données suivant plusieurs perspectives ou dimensions. L'analyse OLAP sur des données relationnelles (structurées) est un processus aujourd'hui parfaitement maîtrisé. Mais ce processus s'avère inadapté pour des documents XML qui présentent une structure hiérarchique profonde et diffèrent des données plates tant au niveau de leur modèle de données que de leur modèles de requêtes [START_REF] Bordawekar | Analytical processing of xml documents: opportunities and challenges[END_REF].

Nous proposons une nouvelle approche permettant de construire un entrepôt sur des documents XML « centré document » [START_REF] Pérez | Data warehouses with web data: A survey, knowledge and data engineering[END_REF] en les intégrant au niveau physique dans un environnement XML natif. L'objectif est de permettre à un décideur de réaliser des analyses multidimensionnelles sur une collection de documents XML. Dans cette approche, le modèle conceptuel est construit à partir du XML Schéma (XSchema) (W3C-Consortium, 2013) représentant la classe de documents analysée ; il est défini sur la base du formalisme de modélisation orientée objet UML (Unified Modeling Language) ((OMG), 2013). Ce modèle permet de représenter la structure de la classe de documents sous la forme d'un schéma en étoile (ou en flocon) [START_REF] Kimbal | The Data Warehouse Toolkit: The Complete Guide to Dimensional Moedeling[END_REF]. Nous présentons donc dans cet article une architecture pour une intégration physique des documents XML « centré document » dans un entrepôt, notre principale contribution étant la définition d'une approche de modélisation conceptuelle d'un entrepôt de documents XML, basé sur le formalisme de modélisation orienté objet UML à partir d'un XSchema.

La suite de l'article est organisée comme suit. Dans la section 2 nous faisons le point sur les travaux relatifs à notre problématique ; la section 3 présente notre architecture et définit notre démarche de modélisation d'un entrepôt ; et enfin nous concluons dans la section 4 en présentant quelques perspectives liées à nos travaux.

Travaux associés

L'analyse OLAP des documents XML soulève des problématiques distinctes de celles liées aux systèmes OLAP traditionnels. Dans [START_REF] Bordawekar | Analytical processing of xml documents: opportunities and challenges[END_REF], les auteurs passent en revue ces problématiques liées à l'implémentation d'un système OLAP pour les documents XML. De même ils proposent une approche basée sur l'utilisation de « modèle d'arbres abstraits » pour l'analyse OLAP des documents XML. Ils décrivent de nouveaux opérateurs pour supporter des « agrégations structurées » sur des documents XML, par le biais du langage XQuery.

Dans [START_REF] Hümmer | Xcube: Xml for data warehouses[END_REF], les auteurs proposent un modèle de document appelé XCube et basé sur le format XML. Ce modèle permet de faciliter l'échange et la manipulation de cubes de données contenus dans les entrepôts de données traditionnels. C'est un modèle dynamique qui est défini par trois schémas XML pour décrire les données échangées, à savoir XCube-Fact pour décrire l'ensemble des faits, XCubeDimension pour décrire les dimensions et leurs hiérarchies, et XCubeSchema pour décrire le schéma multidimensionnel.

Les auteurs de (fei [START_REF] Jiang | Ix-cubes: iceberg cubes for data warehousing and olap on xml data[END_REF] proposent une structure de données appelée IX-Cube (Iceberg XML Cube) permettant de faciliter l'application de requêtes multidimensionnelles OLAP sur des données XML. Ce modèle est défini à partir d'un arbre XML représentant la structure des documents dans la collection. [START_REF] Boussaïd | X-warehousing : Anxmlbased approach for warehousing complex data[END_REF] proposent un outil appelé X-Warehousing pour l'entreposage et la construction des cubes XML en utilisant essentiellement des technologies XML. Ils utilisent le modèle conceptuel multidimensionnel (MCM) pour représenter les besoins d'analyses de l'utilisateur. Ce MCM est traduit en XSchema pour représenter la structure logique de l'entrepôt. Ils utilisent des « arbres d'attributs » pour comparer les documents de la source au XSchema obtenu, afin d'identifier les documents dont la structure est proche des besoins du décideur.

L'ensemble des travaux ci-dessus concerne essentiellement l'analyse des documents XML « centrés-données » [START_REF] Pérez | Data warehouses with web data: A survey, knowledge and data engineering[END_REF], toutefois il est envisageable de les adapter à notre contexte qui est l'analyse OLAP des documents XML « centrés-documents ». Seulement, certains de ces travaux concernent le traitement des données relationnelles et utilisent le format XML pour définir un cube sur ces données [START_REF] Hümmer | Xcube: Xml for data warehouses[END_REF][START_REF] Niemi | Constructing an olap cube from distributed xml data[END_REF]. D'autres travaux, bien que définissant un cube à partir d'une source XML, présentent les limites suivantes :

-Ils ne proposent pas de modèle multidimensionnel représentant la structure des documents analysés -Ils se basent sur les instances de documents constituant la source pour définir les modèles d'arbres XML qu'ils utilisent, or nous basons notre approche sur les XSchemas associés aux documents de la source -Les modèles d'arbres qu'ils ont définis représentent la structure logique servant à définir les cubes de données XML, or nous utilisons un XSchema pour représenter la structure logique de notre entrepôt. Les auteurs de [START_REF] Park | Xml-olap: A multidimensional analysis framework for xml warehouses[END_REF] proposent un outil nommé XML-OLAP pour l'analyse multidimensionnelle des documents XML « centré document ». Cet outil construit un cube XML à partir d'un entrepôt dans lequel les faits et les dimensions sont représentés par des documents XML différents. Le cube est construit et analysé au moyen des langages XQuery utilisé pour le calcul des mesures et l'identification des dimensions. Toutefois ils utilisent l'approche définie par [START_REF] Nassis | Conceptual and systematic design approach for xml document warehouses[END_REF] pour le modèle conceptuel du cube.

Entrepôts de documents XML : modélisation conceptuelle

Notre objectif est de permettre l'analyse multidimensionnelle de documents XML issus du Web en reprenant les principes d'entreposage basés sur les faits et dimensions [START_REF] Kimbal | The Data Warehouse Toolkit: The Complete Guide to Dimensional Moedeling[END_REF]. Il s'agit donc de construire un entrepôt de documents décrit par un schéma en étoile (ou en flocon) et permettant aux décideurs d'effectuer des opérations multidimensionnelles (OLAP). La Figure 1 représente l'architecture globale de notre système. Cette architecture permet l'intégration physique des documents XML « centré document » dans un entrepôt, ainsi que leur analyse OLAP.

Nous avons développé un modèle multidimensionnel qui permet de décrire un entrepôt de documents XML sous la forme d'un schéma en étoile nommé StarCD. Ce schéma d'objets complexes s'appuie sur des diagrammes de classes UML pour représenter le fait et ses dimensions. Il est élaboré à partir de l'analyse des XSchemas des documents XML composant la source. En effet, cette source contient une collection de documents de même thématique, donc présentant des structures proches. Nous considérons dans la suite de l'article que chaque document dans cette collection est valide, et donc associé à un XSchema propre.

De nombreux travaux ont traité de la modélisation multidimensionnelle des documents XML se basant sur UML, notamment [START_REF] Li | Representing uml snowflake diagram from integrating xml data using xml schema[END_REF] ou encore [START_REF] Nassis | Conceptual and systematic design approach for xml document warehouses[END_REF]. Cependant, aucune des approches proposées dans ces travaux ne conserve la structure des documents analysés dans le schéma présenté au décideur. Les auteurs de [START_REF] Nassis | Conceptual and systematic design approach for xml document warehouses[END_REF] proposent néanmoins dans leur modèle xFact une représentation de la dite structure. Toutefois celle-ci est difficilement identifiable par le décideur. Dans notre approche, nous supposons que le décideur connaît la structure des documents qu'il veut analyser, aussi nous lui permettons de retrouver cette structure de façon partielle dans le schéma de l'entrepôt, compte tenu de ses besoins d'analyse.

Unification des structures

Modélisation UML multidimensionnelle

Tout XSchema unifié est transformé en un Diagramme de Classes UML (noté SourceCD pour Source Class Diagram) ; il se présente sous la forme d'un graphe arborescent dont la <?xml version="1.0" encoding="UTF-8"?> <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema"> <xs:element name = "Paper"> <xs:complexType> <xs:sequence> <!--Types simples --> <xs:element name="Title" type="xs:string"/> <!--Types complexes --> <xs:element name = "CoAuthors"> <xs:complexType> <xs:sequence> <xs:element name="Author" maxOccurs="unbounded"> <xs:complexType> <xs:sequence> <xs:element name = "Name" type="xs:string"/> <xs:element name = "FirstName" type="xs:string"/> <xs:element name = "Affiliation" type="xs:string" minOccurs="0"/> <xs:element name = "Mail" type="xs:string" minOccurs="0"/> </xs:sequence> <!--Attributs auteur --> <xs:attribute name = "H-Index" type="xs:integer" use ="required"/> </xs:complexType> </xs:element> <xs:element name = "AffiliationGroup" type="xs:string" minOccurs="0"/> </xs:sequence> </xs:complexType> </xs:element> <xs:element name="Abstract" type="xs:string" minOccurs="0"/> <xs:element name="Résumé" type="xs:string" minOccurs="0"/> <!----> Le SourceCD construit sera traité automatiquement pour en extraire les mesures et dimensions potentielles. Seules les mesures simples (faisant intervenir un seul attribut) sont identifiées par l'algorithme de traitement. Par manque de place, l'algorithme de traitement ne sera pas abordé ici. Le fait ayant déjà été identifié correspond à la racine du SourceCD (classe Paper). D'après [START_REF] Bordawekar | Analytical processing of xml documents: opportunities and challenges[END_REF] tout élément XML peut être analysé autant en tant que dimension que mesure. Ceci est dû au fait que la classification entre les dimensions et les mesures n'est pas rigide, comme c'est le cas pour les données plates. Nous retrouvons cette propriété dans notre modèle, où un élément identifié comme dimension par le décideur peut aussi être identifié comme mesure (à l'exception de l'élément Date, utilisé exclusivement comme dimension). Les dimensions et leurs hiérarchies sont extraites des classes imbriquées, ou des attributs issus de la classe racine. Nous travaillons uniquement avec des hiérarchies simples représentées par des liens de composition dans le StarCD. Nous introduisons néanmoins le concept de hiérarchie inversée dans lequel l'élément de plus haute granularité dans la hiérarchie est l'élément rattaché au fait. Ce type de hiérarchie permet de respecter certaines contraintes de représentation de la structure des documents dans le schéma multidimensionnel.

Traditionnellement les mesures sont des valeurs numériques pré calculées au niveau logique, suivant les agrégations appliquées sur les données transactionnelles pour définir le cube de données. Dans notre modèle, nous prenons aussi en compte les mesures textuelles relatives aux éléments présents dans la structure, bien que ne traitant pas le contenu des documents. En effet notre modèle repose essentiellement sur l'exploitation de la structure des documents analysés, il est donc important que cette structure soit représentée dans le schéma multidimen- -P = {p 1 , . . . , p s } est l'ensemble des paramètres de la dimension D D.

Définitions formelles

-H = {h 1 , . . . , h s } est l'ensemble des hiérarchies dans lesquelles sont organisés les paramètres, avec h défini comme suit :

h = {p 1 , p 2 , . . . , All} où p1 est le paramètre lié au fait (paramètre de plus bas niveau, et All étant le paramètre de plus haut niveau sur la hiérarchie. Dans le StarCD, les dimensions sont décrites sous la forme d'un ensemble de classes ; chaque classe représente un paramètre qui permet de partitionner l'ensemble des instances du fait. Chaque dimension est une arborescence de classes dont la racine est liée au fait par une relation d'association «By». Les attributs faibles des dimensions correspondent aux attributs des classes. Avec ce modèle nous introduisons le concept de hiérarchie inversée. Dans ce type de hiérarchie, le paramètre de plus haute granularité est relié au fait pour respecter la structure du XSchéma de la source. Le paramètre « All » considéré comme paramètre de plus haut niveau dans une hiérarchie dite « normale » n'est plus pris en compte ici.

Conclusions et perspectives

Nous proposons dans cet article une approche de modélisation permettant d'élaborer le schéma conceptuel d'un entrepôt à partir d'une source de documents XML « centré document ». Cette approche est définie pour une pour une intégration physique dans un environnement XML natif. Elle est essentiellement basée sur l'exploitation de la structure des documents. Il est donc important que cette structure soit présentée au décideur afin de faciliter l'expression des requêtes d'analyse multidimensionnelle.

Nous envisageons de développer l'approche présentée dans cet article dans la base de données XML native eXist-DB. Ses mécanismes d'indexation permettent en effet une gestion optimale des collections de documents. Optant pour une intégration physique, une étude de la complexité du chargement de l'entrepôt est à envisager. Nous souhaitons orienter notre réflexion vers la recherche de solution permettant d'optimiser le temps de traitement pendant le chargement. Ceci implique aussi l'étude des problèmes liés à la mise à jour de l'entrepôt, en cas de changement dans les données de la source, ou de modification dans le modèle conceptuel. Par ailleurs, nous envisageons une étude comparative de performance de la solution que nous proposons, par rapport à un système relationnel possédant des fonctionnalités de gestion de documents textuels.

FIG. 1 -

 1 FIG. 1 -Architecture globale.

  Dans la Figure1, le cadre « Conceptual Modeling » représente le processus de modélisation conceptuelle partant de l'unification des schémas de la source. En effet, bien qu'étant de même thématique, les documents ont généralement des structures différentes. Pour résoudre ce problème, un processus d'unification va traiter automatiquement l'ensemble des XSchemas pour en extraire une (ou plusieurs) structure(s) unifiée(s). Cette structure unifiée correspond à un XSchema dont la racine représente le sujet d'analyse. Le processus d'unification n'est pas détaillé dans cet article, aussi nous invitons les lecteurs à se référer à[START_REF] Messaoud | Unification of xml document structures for document warehouse (docw)[END_REF] ou[START_REF] Janga | Schema extraction and integration of heterogeneous xml document collections[END_REF] pour plus de précisions.Une fois le processus d'unification réalisé, la source contient des documents regroupés en classes. Tous les documents appartenant à une même classe sont décrits par un XSchema unique ; le nom de la classe de document est situé au premier niveau du XSchema comme le montre la Figure2. Celle-ci représente un XSchema unifié partiel relatif à une classe de document XML sur une collection d'articles scientifiques.

FIG. 2 -

 2 FIG. 2 -XSchéma de la classe de document Paper.

FIG. 5 -FIG. 6 -

 56 FIG. 5 -Correspondances entre XSchema et SourceCD.

  Nous avons formalisé notre modèle multidimensionnel en définissant les notions de faits, mesures, dimensions et hiérarchies tels que nous les appliquons. Cette formalisation est la suivante : StarCD = (F, D) où : -F correspond au fait, c'est-à-dire à l'élément racine du XSchéma définissant la classe de documents à analyser. -D = {D 1 , . . . , D n } est un ensemble de dimensions associé au fait. Le fait est caractérisé par un ensemble de mesures (numériques ou textuelles). Dans le StarCD, il représente la classe de documents de la source à analyser. Les mesures sont décrites sous forme de classes liées au fait par des liens d'agrégation, ou sous forme d'attributs intégrés au fait ; on retrouve ainsi la structure hiérarchique qui est présente dans le XSchéma de la source. Le fait est défini comme suit : F = (M, Agg) où : -M = {M 1 , . . . , M p } est un ensemble de mesures. -Agg = {ag 1 , . . . , ag p } l'ensemble des fonctions d'agrégation associées aux mesures, avec ag inclus dans {SU M, COU N T, AV G, M AX, M IN }. Les dimensions sont quant à elles caractérisées par des paramètres organisés en hiérarchies. Ces hiérarchies précisent des niveaux de granularité allant du paramètre de plus haut niveau (All) au paramètre de plus bas niveau, qui correspond à la classe liée au fait. Elles sont définies comme suit : D = (P, H) où :

Summary

The XML format is today omnipresent on the Web and also in organizations' information systems. It allows to transport and exchange complex and heterogeneous data representing valuable information, which is barely exploited, even not at all. The current data warehouses systems and OLAP technologies allow the analysis and the storage of transactional data extracted from relational databases. However, these tools are not well suited for the XML documents analysis because of their hierarchical structure or their content being generally textual. We propose in this article an approach that allows building a XML "document-centric" warehouse whose conceptual schema is modeled using the UML formalism ; we also present architecture for a physical integration of these documents in a XML native environment.


Paul Breillat

Alexis Mathian

Flore Rozenberg

Amélie Dutheil

Annick Barbaud

Zahir Amoura

MD François Chasset
email: francois.chasset@aphp.fr

Is there an increased risk of severe COVID-19 among patients with systemic lupus erythematosus treated with anifrolumab?

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Dear Editor, Systemic lupus erythematosus (SLE) is associated with an overexpression of type-I interferons (IFN-I) [START_REF] Crow | Type I interferons in host defence and inflammatory diseases[END_REF]. Recently, anifrolumab, a monoclonal antibody that binds IFN-I receptor subunit 1, has been approved by the US Food and Drug Administration (FDA) and European Medicines Agency for the treatment of SLE. Life-threatening COVID-19 have been recently related to autoantibodies against IFN-I(2,3) raising the question of potentially severe COVID-19 associated with anifrolumab.

Here we report two cases of COVID-19 which occurred in patients treated with anifrolumab for SLE. This work was approved by the ethical committee of Sorbonne Université (CER2020-012) and written informed consent was obtained from participants.

The first case was a 32 years-old woman diagnosed with SLE since the age of 10 years-old.

The main SLE characteristics are summarized in Table 1. She developed refractory discoid lupus and previously failed multiple lines of treatment (see table 1) and anifrolumab was started on November 2021. After 3 infusions of anifrolumab she developed cough, sore throat and headache and a COVID-19 was diagnosed using Polymerase Chain reaction (PCR). The 4th infusion of anifrolumab was postponed for 10 days that has been continued since with improvement of cutaneous lesions. Serological test performed 3 months after COVID-19 showed anti-spike (anti-S) and anti-nucleocapsid (anti-N) antibodies confirming SARS-CoV-2 infection. She reported being previously vaccinated with 3 injections of mRNA BNT162b2 vaccine (last in July 2021). However retrospective analysis of a serum collected in August 2021 showed no anti-S or anti-N antibodies.

The second case was 51 years-old woman diagnosed with SLE 10 years ago. She had active cutaneous and articular involvement with failure to multiple lines (see Table 1). In September 2021, anifrolumab was started with a rapid improvement on both cutaneous and articular symptoms. Before anifrolumab initiation, she had 2 injections of mRNA BNT162b2 and one mRNA-1273 injection was done 2 months after, in December 2021. Retrospective analysis of a serum collected in August 2021 confirmed anti-S antibody response but no anti-N antibodies. After 3 anifrolumab infusions, she developed cough, sore throat, headache, muscle pain and a COVID-19 was confirmed by PCR and serological test (2 months later).

Anifrolumab infusion was postponed for 2 weeks later without SLE flare.

Anifrolumab has been associated with an increased risk of viral infections(4). Since trials on which FDA approval was based were conducted in the COVID-19 pre-pandemic period(5), little is known on the risk of severe COVID-19. During the long-term extension study from a phase III trial, 3 deaths were attributable to COVID-19 in non-vaccinated patients and higher rates of COVID-related serious adverse events was found in anifrolumab group [START_REF] Kalunian | A Randomized, Placebo-Controlled Phase III Extension Trial of the Long-Term Safety and Tolerability of Anifrolumab in Active Systemic Lupus Erythematosus[END_REF]. Moreover, although the 2 present cases seem reassuring, it is important to note that infections occur in January 2022 when omicron variants were the most common in France. This may have contributed to a lower COVID-19 severity regarding the decreased risk of hospitalization related to omicron variants [START_REF] Ward | Risk of covid-19 related deaths for SARS-CoV-2 omicron (B.1.1.529) compared with delta (B.1.617.2): retrospective cohort study[END_REF]. Nevertheless, additional data in larger SLE cohorts are needed to establish proper recommendations for the prevention and management of COVID-19 in patients treated with anifrolumab.

Table 1 Main features of SLE

 1

	Characteristics	Patient n°1	Patient n°2
	Sex category	F	F
	Age	32	51
	Ethnicity	West African	Caucasian
	Chronic medical illness	glucose-6-phosphate dehydrogenase	Depression
		deficiency and Farh syndrome
	Historical SLE features
	clinical involvement	Raynaud phenomenon, discoid lupus,	disseminated discoid lupus, Raynaud
		pericardial effusion	phenomenon, arthritis

Acknowledgment:

Astrazeneca global team was contacted to obtain vaccination status of patients who died from COVID-19 during the long-term extension study from the two phase III trials.

Funding:

No funding was received for this study.

Competing interests:

FC participated in advisory board related to lupus for GSK, Astrazeneca, Celgène, Principa-Bio and received consulting fees from GSK and Astrazeneca.

AM and ZA received consulting fees and participated in advisory board related to lupus for GSK and Astrazeneca.

Contributors:

PB, FR, AD and FC were involved in the acquisition of data. All authors contributed to drafting and/or revising the manuscript.


Donatella Passiatore
email: donatella.passiatore@poliba.it

Luca Sciacovelli
email: luca.sciacovelli@ensam.eu

Paola Cinnella
email: paola.cinnella@sorbonne-universite.fr

Giuseppe Pascazio
email: giuseppe.pascazio@poliba.it

SHOCK-WAVE/BOUNDARY LAYER INTERACTION AT HIGH ENTHALPIES

The dynamics of a shock wave impinging on a freestream-perturbed high-enthalpy boundary layer is investigated by means of direct numerical simulation. The oblique shock impacts on a cooled flat-plate boundary layer with an angle of 10 degrees, generating a reversal flow region. The combination of the freestream disturbances and the shock impingement is such that a transition to a fully turbulent regime occurs downstream of the interaction region. The analysis aims at qualifying and quantifying the role of thermochemical non-equilibrium conditions on the dynamics of the shock-wave/boundarylayer interaction.

INTRODUCTION

Shock-wave boundary layer interactions (SWBLI) have been extensively investigated over the last decades due to their importance for both aeronautical and aerospace applications. The impingement of a shock wave on a fully developed boundary layer may indeed occur for several reasons and both in internal and external flow configurations. The physics underlying such configuration is complex and strongly multiscale. The dynamics of high-speed compressible turbulent boundary layers becomes tightly coupled with strong gradients of the thermodynamic properties, leading to an increase of thermomechanical loads [START_REF] Délery | Some physical aspects of shock wave/boundary layer interactions[END_REF]. In hypersonic and high-enthalpy regimes, thermochemical non-equilibrium effects must be taken into account as well, further complicating the picture. When an incident shock impinges on a fully developed boundary layer, the latter experiences a strong adverse pressure gradient. If the shock is strong enough, a recirculation bubble occurs and the flow separates. Several additional flow features are generated by this interaction, depending on the nature of the incoming boundary layer. Laminar boundary layers have the advantage of a lower drag but are more sensitive to separation in adverse pressure gradients, resulting in wider recirculation bubbles with respect to turbulent flows. In such configurations, investigations have been carried out concerning shock-induced instabilities [START_REF] Hildebrand | Simulation and stability analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92[END_REF] as well as shock-induced transition to turbulence [START_REF] Fu | Shock-induced heating and transition to turbulence in a hypersonic boundary layer[END_REF], that can be obtained when the shock angle is sufficiently high. On the other hand, the interaction with a fully turbulent boundary layer has also been the object of intensive research efforts [START_REF] Andreopoulos | Shock wave-turbulence interactions[END_REF][START_REF] Dupont | Space and time organisation of a shock wave/turbulent boundary layer interaction[END_REF][START_REF] Adler | Dynamic linear response of a shock/turbulent-boundary-layer interaction using constrained perturbations[END_REF]. One of the most remarkable results of the interaction is the amplification of turbulence downstream of the incident shock and the emergence of oscillatory motions. Several parameters can affect the overall SWBLI dynamics, among which it is noteworthy mentioning the effect of non-adiabatic walls. It has been indeed found that wall cooling tends to reduce the interaction scales and the bubble size, while increasing pressure fluctuations [START_REF] Volpiani | Effects of a nonadiabatic wall on hypersonic shock/boundary-layer interactions[END_REF]. More recently, attention has been paid to shockwave/transitional boundary layer interactions [START_REF] Vanstone | Shock induced separation in transitional hypersonic boundary layers[END_REF][START_REF] Nd Sandham | Transitional shock-wave/boundarylayer interactions in hypersonic flow[END_REF][START_REF] Currao | Hypersonic transitional shock-wave-boundary-layer interaction on a flat plate[END_REF]. These studies are meant to mimic more realistic configurations in which the boundary layer is not completely unperturbed, but may be subjected to random disturbances deriving from the external flow or naturally generated in wind tunnel facilities. Of particular interest is the high-enthalpy regime, in which out-of-equilibrium processes can be triggered at the high temperatures induced by the intense wall friction and the strong shock waves. In such configurations, chemical dissociation and vibrational relaxation phenomena interplay with the SWBLI physics. High-enthalpy effects on turbulent flows have gained renewed attention for smooth boundary layer configurations [START_REF] Duan | Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect of high enthalpy[END_REF][START_REF] Passiatore | Finite-rate chemistry effects in turbulent hypersonic boundary layers: A direct numerical simulation study[END_REF][START_REF] Di Renzo | Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies[END_REF][START_REF] Li | Wall heat transfer in high-enthalpy hypersonic turbulent boundary layers[END_REF], where their influence was found to be often important depending on the thermodynamic operating regime. On the other hand, most of the research on SWBLI is limited to low-enthalpy conditions. The main objective of this study is therefore to extend the knowledge about highenthalpy wall-bounded turbulent flows to configurations involving the impingement of shock waves. For that purpose we perform a high-fidelity numerical simulation of a SWBLI in the presence of both chemical and thermal non-equilibrium effects. The paper is organized as follows. Sec. 2 describes the governing equations, the thermochemical models and the numerical strategy used for the computation. The problem setup is reported in Sec. 3, whereas Sec. 4 presents the main results. Concluding remarks are then provided in Sec. 4.

GOVERNING EQUATIONS AND NU-MERICAL METHODOLOGY

The fluid under investigation is air at high-temperature modeled as a mixture of N 2 , O 2 , NO, O and N. Thermochemical non-equilibrium flows are governed by the compressible Navier-Stokes equations for multicomponent chemically-reacting gases. Thermal relaxation is taken into account by means of the classical 2T model of Park [START_REF] Park | Two-temperature interpretation of dissociation rate data for N2 and O2[END_REF], whereby two different temperatures are used to separately compute the internal energy of the translational-rotational (TR) and vibrational (V) modes. After the numerical integration of the conservation equations, the roto-translational temperature T is computed from the specific internal energy (devoid of the vibrational contribution) directly, whereas an iterative Newton-Raphson method is used to compute the vibrational temperature T V from the vibrational energy. The coupling between chemical and thermal nonequilibrium is taken into account by means of a modification of the temperature values used for computing the species reaction rates. Specifically, a geometric-averaged temperature is considered for the dissociation reactions computed as T avg = T q T 1-q V with q = 0.7. Pure species' viscosity and thermal conductivities are computed using curvefits by Blottner [START_REF] Blottner | Chemically reacting viscous flow program for multicomponent gas mixtures[END_REF] and Eucken's relations [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF], respectively. The corresponding mixture properties are evaluated by means of Wilke's mixing rules. Mass diffusion is modeled by means of Fick's law; species diffusion coefficients are computed following Hirschfelder's approximation, starting from the binary diffusion coefficients curvefitted in [START_REF] Gupta | A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K[END_REF]. We refer to ref. [START_REF] Passiatore | Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers[END_REF] for more information about the thermochemical modeling. The numerical solver described in Sciacovelli et al. [START_REF] Sciacovelli | Assessment of a high-order shockcapturing central-difference scheme for hypersonic turbulent flow simulations[END_REF] is used for the present computation. The convective fluxes of the Navier-Stokes equations are discretized by means of central tenth-order differences, supplemented with an adaptive nonlinear artificial dissipation. The latter consists in a blend of a ninth-order-accurate dissipation term based on tenth-order derivatives of the conservative variables, used to damp grid-to-grid oscillations, along with a low-order shock-capturing term. Time integration is carried out using a low-storage 3 rd -order Runge-Kutta scheme. The numerical strategy has been validated for thermochemical nonequilibrium flows, including SWBLI laminar configurations [START_REF] Passiatore | A high-order scheme for the numerical simulation of high-enthalpy hypersonic flows[END_REF].

PROBLEM SETUP

The configuration under investigation consists in a shock wave that impinges a flat-plate boundary layer in thermochemical non-equilibrium conditions. We note in the following with ϑ and β the deflection angle and the shock angle, respectively. The current setup stems from the one of Sandham et al. [START_REF] Nd Sandham | Transitional shock-wave/boundarylayer interactions in hypersonic flow[END_REF], in which inflow freestream perturbations were applied on a M ∞ = 6 laminar perfect-gas boundary layer. Here, we consider the post-shock conditions of a scramjet, approximated by a 6 • planar wedge, flying at Mach 12 at an altitude of 36 km. The freestream conditions are then T ∞ = 405 K, p ∞ = 2258.6 Pa and M ∞ = 9, corresponding to a stagnation enthalpy of H 0 ∞ = 6.86 MJ/kg. For the selected M ∞ and β = 10 • , the Rankine-Hugoniot relations give ϑ ≈ 5 • and the post-shock (PS) variables T PS = 554 K, p PS = 6235 Pa, u PS = 3620 m/s. These conditions are imposed at the left boundary of the rectangular domain as a jump on the inlet profiles, which are are obtained by solving the locally self-similar equations extended to thermochemical non-equilibrium [START_REF] Sciacovelli | Assessment of a high-order shockcapturing central-difference scheme for hypersonic turbulent flow simulations[END_REF]. The inflow plane of the computational domain and the ideal impingement station are located at x 0 = 0.04 m and x sh = 0.7 m from the leading edge, respectively. The wall temperature is fixed equal to 2500 K for both the temperatures, and noncatalytic conditions are applied. Characteristic outflow boundary conditions are imposed at the top and right boundaries, whereas periodicity is enforced in the spanwise direction. The extent of the computational domain is

(L x × L y × L z )/δ ⋆ in = 800 × 80 × 60, δ ⋆ in = 1
.77 × 10 -3 m being the inlet displacement thickness. A total number of N x × N y × N z = 6528 × 402 × 720 grid points is used, with constant grid size in the streamwise and spanwise directions and a constant grid stretching of 1% in the wallnormal direction, the height of the first cell away from the wall being ∆y w = 2.5 × 10 -5 m. The dimensionless streamwise coordinate x = (xx sh )/δ ⋆ in will be used in the following.

Figure 1 reports the pressure and temperature difference (∆T =T -T V ) isocontours of the base flow used to initialize the 3D computation. The adverse pressure gradient induced by the incident shock generates a recirculation bubble; upstream of the latter, a series of compression waves occur which then coalesce into the separation shock. It interacts with the incident shock that penetrates the separated flow. Downstream of the separation bubble, a reattachment shock is generated which readjusts the deflected flow. Globally, the characteristic features of SWBLI are not altered by high-enthalpy effects; on the other hand, such a complex dynamics strongly influences the thermochemical activity. Coherently with the inlet temperature profiles, the amount of thermal non-equilibrium before the bubble is extremely high. The rise of the T and p in the separation zone enhances chemical dissociation whereas the gap between the two temperatures is reduced, moving towards a quasi thermally-equilibrated state right after the recirculation bubble. The ∆T =0 isoline shows that the flow is underexcited everywhere except for the freestream pre-shock region and in the recirculation bubble, where a slight vibrational over-excitation is observed. A comparison of the configurations with and without shock impingement reveals that, in the latter case, the flow remains in a state of stronger thermal non-equilibrium and quasifrozen chemical activity throughout the entire boundary layer. Therefore, the pressure rise caused by the incident shock is responsible for a reduction of the amount of thermal non-equilibrium and an increase of the chemical activity. Laminar-to-turbulent transition for the 3D simulation is favoured by superimposing disturbances on the described base flow. The density self-similar profile is perturbed as in [START_REF] Nd Sandham | Transitional shock-wave/boundarylayer interactions in hypersonic flow[END_REF]; statistics are collected for a period corresponding to T stats ≈ 2050δ ⋆ in /u ∞ , for a total of ≈ 40000 temporal snapshots. The large computational cost of the simulation limits the temporal window of sample collection, and therefore no information about lowfrequency unsteadiness can be provided at the moment.

RESULTS

Profiles of various dynamic, thermodynamic and thermochemical flow quantities are extracted at eight stations in the laminar region, before the shock impingement, in the interaction zone and in the fully turbulent state. The loca-tion of such stations are marked in fig. 2, displaying the isocontours of the streamwise momentum in a xy-slice (top) and a near wall xz-slice (bottom). In the top panel, a shock pattern similar to the one in the base flow of fig. 1 can be appreciated, as well as the effect of the superposed density disturbances. Due to the thickening of the perturbed boundary layer upstream of the impingement, it is possible to detect a distinguishable separation shock only after the interaction with the incident one. The angulation of the separation shock is such that it impacts the reattachment shock, differently from the base flow. Tab. 1 reports some boundary layer properties at the selected positions.

Overview of flow dynamics

We start the analysis with the streamwise distributions of the normalized wall pressure p w = p/p ∞ and the skin friction coefficient C f reported in fig. 3. The vertical lines represent the beginning and the end of the mean separation zone; the laminar base flow solution is also reported with red lines. In the laminar case, the pressure jump across the interaction zone is ≈ 6, whereas it reaches ≈ 7 in the 3D transitional case. A significant reduction of the bubble length with respect to the laminar case is observed. Of particular interest is the different C f trend with respect to the base flow, even before the shock impingement. It follows the laminar distribution in the region -200 < x < -80, deviating from the base flow profile for which the recirculation zone begins at x ≈ -200. The evolution in the upstream zone is in perfect agreement with results from locally self-similar theory. In the fullyturbulent region downstream of the interaction, C f values are approximately four times larger than those registered in the laminar case, as in [START_REF] Nd Sandham | Transitional shock-wave/boundarylayer interactions in hypersonic flow[END_REF]. On the other hand, the picture in the interaction region is rather different: the increase observed after reaching the global minimum, at x ≈ 0, is attributed to the reattachment. As the C f experiences a ramp-like increase, at x ≈ 40, the incident shock penetrates the boundary layer and reaches the wall, causing a sudden increase of wall friction and heating.

The evolution of the two contributions of the normalized wall heat flux are reported in fig. 4. The rototranslational heat flux, q TR w , follows essentially the C f distribution, with a minimum in the separation zone, a peak of almost 10 -4 and a significant overheating in the fully turbulent region. Of particular interest is the trend of the vibrational heat flux: as already observed in flat-plate boundary layer configurations [START_REF] Passiatore | Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers[END_REF], it is one order of magnitude smaller with respect to the rototranslational one. However, thermal non-equilibrium before the interaction is so strong that the wall heats the flow from a vibrational energy standpoint. For the case without perturbation, the vibrational heat flux switches to positive values in the recirculation bubble, then increases in the reattachment region and relaxes to the post shock conditions while keeping

= ρ ∞ u ∞ x/µ ∞ and Re θ = ρ ∞ u ∞ θ /µ ∞ are
the Reynolds numbers based on the distance from the leading edge and on the local momentum thickness, respectively; Re τ = ρ w u τ δ /µ w is the friction Reynolds number, Re δ ⋆ = ρ ∞ u ∞ δ ⋆ /µ ∞ is the Reynolds number based on the displacement thickness and H is the shape factor. Lastly, ∆x + , ∆y + w and ∆z + denote the grid sizes in inner variables in the x-direction, y-direction at the wall and in the z-direction, respectively. positive values. On the other hand, when perturbations are added, q V w keeps negative values almost everywhere, except in the small separation bubble. From the reattachment region onwards, its streamwise evolution is opposed to the one obtained in the laminar regime. The small vibrational heat flux contribution does not affect the Stanton number distribution (not shown) even in the present strong thermochemical non-equilibrium conditions.

Figure 5 shows instantaneous views of the wall pressure (top), skin friction coefficient (middle) and total wall heat flux (bottom) in the neighbourhood of the shock impingement region. The average reversed flow region is also marked with isolines. In the three figures, the footprint of the freestream perturbations is visible in the form of wave packets, corresponding to pressure isolines smaller than p ∞ in the top figure. These wave packets remain coherent up to the separation point and start to destabilize in the bubble at z/δ ⋆ in ≈ 40, albeit they do not completely break. After the reattachment point, breakdown to turbulence begins and C f rapidly increases towards its post-shock value. For the conditions under investigation, the breakdown is particularly sharp as wit-nessed by the large overshoot of C f . This is related to the emergence of energetic structures at x ≈ 40 visible in the middle and bottom panels of fig. 5. Further downstream, the skin friction reaches a local minimum at x ≈ 50 and the flow relaxes to equilibrium turbulence starting from x ≈ 190. Despite the statistically-averaged separation region is small, relatively large structures of negative skin friction coefficient (middle panel of fig. 5) are visible, showing that instantaneous separation exists well upstream and downstream of the average bubble.

An overview of the main turbulent statistics at the last four stations of tab. 1 is presented hereafter. First, the transformations of Van Driest, Trettel & Larsson [START_REF] Trettel | Mean velocity scaling for compressible wall turbulence with heat transfer[END_REF] and Griffin et al. [START_REF] Griffin | Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer[END_REF] for the averaged streamwise velocity are applied to the transitional and fully turbulent stations. Fig. 6 shows the results only for the last two scalings, both providing better predictions than the Van Driest one. The collapse with the classical logarithmic profile is very poor for x = 38 and x = 72, confirming the purely transitional state of the boundary layer in this region. For the two last stations, these transformations fail to collapse the mean velocity profiles on the incompressible logarithmic law, as already observed by many authors [START_REF] Zhang | Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers[END_REF][START_REF] Fu | Shock-induced heating and transition to turbulence in a hypersonic boundary layer[END_REF]. Reasonable self-similarity can be observed for the last two stations, the better collapse being obtained by the Griffin transform. The Reynolds stresses, whose longitudinal and shear components are shown in fig. 7, exhibit a reasonable collapse when plotted in semi-local units. At the transitional stations, the flow is subjected to massive velocity and pressure fluctuations, leading to values of order unity for the mean turbulent Mach number. not be considered. Notwithstanding the cooled boundary condition and the resulting non-monotonic temperature profiles, the largest amount of chemical products is encountered at the wall in each region of the computational domain. The concentrations of species products increase passing from the laminar region to the interaction zone; when entering the recirculation bubble, where the temperature values are the largest, a rise up to an order of magnitude is registered, whereas their amount decreases in the transitional region. The distributions for the last two stations are almost perfectly superposed because of the extremely low Damköhler numbers achieved here, which highlighting a large difference between the characteristic timescales of turbulent motions and chemical activity.

Thermochemical non-equilibrium

Fig. 9 displays the wall-normal profiles of T , T V and ∆ T in panels (a), (b) and (c), respectively, at the selected stations. The amount of thermal non-equilibrium is extremely high along the entire boundary layer, with maximum temperature differences larger than 1000 K registered in the interaction zone. The non-equilibrium state is mostly vibrationally under-excited, with T V lagging behind T almost everywhere apart from the pre-shock freestream region. Upstream of the impingement station, the profiles of the two temperatures keep distinct values due to the low Reynolds numbers. Owing to the presence of a cooled wall, the T always exhibits nonmonotonic distributions. On the other hand, T V displays monotonic profiles with a maximum at the wall, which is therefore vibrationally heating the flow coherently with the q V w evolution. Such a behaviour is partially reversed in the bubble region, where the lower flow speed pro- mote a temperature increase up to values higher than T w . The largest absolute temperatures (as well as their difference) are indeed registered at the reattachment point, peaks of ≈ 3700 K and 2700 K for T and T V , respectively. Here, the gap between the temperatures also reaches a maximum and the wall-normal location of its peak is the farthest from the wall (y/δ ≈ 0.48, compared to y/δ ≈ 0.32 in the laminar region). From this station on, the peak is rapidly shifted towards the wall in the range 0.02 < y/δ < 0.03, due to the sudden decrease of the boundary layer thickness before, and the increase in turbulent activity after. In the last two stations, the turbulent mixing efficiently redistribute the gas [START_REF] Passiatore | Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers[END_REF] such that the relaxation towards equilibrium of the vibrational modes is strongly delayed, resulting in a profoundly different evolution with respect to laminar predictions [START_REF] Passiatore | A high-order scheme for the numerical simulation of high-enthalpy hypersonic flows[END_REF]. The evolution of the rms Favre fluctuations of the is shown in fig. 10 in outer scaling. The level of turbulent fluctuations is high even before the shock impingement, especially for the translational temperature. The profiles of T ′′2 in the fully turbulent region display two peaks, that are a local maximum at y ⋆ < 10 and a global maximum at y ⋆ ≈ 30. These two peaks are more distinguishable when the temperature fluctuations are normalized with the corresponding Favre average [START_REF] Di Renzo | Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies[END_REF][START_REF] Passiatore | Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers[END_REF]. The rms of T V present a radically different behavior: the inner maxima observed for T at all the selected stations are smeared out and vibrational fluctuations are less intense than their translational counterparts everywhere. This is a direct consequence of the under-excited non-equilibrium persisting throughout the boundary layer, with T V values lagging behind T ones. The severe thermal non-equilibrium state is confirmed by inspection of the vibrational Damköhler numbers computed with respect to the flow residence time, i.e. Da m =

x/u δ t m , shown in fig. 11 for two of the three molecules of the mixture (vibrational equilibrium being instantly reached for NO). Molecular nitrogen and oxygen are shown to achieve non-equilibrium conditions in different regions. Specifically, Da O 2 displays values of order unity in the outer part of the boundary layer (0.3 < y/δ < 0.5), from the laminar region up to the recirculation bubble. The peaks are shifted towards the wall in the transitional region, and afterwards N 2 enters a non-equilibrium state with Da N 2 values approaching unity towards the end of the computational domain. An order-of-magnitude analysis shows that e V variations are almost uniquely due to translational-vibrational energy exchanges (not shown), which are particularly large in the transitional and fully turbulent regions. A high exchange rate is registered across the whole boundary layer thickness at x = 38, which corresponds to the C f peak location and to the emergence of the energetic structures observed in fig. 5. Here, the maximum interaction with the chemical activity is also registered, its net effect being however negligible. Fig. 12 and 13 shows correlation coefficients between the Favre-averaged fluctuations of different quantities. First, T ′′ and T ′′ V are strongly correlated almost everywhere except close to the wall, where a slight anticorrelation is registered notwithstanding the same values applied at the walls. This is again linked to the simultaneous vibrational wall heating and translational wall cooling, as shown by the wall heat fluxes and mean temperature profiles in fig. 4 and9, respectively. The trends of the correlations of p ′′ and u ′′ with T ′′ and T ′′ V are qualitatively similar in the outer region of the boundary layer, while significant variations are observed for the inner zone in particular with p ′′ and u ′′ . Specifically, R p ′′ T ′′ is shown to be predominantly positive (albeit in the turbulent region it tends rapidly to zero starting from the buffer layer) whereas p ′′ and T ′′ V are loosely correlated highlighting the important decoupling between the internal vibrational and dynamic fields. The strong correlation observed for R u ′′ T ′′ in the near-wall region is not observed in the profiles of R u ′′ T ′′ V , which are shown to be strongly anticorrelated everywhere. Globally, T ′′ and T ′′ V exhibit a drastically different behaviour not only in the turbulent region [START_REF] Passiatore | Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers[END_REF] but also and above all in the interaction zone, where the amount of thermal nonequilibrium is the largest. Of note, the turbulent Prandtl and vibrational Prandtl numbers are ≈ 0.85 and 0.9 respectively, consistently with the values obtained under largely different thermodynamic conditions [START_REF] Passiatore | Finite-rate chemistry effects in turbulent hypersonic boundary layers: A direct numerical simulation study[END_REF][START_REF] Passiatore | Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers[END_REF].

CONCLUSIONS

A Mach 9 SWBLI is investigated by means of direct numerical simulations. The present thermodynamic conditions are such that the boundary layer is thermally and mildly chemically out-of-equilibrium. The impinging shock is generated by a wedge angle of ϑ ≈ 5 • , leading to tribution is one order of magnitude smaller its rototranslational counterpart and mainly of opposite sign. In the fully turbulent portion downstream the impinging shock, turbulent statistics reveal reasonable self-similarity and corroborate the results previously obtained for turbulent boundary layers. Thermal non-equilibrium is quantified by means of mean and fluctuating temperature values, vibrational Damköhler numbers and contributions of the vibrational source terms. Both O 2 and N 2 exhibit vibrational excitation, but in different portion of the domain; namely, Da O 2 is of order unity in the laminar region up to the recirculation bubble, whereas Da N 2 attains similar values in the fully turbulent zones. Vibrational modes are found to be almost everywhere in an under-excited state, the largest amount of thermal nonequilibrium being achieved in the recirculating bubble. The correlation coefficients of the two temperatures with respect to p and u drastically differ and highlight the important decoupling between the internal vibrational and dynamic fields.

The current study represents a first step towards the understanding of the influence of high-enthalpy effects on shocked turbulent flow configurations. Future investigations on the subject will mainly focus on the characterization of possible low-frequency unsteady motions detected by considering longer integration times.

Figure 1 :

 1 Figure 1: Visualization of the base flow. Top: isocontours of pressure; the white line denotes the extent of the recirculation bubble. Bottom: isocontours of the temperature difference; the white line denotes the ∆T =0 contour.

Figure 2 :

 2 Figure 2: Instantaneous visualization of streamwise momentum in a xy-plane (top) and in a xz-plane at y/δ ⋆ in = 0.5 (bottom). The y axis has been stretched for better visualization.

Figure 3 :

 3 Figure 3: Evolutions of normalized wall pressure p w (a) and skin friction coefficient C f (b); red lines represent the base flow computation. Vertical lines mark the mean separation region in the 3D run, whereas the horizontal line in panel (b) denotes the C f = 0 isoline. Symbols display the results of the locally self-similar theory.

Figure 4 :Figure 5 :

 45 Figure 4: Distributions of the rototranslational (a) and vibrational (b) contributions of the normalized wall heat flux; red lines denote the base flow evolution.

Figure 6 :

 6 Figure 6: Streamwise velocity scalings. Trettel & Larsson transformation (a) and Griffin-Fu-Moin transformation (b).

Figure 7 :

 7 Figure 7: Wall-normal profiles of the Reynolds stresses for the streamwise (a) and shear (b) components.

Figure 8 :

 8 Figure 8: Wall-normal distributions of atomic oxygen (a) and nitric oxide (b) for the different streamwise stations reported in tab. 1.

Figure 9 :

 9 Figure 9: Evolution of normalized mean translational temperature (a), vibrational temperature (b) and temperatures difference (c) in outer scaling.

Figure 10 :

 10 Figure 10: Evolution of translational (a) and vibrational (b) temperature fluctuations, in outer scaling.

Figure 11 :

 11 Figure 11: Wall-normal evolutions of the vibrational Damköhler numbers for N 2 (a) and O 2 (b).

Figure 12 :Figure 13 :

 1213 Figure 12: Wall-normal profiles of the correlation coefficient R T ′′ T ′′ V at the different stations in tab. 1.

Table 1 :

 1 Boundary layer properties at eight selected streamwise stations. Re x

	Laminar	Legend	x -90	Re x × 10 5 16.43	Re θ 864.12	Re τ -	Re δ ⋆ 20635 23.88 H	∆x + ∆z + ∆y + w ---
	Separation		-55	18.57	984.61	-	23550 23.92	-	-	-
	Inside bubble		-30	19.74	1003.0	-	29318 29.23	-	-	-
	Reattachment		-5	21.17	962.57	-	19244 19.99	-	-	-
	Transition		38	23.41	1169.4 245.6 8942	7.64 8.87 6.02 1.02
	Transition		72	25.21	1108.2 392.5 7755	7.00 7.43 5.05 0.86
	Turbulent		240	34.29	1519.8 517.9 13688 9.00 8.89 6.04 1.02
	Turbulent		363	40.90	1957.0 562.4 16858 8.61 8.76 5.96 1.00


Takayuki Ito

Mohammed Bouguerra

Morgane Bourhis

Pascal Perrier

Tongue posture stabilization by reflex mechanism for speech production

Introduction

The stability of tongue posture control is important to produce speech sounds with enough accuracy. Stretch reflex is known as one mechanism that contributes to the stability of human sensorimotor control. When a muscle is stretched by unknown disturbance, the muscle makes a quick contraction to maintain the posture (and then keep its length constant). Although this quick reflex has been quite extensively investigated in limb system, the extent to which it contributes to the motor control of the tongue remains unknown.

Results

Method

Summary

• Reflex response was clearly induced in response to the tongue perturbation. • The peak response in non-speech condition was smaller than the one in speech condition, suggesting the reflex gain was controlled for speech task. • The response latency in resting condition was similar the one of the main reflex response, suggesting no evidence of short-latency reflex corresponding to mono-synaptic reflex. • Using the recorded EMG response, the observed displacement change was successfully reproduced in mathematical simulation.

Reflex mechanism is involved in the compensatory mechanism of the tongue posture stabilization for speech production.

Reflex response in response to the tongue perturbation

Vowel production task

Experimental procedure:

Acknowledgement

This work was supported by Agence National de la Recherche (ANR-21-CE28-0022), and the National Institute on Deafness and Other Communication Disorders Grant R01-DC017439.

Session 1: Speech task

• EMG data was filtered by 30-2000 Hz band-pass filter, rectified and smoothed.

• All data was aligned at the perturbation onset.

• Amplitude was detected using 10 ms temporal window.

Data analysis: References

Alfonso • Sustain the vowels /i/, /e/, /e/, /a/ and /u/ five times each.

• Produce the vowel /i/.

• Produce a maximum contraction when the perturbation was perceived.

Sequence of trials with tongue perturbation

Participants:

• Eight native speaker of French.

Electromyographic recording (EMG)

Tongue perturbation Although the latency of this behavioral response was in the range of reflex delay, the involvement of reflex mechanism is still uncertain due to lack of neurophysiological evidence.

This study aims to show neurophysiological evidence of the tongue stretch reflex during vowel production by the recording of the tongue muscle activity.