Julien Dular
email: julien.dular@uliege.be

Sébastien Brialmont

Philippe Vanderbemden

Christophe Geuzaine

Benoît Vanderheyden

3D Finite Element Models of Stacked Tapes Magnetic Shields

Keywords: high-temperature superconductors, magnetic shielding, finite-element analysis

We present two 3D finite element models for magnetic shields made up of a large number of stacked tapes subjected to a transverse magnetic field. The first model consists in a stack of alternating superconducting and ferromagnetic layers, whereas in the second model, the stack is replaced by an equivalent material for which both superconducting and ferromagnetic properties are homogenized. Both models are solved with an h-φ-formulation and simulation results are compared with experimental measurements.

I. INTRODUCTION

Stacks of flat annular HTS tapes with ferromagnetic (FM) substrates create hollow cylinders with interesting magnetic shielding properties. Under axial fields, superconducting persistent currents in the HTS prevent flux penetration inside the cylinder, while in transverse fields, the high permeability of the substrates helps channelling the flux lines away from the inside.

Modeling systems with both HTS and FM is challenging due to the strong nonlinearities of the material constitutive laws [START_REF] Dular | Finite-element formulations for systems with high-temperature superconductors[END_REF]. In this work, we present 3D models for the transverse field configuration based on the h-φ-formulation. In particular, we propose to replace the stacked materials by an homogeneous HTS-FM hybrid material having anisotropic electric and magnetic properties. This provides results in good agreement with the measurements within a limited amount of computation time.

II. PROBLEM DEFINITION

We consider hollow cylinders that are made up of a stack of N HTS tapes with a FM substrate, and that are maintained at a temperature of 77 K. The volume fraction of the FM substrates is f = 0.9. We apply a transverse field b s from 0 to 60 mT in 1 s, perpendicular to the cylinder axis. One-fourth of the geometry is modeled as represented in Fig. 1. We define the shielding factor SF as where P is the center of the stack.

SF = b s b(P ) , (1)
In this communication, we focus on the numerical model of the system, while the measurements of the magnetic response of the materials are reported in a joint communication by S. Brialmont [START_REF] Brialmont | Annuli of coated conductors with a ferromagnetic substrate: magnetic shielding properties at 77 k and at room temperature[END_REF].

We model the magnetic response of the system with the magneto-quasistatic approximation. In HTS, µ = µ 0 and we assume a power law for the electrical resistivity:

ρ(j) = e c j c j j c n-1 , (2)
with e c = 10 -4 V/m, j c = 10 9 A/m 2 and n = 30. In this work, j c and n are assumed constant. The FM is assumed non-conducting and its permeability µ = µ(h) is interpolated from the measurements at 77 K. We consider two samples for which we have SF measurements: sample A with a height of 22 mm and N = 294 tapes and sample B with a height of 14.9 mm and N = 183. The inner and outer radii, 13 mm and 22.5 mm, respectively, are identical for both samples.

III. FINITE-ELEMENT MODELS

Modelling the exact geometries of samples A and B is not practical because of the large values of N . Instead, we propose two approaches to simulate the magnetic response of the shields.

A. Detailed Model

In the first model, we introduce a limited number N 1 < N of HTS and FM layers, with fictitious thickness so that the total height is the same as the physical sample. We then solve the magneto-quasistatic problem with an h-φ-formulation [START_REF] Dular | Finite-element formulations for systems with high-temperature superconductors[END_REF].

B. Homogeneous Model

In the second approach, we replace the detailed stack of alternating materials by an homogeneous fictitious material having both superconducting and ferromagnetic properties.

To solve the problem with the h-φ-formulation in terms of the average field values, the material properties need to be modified accordingly. Moreover, because of the layered structure of the problem, these properties are anisotropic.

1) Anisotropic Resistivity: The FM is assumed nonconducting and does not carry any current density. In terms of the volume average value j of the current density, the current density in the HTS is therefore j S = j/(1 -f ) with (1 -f ) the filling factor of the HTS phase.

The current density can only flow in the x-y-plane. To prevent current from flowing in the z-direction, a large resistivity ρ ∞ is introduced. In the (x, y, z) Cartesian coordinate system represented in Fig. 1, the resistivity takes the form of a diagonal tensor:

ρ(j) = diag ρ(j S ), ρ(j S ), ρ ∞ . (3)
2) Anisotropic Permeability: In the HTS, µ = µ 0 is a constant. In the FM, the permeability depends on the local magnetic field h F , we have: µ = µ(h F ). From continuity considerations, the relation between the components of the average magnetic field h and those of h F in the FM phase read: h F x = h x , h F y = h y , and

h F z = µ 0 h z / f µ 0 + (1 -f )µ(h F ) . ( 4
)
Extracting h F from h therefore requires to solve an implicit equation.

The permeability also takes the form of a diagonal tensor:

μ(h) = diag μ(h F ), μ(h F ), μ(h F ) , (5)
with μ(h

F ) = f µ(h F ) + (1 -f )µ 0 for the (x, y)-components and μ(h F ) = f /µ(h F )+(1-f )/µ 0 -1 for the z-component.

IV. RESULTS

The models have been implemented in GetDP. An adaptive time-stepping algorithm and a Newton-Raphson method were used during the resolution [START_REF]Life-hts: Liège university finite element models for high-temperature superconductors[END_REF].

One fourth of the geometry is considered for the detailed model. For the homogeneous model, because of the additional symmetry along the z-axis, only one eighth is modeled. The parameter ρ ∞ is fixed to 0.01 Ωm.

Results for the samples A and B solved with the two approaches are shown in Fig. 2. Increasing the number of tapes in the detailed model has a very limited influence on the curves for N 1 8. By contrast, the numerical solution of the detailed model is strongly affected by the mesh resolution inside the FM layers. When the mesh is refined, the SF curves get closer to those obtained with the homogenized model. The homogeneous model is less sensitive to the mesh resolution and therefore requires less computation time than the detailed approach (15 minutes compared to 25-30 minutes). In both methods however, handling the nonlinear permeability is challenging. Usually, mixed formulations involving the reluctivity ν = 1/µ instead of the permeability demonstrate a better efficiency [START_REF] Dular | Finite-element formulations for systems with high-temperature superconductors[END_REF]. In this configuration however, the high surface-to-volume ratio in the detailed model or the anisotropic material properties in the homogeneous approach require a careful implementation of the mixed formulations to maintain their efficiency and accuracy. We will present the associated analysis and a comparison with the h-φ-formulation in the full paper, together with a more detailed verification.

V. CONCLUSION

We presented two methods for evaluating the magnetic shielding properties of a stack of superconducting tapes with ferromagnetic substrates. In the full paper, we will extend the study to an axial field configuration (2D-axisymmetric models). We will also assess the influence of a field-dependent critical current density on the shielding factors curves. In addition, we will evaluate the relevance of mixed formulations in this problem.

Fig. 1 :

 1 Fig. 1: Simplified detailed model of sample A: one fourth of a stack of 16 tapes (height: 24 mm, inner radius: 13 mm, outer radius: 22.5 mm). Yellow regions are HTS and blue regions are the FM substrates.

Fig. 2 :

 2 Fig. 2: Shielding factors for the two samples (up: A, down: B). Comparison of the two 3D finite element models with experimental measurements. The qualitative behavior is reproduced by both

ACKNOWLEDGMENT J. Dular and S. Brialmont are recipients of research grants from F.R.S.-FNRS and FRIA, respectively.


Asef Ghabeli
email: asef.ghabeli@kit.edu

Francesco Grilli
email: francesco.grilli@kit.edu

Jens Hänisch
email: jens.haenisch@kit.edu

Günther Fuchs
email: g.fuchs@evico.dedehaas@evico.de

Oliver De Haas

Pengbo Zhou
email: pengbo.zhou@kit.edu

3D modeling of HTS tape stacks in superconducting magnetic bearings with real thickness

Keywords: Tape Stacks, Magnitization of tape stacks, Numerical modeling, Superconducting magnetic bearing, Lorentz force calculation

Superconducting magnetic bearings (SMB)s offer a passive and contactless technique for rotating machines and, as linear bearings, for superconducting maglev systems. Stacks of superconducting tapes have been recently used as an alternative to the bulk. Modeling has been employed as a cost-effective, fast and reliable tool for improving the performance of SMBs. 2D models have been extensively used in the past, due to offering much faster computations compared to 3D models. However, using the 3D models is sometimes inevitable, especially when the depth of the problem geometry is comparable to the width and height or when the magnet guideway or the passive component geometries are complicated or asymmetrical. In this study, we employ an energy minimization method called MEMEP 3D, developed in C++, for modeling the magnetization of the tape stacks in three dimensions in a reasonable time. This method is significantly faster and more efficient than the previously proposed 3D methods giving the opportunity to model tens of HTS tapes with their real thickness with consideration of J c (B, θ) dependence.

I. INTRODUCTION

The passive superconducting levitation of superconducting magnetic bearings (SMB)s is very promising for the development of levitated trains [START_REF] Bernstein | Superconducting magnetic levitation: principle, materials, physics and models[END_REF]. The advantage is that the generated repulsive force between the magnet guideway and the superconducting part is mechanically stable without using any control system, unlike the repulsive force between two permanent magnets (PM).

Bulk superconductors have been mostly employed as the passive component in SMBs [START_REF] Dias | Simulations and tests of superconducting linear bearings for a MAGLEV prototype[END_REF]- [START_REF] Werfel | Superconductor bearings, flywheels and transportation[END_REF]. However, recently, stacks of superconductor tapes have been utilized as an alternative for the bulks offering better mechanical properties, better thermal conductivity and a simpler production process. [START_REF] Patel | Magnetic levitation using a stack of high temperature superconducting tape annuli[END_REF]- [START_REF] Liu | Testing and comparison of levitation forces and rotational friction in different superconducting tape stacks[END_REF].

Modeling is a cost-effective, fast and reliable tool to optimize or improve the performance of the SMBs. This issue has been investigated in several studies using numerical methods or a combination of analytical and numerical methods. For performing the optimization process, the problem should be solved in a reasonable time, which makes the 2D models a more popular option. However, using a 3D model is sometimes inevitable for the following reasons: when the depth of problem geometry is comparable to the width and height, the 2D model usually leads to a large errors. Moreover, when the magnet guideway or the passive component geometries are complicated or asymmetrical, the 2D model would be either incapable of simulating or subjected to a large error. A fast and efficient 3D model that can be solved in a reasonable time period can be the solution of the above mentioned issues.

There are several numerical models with the purpose of reproducing the performances of tape stacks or cables made of stacks such as 2D models in [START_REF] Quéval | Numerical models for ac loss calculation in large-scale applications of HTS coated conductors[END_REF]- [START_REF] Zhang | Magnetization simulation of ReBCO tape stack with a large number of layers using the ANSYS A-V-A formulation[END_REF] and 3D models in [START_REF] Zermeño | 3D modeling and simulation of 2G HTS stacks and coils[END_REF]- [START_REF] Kapolka | Cross-field demagnetization of stacks of tapes: 3D modelling and measurements[END_REF]. The 2D models take advantage of several strategies to reduce the computational load such as homogenization, densification and multi-scaling. However, these strategies have been mostly implemented and verified on 2D models due to the very high aspect ratio of the HTS tape and enormous numbers of degrees of freedom in 3D models.

In this study, we employ an energy minimization method called minimum electromagnetic entropy production method in 3D (MEMEP 3D), implemented in C++, for solving the problem of magnetization of tape stacks in three dimensions. This method had been presented and verified by experiments and other methods in several works [START_REF] Kapolka | Three-dimensional modeling of the magnetization of superconducting rectangular-based bulks and tape stacks[END_REF]- [START_REF] Ghabeli | 3D modeling of a superconducting dynamo-type flux pump[END_REF]. We develop this method to calculate the levitation force between magnet and tape stacks in field cooling (FC) and zero field cooling (ZFC) cases and compare the results with experimental data. We investigate the implementation of strategies such as homogenization and densification and study the possibility of implementing the real configuration of tape stacks including modeling of each individual HTS tape with its real thickness and J c (B, θ) dependence of the HTS tape. The non-superconducting layers in the stacks are modeled as a conducting material of very high resistivity.

II. PROBLEM DESCRIPTION

Fig. 1 shows the schematic of the problem and Table I lists the parameters related to PM geometry and movement as well as characteristics of the stacks. The passive part of the SMB is comprised of two parallel stacks of SuperOx tapes, each one containing 132 pieces of tapes.

The first investigated case is ZFC in which the magnet traverses the distance from ∆z = 52 mm, where the magnet is far enough from the stack so that the applied field is negligible, up to the distance of ∆z = 2 mm and comes back to its initial position in a full cycle. The goal is to obtain the hysteresis force loop between stacks and PM. The force F is defined as the Lorentz force due to interaction between the PM magnetic field and the screening current generated in the HTS stacks of tapes:

F = v J × B dv ( 1
)
where v is the volume of the HTS domain, J is the screening current in the HTS stacks, and B is the magnetic field of PM.

III. MODELING RESULTS

As the first step, we use the homogenization process to obtain the force loop. Using homogenization, we transform the two parallel HTS tape stacks into a single homogeneous bulk. This is more convenient and faster in terms of computational speed. The calculation time is about one hour for one cycle. Due to unavailable J c (B, θ) data of the SuperOx tape at the present time, we use the trial-and-error process to find the two parameters of isotropic Kim-Anderson model for describing the dependence of the critical current density of the HTS tape to the magnetic field [START_REF] Quéval | Superconducting magnetic bearings simulation using an H-formulation finite element model[END_REF]. Figure 2 shows the MEMEP 3D bulk homogenization modeling result against the experimental data in the ZFC case. Good agreement between modeling and experiment can be observed. We expect even better agreement when the measured J c (B, θ) data of the tape is used instead of the Kim-Anderson model for defining the J c (B, θ) dependence of the HTS tape to the magnetic field.

Fig. 1 .

 1 Fig. 1. Schematic of the problem

Fig. 2 .

 2 Fig. 2. MEMEP 3D bulk homogenization modeling results against experiment for the ZFC case

TABLE I PROBLEM

 I PARAMETERS INCLUDING PM GEOMETRY AND MOVEMENT, AND HTS STACKS OF TAPES CHARACTERISTICS

		Diameter	35 mm
	Permanent Magnet	Height	20 mm
		Remanent flux density, Br	1.22 T
	Magnet displacement	2 mm < ∆z < 52 mm Movement speed 1 mm/s
		Width	24 mm
	2 Stacks of Tapes	Depth	24 mm
		Height	10 mm
		Width	12 mm
		Thickness	76 µm
	HTS Tape	Thickness of Superconducting layer 1 µm
		Tape Critical Current Ic	350 A
		Assumed n-value	25

ACKNOWLEDGMENT

The authors would like to acknowledge the financial support of the German Federal Ministry for Economic Affairs and Energy under BMWi contract no. ZIM KK5082301SH0.


Juntong Hu

Structural Modeling and Optimization for REBCO Ring Magnet Using Coupled Electromagnetic-Thermal-Mechanical T-A Formulation

Keywords: REBCO Ring Magnet, elastoplastic model, coupled T-A formulation, structural optimization

RE)BCO high-temperature superconducting tape(HTS) can be stacked into a compact ring magnet along parallel magnetic field direction, with huge potential to trap strong magnetic fields. However, large mechanical deformation will be introduced in the process of making HTS ring magnets, which may lead to the degradation of the critical current density. This paper simulates the plastic deformation of HTS ring tape during the machining stage based on an elastoplastic bilinear isotropic hardening model. After that, a 3D coupled electromagnetic-thermal-mechanical T-A formulation was used to analyze the field cooling and pulse field magnetization trapping field, and the length and radius of the ring magnet are optimized. It is found that plastic strain will significantly reduce the critical current density resulting in a decrease of trapping fields. The influence of length and radius on the trapping field is restricted by each other. and the relationship between them needs to be reasonably matched.

I. INTRODUCTION

In recent years, superconducting permanent magnet stacked by the second generation high-temperature superconducting (2GHTS) tapes has been able to trap magnetic fields up to 17.89 T [START_REF] Suyama | Trapping a magnetic field of 17.89 T in stacked coated conductors by suppression of flux jumps[END_REF], and have great potential in high-field applications such as electric airplanes, nuclear magnetic resonance instrument(MRI), and magnetic levitation. Benefiting from the high critical current density and high transition temperature of superconducting tapes, trapped field magnets can be made more compact and with lower cooling costs.

The REBCO ring magnet is a jointless magnet separated by laser along the midline of superconducting tape and expanding by machining. Compared with the HTS bulk, the ring magnet has the advantages of flexible size and independent current loop, which can be made into a superconducting magnet with a diameter of more than 50 mm [START_REF] Qiu | Experiment and numerical analysis on magnetic field stability of persistent current mode coil made of HTS-coated conductors[END_REF]. Moreover, it can also be magnetized along the parallel direction of the magnetic field, which means a higher critical current density than the stack. The reason is the a-b plane of the REBCO crystal and the loop current are parallel to the magnetic field, leading to the Lorentz force helping the flux vortex overcome the pinning forces are close to 0, and effectively reducing the influence of the magnetic field on the critical current density. At present, the trapped field of the ring magnet at 25 K has already reached 4.6 T [START_REF] Ali | 4.6 T generated by a hightemperature superconducting ring magnet[END_REF].

The structural deformation of superconducting tapes will significantly reduce the critical current density. According to different practical applications, structural deformation including tensile, shear, torsion, bending, and delamination may occur in the production, processing, and operation of superconducting tape [START_REF] Fu | Out-of-plane bending characteristics of second generation high temperature superconducting tapes[END_REF][5]. In the above deformation mode, the superconducting tape will have a certain critical current recession. In general, the irreversible strain of the REBCO layer can only reach 0.45 %. Since the residual strain of the REBCO super-conducting layer can reach -0.237% when cooling it to 77K, the strain of recession point can reach 0.7 %. Moreover, the critical current density of the superconducting tape will quickly decay to 0 after the plastic yield happens [START_REF] Ilin | Experiments and FE modeling of stress-strain state in ReBCO tape under tensile, torsional and transverse load[END_REF] . T-A formulation is currently used for electromagnetic field simulation of superconducting tapes, and its calculation speed has been greatly improved compared with the traditional H-formulation [START_REF] Berrospe-Juarez | Real-time simulation of large-scale HTS systems: Multi-scale and homogeneous models using the T-A formulation[END_REF]. Its advantage is that the superconducting tape is regarded as an infinitely thin shell, ignoring the thin layer structure in the thickness direction, which effectively reduces the meshing and greatly improves the calculation speed. The main idea of this method is to apply the T formulation to the superconducting thin shell to calculate the current density, and the A formulation to the non-superconducting region to calculate the magnetic field. The two are coupled by applying the boundary conditions of magnetic field and current density. Today, in the threedimensional magnet structure, such as CORC cables and Roebel cables, the calculation advantage of the T-A formulation is obvious [START_REF] Wang | Study of the magnetization loss of CORC® cables using a 3D TA formulation[END_REF].

This work focuses on the construction of a 3D elastoplastic model of the mechanical expansion stage of the REBCO ring magnet. The key is to evaluate whether the strain of the REBCO layer exceeds its irreversible strain during the expansion of the superconducting tapes, resulting in a decline in the critical current density. Based on the threedimensional structure of the superconducting ring after deformation, the thermodynamic parameters and mechanical parameters are equivalent in one dimension, and the electromagnetic-thermal-mechanical coupled T-A formulation is constructed. Finally, based on the above multi-field calculation results, the length and expansion radius of the REBCO ring magnet is optimized and analyzed with the maximum capture field as the optimization objective.

II. NUMERICAL MODELING

A. Elastoplastic model

The superconducting tape is a kind of multi-layer composite structure material. The materials include copper, Hastelloy alloy, silver, REBCO, etc. the cross-section diagram is shown in Fig. 1. When the superconducting tape is expanded into a ring, it will inevitably produce large deformation. In this process, metal materials such as copper bear a large amount of plastic deformation, which reduces the bending stress of the REBCO layer. With the increase of deformation, the stress in the REBCO layer reaches the fracture strength, and the critical current density of the superconducting tape is irreversible degradation. The 3D deformation diagrams of the ring tape at the expansion and non-expansion stage are shown in Fig. 2. The elastic-plastic model used in this paper is the linear hardening model, and the mechanical constitutive relation is :

si i i i i i si si i i si i i i T i E if E E if E E                          (1)
σi, εi are the stress and strain of each layer of the superconducting tape, σsi is the yield strength of the metal materials of each layer of the superconducting tape, Ei is the elastic modulus of each layer, and ETi is the tangent modulus of the metal materials of each layer after yield. The above parameters are isotropic. At the same time, the isotropic hardening model is adopted, and the kinematic hardening is ignored [START_REF] Michalcová | Structural modeling of REBCO coated conductor tapes in TORT cables[END_REF]. Since REBCO is a brittle material, yield strength and tangent modulus are not set. i denotes layers of superconducting tape

The 3D model of superconducting tape is a thin shell, which is modeled by the Layerwise theory (LWT). In this method, the elements and integral points are constructed by the thickness of the shell and different layers. This means that only translational degrees of freedom are solved at each node, thus providing more accurate full-thickness stress and strain results than the equivalent single-layer method (ESL). The cost is that the simulation time is longer (the total number of degrees of freedom is more).

B. T-A formulation

The REBCO ring tape has no symmetrical structure in space. In order to accurately simulate the electromagnetic field of the REBCO ring magnet, the 3D configuration of the ring superconducting tape after the elastoplastic simulation is adopted. On the basis of the configuration, the T-A formulation is used to model the electromagnetic-thermalmechanical coupling characteristics of the REBCO ring magnet during magnetization.

C. Multi-field coupling model

Since the T-A formulation does not consider the thickness direction of the superconducting tape, it cannot directly couple the solid heat transfer module as the H formulation [START_REF] Li | Calculation of CORC Cable Loss Using a Coupled Electromagnetic-Thermal TA Formulation Model[END_REF]. In this paper, the thermodynamic parameters of each layer of the superconducting tape along the thickness direction are equivalent, and the heat transfer formulation the width direction is obtained :

    eff eff tape -eff -eff - sc l l l T C h k T k T Q t               (2)
Where τ, l are the transverse and longitudinal components of the superconducting tape, and ρeff, Ceff, kτ-eff, kl-eff respectively, are the equivalent density, equivalent specific heat capacity, equivalent transverse thermal conductivity and longitudinal thermal conductivity of the superconducting tape. T is the temperature of superconducting tape, Qsc representing the heat source of the superconducting tape, which is generated by the thermal effect of current, and its value is Qsc=E×J.

In order to couple the mechanics in the T-A formulation, the influence of the deformation of superconducting tape on the critical current density needs to be considered. Here, the empirical model is used to fit the influence of strain on the critical current density:

    , , cc J k J B T    (3)
Here, k(ε) denotes the influence factor of strain on the critical current density, and its specific form is referred to Yan [START_REF] Yan | Screening-current-induced mechanical strains in REBCO insert coils[END_REF] The calculation of stress and strain needs to consider the effect of Lorentz force FL=J×B, which is brought into the elastic equation to obtain : 0     L σ F [START_REF] Fu | Out-of-plane bending characteristics of second generation high temperature superconducting tapes[END_REF]

Fig. 1 .

 1 Fig. 1. Cross-section of REBCO HTS tape

Fig. 2 .

 2 Fig. 2. 3D deformation diagrams of REBCO ring tape


Sirois Frédéric

Lacroix Christian

A physics-guided recurrent machine learning model for long-time prediction of nonlinear partial differential equation

Keywords: Physics-guided machine learning, physicsinformed neural network, nonlinear partial differential equations and deep learning

I. Introduction

The apparition of hot spots is one of many challenges that slow the adoption of second-generation high temperature superconductor coated conductor (2G HTS CC). Hot spots appear due to the variation of the critical current along the length of the tape. When the injected current reaches a low local critical current, it results in the generation of heat and a rapid rise of the local temperature (hot spot). This generation of heat can lead to the formation of a normal zone (quench) and its propagation under certain conditions. It is possible to simulate the quench dynamics of 2G HTS CC by solving the coupled electro-thermal equations using a finite element method. Indeed, the heat equation and the current continuity equation are coupled by the heat source, which is defined by the Joule losses generated by the hot spots. One of the challenges of this problem is the nonlinear nature of superconductor conductivity which can make the computation expensive and unstable. Moreover, for particular architecture of HTS tape, the simulation has to be done in 3D, which leads to simulations that last many hours. Instead of using deterministic methods like the finite element method to simulate the quench dynamics, we propose in this work to use a "physics-guided" data-driven method in order to speed up the computation. The model we propose is inspired by recent work on machine learning (ML) models that have been developed to solve nonlinear dynamical systems [1], [2]. It is also inspired by some studies who tried to incorporate some structure of classical numerical methods (like finite difference and finite volume methods) in their model architecture [3].

II. Machine learning model

The model we propose is a physics-guided recurrent ML model used to make long-time predictions of the temper-ature evolution over time in the presence of hotspots of a 2G HTS CC. Our model speeds up substantially the resolution of the full 3D electro-thermal coupled problem. The ML model is trained with multiple simulations of quench propagation generated by a standard finite element solver (COMSOL). The different simulations are run with randomly generated parameters like the tape architecture, the initial conditions and the heat source. The model is expected to predict the quench dynamics for any architecture and initial condition without the need for retraining. The model is then used in a recursive way to predict the temperature along the tape at every time step. To test the ML model progressively, we decided to decouple the thermal and electrical problem. To do so, two ML models are defined: a model to predict the electric field (f E ) and a model to predict the temperature (f T ). The architecture of f E is a simple neural network. This model is trained using values of temperature (T ) and electric field (E) along the tape, extracted directly from the 3D COMSOL simulation. This model is relatively easy to fit since the relationship between T and E is related to the power law (imposed in the COMSOL simulation) and the current sharing between the layers of the HTS tape. The model f T is the real innovation of this work. It is characterized by an architecture that uses hard physical constraints under a Dufort-Frankel discretization scheme of the nonlinear heat equation in order to guide the solution to respect the conservation of energy and heat fluxes. The model is implemented using the deep learning library PyTorch. The material properties (defined as a function of temperature) are implemented as two neural networks, which give some degree of freedom to the model. The spatial derivatives of the material properties are obtained using the "automatic differentiation" described by Raissi [4]. Also, the finite differences, defined by the Dufort-Frankel discretization scheme are implemented using convolution layers implemented with PyTorch. The weights of the different filters of these layers add additional degrees of freedom to the model. The two models (f E and f T ) are used in a recursive, way as describe in figure 1. The model f T is first used to predict the temperature at the next time step. Then, f E predicts the electric field at this new time step. The same process is repeated every time step in a recursive manner. In order to reduce the accumulation of errors due to the recursive nature of the model, an adaptive training strategy is used [1]. One could say that, to avoid the accumulation of error, a non-recursive technique could be employed in order to avoid the problem of error accumulation. However, because the heat source changes every time step and depends on the previous predictions, the model has to be recurrent and the problem has to be solved step-by-step.

Many COMSOL simulations were generated for different heat source profiles in order to generate a dataset that can feed f T . Ten simulations were run using a randomly generated time-varying heat source that emulates the dynamics of hot spots. The nonlinear heat equation was solved in 3D using the heat transfer module of COMSOL on a geometry consisting in a stack of silver, YBCO and hastelloy thin films. The problem could have been solved in 1D, but we created a 3D COMSOL model in order to consider 3D effects on the quench dynamics in a near future.

III. Results Figure 2 shows the root mean squared error (RMSE) of the ML model on the test set compared to the finite element true solution (COMSOL) along time. The error is the average of the temperature distribution along the tape at each time step. The predictions are compared with a solution computed using a standard finite difference method (FDM) in 1D. One can see that the ML model (trained with the 3D COMSOL simulations) outperform the standard FDM and seems less affected by the accumulation of error. Figure 3 shows an example of prediction of the material properties learned during the training. The neural networks learned properly the temperature-dependent material properties in the range of temperature seen during the training (vertical dotted lines).

IV. Conclusion We showed that our machine learning model can minimize the accumulation of error compared to a standard numerical method (here the finite difference method). We also showed that the temperature-dependent material properties can be learned from finite element simulation results. Finally, we showed that for simple cases, the model converges to a classical finite difference method, but it has the potential to generalize to more complex cases and include effects that a simple classical numerical methods cannot take into account.

Fig. 1 .

 1 Fig. 1. Decoupling of the thermal and electric problem with two ML models (f E and f T )

Fig. 2 .Fig. 3 .

 23 Fig. 2. Error of the ML model and the finite difference method vs. time

Acknowledgment

The authors gratefully acknowledge the financial support from the National Research Council of Canada (NRC) through the AI for Design program. The support from NRC collaborators Julio Valdez and Alain Tchagang is also acknowledged.


So Noguchi
email: noguchi@ssi.ist.hokudai.ac.jp

Takanobu Mato
email: mato@em.ist.hokudai.ac.jp

Seokbeom Kim
email: kim@ec.okayama-u.ac.jp

Current distribution simulation for REBCO pancake coils applying low-frequency-ac current method

Keywords: numerical simulation, REBCO magnet, turn-to-turn contact resistance

In recent years, the no-insulation (NI) winding technique for rare-earth barium copper oxide (REBCO) pancake coils have been attracted in the field of high magnetic field generation. A contact resistance between turns characterize the stability of REBCO pancake coils. Hence, it is important to control the contact resistance, as well as it is necessary to measure it.

The sudden-discharging method is a popular way to measure the turn-to-turn contact resistance. It is, however, not robust against various conditions, e.g. external field, varying temperature, etc. A few years ago, we have been proposed a method to measure a contact resistance of an NI REBCO pancake coil applying a low-frequency-ac current, so called an LFAC method.

We present the validity of LFAC method through a simulation. Since the original LFAC method contains some errors, we will show a correction method together with simulation results.

I. INTRODUCTION

The no-insulation winding technique brings great stability to rare-earth barium copper oxide (REBCO) pancake coils [START_REF] Hahn | HTS pancake coils without turn-to-turn insulation[END_REF]. A key parameter of stabilization is a contact resistance between turns of NI REBCO pancake coils [START_REF] Katsumata | Influence of the turn-to-turn contact electrical resistance on the thermal stability in meter-class no-insulation REBCO pancake coils during a local normal-state transition[END_REF], [START_REF] Noguchi | A simple protection evaluation method for no-insulation REBCO pancake coils during local normal-state transition[END_REF]. In common, a contact resistance is measured with a sudden-discharging method [START_REF] Wang | Turn-to-turn contact characteristics for an equivalent circuit model of no-insulation ReBCO pancake coil[END_REF]. Although the contact resistance varies depending on operating current, magnetic field, and temperature, the sudden-discharging method is not applicable under such varying conditions.

To overcome such difficulties, we have proposed a new measurement method applying low-frequency-ac current to an NI REBCO pancake coil [START_REF] Noguchi | Turn-to-turn contact resistance measurement of noinsulation REBCO pancake coils[END_REF]. Using the proposed method, so named LFAC (low-frequency-ac current) method, it was succeeded that turn-to-turn contact resistances were measured during an external field excitation or a dc current operation [START_REF] Noguchi | Turn-toturn contact resistance measurement of no-insulation REBCO pancake coil at DC current operation[END_REF], [START_REF] Noguchi | Turn-to-turn contact resistance measurement of noinsulation REBCO pancake coil: external field dependence[END_REF]. Meanwhile, since the phase of the measured voltages differed from expected ones, the current distribution on NI REBCO pancake coil is investigated through a numerical simulation when applying the LFAC method.

II. THEORY OF LFAC METHOD

It is well known that an NI REBCO pancake coil can be simply expressed as a parallel circuit, as shown in Fig. 1 [1], [START_REF] Wang | Turn-to-turn contact characteristics for an equivalent circuit model of no-insulation ReBCO pancake coil[END_REF]- [START_REF] Noguchi | Turn-to-turn contact resistance measurement of noinsulation REBCO pancake coil: external field dependence[END_REF]. When applying a sinusoidal current to an NI REBCO pancake coil, the coil impedance Z at R sc = 0 is

Z = jωLR ct jωL + R ct (1)
where j and ω are the imaginary unit and the angular frequency, respectively. Here, taking a condition of R ct ≪ ωL, Z ≈ R ct . That is, when ac current with high frequency carries on an NI REBCO pancake coil, the current mostly flows in the radial direction with resistance of R ct . According to [START_REF] Noguchi | Turn-to-turn contact resistance measurement of noinsulation REBCO pancake coils[END_REF], the frequency range of 10-100 Hz is suitable for contact resistance measurement, because a current with higher frequency generates an error due to ac loss. Fig. 2 shows the measured current and the voltage of NI REBCO pancake coil. Reference [START_REF] Noguchi | Turn-toturn contact resistance measurement of no-insulation REBCO pancake coil at DC current operation[END_REF] concluded that the turnto-turn contact resistance corresponded to V p /I p (= 0.143 mΩ), where V p (= 1.43 mV) and I p (= 10 A) are the peak voltage and the peak current, respectively, despite the phase difference between voltage and current (θ = 10.8 deg.). The phase difference is ideally zero; however, since the phase difference of 10.8 deg. appeared, it is necessary to investigate whether it is measurement error or incompleteness of the LFAC method, with an accurate simulation. Even if the phase difference is considered, a theoretically estimated contact resistance is 0.140 mΩ (= V p /I p cos θ).

I θ I r I r I θ R ct L R sc

III. PEEC SIMULATION

The current distribution is simulated with a partial element equivalent circuit (PEEC) model [START_REF] Wang | Analyses of transient behaviors of no-insulation REBCO pancake coils during sudden discharging and overcurrent[END_REF]. Table I shows the specifications of the simulated NI REBCO pancake coil [START_REF] Noguchi | Turn-toturn contact resistance measurement of no-insulation REBCO pancake coil at DC current operation[END_REF]. The turn-to-turn contact resistance and resistivity estimated with the original LFAC method are 0.143 mΩ and 122 µΩ•cm 2 , respectively. In the simulation, a current of 10 A, 10 Hz, which is the same condition as the experiment, is applied to the NI REBCO pancake coil. Fig. 2 also shows the simulated voltage waveform with the contact resistivity of 122 µΩ•cm 2 . The simulated voltage is obviously higher than the measured one despite almost the same phase.

Fig. 3 shows the radial and azimuthal current distribution maps, where it is assumed that the same contact resistivity is uniformly distributed. At the peak of current, the current uniformly distributes in the radial direction [Fig. 3(e)]; however, the azimuthal currents remain on the innermost and outermost turns [Fig. 3(a)].

A. Correction

To fit the simulated voltage with the measured one, we investigated the value of contact resistivity. When the contact resistivity is 91 µΩ•cm 2 (R ct = 0.107 mΩ), the waveform of simulated voltage agrees with the measured one well. The new contact resistance value is much smaller than the values estimated with LFAC method (0.143 mΩ) and theoretically derived (0.140 mΩ).

The current behaviors are more complicated than the behaviors expressed form the RL parallel circuit as shown in Fig. 1. The newly obtained contact resistance is approximately 75% of the LFAC-method one. IV. SUMMARY

We have previously proposed the turn-to-turn contact resistance with low-frequency-ac current (LFAC). When the resistance is much smaller than the inductor impedance, the coil impedance ideally matches with the turn-to-turn contact resistance without the phase difference between current and voltage. However, the phase difference was observed in experiments, and the contact resistance was inaccurately estimated.

The current distribution is investigated using the partial element equivalent circuit (PEEC) model. It is obvious that although the current uniformly flows in the radial direction, the current azimuthally flows in the innermost and outermost turns. Using the PEEC, the contact resistance of 0.107 mΩ is newly obtained, 75% of the LFAC method.

Fig. 1 .

 1 Fig.1. NI REBCO pancake coil and its equivalent circuit model consisting of R and L in parallel. I θ and Ir are the current in the azimuthal and radial directions, respectively. L, Rct, and Rsc are the coil inductance, the turn-toturn contact resistance, and the longitudinal REBCO tape resistance.

Fig. 2 .

 2 Fig. 2. Measured and simulated waveforms of voltage and current at 10 Hz.

Fig. 3 .

 3 Fig. 3. Current distribution map in (a)-(d) the azimuthal and (e)-(h) the radial directions.


Édouard Lansiaux
email: edouard.lansiaux@orange.fr

Ph.D Philippe P Pébaÿ
email: philippe.pebay@ng-analytics.com

M.Sc Jean-Laurent Picard

M.D Joachim Forget
email: joachim.son-forget@assemblee-nationale.fr

Edouard Lansiaux
email: edouard.lansiaux.etu@univ-lille.fr

Response to Naudet et al

Response to Naudet et al.

Obviously, correlation doesn't mean causality. However, in sciences and especially in medecine, when a physio-pathological context is added, evidences were reinforced.

Legitimate reviews were done on our previous modest study, we will try to reply here.

General considerations

The correlation between vitamin D and sunlight exposure has been broadly documented and known for a long time [START_REF] Holick | Biological Effects of Sunlight, Ultraviolet Radiation, Visible Light, Infrared Radiation and Vitamin D for Health[END_REF] 1.

Our hypothesis was initially based upon COVID-19 outcomes differences between BAME (Black, Asian, Middle East) and White people living at the same latitudes , that could be explained by vitamin D deficiency in the BAME population it was not the case at the time of submission date. Furthermore, to assess this, the French National Academy of Medicine has recommended the rapid serum vitamin D (i.e. 25 OHD) testing in people over 60 years of age with Covid-19, and a loading dose of 50,000 to 100,000 IU in case of deficiency, which could help limit respiratory complications 4 4.

Our manuscript

Specific considerations

The sunlight exposure average has been measured since 2018 (not the same data as correspondents have used 6 6).

Weather data are actually unreachable due to a recent website update [START_REF]Bienvenue sur le nouveau site de Météo-France ![END_REF] 7.

In more, COVID-19 outcomes data were extracted after the daily update so we have different numbers (as presented on our first manuscript), so the 25/05/2020 data were included in our manuscript and not in their letter and they were published online on the 26/05/2020 by Santé Publique France.

Firstly, concerning the so-called mistake of «assumption of binormal distribution» 6 , we are sure that it has not escaped to the authors that we have used a Shapiro-Wilk test, as it is assessed in our previous manuscript and described in As the p-value for the sunlight exposure is 0.3697 (which is higher than the traditional 0,05 p-value and especially higher than the 0,001 p-value that we have fixed as the limit), we can't reject the null hypothesis. In this way, as we have assessed the normal distribution of each variable (including sunlight exposure), we don't violate any Pearson's correlation law because:

1) we have established the link between the sunlight exposure and the COVID-19 mortality (by r computation: R= -0.635688603).

2) We have obtained the regression line y = -55,459x + 2888,5.

3) According to our correspondents, if we use their analysis upon the 12 regions as N, we obtain t= 2.604 and a p-value of 0,0263 (the correlation stays significant with this p-value).

In this way, the use of Spearman's correlation would be inappropriate here.

In a second hand, we formally disagree on the follow statement «at least for sunlight exposure, since two neighboring regions have more similar climates than two distant regions» 6 . Indeed, for example in the «Provence-Alpes-Côte d'Azur» region, we can observe a diversity of climate (mountain, mediterranean); in more, «Auvergne-Rhônes-Alpes» region has mountain, but borderline regions have different climates (for instance, semi-oceanic and oceanic for «Nouvelle-Aquitaine» region) [START_REF]Le climat en France métropolitaine[END_REF] 9.

To prove this statement, firstly, we invite our opponents to use of basic knowledges which assess that regions, with an average size of 43,925.875 km² (Table 2), have climate more independent than neighboring towns. This is all the more reinforced as we reason on sunlight exposure average by region. Then, to use the Shapiro-Wilk test (as we have done in our manuscript [START_REF] Lansiaux | Covid-19 And Vit-D: Disease Mortality Negatively Correlates With Sunlight Exposure[END_REF] ), we have to prove the pseudoindependence (indeed, the perfect independence can't be prove) of a same variable different values between them. In order to do this, we have used the «turning point test» (published by Irénée-Jules Bienaymé in 1874 10 10) , the time on the abscissa axe was replaced by French regions (therefore it's not a time-series data as usual but a geographical series data). This method «is reasonable for a test against cyclicity but poor as a test against trend». As we wanted to study the inner-independence of variables (and especially for the sunlight exposure), we had to reduce the bruit due to cyclicity thanks to the turning points test. Our null hypothesis was that they are independently, identically distributed random variables.

As we have 128 (or 140 if Corsica is included) turning points (Table 3), we obtained a z of 0.205 with 12 regions (without Corsica) and z of 0.393 with Corsica inclusion (Table 4). As the observed number of turning points is in the 95% trust interval, we can't reject the null hypothesis; we may have used, in our manuscript, innerindependent identically distributed random variables.

To respond to the reductio ad absurdum, we are extremely disappointed thatour correspondents can't read and can't interpret correctly a Pearson/Spearman coefficient. In fact, a negative coefficient indicates a negative correlation and not a positive one as our correspondents assess 6 6:

«sunlight exposure makes people building nursing homes». With a Pearson/Spearman coefficient of -0,69, the correct statement would be «sunlight exposure makes people building less nursing homes», if we interpret correctly the negative coefficient.

Concerning the exclusion of the Corsican region, we have done it after the data extraction from the different public health already quoted in our manuscript In order to justify, we used two indicators: the eldery equipment rate (in view of the large aged people infected by the COVID-19) and the hospitalization bed density (indeed, infected seniors require an hospitalization due to theirs comorbidities and not only a lockdown). Two of three trackers (the last one, the Corsican medical doctor density, had no significant difference with others regions) had significant differences with the others French regions (Tables 5 &6) 5 5.

Therefore, they have conducted us to exclude the Corsican region before the sunlight exposure data extraction (so it was an a priori choice), and not in order to «hack» the pvalue what we have been accused of.

Finally, if our correspondents persist in their thesis of p-hacking, we will oppose them that their computed p-value 0,03 6

Using a ratione absurdum, this one stays above the usual medical significance threshold of 5%. In fact, thanks to this «negators» (according to the antique definition), even if we are wrong we are right. Therefore, we thank them for the fact that they, thus ,ensure the validity of our hypothesis, despite the mistakes they think have discovered.

Conclusion

We are extremely enthusiastic about debating in a relaxing manner. Although the heart has its reasons that reason ignores, we must show restraint and rigor, especially in these sanitary hard times. This formal correspondence was very instructive for us (on modesty, respect...), we hope that it was and will for our correspondents.

2

 2

5

 5

Table 1 .

 1 As

a reminder, it is a test of normality in frequentist statistics which test the null hypothesis that a sample came from a normally distributed population. Monte Carlo simulation has found that Shapiro-Wilk test has the best power for a given significance 8 8.

Table 6 .

 6 Healthcare access statistical parameters with the inclusion of the Corse region

	Eldery equipment rate (‰)	144,5	707,103 26,591 130,045	147,303
	Medical doctor density (‰ₒₒ)	326,7	1769,244 42,062 303,835	330,226
	Hospitalization bed density (‰ₒₒ)	387,5	933,923 30,56	370,887	390,505

Death rate (‰) 5 4

Life conditions

Imposed fiscal menages rate (%) 6 5

Health status

Current smokers prevalence 7

Chronic pulmonary insuffisance prevalence 9 9

Severe renal chronic insuffisance prevalence 7 7

Obesity prevalence 7 7

Healthcare access

Eldery equipment rate (‰) 7 7

Medical doctor density (‰ₒₒ) 10 9

Hospitalization bed density 7 6

Sunlight exposure 9 8

Infection

Confirmed cases

Infection rate (%) 8 7

Healed cases

Healed rate(%) 10 9

Deceased cases

Mortality rate (%) 6 5

Turning points sum 140 128


Munakata Yuka

Carole Gavira

Julie Genestier

Frédéric Bourgaud

Alain Hehn

S Slezack

Yuka Munakata

Sophie Slezack-Deschaumes

Composition and functional comparison of vetiver root endophytic microbiota originating from different geographic locations that show antagonistic activity towards Fusarium graminearum

Keywords: Conceptualization, methodology, investigation, writing -review Bacterial endophytes, Fusarium graminearum, antagonistic activity, vetiver root microbiome, geographic location, 16S rDNA high-throughput sequencing

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

Introduction

Fusarium graminearum is a causal agent of important diseases in small-grain cereals such as wheat [START_REF] Dean | The Top 10 fungal pathogens in molecular plant pathology: Top 10 fungal pathogens[END_REF][START_REF] Taheri | Cereal diseases caused by Fusarium graminearum: from biology of the pathogen to oxidative burst-related host defense responses[END_REF]. This pathogen can induce seedling blight, root and stem-based rots and ear blight, which can lead to significant yield losses [START_REF] Bottalico | Toxigenic Fusarium species and mycotoxins associated with head blight in small-grain cereals in Europe[END_REF]. In addition, as this pathogenic fungus is able to contaminate cereals with mycotoxins, it can threaten human and animal health [START_REF] Xu | Community Ecology of Fungal Pathogens Causing Wheat Head Blight[END_REF].

Agricultural practices such as crop rotation, soil tillage, the application of chemical fungicides and the use of resistant cultivars are considered as the most effective strategies for controlling F. graminearum. However, these strategies are not always fully effective in controlling disease symptoms and preventing the accumulation of mycotoxins [START_REF] Lamichhane | Toward a Reduced Reliance on Conventional Pesticides in European Agriculture[END_REF][START_REF] Van Lenteren | Biological control using invertebrates and microorganisms: plenty of new opportunities[END_REF][START_REF] Wegulo | Management of Fusarium head blight of wheat and barley[END_REF]. The use of chemical fungicides may also cause concern for human health and the environment [START_REF] Lamichhane | Toward a Reduced Reliance on Conventional Pesticides in European Agriculture[END_REF].

Therefore, reducing the use of these chemicals has become a major concern in European regulations in recent years. In this context, biocontrol agents, within the framework of integrated pest management strategies, are promising solutions that protect plants from biotic stresses and considered relatively environmentally friendly [START_REF] Köhl | Mode of Action of Microbial Biological Control Agents Against Plant Diseases: Relevance Beyond Efficacy[END_REF][START_REF] Van Lenteren | Biological control using invertebrates and microorganisms: plenty of new opportunities[END_REF][START_REF] Wegulo | Management of Fusarium head blight of wheat and barley[END_REF].

Many bacterial and fungal microorganisms isolated from different environments, such as the rhizosphere or the surface of wheat anthers, were investigated in both in vitro assays and field experiments for their antagonistic activity towards F. graminearum [START_REF] Shahzad | What Is There in Seeds? Vertically Transmitted Endophytic Resources for Sustainable Improvement in Plant Growth[END_REF][START_REF] Tian | Functional Agents to Biologically Control Deoxynivalenol Contamination in Cereal Grains[END_REF]. Recently, microbial endophytes that colonize inner plant tissues during at least part of their life cycle have attracted attention. It is assumed that they might protect plants more efficiently than rhizospheric and epiphytic microorganisms [START_REF] Backman | Endophytes: An emerging tool for biological control[END_REF][START_REF] Brader | Metabolic potential of endophytic bacteria[END_REF]. These beneficial effects on plant health might be specifically related to the ability of endophytic microorganisms to produce antimicrobial substances [START_REF] Ek-Ramos | Bioactive Products From Plant-Endophytic Gram-Positive Bacteria[END_REF][START_REF] Gouda | Endophytes: A Treasure House of Bioactive Compounds of Medicinal Importance[END_REF][START_REF] Singh | Endophytic bacteria: a new source of bioactive compounds[END_REF]. Since endophytes have to survive in very different environmental conditions, they might be able to produce a greater diversity of antimicrobial metabolites than free-living microorganisms [START_REF] Brader | Metabolic potential of endophytic bacteria[END_REF][START_REF] Hardoim | The Hidden World within Plants: Ecological and Evolutionary Considerations for Defining Functioning of Microbial Endophytes[END_REF]. Endophytes represent, therefore, pathways for identifying new sources of biocontrol agents, and their diversity needs to be further investigated [START_REF] Hardoim | The Hidden World within Plants: Ecological and Evolutionary Considerations for Defining Functioning of Microbial Endophytes[END_REF][START_REF] Lebeis | Salicylic acid modulates colonization of the root microbiome by specific bacterial taxa[END_REF][START_REF] Thiergart | Root microbiota assembly and adaptive differentiation among European Arabidopsis populations[END_REF][START_REF] Toju | Factors Influencing Leaf-and Root-Associated Communities of Bacteria and Fungi Across 33 Plant Orders in a Grassland[END_REF].

Vetiver (Chryzopogon zizanioides (L.) Roberty) is a perennial poaceous plant that is native to India. This plant was introduced in tropical and subtropical regions such as Haiti and Reunion Island by traders and has spread worldwide [START_REF] Belhassen | Volatile constituents of vetiver: a review: Volatile constituents of vetiver[END_REF]. Vetiver is cultivated mainly for its essential oil, extracted from its roots, which is used for perfume production, cosmetics and aromatherapy [START_REF] Burger | Vetiver Essential Oil in Cosmetics: What Is New?[END_REF]. A study showed that vetiver essential oil also displays antimicrobial activities against several plant fungal pathogens [START_REF] Sharma | Evaluation of the antifungal and phytotoxic effects of various essential oils against Sclerotium rolfsii (Sacc) and Rhizoctonia bataticola (Taub)[END_REF].

Vetiver essential oil is composed of highly diverse sesquiterpene derivatives [START_REF] Belhassen | Volatile constituents of vetiver: a review: Volatile constituents of vetiver[END_REF][START_REF] Champagnat | A Study on the Composition of Commercial Vetiveria zizanioides Oils from Different Geographical Origins[END_REF]. Its composition is known to depend on different factors, including environmental conditions and root-associated bacteria [START_REF] Adams | Preliminary comparison of vetiver root essential oils from cleansed (bacteria-and fungus-free) versus non-cleansed (normal) vetiver plants[END_REF][START_REF] Adams | Vetiver DNA-Fingerprinted Cultivars: Effects of Environment on Growth, Oil Yields and Composition[END_REF]. Del Guidice and coworkers [START_REF] Del Giudice | The microbial community of Vetiver root and its involvement into essential oil biogenesis: Vetiver root bacteria and essential oil biogenesis[END_REF] showed that some bacteria isolated from vetiver roots could metabolize sesquiterpenes into the compounds that are present in vetiver essential oil. These results therefore suggest that the endophytic bacterial community from vetiver roots may contribute to the overall metabolic composition of the essential oil, which has been reported to have antifungal activities [START_REF] Del Giudice | The microbial community of Vetiver root and its involvement into essential oil biogenesis: Vetiver root bacteria and essential oil biogenesis[END_REF][START_REF] Hammer | Antimicrobial activity of essential oils and other plant extracts[END_REF][START_REF] Monteiro | Bacterial communities within the rhizosphere and roots of vetiver (Chrysopogon zizanioides (L.) Roberty) sampled at different growth stages[END_REF].

In this report, we assumed that the endophytic bacterial community of vetiver roots contributes to bioactivity against F. graminearum. Since bacterial communities are influenced by the surrounding environmental conditions, we investigated vetiver roots originating from different geographical locations assuming that the endophytic bacterial communities would differ in their taxonomical composition and bioactivity against F. graminearum. The results described here are related to Sunshine vetiver roots collected in four different geographical regions i.e., Madagascar, Portugal, Reunion Island, and Senegal.

To thoroughly describe endophytic bacterial community of vetiver roots, culture dependent and independent approaches were used. Using the high resolutive meta-barcoding approach, we assessed the structure and diversity of the bacterial endophytes. Through a complementary culture-dependent approach, we functionally characterized the bacterial endophytes with antagonistic activity towards F. graminearum. This allowed us to better understand the role that these microorganisms can have and it also revealed which microorganisms could be used in subsequent studies to develop biocontrol solutions with respect to F. graminearum.

Materials and methods

Sampling of vetiver roots

Preparation of root samples

The vetiver roots were first rinsed in running tap water to eliminate soil and surface debris prior to surface sterilization under sterile conditions. For this purpose, they were cut into small pieces of approximately 3 to 4 cm in length. The root pieces were treated with 70% ethanol for 1 min 5 times, followed by immersion in 2.6% sodium hypochlorite solution for 15 min. The samples were then rinsed three times with sterile water for 1 min. After root surface sterilization, four grams of plant material were stored at -80°C until DNA extraction, and 1 g of root tissues was used for the isolation of bacterial endophytes.

Isolation of bacteria

The root samples were cut into smaller pieces (0.5 mm to 1 cm in length) and ground using a Potter homogenizer. The samples were macerated in 10 ml of M9 medium without a carbon source containing 100 mg L -1 cycloheximide (Sigma-Aldrich™, USA) for 1 h at 28°C under gentle agitation. A serial dilution of the homogenate from 10 -1 to 10 -6 was prepared in phosphate buffer PBS, and 100 μl of each dilution was plated on 10% tryptic soy agar (TSA, Sigma-Aldrich™, USA) media containing 100 mg L -1 cycloheximide. The plates were incubated at 28°C for 10 days. Three replicates per dilution were prepared. Similarly, the efficacy of the root surface sterilization was evaluated by plating 100 μl of the last root washing water on 10% TSA media containing 100 mg L -1 cycloheximide for 10 days at 28°C.

The number of microbial colonies was counted 10 days after isolation and expressed as log CFU g -1 of root dry matter. Bacterial colonies were randomly removed from the plates and purified by repeated subculturing. The purified bacterial isolates were stored frozen at -80°C in 15% glycerol.

DNA extraction from surface-sterilized vetiver roots

Total genomic DNA was extracted from 3 g of surface-sterilized vetiver roots according to [START_REF] Ranjard | Sampling strategy in molecular microbial ecology: influence of soil sample size on DNA fingerprinting analysis of fungal and bacterial communities[END_REF] with minor modifications. Briefly, frozen root materials were ground in liquid nitrogen with a mortar and a pestle, both of which were autoclaved in advance. Three grams of the ground material was distributed into 5 microtubes, and the aliquots were mixed in 1 ml of lysis buffer [START_REF] Ranjard | Sampling strategy in molecular microbial ecology: influence of soil sample size on DNA fingerprinting analysis of fungal and bacterial communities[END_REF] using a Retsch® MM400 agitator at 30 per sec for 2.5 min. After incubation at 70°C for 30 min, supernatants were collected after centrifugation at 7000 g for 5 min at 15 -20°C. The supernatants from the same original root material were combined as a crude DNA solution. The obtained crude extracts were purified using the GENECLEAN® Turbo Nucleic Acid Purification kit (MP Biomedicals, France).

Metabarcoding Amplicon libraries

Target V5-V7 regions of 16S rRNA were prepared using the Metabiote® v 2.0 procedure (Genoscreen, Lille, France) and were paired-end sequenced (2 × 250 bp) using an Illumina MiSeq instrument.

Demultiplexed sequence reads were obtained using the CASAVA v 1.0 tool (Illumina) by

Genoscreen. Sequence reads were processed with the FROGS (Find Rapidly OTUs with Galaxy Solution) pipeline [START_REF] Escudié | FROGS: Find, Rapidly, OTUs with Galaxy Solution[END_REF]. Reads 1 and 2 were merged under conditions of 10 bp minimum overlap and 10% mismatch allowance using the VSEARCH algorithm [START_REF] Rognes | VSEARCH: a versatile open source tool for metagenomics[END_REF]. Contigs were selected in the range of 380 bp to 500 bp, and those including ambiguous bases were eliminated. These sequences were clustered with Swarm [START_REF] Mahé | Swarm: robust and fast clustering method for amplicon-based studies[END_REF]. Chimaeras were removed using a filtering tool with the following criteria: OTUs needed to contain sequences shared by at least three samples and with a read abundance higher than 0.005% of the total number of reads. The OTUs were taxonomically associated using the Silva138 16S rRNA gene database [START_REF] Quast | The SILVA ribosomal RNA gene database project: improved data processing and web-based tools[END_REF].

Although the Genome Taxonomy Database recently proposed the repositioning of Betaproteobacteria as an order (Burkholderiales) in Gammaproteobacteria [START_REF] Parks | A standardized bacterial taxonomy based on genome phylogeny substantially revises the tree of life[END_REF], we decided to conserve the old classification to maintain consistency with previous studies. OTUs were further filtered with a threshold of at least 99% BLAST identity and 100% coverage. The number of remaining reads after the 2 nd filtration was in the range of 10,440 to 23,950 reads, with an average of 14,805 reads per plant. To compare the data coming from the different vetiver samples, the sequencing results were normalized to the same number of reads as that in the sample with the lowest total count (10,440 reads).

Rarefaction curves were depicted in parallel with the R packages vegan and phyloseq (McMurdie and Holmes, 2013) (Figure S2). Phylogenetic tree data were prepared with FastTree, following a multiple alignment by PyNAST in FROGS.

Dual inoculation test with F. graminearum

The antagonistic activities of bacterial isolates were analysed using an in vitro dual-inoculation method. F. graminearum was cultivated on potato dextrose agar medium (PDA) (Sigma-Aldrich™, USA) for 4 days. A 5-mm-diameter mycelial plug of fresh F.

graminearum cultures was inoculated at the centre of a 9 cm diameter plate containing 12 mL of PDA. Fifty microlitres of a bacterial suspension obtained from a liquid culture of an isolated bacterium incubated in 2 ml of nutrient broth (Sigma-Aldrich™, USA) at 28°C for 12

h was placed at 4 points 3 cm from the centre of the Petri dish. Three independent replicates were performed for each bacterial isolate. The plates were incubated at 28°C for 5 days.

The diameter of the fungus was measured and averaged among the replicates. Plates inoculated with only F. graminearum were used as controls. Antagonistic activity was expressed as the inhibition rate (%), calculated as follows: ((dcontrol -dassay)/dcontrol) x 100),

where d means the diameter of the F. graminearum mycelium.

Sequencing of the 16S rRNA gene of cultured bacterial endophytes

Selected bacterial strains were cultured on 10% TSA medium for 1 to 4 days. 16S rDNA amplification was performed on one single colony, as described in [START_REF] Cregut | Density, structure, and diversity of the cultivable arylsulfatase-producing bacterial community in the rhizosphere of field-grown rape and barley[END_REF]. PCR products were purified with the NucleoSpin® Gel and PCR Clean-up Kit (Macherey-Nagel, Germany) according to the manufacturer's recommendations. The clean amplicons were sequenced by Eurofins (Luxembourg). The sequences were compared to the GenBank database using BLASTn (http://www.ncbi.nlm.nih.gov/), and their taxonomic associations were determined using the Silva138 16S rRNA gene database.

Diversity and compositional analysis of the bacterial communities

All data treatments herein were performed using R (version 3.6.3) unless otherwise noted.

For the calculation and illustration of the number of shared OTUs and genera across locations, we used the Venn diagram R package. The number of observed OTUs and the Chao1, Shannon, and inverse-Simpson indices were used to describe richness and evenness within a location and were calculated with phyloseq. To evaluate the recovery rate of richness in our samples, the coverage ratio (%) was calculated by dividing the number of observed OTUs by the estimated richness, i.e., the Chao1 values [START_REF] Marzano | Complexity and Dynamics of the Winemaking Bacterial Communities in Berries, Musts, and Wines from Apulian Grape Cultivars through Time and Space[END_REF].

The beta diversity among vetiver bacterial communities by weighted UniFrac distance was visualized through principal coordinate analysis (PCoA) using the phyloseq and ggplot2 R packages.

The composition of the functionally selected endophyte communities was converted into a table that includes the relative abundance at the genus level. These data were visualized using the ggplot2 R package. The table was used to measure the beta diversity among samples with a distance metric, Bray-Curtis dissimilarity, using vegdist in the vegan R package. The result was visualized by PCoA with ggplot2 and ggpubr R packages.

Statistical analyses

The inhibition rate was visualized with ggplot2 and tested by the Tukey-Kramer method with the multcomp R package. Multiple comparisons of alpha diversity indices and the relative abundance of taxa were performed with the Tukey-Kramer method using the multcomp R package. For the meta-barcoding analysis, the influence of the location factor was tested by PERMANOVA (permutations = 9999) with Adonis available in the vegan R package equipped in FROGS. The influence of the location factor on the variation in the Bray-Curtis dissimilarity metric among the culturable endophyte communities was tested by PERMANOVA (permutations = 10000) with adonis in the vegan R package.

Results

Biodiversity analysis of endophytic bacterial microbiota in vetiver

Vetiver roots were sampled from different places located in Madagascar, Portugal, Senegal and Reunion Island (Figure S1). Illumina sequencing performed on the DNA extracted from each sample generated a total of 366,169 raw sequences, and after a FROGS process (29), 222,081 sequences were retained. These sequences were clustered into 894 different OTUs (between 233 and 500 OTUs per sample) (Table S1). Among them, 55 OTUs were shared by all samples, whereas 32, 38, 100, 115 and 64 specific OTUs were detected only in the Madagascar, Portugal, Reunion1, Reunion2 and Senegal vetiver root samples, respectively (Figure S3). The observed number of OTUs differed according to the geographic origin of the vetiver roots and was significantly higher in the samples from Reunion Island than in the samples from the other geographic locations (Table 1). The Chao1, Shannon, and inverse-Simpson indices were calculated to characterize the alpha diversity of the bacterial communities associated with vetiver roots (Table 1). Overall, although the differences were not always significant, our results show that the values of all diversity indices were higher in the Reunion Island samples. This could indicate more diverse bacterial communities in vetiver root samples from Reunion Island than in samples from the other geographic locations (Table 1). To evaluate how our data reflect the diversity, we calculated the ratio of observed OTUs to the Chao1 index values for each location. The analysis showed that the Madagascar samples had significantly lower diversity coverage than the Reunion samples (Table 1).

Principal coordinate analysis (PCoA) based on weighted UniFrac distances among samples showed that the endophytic root bacterial communities from the 5 vetiver geographic locations were clearly separated from each other (Figure 1). The first two axes explained 78.4% of the variation. The samples from Reunion Island and Madagascar were separated along the first axis (PCoA 1 = 51.6%), whereas the samples from Senegal and Portugal were separated along the second axis (PCoA 2 = 26.8%). These results, which were further validated statistically by PERMANOVA (Df=4, R 2 = 85%, P=0.0001), indicated that the endophytic bacterial communities from vetiver roots are structured by geographic location.

Taxonomic composition of endophytic bacterial communities in vetiver roots from different geographic locations

The detected vetiver root bacterial OTUs were affiliated with 13 bacterial phyla (Figure 2A). However, almost all OTUs were distributed in 4 phyla that represented 98.7% of the total abundance. These phyla were Proteobacteria (70.3% +/-12.1), Bacteroidota (13.7%

+/-8.2), Firmicutes (7.8% +/-9.7) and Actinobacteria (5.5% +/-8.5). Proteobacteria were common to all samples in relatively equal abundance, with three main subphyla, Gammaproteobacteria (67.6% +/-13.7), Alphaproteobacteria (29.7% +/-13.2) and Betaproteobacteria (2.6% +/-2.5). In contrast, the other dominant phyla were more specifically enriched the certain vetiver locations (Figure 2A). Bacteroidota were more abundant in root samples from Reunion and Senegal (from 13.1% to 23.1%) than in the samples from the other locations (Figure 2A). The abundances of Firmicutes and Actinobacteriota also varied greatly among vetiver locations. The Firmicutes abundance in vetiver roots originating from Senegal was 20.6% (4.0% on average in the other samples),

whereas Actinobacteria was mostly represented in samples from Portugal (20.6%) (1.7% on average in the other samples) (Figure 2A). At the genus level, a total of 258 genera were found in our samples. Among them, 53 genera were shared across geographic sites; these genera accounted for 20.5% of the total genera (Figure 3). The shared genera belonged to 6 phyla (Proteobacteria, Myxococcota, Firmicutes, Bdellovibrionota, Bacteroidota, and Actinobacteriota) and made up an average relative abundance of 72.5% +/-12.7 of the total abundance at each location.

Except in the Senegal samples, in which Exigobacterium dominated, the most abundant genus was Pseudomonas (3.7 -59.7% of the total abundance) (Figure 2B,4A).

The abundance of other dominant genera differed significantly depending on the vetiver geographic location (p value < 0.05, Figure 4A). Some genera, such as Pantoea, Rhizobium, Bradyrhizobium, Acidibacter, Enterobacter and Kosakonia, were specifically enriched in samples originating from specific geographic locations, whereas Flavobacterium was shown to be enriched in samples from Senegal and Reunion Island (Figure 5).

Bacterial endophyte isolation and antagonistic activity towards F. graminearum

We isolated bacteria from the same vetiver roots that were used for the metagenomic approach. First, the density of cultivable endophytic bacteria from the vetiver root samples was estimated. We observed that the average density of cultivable endophytic bacteria in vetiver roots did not differ significantly between each geographic location (5.2 to 6.2 log10 CFU g -1 root dry weight) (Table 2). A total of 381 endophytes were recovered from vetiver root samples and were tested for their ability to inhibit F. graminearum mycelial growth in in vitro culture. The inhibition rate varied greatly among bacterial isolates (from -3.3 to 93.3), but nearly all isolates (99.7%, Table S2) presented this functional trait. The mean inhibition rate of the bacterial isolates was significantly lower in the isolates from Reunion1 (p<0.05, 31.7% +/-14.9) than in the isolates from the other samples (Table 2). The endophytic bacterial isolates with an inhibitory rate of at least 50% were selected for further analyses.

They represented 49% (176 isolates) of the total isolates, and 20% (36 isolates) of them had an inhibition rate of at least 70% against F. graminearum (Table S2). The relative frequency of these functional isolates differed significantly among the vetiver samples (p-value<0.05, Table 2). In particular, only 14% of isolates from Reunion1 showed an inhibition rate ≥ 50%, while 77% of the isolates from Madagascar showed an inhibition rate ≥ 50%. The isolates with inhibition rate ≥ 70% were isolated from vetiver originating from Madagascar (2 isolates), Portugal (20 isolates), Reunion2 (11 isolates) and Senegal (3 isolates) (Table S4).

Based on partial 16S rDNA sequencing, 153 of these bacterial isolates were taxonomically characterized (Table S3). They included Proteobacteria (86.2% +/-22.0), Firmicutes (12.2% +/-22.4) and Actinobacteriota (1.4% +/-3.0) (Figure S5). A total of 15 genera were identified (Figure 5). Among them, 8 genera had already been described using 16S rDNA high-throughput sequencing (Figure 6).

Pseudomonas was the dominant genus (47.0% +/-36.3) and was observed in all samples except those from Madagascar (Figure 5). Bacillus was mostly identified in samples from Reunion 2, whereas Kosakonia was mostly observed in Madagascar samples (Figure 5). The presence and/or proportion of each genus varied according to the samples.

It should be noted that the bacterial isolates possessing the highest inhibition rates (≥ 70%) against F. graminearum were mainly affiliated with the Pseudomonas, Serratia and Bacillus genera (Table 3). The Pseudomonas isolates seemed to be most closely related to 3 species, P. koreensis, P. vancouverensis and P. nitroreducens, whereas the Serratia isolates belonged to 2 species, S. marcescens and S. grimesii, and the Bacillus isolates were B.

subtilis and B. cereus.

The table of the relative abundance of genera was used to generate a Bray-Curtis distance matrix that was subjected to PCoA (Figure 7). This analysis showed that the functional microbial communities from Reunion2 and Madagascar were distinct from each other and from a cluster composed of the microbial communities from the Reunion1, Portugal and Senegal samples. These results were validated with PERMANOVA showing that the geographic location factor significantly altered the composition of the cultivable endophytic communities with antagonistic activity towards F. graminearum in vetiver roots (Df =4, R 2 = 66.4%, p< 0.001).

Discussion

Diseases caused by F. graminearum are among the most important diseases in grain cereals. Chemical fungicides are still widely used to control this fungus, although their detrimental impacts on the environment and human health are now well known. To reduce the use of such chemicals while maintaining crop yields, it is now necessary to find and develop alternative crop protection solutions. A number of previous studies revealed that bacterial endophytes may help plants cope with pathogens [START_REF] Berg | Next-Generation Bio-Products Sowing the Seeds of Success for Sustainable Agriculture[END_REF][START_REF] Card | Beneficial endophytic microorganisms of Brassica -A review[END_REF][START_REF] Eljounaidi | Bacterial endophytes as potential biocontrol agents of vascular wilt diseases -Review and future prospects[END_REF][START_REF] Liu | Biological control of take-all in wheat by endophytic Bacillus subtilis E1R-j and potential mode of action[END_REF][START_REF] Mancini | Seed treatments to control seedborne fungal pathogens of vegetable crops: Seed treatments to control seedborne fungi[END_REF][START_REF] Mousa | Root-hair endophyte stacking in finger millet creates a physicochemical barrier to trap the fungal pathogen Fusarium graminearum[END_REF]. In particular, bacterial endophytes are able to produce a range of specialized metabolites that have antimicrobial activity [START_REF] Brader | Metabolic potential of endophytic bacteria[END_REF]. In addition, coevolution processes with their hosts led endophytes to mimic natural plant compounds [START_REF] Baltrus | Adaptation, specialization, and coevolution within phytobiomes[END_REF].

Because of these findings, it is now accepted that bacterial endophytes contribute to the biological activity of plant extracts, including their antimicrobial activity [START_REF] Miller | Investigation of the Biosynthetic Potential of Endophytes in Traditional Chinese Anticancer Herbs[END_REF][START_REF] Strobel | Natural Products from Endophytic Microorganisms[END_REF]. The metabolic potential of bacterial endophytes suggests the possibility of exploiting these microorganisms for biocontrol applications. In this study, we focused on the bacterial endophytic community of vetiver roots since it has been shown that some members of this community are involved in the synthesis of vetiver essential oil, which has been reported to display antimicrobial activity [START_REF] Chahal | Chemical composition and biological properties of Chrysopogon zizanioides (L.) Roberty syn. Vetiveria zizanioides[END_REF][START_REF] Del Giudice | The microbial community of Vetiver root and its involvement into essential oil biogenesis: Vetiver root bacteria and essential oil biogenesis[END_REF][START_REF] Hammer | Antimicrobial activity of essential oils and other plant extracts[END_REF][START_REF] Powers | Antifungal and Cytotoxic Activities of Sixty Commercially-Available Essential Oils[END_REF].

The vetiver roots we investigated mainly harbour endophytic bacteria belonging to four major phyla, i.e., Proteobacteria, Bacteroidetes, Firmicutes and Actinobacteriota. These results are consistent with those of several previous studies showing that these phyla are preferentially enriched in plant roots compared to their levels in the soil and rhizosphere [START_REF] Bulgarelli | Structure and Functions of the Bacterial Microbiota of Plants[END_REF][START_REF] Hardoim | The Hidden World within Plants: Ecological and Evolutionary Considerations for Defining Functioning of Microbial Endophytes[END_REF][START_REF] Lundberg | Defining the core Arabidopsis thaliana root microbiome[END_REF]. Additionally, among them, Proteobacteria were overrepresented in all vetiver roots sampled, which is similar to the results obtained by [START_REF] Monteiro | Bacterial communities within the rhizosphere and roots of vetiver (Chrysopogon zizanioides (L.) Roberty) sampled at different growth stages[END_REF]. This predominance might be related to the fact that such copiotrophic microorganisms prefer a C-rich environment [START_REF] Fierer | TOWARD AN ECOLOGICAL CLASSIFICATION OF SOIL BACTERIA[END_REF][START_REF] Yang | Comparative analysis of bacterial community structure in the rhizosphere of maize by high-throughput pyrosequencing[END_REF]. They may therefore benefit from the flow of photoassimilates from shoots to roots, which creates a nutrient-rich environment inside the roots. We showed that the Proteobacteria were mostly Gammaproteobacteria and were dominated by a few families and genera. Among them, the genus Pseudomonas is a good root colonizer and was prevalent. However, other genera, such as Kosakonia, Enterobacter and Pantoea, were also observed. Most of these genera can benefit plants by promoting plant growth and/or protection, although some of them have been described as pathogens [START_REF] Bulgarelli | Structure and Functions of the Bacterial Microbiota of Plants[END_REF]. Bacteroidetes were represented by the dominant Flavobacterium genus, which is often reported as an important member of root microbiomes, and some strains have traits that are beneficial to plants [START_REF] Kolton | The Flavobacterium Genus in the Plant Holobiont: Ecological, Physiological, and Applicative Insights[END_REF]. Finally, Actinobacteria and Firmicutes were represented by the Streptomyces and Exiguobacterium genera, respectively, which are known to produce antimicrobial compounds [START_REF] Hardoim | The Hidden World within Plants: Ecological and Evolutionary Considerations for Defining Functioning of Microbial Endophytes[END_REF][START_REF] Kasana | Exiguobacterium: an overview of a versatile genus with potential in industry and agriculture[END_REF]. Our study also provides additional insights since we showed that the geographic location of the vetiver samples seemed to influence the composition and the relative abundance of some of the taxa in the roots. Recently, [START_REF] Thiergart | Root microbiota assembly and adaptive differentiation among European Arabidopsis populations[END_REF] provided evidence that soil is the primary factor that influences root endophytic bacterial communities, regardless of the spatial scale of the analysis or the host genotype. These data support the findings of previous studies and led us to suggest that the variations we observed within the vetiver root bacterial communities might be related to the differences in soil properties across a geographic gradient from Europe to Africa [START_REF] Bulgarelli | Structure and Functions of the Bacterial Microbiota of Plants[END_REF][START_REF] Chen | Soil Characteristics Overwhelm Cultivar Effects on the Structure and Assembly of Root-Associated Microbiomes of Modern Maize[END_REF][START_REF] Fierer | TOWARD AN ECOLOGICAL CLASSIFICATION OF SOIL BACTERIA[END_REF][START_REF] Lundberg | Defining the core Arabidopsis thaliana root microbiome[END_REF].

As some of the microbial groups we identified in vetiver roots have been described as potential biocontrol agents against plant pathogens, we evaluated the ability of this microbiota to suppress the growth of F. graminearum. For that purpose, the bacteria were isolated and profiled in in vitro dual-culture assays with F. graminearum. Among the 381 isolates, most displayed antagonistic activity towards F. graminearum, with almost 50%

producing an inhibition rate of more than 50%. These bioactivities might be related to the ability of the isolates to synthesize diverse antimicrobial compounds (specialized metabolites) [START_REF] Saleh | Diversity, distribution and multi-functional attributes of bacterial communities associated with the rhizosphere and endosphere of timothy (Phleum pratense L.)[END_REF][START_REF] Strobel | Natural Products from Endophytic Microorganisms[END_REF]. Furthermore, these results reinforce the hypothesis that microbial endophytes can contribute to the bioactivity of plant extracts and, in our case, to the antimicrobial properties of the vetiver essential oil [START_REF] Chahal | Chemical composition and biological properties of Chrysopogon zizanioides (L.) Roberty syn. Vetiveria zizanioides[END_REF][START_REF] Del Giudice | The microbial community of Vetiver root and its involvement into essential oil biogenesis: Vetiver root bacteria and essential oil biogenesis[END_REF][START_REF] Egamberdieva | Antimicrobial Activity of Medicinal Plants Correlates with the Proportion of Antagonistic Endophytes[END_REF][START_REF] Miller | Investigation of the Biosynthetic Potential of Endophytes in Traditional Chinese Anticancer Herbs[END_REF].

The metagenomic data showed that the bacterial isolates mostly belong to Proteobacteria, followed by Firmicutes and Actinobacteriota, and that their distribution is related to their geographic location. Our results also showed, at lower taxonomic levels, that the geographic location shapes the cultivable bacteria in vetiver roots. As previously suggested by [START_REF] Monteiro | Bacterial communities within the rhizosphere and roots of vetiver (Chrysopogon zizanioides (L.) Roberty) sampled at different growth stages[END_REF], soil could be an important factor influencing bacterial communities from vetiver. Interestingly, the culture-based and molecular-based datasets do not completely overlap. For instance, in the metagenomic data, Pseudomonas was highly represented in the Madagascar samples, whereas most of the bacterial isolates in these samples were affiliated with Kosakonia and Pantoea. This relative discrepancy could result from the fact that most of the bacteria present in a sample cannot grow on the traditionally used culture media [START_REF] Eevers | Optimization of isolation and cultivation of bacterial endophytes through addition of plant extract to nutrient media[END_REF][START_REF] Pascual | Assessing Bacterial Diversity in the Rhizosphere of Thymus zygis Growing in the Sierra Nevada National Park (Spain) through Culture-Dependent and Independent Approaches[END_REF]. Bacteria with the capacity to inhibit the in vitro growth of F. graminearum were affiliated with 15 genera. Some of these genera, such as Pseudomonas, Enterobacter, and Serratia, have already been identified in vetiver roots [START_REF] Del Giudice | The microbial community of Vetiver root and its involvement into essential oil biogenesis: Vetiver root bacteria and essential oil biogenesis[END_REF].

This study performed on vetiver roots resulted in the isolation and identification of 32 highly bioactive isolates displaying at least 70% inhibition rates against F. graminearum.

These isolates were mostly from the genera Pseudomonas, Serratia, and Bacillus. Only 4 isolates were affiliated with different genera, i.e., Kosakonia, Janthinobacterium and Microbacterium. Various reports have described bacteria affiliated with these dominant genera that were isolated from different cultivated plants and display in vitro inhibition activity against Fusarium spp. including F. graminearum [START_REF] Bredow | In silico analysis of the 16S rRNA gene of endophytic bacteria, isolated from the aerial parts and seeds of important agricultural crops[END_REF][START_REF] Haas | Biological control of soil-borne pathogens by fluorescent pseudomonads[END_REF][START_REF] Ju | Identification and evaluation of a potential biocontrol agent, Bacillus subtilis, against Fusarium sp. in apple seedlings[END_REF]. Furthermore, Serratia, Pseudomonas, Bacillus, and Microbacterium have been reported to produce antimicrobial compounds. Bacillus, which is one of the most investigated and commercially utilized genera worldwide [START_REF] Lopes | A look into a multifunctional toolbox: endophytic Bacillus species provide broad and underexploited benefits for plants[END_REF], is known to produce antimicrobial compounds such as lipopeptides, exopolysaccharides, siderophores and polyketides [START_REF] Ek-Ramos | Bioactive Products From Plant-Endophytic Gram-Positive Bacteria[END_REF]. In addition to Bacillus, Pseudomonas strains, including those affiliated with P. koreensis, are also known to produce structurally diverse specialized metabolites with antimicrobial properties [START_REF] Kaur | Pseudomonas koreensis Recovered From Raw Yak Milk Synthesizes a β-Carboline Derivative With Antimicrobial Properties[END_REF][START_REF] Raaijmakers | Diversity and Natural Functions of Antibiotics Produced by Beneficial and Plant Pathogenic Bacteria[END_REF]. Likewise, some strains in the Serratia genus can produce antibiotics whose synthesis is regulated by carbon sources [START_REF] Mai | Serratia A Novel Source of Secondary Metabolites[END_REF].

Another study performed on Janthinobacterium strains revealed that one of the modes of action of this genus against F. graminearum occurs through biofilm formation following quorum sensing [START_REF] Haack | Molecular Keys to the Janthinobacterium and Duganella spp. Interaction with the Plant Pathogen Fusarium graminearum[END_REF]. More recently, new antifungal compounds, such as janthinopolyenemycins, were identified through the co-culturing of two Janthinobacterium strains isolated from marine sediments [START_REF] Anjum | Novel antifungal janthinopolyenemycins A and B from a co-culture of marine-associated Janthinobacterium spp. ZZ145 and ZZ148[END_REF].

Conclusions

By combining culture-based and molecular-based approaches, we provided new insights into the composition of the endophytic bacterial communities of vetiver roots. We showed that the taxonomic composition as well as the ability of the members of the endophytic community to exhibit in vitro antagonistic activity towards F. graminearum were influenced by the geographic location of the vetiver roots. These results open new pathways for accessing a wider diversity of bacteria and therefore identifying new functional bacteria.

The most effective bacteria for inhibiting the growth of F. graminearum in vitro might be further studied as promising biological control solutions. The next step will now consist of confirming the bioactivity of these isolates in plant inoculation assays and/or characterizing the antimicrobial compounds produced.

Table 1|. Alpha diversity of Vetiver bacterial communities in five locations using the indices of richness

  Roots ofChrysopogon zizanioides (L.) Roberty were collected in summer 2013 in Portugal in Sao Bartolomeu de Messines, in Madagascar on the Bemasoandro plantation in Antananarivo, in Senegal at the Naac Baal nursery in Sebikotane, and on Reunion Island in the areas Pierrefonds (Reunion1) and Domaine Vidot (Reunion2) (Figure S1). Three individual plants were obtained from each geographical location. The collected fresh plants were shipped at cold temperatures and processed immediately after being received. The map of vetiver origins (Figure S1) was based on Global Map Version 1//maps.gsi.go.jp/development/ichiran.html); this map was edited and points representing the sampling locations were added.

  Similar patterns were observed at lower levels of taxonomical classification. At the family level, Pseudomonadaceae were dominant (from 19% to almost 50% in abundance), with the exception of the samples from Senegal in which Enterobacteriaceae dominated (FigureS4). The abundance of other dominant families differed depending on the geographic origin of the vetiver. In particular, Streptomycetaceae and Exiguobacteraceae were only abundant in the Portugal and Senegal samples, respectively, whereas Flavobacteriaceae was shown to be more abundant in the Senegal and Reunion samples.

(

  the number of observed OTUs and Chao 1), coverage (the ratio of observed OTUs and Chao 1), and the indices of evenness (Shannon and InvSimpson), with ± standard deviation. Different letters besides the values indicate differences with p value < 0.05 within an index by location group.

Figure

  Figure 1| PCoA plot based on weighted UniFrac distance of Vetiver samples. Points represent individual plants, Points represent individual plants, and squares and ellipses show the center of gravity and a 95% confidential zone of each locational group, respectively.

Figure

  Figure 3| Venn diagram of the number of shared genera over locations and specific genera for each location. The shown percentages are percentage of shared or specific genera against total number of genera found through all samples.

Figure

  Figure 4| Relative abundance of dominant genera in 4 phyla, in Vetiver root endophyte communities. (A) Proteobacteria, (B) Bacillus and Exiguobacterium (Firmicutes), Flavobacterium (Bacteroidota), Streptomyces (Actinobacteriota). The same letters within a genus mean no differences with p value <0.05 (Tukey-Kramer test)

Figure

  Figure 6| Venn diagram of the number of common or unique genera in the metabarcoding data and the culturable communities.

Figure

  Figure 7| PCoA ordination of isolated endophyte communities with bioactivities against F. graminearum using Bray-Curtis distance. Points represent individual plants, and squares and ellipses show the center of gravity and a 95% confidential zone of each locational group, respectively.

Table 2|

 2| Summary of isolation and antagonistic activities of endophytic isolates of Vetiver roots from 5 different locations. Colony forming unit (CFU) of Vetiver root endophytes per 1 g of dried root materials (dry weight, DW). The same letters within a column indicate no significant difference among locations with p value <0.05 (Tukey-Kramer test).

				Inhibition rate against F. graminearum	Isolates with ≥50% antagonism
	Site	Log 10 CFU/g of DW	Total number of isolates	Min.	Max.	(%)	Average ± SD		Number of isolates against F. graminearum Population within a site
	Madagascar	6.1 ± 0.3 a	48	0.5	83.5	55.1 ± 11.6	a	37	77% a
	Portugal	5.7 ± 0.5 a	89	28.7	79.9	54.2 ± 14.9	a	46	52% ab
	Reunion 1	5.6 ± 0.2 a	86	-3.3	65.0	31.7 ± 14.9	b	12	14% b
	Reunion 2	5.6 ± 0.3 a	76	18.3	93.3	52.0 ± 17.2	a	43	57% ab
	Senegal	6.2 ± 0.3 a	82	22.9	82.8	52.9 ± 12.6	a	38	46% ab
	total		381						176
	Figure 5| Taxonomical compositions of 15 genera in functionally selected bacterial endophyte
	communities of Vetiver roots in 5 sites

  Table 3| Bacterial endophyte isolates that exhibited more than 70% of inhibition activity against F. graminearum mycelia

	Site	Accession	Inhibition rate (%)	Phylum	Genus	Top hit	Identity (%)
	Madagascar M1_08	71.3 Proteobacteria	Serratia	Serratia marcescens subsp. marcescens ATCC 13880 strain DSM 30121	100
	Portugal	P2_28	70.6 Actinobacteriota Microbacterium	Microbacterium hominis strain IFO 15708	100
		P2_02	73.5			Pseudomonas koreensis strain Ps 9-14	100
		P2_16 P2_06	72.1 78.5	Proteobacteria	Pseudomonas	Pseudomonas vancouverensis strain DhA-51 Pseudomonas vancouverensis strain DhA-51	100 99.61
		P2_25	79.2			Pseudomonas vancouverensis strain DhA-51	100
		P2_15	73.1		Serratia	Serratia grimesii strain DSM 30063	99.67
		P3_18	70.6			Pseudomonas koreensis strain Ps 9-14	99.44
		P3_08	71.0			Pseudomonas koreensis strain Ps 9-14	100
		P3_19 P3_26	71.7 72.1		Pseudomonas	Pseudomonas koreensis strain Ps 9-14 Pseudomonas koreensis strain Ps 9-14	99.42 99.79
		P3_27	73.8			Pseudomonas koreensis strain Ps 9-14	99.51
		P3_24	74.2			Pseudomonas koreensis strain Ps 9-14	99.45
		P3_01 P3_07	72.1 73.1	Proteobacteria		Serratia grimesii strain DSM 30063 Serratia grimesii strain DSM 30063	99.69 99.68
		P3_25	73.1			Serratia grimesii strain DSM 30063	99.65
		P3_30 P3_17	73.5 73.8		Serratia	Serratia grimesii strain DSM 30063 Serratia grimesii strain DSM 30063	99.7 99.67
		P3_13	74.9			Serratia grimesii strain DSM 30063	99.67
		P3_28	78.1			Serratia grimesii strain DSM 30063	99.67
		P3_29	79.9			Serratia grimesii strain DSM 30063	99.71
	Reunion2	R22_05	81.7			Bacillus subtilis strain IAM 12118	99.83
		R22_06	81.7	Firmicutes	Bacillus	Bacillus subtilis strain IAM 12118	100
		R22_17	93.3			Bacillus subtilis strain IAM 12118	97.95
		R22_08	70.0 Proteobacteria	Pseudomonas	Pseudomonas nitroreducens strain NBRC 12694	100
		R23_17	78.3			Bacillus cereus ATCC 14579	100
		R23_12 R23_28	70.0 73.3	Firmicutes	Bacillus	Bacillus subtilis strain IAM 12118 Bacillus subtilis strain IAM 12118	99.86 100
		R23_08	75.0			Bacillus subtilis strain IAM 12118	100
	Senegal	S1_29	82.8 Proteobacteria	Kosakonia	Kosakonia oryzendophytica strain REICA_082	100
		S2_18 S2_11	76.0 82.5	Proteobacteria	Janthinobacterium	Janthinobacterium agaricidamnosum strain NBRC 102515 Janthinobacterium lividum strain DSM 1522	100 99.71

Acknowledgments

This work was financially supported by the "Impact Biomolecules" project of the "Lorraine Université d'Excellence" (Investissements d'avenir-ANR)