Florent Brenguier
email: florent.brenguier@ujf-grenoble.fr.

Nikolai M Shapiro

Michel Campillo

Valérie Ferrazzini

Zacharie Duputel

Olivier Coutant

Alexandre Nercessian

Toward Forecasting Volcanic Eruptions using Seismic Noise

During inter-eruption periods, magma pressurization yields subtle changes of the elastic properties of volcanic edifices. We use the reproducibility properties of the ambient seismic noise recorded on the Piton de la Fournaise volcano to measure relative seismic velocity variations of less than 0.1 % with a temporal resolution of one day. Our results show that five studied volcanic eruptions were preceded by clearly detectable seismic velocity decreases within the zone of magma injection. These precursors reflect the edifice dilatation induced by magma pressurization and can be useful indicators to improve the forecasting of volcanic eruptions.

Volcanoes are among the most dynamic geological objects and their eruptions provide a dramatic manifestation of the Earth's internal activity. However, strong eruptions are only short

episodes in the history of volcanoes which remain quiescent most of time. During this intereruption periods, slow processes such as changes in the magma supply to the reservoir and changes of the magma physical or chemical properties lead to perturbations of the reservoir pressure and to preparation of new eruptions. It is, therefore, very important to better describe these processes to fully understand the functioning of active magmatic systems and to improve our ability to forecast volcanic eruptions.

The inter-eruptive magma pressurization and/or intrusions of dykes result in subtle changes in the shape of the volcanic edifices that may be detected by modern strainmeters and tiltmeters (1) or by satellites (2). The main limitation of these geodetic methods is that they are based on the interpretation of displacements or tilts observed near the surface, which limits their sensitivity to changes located at depth. Volcanic seismicity provides informations about shortterm (few seconds to few days) mechanical processes occurring within volcanoes at depth. The spatio-temporal evolution of magma migration can be retrieved by precise location of seismic events (3) and by accurate determination of seismic source properties (4,5). However, analysis of volcanic seismicity can not be used to detect the aseismic magma pressurization preceding fracturing and magma migration. The inter-eruptive processes also produce perturbations of the elastic properties of volcanic edifices. They can be detected as changes in the travel times of seismic waves propagating within the volcanic edifices by using coda waves from repetitive seismic sources such as multiplets (6,7,8) or small summital volcanic explosions (9,10) or correlations of a diffuse seismic wavefield excited by long-period seismo-volcanic events (11).

However, these methods based on seismo-volcanic sources do not provide information about time periods when volcanoes are seismically quiescent. More recently, repeated seismic tomographies (12) has been used to detect seismic velocity variations within Mount Etna over periods of a few years. This method reveals variations of the internal volcanic structure before and after an eruption. However, the construction of repetitive tomographic images requires long time periods of observation of seismicity and cannot be done continuously. Moreover, the accuracy of repetitive tomographies is limited and may be insufficient to detect small velocity variations (less than 1 %) associated with magma pressurization processes.

In this paper, we go beyond the limitations of methods based on seismo-volcanic sources by recovering temporal velocity variations within the Piton de la Fournaise volcano using continuous ambient seismic noise records. The basic idea is that a cross-correlation of random seismic wavefields such as coda or noise recorded at two receivers yields the Green function, i.e., the impulse response of the medium at one receiver as if there was a source at the other (13,14,15,16). This property has been used for imaging the crust at regional scales (17,18,19) and, more recently, has been applied to infer the internal structure of the Piton de la Fournaise volcano at La Réunion island (20). By computing noise cross-correlations between different receiver pairs for consecutive time periods, we make each receiver to act as a virtual highly repetitive seismic source. The associated reconstructed seismic waves (Green functions) can then be used to detect temporal perturbations associated to small velocity changes (less than 1 %), (21).

We applied this method to study the Piton de la Fournaise volcano on La Réunion island (Fig. 1A). During the past two centuries the average time between consecutive eruptions of this volcano has been about 10 months (22). Geodetic and seismic data suggest that the Piton de la Fournaise eruptions are triggered by magma over-pressure within a magma reservoir located below the main vent (Fig. 1B) at approximately sea level (23,1). We used the continuous seismic noise recorded between July 1999 and December 2000 by 21 vertical short period receivers operated by the Observatoire Volcanologique du Piton de la Fournaise to compute 210 cross-correlation functions corresponding to all possible receiver pairs [see Fig. S1 and (20) for details]. We used the spectral band between 0.1 and 0.9 Hz where the recovered Green functions has been demonstrated to consist of Rayleigh waves that are sensitive to the structure at depths down to 2 km below the edifice surface. The cross-correlation functions obtained by correlating 18 months of seismic noise are called the reference Green functions. The temporal evolution was then tracked by comparing the reference Green functions with current Green functions computed by correlating the noise from a ten-days-long moving window.

If the medium exhibits a spatially homogeneous relative velocity change ∆v/v, the relative travel-time shifts (∆τ ) between the perturbed and reference Green functions is independent of the lapse time (τ ) at which it is measured and ∆v/v = -∆τ /τ = const. Therefore, when computing a local time shift ∆τ between the reference and the current cross-correlations in a short window centered at time τ , we would expect to find ∆τ to be a linear function of τ (Fig. S2). By measuring the slope of the travel time shifts ∆τ as function of time τ , we finally estimate the Relative Time Perturbation (RTP) that is the opposite value of the medium's uniform relative velocity change (∆v/v). Fig. 1C shows the reference and the current Green functions for one pair of receivers (PBRZ-NCR) computed 40 days , 14 days, and one day before the eruption of June 2000 (day 359). Fig. 1D shows the respective travel time shifts measured in the frequency band [0.1-0.9] Hz using the Moving Window Cross Spectrum technique (7,[START_REF]Materials, methods are available as supporting material on Science Online[END_REF]. It can be seen in these measurements obtained just with one pair of receivers that the RTP changes from a negative to a nearly zero and then to a positive value 40 days, 14 days, and one day prior to the eruption, respectively. However, the RTP can be measured only very approximately when using only one pair of receivers. The accuracy of the linear trend measurements is significantly improved by averaging local time shifts for different receiver pairs assuming that the seismic velocities are perturbed uniformly within the sampled medium. We selected 13 receiver pairs located near the caldera and showing good quality measurements (Fig. 1E) to compute the averaged time shifts (Fig. 1F) and to obtain accurate RTP estimates. Fig. 2A presents the relative time perturbations (∆τ /τ ) measured over 18 months (June 1999 to December 2000). Intervals with low-quality measurements that correspond to periods of intense seismo-volcanic activity (Fig. 2C) and to strong tropical cyclones (days 150-200) are excluded from the analysis (Fig. 2B). The remaining time series show that the volcano interior exhibits changes at different time scales varying from a few months to a few days. To simplify the analysis, we separate the short-and the long term-variations. We fit the Long Term Variations (LTV) by a polynomial function and then subtract it from the raw RTP to obtain the Short-Term Variations (STV, Fig. 2B). The STV curve shows clear precursors to the volcanic eruptions characterized by an increase in the RTP and thus a decrease of seismic velocities.

These precursors start about 20 days before the eruptions and correspond to relative velocity perturbations as small as 0.1 %.

We interpret the observed decreases in seismic velocities as an effect of the dilatation of a part of the edifice resulting from the magma pressurization within the volcano plumbing system similar to observations at Mount Etna [START_REF] Patanè | [END_REF]. This interpretation is also supported by the clear opening of an individual fracture detected by an extensometer (26) prior to the eruption n • 4 (day 360, June 2000) synchronously with the RTP precursor (Fig. S3A). The lack of clear fracture opening precursors for the other eruptions would suggest that the detected dilatation may occur in a restricted zone and have non-measurable effects at the extensometer location. The relative velocity changes return to a nearly background level during the eruption periods (Fig. 2B). This observation is consistent with deflation associated to depressurization of the magma during its extrusion to the surface only few minutes after the beginning of the eruptions (26).

The presented RTP curve required to spatially average the measured time shifts for different receiver pairs located in the vicinity of the main caldera. The same procedure applied to receiver pairs located outside the main caldera do not show eruption precursors. This suggests that the velocity variations are spatially localized. We apply a regionalization procedure (24) in order to localize more precisely the observed perturbations. We estimate the relative velocity variations for 28 individual receiver pairs selected according to quality criteria, subtract the long-term component from the raw measurements to obtain the short-term variations (STV) and then compute, in every grid cell, an average value from its neighborhood receiver pair paths. As a result, we obtain for every day a two-dimensional map of relative velocity perturbations. A full set of this maps is shown in Movie S1 and a snapshot taken five days before eruption n • 2 is presented in Fig. 3A. The movie and snapshot show that the precursors are not distributed homogeneously in space but are mainly located in an area a few kilometers East from the main vent. This location nearly coincides with the fast velocity anomaly imaged by surface wave tomography at 1.3 km above sea level (Fig. 3B), (20), and interpreted as an effect of solidified dykes associated to the zone of magma injection. This coincidence is an additional argument suggesting that the observed short-term seismic velocity decreases are produced by a dilatation associated with the pressurization within the volcano plumbing system.

The presented measurements are based on Rayleigh waves that dominate the noise crosscorrelations. Therefore, the observed travel time variations mainly correspond to perturbations of shear wave velocity β. We use empirical laws for porous media [START_REF] Pride | Hydrogeophysics[END_REF] to link the relative shear wave velocity perturbations to relative perturbations of porosity φ and volume V :

-∆τ /τ = ∆β/β = - 1 2 × ∆φ/φ = - 1 2 × ∆V V × φ (1)
that can be, in turn, related to the over-pressure ∆P induced in the medium by the magma using a model of dilatancy:

∆V /V = ∆P/K ( 2
)
where K is the incompressibility factor of the media that can be estimated as approximately 10

GPa by considering an average P-wave speed of 3400 m/s (20), a density of 2000 kg/m 3 , and a shear modulus value of 10 GPa. We then take ∆β/β = -1 × 10 -3 and an average realistic porosity of 0.1 and find ∆P to be approximately equal to 2 MPa or 20 bar. This over-pressure level is consistent with theoretical and experimental models of dike migration [START_REF] Tait | [END_REF]29), with recent interpretation of strain data on the Soufrière Hills volcano of Montserrat (30) as well as with the model of dyke propagation developed to explain the geodetic observations on the Piton de la Fournaise (26).

The analysis of the long-term velocity variations show that they are associated to processes varying over several months (Fig. 2A) with a possible seasonality. A clear seasonal dependance of the seismic velocity perturbations was observed from the analysis of short-period noise crosscorrelations at the Merapi volcano (31) and was related to variations of the depth of the superficial ground water layer because of precipitation. In the case of the Piton de la Fournaise, the observed LTV are not correlated with the pluviometric record on La Réunion island (Fig. S3B).

Moreover, the LTV amplitude and location (east of main vent) are very similar to what was observed for the short-term precursors (Fig. 2B, S4E and Movie S2) suggesting that the long-term velocity variations reported in this study are related to the dynamics of the volcano-magmatic system.

Our results demonstrated that relative seismic velocity changes can be measured with an accuracy lower than 0.1% by following the time evolution of the waveforms extracted from correlations of seismic noise. Application of this method to the data of the seismic network on the Piton de la Fournaise volcano revealed the evolution of the elastic properties of the upper volcano edifice during inter-eruption periods between July 1999 and December 2000.

We detected systematic velocity decreases of the volcanic edifice preceding volcanic eruptions.

These precursors clearly appeared approximately 20 days before four eruptions that occurred during the studied period. Approximate lateral positions of the maxima of observed velocity perturbations and a correlation with available geodetic data strongly indicate that the velocity variations are caused by dilatation of a part of the edifice. This process is caused by the preeruptive magma pressurization.

As a pilot experiment, we began to monitor the Piton de la Fournaise volcano by computing

  in real time the noise cross-correlations and measuring the velocity variations since spring 2006. This allowed us to identify a clear precursor for the last eruption that occurred in July 2006 (Fig.3C, D). Observation of such precursors may have important implications for monitoring volcano unrest and for improving the forecasting of volcanic eruptions. Detection of changes in elastic properties based on correlations of seismic noise may also be useful in other geophysical, engineering, and geotechnical applications that require non destructive monitoring of the media.

Figure 1 :Figure 2 :

 12 Figure 1: Measurements of relative velocity perturbations (∆v/v). (A) La Réunion Island. (B) Topographic map showing a direct path between two seismic receivers (PBRZ-NCR) indicated with inverted triangles. (C) Comparison between reference (black curves) and current (red curves) cross-correlation functions computed 40 days, 14 days, and one day prior to the eruption of June 2000 (day 359). (D) Time shifts measured between the reference and current crosscorrelation functions computed between PBRZ and NCR. Red lines show results of the linear regressions. (E) Topographic map showing 13 receiver pairs used for averaging the time shift measurements. (F) Averaged time shifts. Resulting measurements of relative time perturbations (RTP, ∆τ /τ = -∆v/v) estimated by linear regressions are illustrated with red lines.

Figure 3 :

 3 Figure 3: (A) Regionalization of the relative velocity perturbations associated with the second eruption precursor (day 85, Sept. 1999). The gray dashed line represents the limits of ray coverage. (B) Fast shear velocity anomaly imaged by passive surface wave tomography (20) and interpreted as an effect of solidified dykes associated with the zone of magma injection. (C) Relative time perturbations before the eruption of July 2006. (D) Associated regionalized relative velocity perturbations one day before the beginning of the eruption.

thank L. Stehly, P. Gouédard, P. Roux, L. de Barros and C. Sens-Schönfelder for helpful discussions. We are grateful to A. Peltier and Meteo France for providing us with respectively extensometer and meteorological data. We thank F. Renard, I. Manighetti, and G. Poupinet for constructive comments concerning the manuscript. This work was supported by ANR (France) under contracts 05-CATT-010-01 (PRECORSIS) and COHERSIS.


Sarra Nouaoura

Nahla Abdellatif
email: nahla.abdellatif@ensi-uma.tn

Radhouane Fekih-Salem
email: radhouene.fs@gmail.com

Tewfik Sari
email: tewfik.sari@irstea.fr

Tewfik Sari Mathematical

R Fekih

Mathematical analysis of a three-tiered microbial food-web model with new input substrates

Keywords: Anaerobic digestion, Microbial ecology, Local stability, Operating diagram

Introduction

The anaerobic digestion (AD) is a natural process in which organic material is converted into biogas in an environment without oxygen by the action of a microbial ecosystem. It is used for the treatment of waste or wastewater and has the advantage of producing methane or hydrogen under appropriate conditions. The three-tiered model analysed here is based on Anaerobic Digestion Model No.1(ADM1) and has three substrates and three biomass variables. In this model, a chlorophenol-dechloronating bacterium is introduced in a two-tiered model involving two other organisms which are a phenol degrader and a hydrogenotrophic methanogen, see [START_REF] Wade | Emergent behaviour in a chlorophenol-mineralising three-tiered microbial food web[END_REF] and [START_REF] Sari | Generalised approach to modelling a three-tiered microbial food-web[END_REF]. The chlorophenol degrader uses both chlorophenol and hydrogen for growth, giving phenol as a product. Phenol is consumed by the phenol degrader forming hydrogen, which inhibits its own growth. The methanogen scavenges this hydrogen and acts as the primary syntroph. The aim of this study is to give a comprehensive analysis of the three-tiered model of [START_REF] Wade | Emergent behaviour in a chlorophenol-mineralising three-tiered microbial food web[END_REF], taking into account the three input substrates. We present a description of the model to be investigated and we give assumptions on the growth functions. We describe all steady states and their stability properties, in the case where the mortality terms are neglected. To describe the qualitative behavior of the system, we determine the operating diagrams of the model according to the operating parameters. The operating diagrams can be useful to interpret experimental results.

Conclusion

We have considered a mathematical model of three microbial species competing on three resources. We prove that the system can have eight types of steady-states. We give sufficient and necessary conditions for their existence and stability. We present numerical simulations which illustrate the demonstrated mathematical results.

Mathematical analysis of a three-tiered microbial food-web model

The model

We are interested in the mathematical analysis of the following system, obtained from the threetiered food-web model of [START_REF] Wade | Emergent behaviour in a chlorophenol-mineralising three-tiered microbial food web[END_REF], by using change variables and simplified notations:

where s 0 , x 0 , s 1 , x 1 , s 2 and x 2 represent the chlorophenol, the phenol and the hydrogen substrate and degrader concentrations, respectively. s in 0 , s in 1 and s in 2 are the inflowing concentrations and µ 0 (•, •), µ 1 (•, •) and µ 2 (•) are the growth functions. Under general hypotheses on the growth functions, we first prove the positivity and the boundedness of the solution of system (1)-(6).

Analysis of the steady-states

The analysis of the steady-states of model ( 1)-( 6) prove the existence of eight steady-states: the washout steady-state which always exists, a positive steady-state where all degrader populations are maintained and six other steady-states corresponding to the extinction of one or two degrader populations. We give the existence conditions of these steady-states as functions of the operating parameters. The local stability conditions of all identified steady-states are obtained using the Jacobian matrix. Without mortality terms, the latter matrix has a block triangular form. The stability of the system is determined by calculating eigen-values of three-order matrices and using the Routh-Hurwitz criterion.

Operating diagrams

The operating diagrams define regions of existence and local stability of equilibria. They show how the system behaves when we vary the four operating parameters s in 0 , s in 1 , s in 2 and D, the biological parameters being fixed. To plot the operating diagrams in the plane, we must fix two of the four operating parameters.


R Fekih-Salem

-T Sari

Operating diagram of a flocculation model in the chemostat

Keywords: Bi-stability, Chemostat, Flocculation, Limit cycles, Operating diagram MOTS-CLÉS : Bi-stabilité, Chémostat, Floculation, Cycles limites, Diagramme opératoire

The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. We show that the model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles.

RÉSUMÉ. L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. De plus, nous déterminons le diagramme opératoire qui décrit le comportement asymptotique du système par rapport aux paramètres de contrôle. Nous montrons que le modèle présente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables.

Introduction

In the culture of microorganisms, the processes of attachment and detachment of bacteria are well known and frequently observed. This phenomenon is manifested either by a fixation of microorganisms on a support as in the growth of biofilms or simply by an aggregation such as the formation of flocs or granules [START_REF]Mathematical modeling of biofilms[END_REF][START_REF] Thomas | Flocculation modelling: a review[END_REF]. In fact, the formation of flocs has a direct impact on growth dynamics, since the access to the substrate is limited for microorganisms within such structures. Nevertheless, it is only recently that they have been explicitly taken into account in mathematical models based on the chemostat (see the monograph [START_REF] Harmand | The Chemostat: Mathematical Theory of Microorganism Cultures[END_REF]).

This flocculation mechanism may explain the coexistence of microbial species when the most competitive species inhibits its own growth by the formation of flocs [START_REF] Haegeman | How flocculation can explain coexistence in the chemostat[END_REF]. In fact, these bacteria in flocs consume less substrate than planktonic bacteria since the attached bacteria have less access to the substrate, given that this access to the substrate is proportional to the outside surface of flocs. An extension of the model [START_REF] Haegeman | How flocculation can explain coexistence in the chemostat[END_REF] has been studied in [START_REF] Fekih-Salem | Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses[END_REF] when the growth rate of isolated bacteria of the most competitive species exhibits an inhibition. In this case, there may be coexistence around a stable limit cycle. The interested reader can refer to [START_REF] Fekih-Salem | Extensions of the chemostat model with flocculation[END_REF][START_REF] Fekih-Salem | Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses[END_REF] for a review of the different specific attachment and detachment rates used in the literature.

In this work, we consider the flocculation model of one species introduced in [START_REF] Fekih-Salem | Extensions of the chemostat model with flocculation[END_REF]. This model, which has been studied also in [START_REF] Fekih-Salem | Modèles mathématiques pour la compétition et la coexistence des espèces microbiennes dans un chémostat[END_REF][START_REF] Harmand | The Chemostat: Mathematical Theory of Microorganism Cultures[END_REF][START_REF] Rapaport | Properties of the chemostat model with aggregated biomass[END_REF][START_REF] Sari | Analysis of a model of flocculation in the chemostatguilf[END_REF], is written as follows: 8 > < > :

Ṡ = D(S in S) f (S)u g(S)v u = [f (S) D u ]u a(u + v)u + bv v = [g(S) D v ]v + a(u + v)u bv (1)
where S(t) is the concentration of the substrate at time t; u(t) and v(t) are, respectively, the concentrations of planktonic and attached bacteria at time t; f (S) and g(S) represent, respectively, the growth rates of isolated and attached bacteria; D and S in are, respectively, the dilution rate and the concentration of the substrate in the feed device; D u and D v represent, respectively, the disappearance rates of planktonic and attached bacteria.

We assume that isolated bacteria can aggregate with isolated bacteria or flocs to form new flocs with a rate a(u + v)u, where a is a positive constant, proportional to both the density of isolated bacteria u and the total biomass density u + v. Furthermore, the flocs can split and liberate isolated bacteria with rate bv, where b is a positive constant, proportional to their density v.

The study of this model [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF] has been limited to the biologically interesting case D v  D u  D, where D u = ↵D and D v = D, ↵ and belong to [0, 1] and represent, respectively, the fraction of planktonic and attached bacteria leaving the reactor. This case was proposed by [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF] to model a reactor with biomass attached to the support or to decouple the residence time of solids and the hydraulic residence time (1/D).

In this work, we study the model [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF] where D u and D v can be modeled as in [START_REF] Marsili-Libelli | Shock load modelling in the anaerobic digestion process[END_REF][START_REF] Shen | Bifurcation and stability analysis of an anaerobic digestion model[END_REF] by:

D u = ↵D + m u , D v = D + m v
where the non-negative parameters m u and m v representing mortality (or maintenance) rate are taken into consideration. Therefore, our study will not be restricted to the cases [START_REF] Fekih-Salem | Modèles mathématiques pour la compétition et la coexistence des espèces microbiennes dans un chémostat[END_REF][START_REF] Fekih-Salem | Extensions of the chemostat model with flocculation[END_REF][START_REF] Harmand | The Chemostat: Mathematical Theory of Microorganism Cultures[END_REF][START_REF] Rapaport | Properties of the chemostat model with aggregated biomass[END_REF][START_REF] Sari | Analysis of a model of flocculation in the chemostatguilf[END_REF], and the cases D < D u , D < D v or D u < D v , which are also of biological interest, will be investigated. Thus, our main objective in this article is to give a complete analysis of model ( 1) and to study its operating diagram in order to illustrate the behavior of the system according to the control parameters D and S in .

D v  D u  D, as in
This paper is organized as follows. First, we present in Section 2 some general hypotheses about the growth functions of flocculation model [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF]. Then, we analyze the existence and the local stability of steady states according to the dilution rate and the disappearance rates of planktonic and attached bacteria. In Section 3, we present the operating diagram in order to show the regions of emergence of multiplicity of positive equilibria according to the control parameters. Finally, conclusions are drawn in the last Section 4.

Hypotheses and model analysis

We use the following general hypotheses for growth functions f (S) and g(S):

(H1) f (0) = g(0) = 0 and f 0 (S) > 0 and g 0 (S) > 0 for all S > 0.

(H1) f (S) > g(S) for all S > 0.

Assumption (H1) means that the growth can take place if and only if the substrate is present. In addition, the growth rates of isolated and attached bacteria increase with the concentration of substrate. Assumption (H2) means that bacteria in flocs consume less substrate than isolated bacteria.

The following result shows that our model (1) preserves the biological meaning.

Proposition 2.1 For any non-negative initial condition, the solutions of system (1) remain non-negative and positively bounded. In addition, the set

⌦ = ⇢ (S, u, v) 2 R 3 + : S + u + v  D D min S in , where D min = min(D, D u , D v ),
is positively invariant and is a global attractor for the dynamics [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF].

The proofs of all results of this section are detailed in [START_REF] Fekih-Salem | Properties of the chemostat model with aggregated biomass and distinct dilution rates[END_REF]. In the following, we use the following notations:

'(S) = f (S) D u and (S) = g(S) D v , (2)
U (S) := '(S) ( (S) b) a [ (S) '(S)] and V (S) := ' 2 (S) ( (S) b) a [ (S) '(S)] (S) , (3)
H(S) := f (S)U (S) + g(S)V (S). (4)
From (H1), when equations f (S) = D u , g(S) = D v and (S) = b have solutions, they are unique and we define the usual break-even concentrations

u = f 1 (D u ), v = g 1 (D v ) and b = 1 (b). From (H2), if in addition D v D u , then v > u . When equations f (S) = D u or g(S) = D v or (S) = b have no solution, we put u = 1 or v = 1 or b = 1.

Existence of steady states

In order to study the existence of equilibria of model ( 1), we define the interval I by:

I = ( ] u , v [ if u < v ] v , min( u , b )[ if u > v .
(

) 5
We can state the following result:

Lemme 2.1 Under the assumptions (H1-H2), system (1) has the following steady states:

1) the washout E 0 = (S in , 0, 0), that always exists, 2) a positive steady state,

E 1 = (S ⇤ , u ⇤ , v ⇤ ) with S ⇤ solution of equation D(S in S ⇤ ) = H(S ⇤ ) (6)
where H is given by ( 4), u ⇤ = U (S ⇤ ) and v ⇤ = V (S ⇤ ), where U and V are given by ( 3). This coexistence steady state exists if and only if S ⇤ 2 I where I is defined by [START_REF] Fekih-Salem | Properties of the chemostat model with aggregated biomass and distinct dilution rates[END_REF].

The following proposition presents the number of positive steady states of (1).

Proposition 2.2 -When D u  D v , then the positive steady state E 1 = (S ⇤ , u ⇤ , v ⇤ ) exists if and only if S in > u . If it exists, it is unique.
-When D u > D v , then there exists at least one positive steady state in the case u < min( v , S in ) or v < min( u , b ) < S in . Generically, the system can have generically an odd number of positive steady states. When S in < min( u , b ) and v < u , then generically the system has no positive steady state or an even number of positive steady states.

Stability of steady states

In this section, we study the local asymptotic stability of each steady state of system (1). Let J be the Jacobian matrix of (1) at (S, u, v), that is given by

J = 2 4 D f 0 (S)u g 0 (S)v f (S) g(S) f 0 (S)u ' (S) a(2u + v) au + b g 0 (S)v a(2u + v) (S) + au b 3 5 . ( 7
)
The stability of the washout steady state is given as follows:

Proposition 2.3 E 0 is Locally Exponentially Stable (LES) if and only if S in < u and S in < b .
In the following, we analyze the stability of positive steady states. At E 1 = (S ⇤ , u ⇤ , v ⇤ ), the Jacobian matrix is given by

J 1 =
m 11 = D + f 0 (S ⇤ )u ⇤ + g 0 (S ⇤ )v ⇤ , m 12 = f (S ⇤ ), m 13 = g(S ⇤ ), m 21 = f 0 (S ⇤ )u ⇤ , m 22 = a(2u ⇤ + v ⇤ ) '(S ⇤ ), a 23 = b au ⇤ , m 31 = g 0 (S ⇤ )v ⇤ , m 32 = a(2u ⇤ + v ⇤ ) and m 33 = b au ⇤ (S ⇤ ). (8)
Operating diagram of a flocculation model in the chemostat 67

The characteristic polynomial is given by (9) According to Routh-Hurwitz criterion, E 1 is LES if and only if

P ( ) = 3 + c 1 2 + c 2 + c 3 , c 1 = m 11 + m 22 + m
c 1 > 0, c 3 > 0 and c 4 = c 1 c 2 c 3 > 0. ( 10
)
We have the following results:

Lemme 2.2 All m ij are positive for all i, j = 1, . . . , 3 with (i, j) 6 = (2, 3) and we have

c 1 > 0.
The next lemma shows that the sign of c 3 is given by the position of the curve of the function H(•) with respect to the line of equation y = D(S in S). More precisely, we give the link between the determinant of the Jacobian matrix J 1 at E 1 = (S ⇤ , u ⇤ , v ⇤ ) and D + H 0 (S ⇤ ). Proposition 2.4 One has c 3 = det(J 1 ) = '(S ⇤ )( (S ⇤ ) b)(D + H 0 (S ⇤ )).

Since the condition c 4 > 0 of the Routh-Hurwitz criterion (10) could be unfulfilled, we will study the behavior of flocculation model (1) according to the dilution rate and the disappearance rates of planktonic and attached bacteria. In fact, there exist four cases that must be distinguished:

Case 1: D u  D v  D, Case 2: D v < D u  D, Case 3: D v < D u and D < D u , Case 4: D u  D v and D < D v . (11)
To determine the local stability of the positive steady state in the first and second cases of (11), we will have need of the following. It was shown in [START_REF] Harmand | The Chemostat: Mathematical Theory of Microorganism Cultures[END_REF], see also [START_REF] Rapaport | Properties of the chemostat model with aggregated biomass[END_REF][START_REF] Sari | Analysis of a model of flocculation in the chemostatguilf[END_REF] that if D u = D v = D then the positive steady E 1 exists and is unique and LES if and only if S in > u . Actually, this result holds in case 1.

Proposition 2.6 In the case 1 (D u  D v  D), the positive steady state E 1 = (S ⇤ , u ⇤ , v ⇤ ) exists if and only if S in > u . If it exists, it is unique and LES.

The case 2 was solved in [START_REF] Fekih-Salem | Modèles mathématiques pour la compétition et la coexistence des espèces microbiennes dans un chémostat[END_REF] where it was shown that the stability depends only on the relative position of the curve of function y = H(S) and the straight line of equation y = D(S in S) that is to say, on the sign of D + H 0 (S ⇤ ). More precisely, we have:

Proposition 2.7 Let E 1 = (S ⇤
, u ⇤ , v ⇤ ) be a positive steady state. Assume that case 2 holds.

1

) If u < v : E 1 is LES if H 0 (S ⇤ ) > D and is unstable if H 0 (S ⇤ ) < D. 2) If u > v : E 1 is LES if H 0 (S ⇤ ) < D and is unstable if H 0 (S ⇤ ) > D.
In the case 3 of ( 11), when

D < D v  D u or D v < D  D u
c 4 can change sign by varying the control parameter S in such that the positive steady state E 1 could change its behavior without any collision with another steady state [START_REF] Fekih-Salem | Properties of the chemostat model with aggregated biomass and distinct dilution rates[END_REF]. In fact, numerical simulations show the emergence of stable limit cycles by Hopf bifurcations.

In the case 4 of ( 11), we always have u < v and H 0 (S) > 0. Therefore, from Prop. 2.4, it is deduced that in the case 4 of ( 11) we always have c 3 > 0. We were not able to find a set of parameters for which c 4 < 0, as in the case 3 of ( 11) and we conjecture that in this case the positive steady state E 1 which is unique as soon as it exists, is also LES as soon as it exists.

Operating diagram

The operating diagram shows how the system behaves when we vary the two control parameters S in and D in [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF]. All other parameters in (1) are fixed, such as growth functions and specific attachment and detachment velocities. In fact, they depend on the nature of the organisms and the substrate introduced into the chemostat. Note that this operating diagram has not been studied in the existing literature in the generic case where the disappearance rates are distinct.

If m u f (+1) then equation

f (S) = ↵D + m u (12)
has no solution. We assume that m u < f(+1). The equation ( 12) is equivalent to

D = f (S) := f (S) mu ↵
. Since f is increasing, then there exists a unique increasing function

F 0 : [0, Du [ ! [f 1 (m u ), +1[ D ! F 0 (D) = f 1 (D)
solution of equation [START_REF] Sari | Analysis of a model of flocculation in the chemostatguilf[END_REF] where Du = f (+1) mu ↵ . Note that if D Du , then equation ( 12) has no solution and we put F 0 (D) = +1. If m v g(+1) then equation

g(S) = D + m v (13)
has no solution. We assume that m v < g(+1). The equation ( 13) is equivalent to D = g(S) := g(S) mv . Since g is increasing, then there exists a unique increasing function

F 1 : [0, Dv [ ! [g 1 (m v ), +1[ D ! F 1 (D) = g 1 (D)
solution of equation [START_REF] Shen | Bifurcation and stability analysis of an anaerobic digestion model[END_REF] where Dv = g(+1) mv . Note that if D Dv , then equation [START_REF] Shen | Bifurcation and stability analysis of an anaerobic digestion model[END_REF] has no solution and we put

F 1 (D) = +1. If m v + b g(+1) then equation g(S) = D + m v + b (14)
has no solution. We assume that m v + b < g(+1). The equation ( 14) is equivalent to D = gb (S) := g(S) mv b . Since g is increasing, then there exists a unique increasing function

F 2 : [0, Db [ ! [g 1 (m v + b), +1[ D ! F 2 (D) = g 1 b (D)
solution of equation ( 14) where Db = g(+1) mv b . Note that if D Db , then equation [START_REF] Smith | The Theory of the Chemostat: Dynamics of Microbial Competition[END_REF] has no solution and we put F 2 (D) = +1.

In the following, we show the emergence of the bi-stability region with multiplicity of positive steady states in the case which corresponds to the saddle-node bifurcation with the appearance of two positive steady states. In order to illustrate the operating diagram, we considered the parameter values provided in Table 2 with the growth rates f and g of Monod-type:

f (S) = m 1 S k 1 + S and g(S) = m 2 S k 2 + S , (15)
where m i denotes the maximum growth rate and k i the Michaelis-Menten constant, i = 1, 2. Table 1 shows the existence and local stability of steady states E 0 , E 1 and E 2 in the regions I k , k = 0, 1, 2, of the operating diagram shown in figure 1 (b). The letter S (resp. U) means stable (resp. unstable). Absence of letter means that the corresponding steady state does not exist. Let i , i = 0, . . . , 3, be the respective curves of equations S in = F i (D) (see Fig. 1(a)). 0 and 3 separate the operative plan (D, S in ) at most in three regions, denoted I k , k = 0, 1, 2 (see Fig. 1(b)). The transition from the region I 0 to the region I 1 by the curve 3 (in magenta) corresponds to a saddle-node bifurcation with the appearance of two positive equilibria E 1 which is LES and E 2 which is unstable. The transition from the region I 1 to the region I 2 by the curve 0 (in red) corresponds to a transcritical bifurcation when the unstable steady state E 2 disappears and E 0 becomes unstable. For this set of parameters mentioned in Table 2, the numerical simulations show that the condition c 4 > 0 of the Routh-Hurwitz criterion is satisfied in the region I 1 , that is, the steady state E 1 is LES as long as it exists. However, this condition may not be satisfied for another set of parameters where the positive steady state can change behavior by a Hopf bifurcation with the emergence of stable limit cycle. In this case, the analysis of the operating diagram is the subject of on-going investigations.

Condition Region E 0 E 1 E 2 S in < F 3 (D) (Sin, D) 2 I0 S F 3 (D) < S in < F 0 (D) (Sin, D) 2 I1 S S I F 0 (D) < S in (Sin, D) 2 I2 I S

Conclusion

In this work, we have analyzed mathematically and through numerical simulations a model of the chemostat where one species is present in two forms, isolated and attached with the presence of a single resource. The new feature was that maintenance terms are added to removal rates in order to give a complete analysis of the flocculation model [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF]. The operating diagram shows the occurrence of the bi-stability region with multiplicity of coexistence steady states that can bifurcate through saddle-node bifurcations or transcritical bifurcations. However, the bi-stability could occur in the classic chemostat model [START_REF] Smith | The Theory of the Chemostat: Dynamics of Microbial Competition[END_REF] only when the growth rate is non-monotonic.

  33 , c 2 = m 12 m 21 + m 13 m 31 m 32 a 23 + m 11 m 22 + m 11 m 33 + m 22 m 33 , c 3 = m 11 (m 22 m 33 m 32 a 23 ) + m 21 (m 12 m 33 + m 32 m 13 ) + m 31 (m 12 a 23 + m 13 m 22 ).

Proposition 2 . 5

 25 In the cases 1 and 2 (D u  D and D v  D), we have c 4 > 0.

F 1 ( 1 DH

 11 D) < F 0 (D) < F 2 (D) for all D 2 [0, min( Du , Dv , Db )[. In this case, the function H is defined and decreasing on the interval I =] v , u [. It vanishes at u and tends to infinity as S tends to v (see Fig. 1(c)). Assume that H is convex. Thus, equation H 0 (S) = D has a unique solution S(D) 2 I =] v , u [ if and only if H 0 ( u )+D > 0, or also D > D with D solution of equation H 0 (F 0 (D))+D = 0. More precisely, since the function H 0 is increasing, then there exists a unique decreasing function S : [ D, Dv [ ! ] v , u [ D ! S(D) = H 1 (D) solution of equation H 0 (S) = D with H(S) = H 0 (S). Thus, we define the curve 3 of equation S in = F 3 (D) := ( S(D)) + S(D)

Figure 1 .

 1 Figure 1. (a) The case F1(D) < F0(D) < F2(D). (b) Operating diagram of (15). (c) Bi-stability and multiplicity of positive steady states when (D, Sin) = (2, 6) 2 I1.

Table 1 .

 1 Existence and local stability of steady states according to the regions in the operating diagram of figure 1.

Acknowledgments. We thank the financial support of the PHC UTIQUE project No. 13G1120 and of the Euro-Mediterranean research network TREASURE ( )

Operating diagram of a flocculation model in the chemostat 71

A. Parameters used in numerical simulations

Table 2. Parameter values used for (1) when the growth rates f and g are given by [START_REF] Thomas | Flocculation modelling: a review[END_REF].

B. References


Catalin Daniel Galatanu
email: catalin.galatanu@tuiasi.ro

Laurent Canale
email: laurent.canale@laplace.univ-tlse.fr

Measurement of Reflectance Properties of Asphalt using Photographical Methods

Keywords: EN 13201, Reduced Luminance Coefficient, Asphalt albedo, Luminance map, Reflectance uncertainty, street lighting, light pollution I

HAL is

INTRODUCTION

The paper identified a parameter that underlies the calculation of the luminance of a street lighting system, the reflectance qualities of the asphalt. Usually predetermined data are used, defined for large categories of asphalt (Europe or USA), with few possibilities to estimate the real state of the materials. It is a challenge that while looking for highly accurate results in terms of calculation, for example, the reflectance factor is responsible for a high degree of approximations.

II. DIFFERENT MOTIFS FOR REFLECTANCE MEASUREMENT

The problem of asphalt, as a solution for roads, is beginning to be questioned. In this very recent article [START_REF] Williams | End of the asphalt road?[END_REF] we are challenged with the vision that the asphalt, as we know it, will be replaced by entirely other material, with various reasons (solar energy with photovoltaic or thermoelectric conversion, reuse of waste material). For these new materials, for which their behavior over time is not known, it is all the more important to measure the reflection factor.

A. Harvesting Solar Energy and Reflectance Factor

One of the most promising directions of road evolution is the production of electricity through photovoltaic conversion [START_REF] Duarte | A new pavement energy harvest system[END_REF]. Obviously, the main objective will be the transparency and durability of the surface, so measuring reflexivity is a need. But there is also the possibility of harvesting solar energy through thermal or thermoelectric conversion [START_REF] Papadimitriou | A review on the latest trend of Solar Pavements in Urban Environments[END_REF]. Even if the amplitude of this method is less developed compared with PV conversion, the main objective becomes to obtain as high absorption coefficient as possible (albedo as low as possible), which needles contradict the requirement to obtain high luminances during night time, for good visibility.

In other research concerning global warming and infrared asphalt response [START_REF] Baumgartner | Infrared reflectance factor of various asphalts[END_REF] one discover the confirmation that the various types of asphalt have responded very differently to each other, depending on composition (structure) and wear or age. An important conclusion in [START_REF] Baumgartner | Infrared reflectance factor of various asphalts[END_REF] is that "the dependence of the diffuse reflectance factor on the light spot size, in order to determine a minimum light spot size for any further optical study. By comparing the BRF (bidirectional reflectance factor) to a nearly-Lambertian Spectralon® white standard", the conclusions are that the asphalt is in general a good diffuse scatterer. This statement will be contradicted later, and we will confront it with our own measurements.

When a lower IR response is required, the asphalt with high albedo is reached, but it contradicts other very current objectives, such as lane border detection [START_REF] Schomerus | Camera-based Lane Border Detection in Arbitrarily Structured Environments[END_REF]. In this working hypothesis the light color is a disadvantage, because the vision requires a high luminance contrast between asphalt and markings, in order to achieve good visibility.

B. Promoting Energy Efficiency and Reflectance Factor

Another distinct direction where asphalt is involved is that of energy efficiency of lighting systems. This can be achieved through the light sources themselves (and we have seen the obvious progress of LED sources), but there may be other ways to increase energy efficiency. One of them is dimming, but not in traditional manner. Dimming that follows an original philosophy is presented in [START_REF] Rusu | Calculation of energy economy by dimming led lamps with maximum performance[END_REF]. Here it is based on the finding that in the field it is not possible to ensure the constant step between the lighting poles, as is taken into account in the design phase. The distance between poles is almost nonstop reduced by several meters, due to the intersections and the access paths in the properties. These reductions can be offset with custom dim ratio for almost every pole. In relation to this strategy one can propose another factor of dimming, which takes into account that in the project calculations are carried out for new asphalt, so it is a dimming reserve that can be applied after a number of years, along with the wear of the asphalt. For this, however, we need to measure in-situ reflectance, which is also our objective.

There are also classical approaches, where the lighting system is to be modernized [START_REF] Zdunic | Public lighting -road to energy efficiency[END_REF], but the problem of measuring reflectance factor is neglected, and it is mentioned only:

-Data on poles; -Geometry arrangements.

Energy efficiency can also be achieved by precise calculations, as in [START_REF] Lipnický | Influence of the calculation grid density to the selected photometric parameters for road lighting[END_REF], which is a classic and traditional approach. But if there is a purpose of reducing the approximations from 20% to 10% and then even to 5% and finally to 1% it is not allowed to avoid the parameter on which the luminance directly depends, i.e. reflectance factor of asphalt, as seen in [START_REF] Lipnický | Influence of the calculation grid density to the selected photometric parameters for road lighting[END_REF].

Retrofit solutions can be another approach to energy efficiency. In [START_REF] Ciobanu | Analysis on the possibility of using retrofit solutions for increasing the energy efficiency of public lighting systems[END_REF] the optimization of solutions with the help of the computing power of DIALUX is used, but the reflectance answer of asphalt influence is not accessible, nor is it mentioned, which calls into question the entire optimization of [START_REF] Ciobanu | Analysis on the possibility of using retrofit solutions for increasing the energy efficiency of public lighting systems[END_REF].

Energy efficiency is also obtained by considering natural lighting during twilight, which changes the time and manner of connecting artificial lighting [START_REF] Sedziwy | A New Approach to Power Consumption Reduction of Street Lighting[END_REF]. After finding that natural lighting is isotropic (after sunset, when the sky is still bright), it reaffirms what was actually known, that artificial lighting is anisotropic, thus contradicting the statement that asphalt is perfectly diffuse, from [START_REF] Baumgartner | Infrared reflectance factor of various asphalts[END_REF].

C. Asphalt Reflectance and Light Pollution

The problem of asphalt reflection can't be dissociated from that of light pollution. Even if light incident on the road is not considered light pollution, what is reflected contributes to light pollution. In [START_REF] Fryc | Lighting of recreation grounds as a source of sky glow -The influence of luminaire type on this phenomenon[END_REF] is found the exact study of this parameter, the reflective properties of the soil (clear spectral reflection of soil, asphalt, and concrete) and the sky glow.

In [START_REF] Tabaka | Landscape Lighting as a Source of Light Pollution -the Effect of the Seasons on this Phenomenon[END_REF] this analysis is continued, by extending it to the extreme situation of summer -winter. The crowns (branches) of the trees are also clearly modeled, with or without the presence of leaves or snow. However, the arguments in [START_REF] Tabaka | Landscape Lighting as a Source of Light Pollution -the Effect of the Seasons on this Phenomenon[END_REF] are also valid for street lighting, without the need for additional arguments.

Optimization of lighting systems can benefit from modern tools, such as genetic algorithm [START_REF] Bayer | Road lighting design by means of genetic algorithm[END_REF]. Here, however, an interesting thing can be found, because the whole optimization refers to the lighting level. Or, if the reflection factor is not considered, then the calculation depending on the lighting can generate oversizing. The approach method is even more surprising when the precise modeling of the light pollution is desired, for which the level of illumination in the areas near the road is evaluated.

There are also fewer approaches, such as [START_REF] Doulos | A decision support system for assessment of street lighting tenders based on energy performance indicators and environmental criteria: Overview, methodology and case study[END_REF], where ESCO-type projects are pursued several years after commissioning. It is shown that there are parameters that are not yet in current use. Utilance [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF] is one of them, and essentially expresses the ratio between the incident luminous flux on the road and the actual luminous flux emitted by the luminaire. More interestingly, it is emphasized in [START_REF] Doulos | A decision support system for assessment of street lighting tenders based on energy performance indicators and environmental criteria: Overview, methodology and case study[END_REF], it is the Installation Lighting Factor, which includes the average luminance of the road and therefore reflectance of the road, with another argument for the necessity of its measurement. Global image of all these factors are presented in Fig. 1.

III. THE COMPLEXITY OF REFLECTANCE MEASUREMENT

AND THE STREET LIGHTING PERFORMANCE All the arguments so far lead us to the importance of measurement of reflectance factor of the asphalt. In such situations, as those of entrances to road tunnels [START_REF] Doulos | Minimizing lighting consumption in existing tunnels using a no-cost fine-tuning method for switching lighting stages according revised luminance levels[END_REF], the contrast of luminances is important to obtain a safe visibility. In these visual scenes, the reflectance of the asphalt is evaluated in the context of the other parameters:

-The brightness of the sky (clear or cloudy); -Road luminance (day, night); -Reflectance and luminance of vegetation; -Emissivity of buildings; -The luminance of the rocks and the mountainous landscape. In contrast to [START_REF] Doulos | Minimizing lighting consumption in existing tunnels using a no-cost fine-tuning method for switching lighting stages according revised luminance levels[END_REF] is [START_REF] Li | The development of LED street lamp pavement lighting effects testing system[END_REF], where there is presented a very complex system of in-situ measurement of road lighting systems, which uses a frame equipped with multiple sensors, a frame carried by a vehicle on the road. Global results of illumination and level of uniformity are obtained, but we do not find any information about luminance. However, a positive example is [START_REF] Rusu | Assessment of Conflict Area Parameters Measurements by Using Photographic Methods[END_REF], which demonstrates the importance of analyzing the distribution of luminances, even if only illumination can be accepted for conflict areas [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF]. Acceptance of illumination is justified by the fact that in conflict areas (junctions) visibility must be ensured for multiple relative driver-target configurations. The photographic method in [START_REF] Rusu | Assessment of Conflict Area Parameters Measurements by Using Photographic Methods[END_REF] demonstrates that global (otherwise unavailable) information can be obtained that includes reflectance of asphalt, including lines or other signs.

However, about the complexity of the problem we are warned in [START_REF] Zhang | Influence analysis of road reflective characteristic on roadway luminary design[END_REF], where it is stated that for certain luminance coefficients q(β, r) [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF], since specular reflection of road surface, "optimal values for luminance and illumination cannot be obtained simultaneously". This contradiction is an additional argument for measuring the reflectance factor of asphalt.

The same parameter acquires another relevance for tropical areas, where high reflectance asphalt is pursued [START_REF] Tran | Strategies for Design and Construction of High-Reflectance Asphalt Pavements[END_REF]. It is interesting that the implications are analyzed only in the diurnal hypothesis, while the benefits on street lighting could be much more spectacular.

But the actual measurements of these parameters are not simple, as seen in [START_REF] Puttonen | Measurement of Reflectance Properties of Asphalt Surfaces and Their Usability as Reference Targets for Aerial Photos[END_REF], for which some aspects of the experimental program are noted:

-Measurements carried out over three years; -Nine types of asphalt; -Two types of wear materials; -Asphalt concrete with particles of 11 -16mm; -Different ages, between 2 and 10 years; -Different but moderate wear.

It is obvious that such a systematic approach exceeds the objective of a street lighting project, which needs to be able to achieve an optimal sizing for the situation at a given time.

The final argument for this research is found in the reference work, with monographic character [START_REF] Fotios | Road lighting research for drivers and pedestrians: The basis of luminance and illuminance recommendations[END_REF], where the specific standards for street lighting are analyzed, in their evolution. It turns out that many of the imposed values are quite arbitrary. There are also interesting statements, namely "in-situ luminance measurement could indicate variations up to 45% from the design value". The explanation is also provided: "One contribution to this difference is uncertainty in the road surface reflectance data, for example the age and the traffic volumes".

The main situations related to reflectance measurement of the asphalt is presented in Fig. 2: Fig. 2. The problems related to the reflectance measurement of asphalt.

Overall, the uncertainty that exist in many lighting designs due the lack of measurements of asphalt reflectance must be reduced.

IV. REDUCED LUMINANCE COEFFICIENT ASSESSMENT

FOR ASPHALT TYPE C2, N1 AND W4 In order to prepare the measurement program for reduced luminance coefficient r it is necessary to analyze in advance the range of variation of this parameter for the existing data [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF], respectively for some types of asphalt. The values are analyzed for the points for which in [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF] the calculation of the luminance for an observer located at a height of 1.5 m and a distance of 60 -100 m is indicated. In Fig. 3 are indicated a number of 13 calculation points, distributed with a step of 3 m along the traffic lane in the vicinity of the poles (H=10m). The values of the angles β and ε in Fig. 3 for the measuring points are indicated in Table 1. It should be noted that for the following series of measuring points (towards the road axis) these values are very close, which allows us to significantly reduce the number of values for which reduced luminance coefficient r must be measured, without the need to complete the whole value matrix, as indicated in [15, p.17] for tgβ between 0 and 12 and ε between 0 and 180°. This greatly limits the number of elements in the matrix with values of reduced luminance coefficient. Fig. 3. Points for luminance calculation, according to [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF].

In Table 1 it can be seen that after the first 3-4 calculation points near the pillar, the angle β reaches 10° ÷ 5°, and the angle ε reaches 55° ÷ 75°. These areas can reduce the amount of data that needs to be measured and analyzed. The next preparatory stage for the measurement program is the estimation of the range of variation of the reflectance factor, for various types of asphalt. In [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF] one use another variable, namely reduced luminance coefficient, which is used to calculate the road luminance L for the standard observer, according to [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF]:

= × × ∅ × × 10 (1)
Where I -Lighting intensity (cd/klm); r -Reduced luminance coefficient; Ø -Luminous flux;

MF -Maintenance factor;

H -Mounting height of the luminaire.

Equation ( 1) is valid for specular reflection, for which the reduced luminance coefficient r models this reflection. If we accept the hypothesis that the reflection would be perfectly diffuse, then the asphalt would be described with a material with reflectance factor ρ that would produce, for the considered angles, the same luminance L:

= × (2)
Where E is the illuminance on the calculation point, produced by the same lighting intensity I:

= × cos × ( 3
)
Where l is the distance between the luminaire and the calculation point.

In (2) one include (3) and we write the equality with (1):

× × ∅ × × 10 = × cos × (4)
Making the necessary operation the reflectance factor will be:

= × 10 (cos ) (5)
It is necessary to specify that since reduced luminance coefficient r is not constant, neither reflectance ρ will be a constant, but a function of β and ε that is:

( , ) = ( , ) × 10 (cos ) (6)
For the first 14 calculation points in the vicinity of the column and asphalt type C2, a variation presented in Fig. 4 is obtained. It is observed that one start from reflection coefficients of ρ = 0,15 under the column (ε = 0°) and the values increase as the angle of incidence increases to 75° -85°. The results for reflectance factor for W4 asphalt is presented in Fig. 6: The results shown in Fig. 6 do not allow us to accept that it could be a reflectance factor, being visible an obvious amplification effect. Our conclusion is that the hypotheses that led us to (6) are valid for asphalt with porous structure, and lose their validity for glossy asphalt, and even more so with wet surface. For specular reflection certainly a reflectance factor as (6) does not make sense. These observations are useful in the processing and careful interpretation of data from the reflectance factor measurement.

V. EXPERIMENTAL MEASUREMENTS

For the measurement program we started from the sourcepoint geometry of measurement in Fig. 3 [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF] and with the range of values for ε and β from matrix of the reduced luminance coefficient r [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF]. Especially to cover the maximum range for tgε, a distance of max. 12m of the target point with respect to the optical axis of the light source is necessary, if lighting source is located at a height of 1m, a configuration that generates a scale factor of 1:10. To test the measuring principle, a working surface of 5 m length was used, according to Fig. 7. The digital camera calibrated for luminance measurement is placed at a height of 15 cm and a distance of 6 m, to keep the angles σ of the observer as in Fig. 3 [START_REF]EN 13201, Road lighting -Part 3: Calculation of performance[END_REF]. For the simplicity of the presentation, we will work only on the observer-light source direction, ie β=0° and β =180°. The obtained luminance field is presented in Fig. 8: In Fig. 8, the AB line is the measurement domain, corresponding to tg ε = (0 to 2.5), β = 0 and β =180. The test surface was a perfect Lambertian material (gray cardboard), with the intention of obtaining a controlled illumination (from a punctiform source), respectively the known incident intensity in each point for which the luminance is measured. The distribution of the illuminations measured and calculated on the AB direction are available in Fig. 9: With this known distribution for illumination and therefore for the incident light intensity at each point, it was intended to check the diffuse reflection of the cardboard, respectively to validate the entire measuring chain. The obtained results showed, however, that the cardboard reflection is not perfectly diffuse, having a fairly obvious directional component. This aspect can also be seen in Fig. 8. In Fig. 9 the luminance distribution (cd/m 2 ) is indicated for 250 elements in the vector with results (abscissa). For the 5 m long (AB), i.e. a measurement density of 2 cm. An important observation is necessary, the power of the punctiform lamp and the level of luminance on the test surface was chosen to make luminaires with two orders of magnitude higher than those in street lighting, so that measurements can be made in the presence of street lighting. Fig. 10 indicates that the cardboard reflection is not perfectly diffuse. Zone AO, for which β = 180° has a much lower reflection than zone OB, for β = 0°. The results represent a demonstration of the method by which the luminance values of an area with a determined geometry can be extracted, by a single imaging measurement. From which then the reduced luminance coefficient could be calculated.

VI. CONCLUSIONS

Fig. 1 .

 1 Fig. 1. Influence of reflectance factor of asphalt on other lighting connected aspects.

Fig. 4 .

 4 Fig. 4. Reflectance factor in polar coordinates (ε) for asphalt type C2.

Fig. 4

 4 Fig. 4 also forces us to analyze what happens to the reflectance factor for other types of asphalt. In Fig.5 the variation of reflectance factor for C2 asphalt together with N2 type asphalt is presented. A different range of variation is observed, but with the same tendency to increase the reflection for large, sharp incident angles. The relative brightness of N2 asphalt is much lower than that of C2 asphalt. Even if weighted average luminance coefficient (Q0) of C2 Asphalt (CIE) is equal with weighted average luminance coefficient of

Fig. 5 .

 5 Fig. 5. Reflectance factor in polar coordinates (ε) for asphalt type C2 (blue and '+' and asphalt type N2 (red and 'x').

Fig. 6 .

 6 Fig. 6. Reflectance factor in polar coordinates (ε) for asphalt type W4.

Fig. 7 .

 7 Fig. 7. The mock-up for measurements using imageing method.

Fig. 8 .

 8 Fig. 8. Luminance map (cd/m 2 ) for the mock-up scene, AB is the measurement domain.

Fig. 9 .

 9 Fig. 9. The illumination level (lux) for the AB direction in Fig.8.

Fig. 10 .

 10 Fig. 10. Luminance distribution (cd/m 2 ) for AB direction from Fig.7 and Fig.8.

TABLE I .

 I VALUES FOR ANGLES BETA AND EPSILON FOT THE POINTS FROM FIG.3

		D1	D2	β	ε
	Point no.	m	m	grades	grades
	1.	3	0	90.00	16.70
	2.	3	3	45.00	22.99
	3.	3	6	26.57	33.85
	4.	3	9	18.43	43.49
	5.	3	12	14.04	51.05
	6.	3	15	11.31	56.83
	7.	3	18	9.46	61.28
	8.	3	21	8.13	64.76
	9.	3	24	7.13	67.54
	10.	3	27	6.34	69.79
	11.	3	30	5.71	71.65
	12.	3	33	5.19	73.21
	13.	3	36	4.76	74.53


Soukaina Sekkal
email: sekkalsoukaina92@gmail.com

Laurent Canale
email: laurent.canale@laplace.univ-tlse.fr

Adel Asselman
email: adelasselman@gmail.com

Flexible Textile Antenna Design with Transparent Conductive Fabric Integrated in OLED for WiMAX Wireless Communication Systems

Keywords: flexible antenna, OLED, VeilShield, wireless communication, 100% polyester, transparent conductive fabric. I

A new flexible antenna made entirely from a transparent conductive fabric VeilShield has been designed to be integrated in OLED light sources as well as flexible or rollable displays. It was layered on a 100% polyester support with a thickness of 1.5 mm and achieves a good adaptation and high gain. The simple and flexible patch antenna has been designed to operate at two frequencies bands: the first one operating at 3.15 GHz in S-band and the second operating at 3.5 GHz for WiMAX wireless communication systems. We have evaluated and tested its performances, including the reflection coefficient, the gain, the radiation pattern and the surface current distribution, with gain values of 5.76 dB and 1.66 dB respectively. This article demonstrates the applicability of the material proposed for the design of flexible antennas integrated into OLED light sources while maintaining gain performance comparable to conventional planar antennas.

INTRODUCTION

The growing need for data throughput will require diversification and multiplication of communication channels which will lead to the development of antennas integrated into existing products. On the other hand, due to their long lifespan, easy-to-make products, efficiency and high quality of light, OLED technologies are likely to be the next generation of light sources [START_REF] Zou | Recent Advances in Organic Light-Emitting Diodes: Toward Smart Lighting and Displays[END_REF]. Among its many advantages that can be useful for lighting as well as displays, let us mention that they are also flexible and even rollable. With the development of smart windows, these will integrate OLED as well as other versatile functions [START_REF] Andrade | Novel Smart Windows Based on Transparent Phosphorescent OLEDs[END_REF][START_REF] Canale | Imaginons l'éclairage du Futur », Dossier Mieux Voir[END_REF]. In the same spirit of integration, we present here the first technological step of a flexible antenna aiming at being integrated into OLED light sources. Textiles have emerged in recent years as promising materials for the development of antennas. This allows the many smart wearable wireless electronic systems to communicate through wireless networks like WLAN and WiMAX.

A lot of research has been performed on the various materials for the construction of wearable antennas since 1997 when wearable antenna was initially defined as an antenna designed to be an integral part of clothing [START_REF] Abramo | Fabrication and testing of the COMWIN vest antenna[END_REF][START_REF] Salonen | Effect of conductive material on wearable antenna performance: a case study of WLAN antennas[END_REF]. A flexible antenna is a key component in emerging wearable wireless electronic devices which often should have additional characteristics such as flexibility and robustness which demands the consideration of flexible nonconventional materials to replace traditional printed circuit boards.

Significant amount of research efforts can be found in the literature for nonconventional materials which opens up new trends in wireless communications such as conductive fabrics [START_REF] Cicchetti | Wideband and UWB antennas for wireless applications: A comprehensive review[END_REF], copper tapes [START_REF] Hu | Bending and On-Arm Effects on a Wearable Antenna for 2.45 GHz Body Area Network[END_REF], silver paste [START_REF] Ha | Reconfigurable Beam Steering Using a Microstrip Patch Antenna With a U-Slot for Wearable Fabric Applications[END_REF], conductive ink [START_REF] Yang | RFID Tag and RF Structures on a Paper Substrate Using Inkjet-Printing Technology[END_REF], and conductive threads [START_REF] Zhang | Embroidered wearable antennas using conductive threads with different stitch spacings[END_REF] are used to form the antenna radiating element and polymer, using cotton and felt [START_REF] Cicchetti | Wideband and UWB antennas for wireless applications: A comprehensive review[END_REF] as substrate. These materials are widely used in industry, for various applications in fields ranging from energy to electronics or security. They are for example required in the manufacture of touch screens (telephones, tablet PCs, GPS, game consoles, automatic ticketing ...).

In this work, the flexibility was integrated to design a fully fabric flexible antenna employing a transparent conductive fabric VeilShield and insulating 100% polyester fabric. The simple patch antenna has been proposed for high gain operation at 3.15GHz and to be used for WiMAX Wireless communication systems at 3.5GHz.

II. MATERIAL CHARACTERISTICS

A. Conductive Fabric

For the rectangular patch, radiating element and the ground plane of the antenna conductive parts we used the parameters of the transparent fabric VeilShield. This fabric consists of woven meshed polyester fibers, coated with nickel/zinc-blackened copper for greater corrosion resistance. Its thickness is 0.057 mm, it has a very low sheet resistance of 0.089 Ω/sq. The electrical conductivity was calculated based on :

(1)

Where and are the sheet resistivity and the sheet thickness respectively.

The calculated theoretical transparency of the fabric is , using [START_REF] Hautcoeur | Transparency and electrical properties of meshed metal films[END_REF]: Where p is the pitch of the mesh with a size of about 620 µm and s was the strip width had a size of 90 µm, as shown in Fig. 1.

  (2)

B. Dielectric Properties of 100% Polyester

This fabric or textile is made of polyester threads or fibers. Its dielectric constant is Ɛ = 2.85, while the loss tangent is δ = 0.02. In addition, polyester is very stable to humidity and to attack moisture, flexible, even having greater resistance and resilience of the deformations of 40 % [START_REF] Rey | Mechanical strength parameters on polyester fabrics. Treatment applied in support of large canvas painting:" the expulsion of the merchants from the temple[END_REF].

III.

ANTENNA DESIGN One fully fabric antenna was designed to operate at 3.15 GHz and 3.5 GHz measured at (

) to demonstrate the proposed concept of 100 % polyester embedding of transparent fabric to design flexible antennas.

The antenna had a size of , whereby the microstrip feed line is applied with a width Wf = 4.12 mm to ensure a 50 Ω input impedance. The antenna geometry and its parameters are shown in Fig. 2 In the proposed antenna design, a full ground plane is used to reduce back radiation. Polyester was chosen for antenna substrate due to its high resistance to air pollutants, toughness and good elastic recovery strain [START_REF] Rey | Mechanical strength parameters on polyester fabrics. Treatment applied in support of large canvas painting:" the expulsion of the merchants from the temple[END_REF].

IV. SIMULATION AND RESULT

The performance of the flexible antenna in terms of reflection coefficient and gain is demonstrated in Fig. 3 and Fig. 4, respectively.

From the reflection coefficient of the proposed antenna, it appears that the antenna is exhibiting resonance at two frequencies: the first operating at 3.15GHz, suitable for S band applications (2 to 4GHz), the second at 3.5 GHz for WiMAX Wireless communication systems.

The variation of the gain of the flexible patch antenna is represented in Fig. 3 in the frequency band from 3 GHz to 3.6 GHz.

It can be observed that the proposed antenna has a high gain of 5.76 dB at 3.15 GHz and a gain of 1.66 dB at 3.5 GHz. The gain tends to decrease as the operating frequency increases. This results from increase with frequency of the dominant losses of the conductive fabric. It can be noted that the overall performance of the proposed design in terms of gain at the frequency 3.15Ghz and 3.5GHz is better than in other bandwidths.

The 3D radiation pattern for the proposed antenna is shown in Fig. 5, illustrating the orientation and the level of the main lobe. This antenna exhibits an omnidirectional radiation pattern with a maximum gain of 1.66 dB. The far field radiation patterns of the proposed patch antenna in E plane and H plane at the frequency 3.5GHz are illustrated in Fig. 6. In general, the figure depicts stable power distribution in the different radiation planes at the resonant frequency 3.5 GHz. Fig. 6 (a) shows E-plane radiation pattern at 3.5 GHz frequency, its main lobe magnitude is 1.07 dB. It can be seen that E-plane radiation pattern is close to omnidirectional. To further study the property of the proposed antenna, we also simulate the surface current distribution for the highest resonant frequency at 3.5 GHz (Fig. 7).

As expected, in the same figure, the strong resonant current flows along the patch surface. More precisely the high density current flows occur at the edge of the conductive layer.

V. CONCLUSIONS

In this work, a flexible and optically transparent purely textile patch antenna for wireless communications was studied with the purpose of being integrated into OLED devices, as well as light sources or flexible displays. This way, the same device is equipped with both lighting and communications functions. The substrate uses micro-strip line for Wireless communication systems WiMAX operating at 3.5 GHz. We have shown that antenna design techniques perform well even for textile substrates and conductive textiles consisting of transparent conductive fabric integrated with polyester. The antenna exhibits omnidirectional radiation coverage with a gain of 1.07 dB at 3.5 GHz for E-Plane polarization (TABLE II). The only drawback is a decrease of the gain at higher frequencies as the dominant losses of the conductive fabric increase with frequency [START_REF] Xu | Wearable Textile Shielded Stripline for Broadband Operation[END_REF].

  Funded by French Ministry of Europe and Foreign Affairs and Moroccan Ministry of Higher Education and Scientific Research as a part of Program Hubert Curien "Maghreb" MELINA (Mastering Efficient Lighting in North Africa) granted to L.C.

Fig. 1 .

 1 Fig.1. Transparent fabric tissue (a) zoomed view and (b) photo.[START_REF] Elmobarak Elobaid | A Transparent and Flexible Polymer-Fabric Tissue UWB Antenna for Future Wireless Networks[END_REF]

Fig. 2 .

 2 Fig. 2. Configuration of the flexible antenna using microstrip line

Fig. 3

 3 Fig. 3 Performance of the proposed fully fabric and flexible antenna in terms of reflection coefficient.

Fig. 4 .

 4 Fig. 4. Performance of the proposed fully fabric and flexible antenna in terms of Gain.

Fig. 5 .

 5 Fig. 5. The 3D radiation pattern for the proposed antenna at 3.5GHz.

Fig. 6 (

 6 Fig.6 (b) shows the global visualization of the H-plane radiation pattern at 3.5 GHz frequency, its main lobe magnitude is -1.1 dB. Characteristics of radiation pattern are given in TABLE II.

Fig. 6 .

 6 Fig. 6. Simulated radiation pattern of the proposed antenna at 3.5 GHz (a) E-Plane, (b) H-Plane

Fig. 7 .

 7 Fig. 7. Surface current distribution of the WiMAX antenna at 3.5GHz.

TABLE I .

 I DIMENSIONS OF THE PROPOSED DESIGN

	Design	Value(mm)
	Parameters
	Wp	60
	Lp	35
	Wg	58
	Lg	52
	Lf	10
	Wf	4.12
	Lf1	9
	Wf1	10

TABLE II

 II

	.	RADIATION CHARACTERISTICPATTERN OF THE PROPOSED
			ANTENNA AT 3.5 GHZ
		Plane	E	H
	Property
	Frequency	3.5	3.5
	Main lobe	1.07	-1.1
	magnitude
	Main lobe	323	325
	direction
	Angular width	61.1	122.1
	(3 dB)
	Side lobe level	-3.4	-9.9

ACKNOLEDGMENT

This research is part of the PHC "Maghreb" (Programme Hubert Curien) MELINA (Mastering Efficient Lighting In North Africa) and benefits from the financial support of the French Ministry of Europe and Foreign Affairs and Moroccan Ministry of Higher Education and Scientific Research.

The authors would like to thank their colleague Pascal Dupuis from University Paul Sabatier, Toulouse, France, for proofreading this document and making valuable suggestions.


Maurras Ulbricht Togbe

Yousra Chabchoub

Aliou Outliers Boly

Detection

OUTLIERS DETECTION METHODS: A SURVEY

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

OUTLIERS DETECTION METHODS: A SURVEY

Maurras U. TOGBE 1 , Yousra CHABCHOUB 2 , Aliou BOLY 3 1 maurras.togbe@isep.fr, 2 yousra.chabchoub@isep.fr, 3 aliou.boly@ucad.edu.sn

Context

• The emergence of data streams issued from a variety of sources with an always increasing rate requires efficient anomalies detection algorithms to identify suspicious behavior.

• According to the knowldege about the available dataset many supervised, semi-supervised or unsupervised anomalies detection techniques can be applied.

Application Domains

Anomalies detection is an actual issue in many fields:

Constraints and challenges

Constraints of the data stream context:

• A continuous generation and reception of the data stream for analysis

• A high and variable data stream rate

• A poor quality, so that the data stream needs to be first cleaned Data stream constraints engender several challenges for the online outliers detection methods:

• A single pass over the data stream

• A fast online analysis (low complexity)

• No a priori knowledge on data distribution

• Adaptation for distributed processing

• Ability to provide Specific information about the anomaly (start-time, intensity)

Classification of the outliers detection methods

Only certain existing anomalies detection methods are adapted to data streams and time series [START_REF] Charu | Outlier Analysis[END_REF].

Performance metrics: -Detection accuracy (False positives, False negatives) -Response time (anomalies detection delay) -Assumptions on data distribution -Scalability (adaptation to a high data dimension or high rate data stream) -Adaptation for distributed processing -Complexity -Memory consumption

Comparison of outliers detection methods

Approaches

Future Works

• Benchmark of several existing outliers detection methods based on the different performance metrics.

• Focus on the distributed outliers detection methods and design a distributed version for some existing outliers detection techniques.

  parametric methods are adapted to data stream context -Parametric method can't be used in data stream -Non-parametric methods can only be used for low dimensional data stream Distance-based -Adapted for global outliers detection -Not adapted for non-homogeneous densities -High computational cost for high dimensional data stream Density-based -Adapted for local outliers detection -High complexity -More efficient than distance-based methods -Not effective for high dimensional data stream Clustering-based -Adapted for clusters identification -Not optimized for outliers identification


New approaches to the synthesis of aminoalkyl-o-carboranes

1. Lewis acid-catalyzed amination of alcohols 5

Application to o-carboranylmethyl alcohols

X

One simple and practical access to benzylic amines is the direct amination of the corresponding alcohols (easily available compounds) catalyzed by Lewis acids. In this way, it is avoided the necessary previous transformation of the hydroxyl function into a good leaving group that could then be displaced by an amine.

The reaction of diphenylmethanol with non-coordinating amines gives the desired amine products 1, but also the undesirable symmetrical ether 2, due to competition of the alcohol as a nucleophile (Scheme 1).

Scheme 1

The proportions of the resulting compounds depend on the nature of both the Lewis acid and the amine derivatives. Although nitroaniline gives similar yields of the amination products with Au(III), Fe(III) and BF 3 as catalysts (Table 1), for other amines, NaAuCl 4 seems to be the best catalyst in terms of reaction selectivity.

Table 1 Scheme 2

The reaction also gives good results replacing one or two phenyl groups in diphenylmethanol by thiophene units (Scheme 2), by substituting the phenyl group with electron donating (-OMe) or mild electron withdrawing functions (-CF 3 ). Monobenzylic substrates also react under the same reaction conditions to give the amination product in good yields.

Table 2

Scheme 3

Scheme 4

In order to apply our strategy to o-carborane substituted benzylic alcohols, we have synthesized several new alcohols, following a previously described procedure (Scheme 3). 6

Scheme 5

High yields of benzylic alcohols are obtained by the reaction of ocarboranyl lithium with (hetero)aromatic aldehydes, either with π-donor or π-acceptor properties (Table 2).

Unfortunately, the reaction of these alcohols with nitroaniline in the presence of Lewis acid catalysts (Fe(III) or BF 3 ) does not lead to the amination product. In all cases, no reaction was observed at room temperature or refluxing conditions (Scheme 4).

The electron-withdrawing effect of the carborane seems to be strong enough to prevent the reaction, which is assumed to proceed through an S N 1-type mechanism, by destabilizing the benzylic cation intermediate. Since the direct (catalyzed) amination of these alcohols did not work, we have changed our focus to conventional amination routes. For this, it is necessary to convert the hydroxyl group into a good leaving group such as tosylate in order to obtain the desired amines (Scheme 5).

Although the formation of the tosylate is observed (δ = 5.75 ppm in RMN 1 H for the benzylic hydrogen instead of 5.10 ppm for the alcohol with R 1 = Me and R 2 = Ph), the reaction proceeds very slowly converting only 20 % of the alcohol into the tosylate after 18 hours at reflux. Improvements of this strategy are in progress.

OEt 2 85 12 2,4-DNPH NaAuCl 4 68 28 BF 3 .OEt 2 13 82 TMS-N 3 NaAuCl 4 93 0 BF 3 .OEt 2 84 6

				OH
				Li
	OH Amines : 4-nitroaniline + Ts-NH 2	R	NH 2	5% L.A. CH 2 Cl 2 RT, 16h Lewis Acids : NaAuCl 4 FeCl 3 BF 3 .OEt 2 NaAuCl 4 BF 3 .R 1 R 2 NH R 1 + Ph Ph O Ph Ph 2 Yield 1 (%) : Yield 2 (%) : 91 0 90 5 86 10 95 0 R 1 THF + R 2 -CHO -78 C, 1h R 1 R 2 Yield (%) : Me Phenyl 95 Me 2-

Pyridinyl 87 Me Ferrocene 93 Ph 2-Furanyl 91 R 1 R 2 OH + 10 % L.A. CH 2 Cl 2 , 16h NH 2 O 2 N

Aminoalkyl-o-carboranes have attracted interest due to their potential use in boron neutron capture therapy (BNCT)1 and as ligands for transition metal catalysts.2 The synthesis of aminoalkyl-o-carboranes is commonly carried out by the addition of terminal alkynes to activated boranes B 10 H 12 L 2 . 3 However this methodology often gives low yields. Other approaches include the reaction of lithio-o-carborane with preformed amines.4 It is therefore of interest to investigate new synthetic routes that produce aminoalkyl-o-carboranes in good yields and from other functional groups that allow the preparation of a variety of amines. In this sense, we have recently reported a synthesis of amines by Lewis acid-catalyzed direct amination of benzylic alcohols.5 Thus, we are now interested in utilizing this organic synthetic procedure to introduce the o-carborane fragments, as part of several projects directed towards the preparation of new metal complexes and their application in catalysis and materials science.

We thank CICYT (Project MAT2006-05339), Generalitat de Catalunya (2005/SGR/00709), Spanish Government (RyC to J.G.P.), MENRT-France (grant to V.T.), CNRS and Université de Versailles-Saint Quentin en Yvelines for financial support.


N-Heterocyclic Benzhydrylamines as Ligands in Palladium Complexes: Catalytic Activity in Suzuki Coupling Reaction

Vincent Terrasson, Damien Prim, Jérome Marrot

Synthesis of palladium (II) complexes:

N-heterocyclic benzhydrylamines 1a-c were obtained according to our previously described one-pot procedure (Figure 1). [3] This strategy was applied to three different π-deficient heterocycles in order to modulate the electronic effects in the new N,N-bidentate ligand series.

Benzylation of 1 a-c to obtain the secondary amines 2 a-c proved judicious in increasing solubility of the complexes in common solvents, making purification and characterization easier.

Further alkylation of the nitrogen atom of 2a leading to tertiary amine 2d was also envisioned to study the influence of steric effects over catalytic activity (Figure 1).

Institut Lavoisier de Versailles

Over the last decades, the Suzuki-Miyaura coupling reaction has become one of the most popular way to create carbone-carbone bounds and found widespread applications in organic synthesis. [1] This Pd-assisted process offers many advantages over other metal-catalyzed reactions such as commercial availability of a large panel of boronic acids, easy handling and high functional group tolerance, explaining the increasing interest in the scientific community. N,N-bidentate ligands recently proved to efficiently compete with classical phosphine-based ligands and to overcome some of their known drawbacks such as their cost and low air-stability. [2] Development of new series of N,N-bidentate palladium complexes more efficient and easier to prepare is therefore of great interest. These complexes were fully characterized by NMR spectroscopy and X-ray structure determination (Figure 3). [4] Figure 3 : X-ray structures.

Acknowledgments

Catalytic activities of these Pd-complexes in the Suzuki coupling reaction were next studied.

Comparison of our four different complexes in a model reaction proved complex 3c bearing a pyrazine heterocycle was the most efficient (Figure 4, Table1). Catalyst loadings as low as 0.01 mol.% could be successfully used.

The substitution on both boronic acids and aromatic halides were surveyed (Figure 5). Results are gathered in Table 2.

Table 2

Good results are obtained with halides and boronic acids bearing either electron donating or withdrawing groups. It is also worth noting that the use of pure water as a solvent seemed to afford increased yields of biphenyl products in some cases. Our catalytic system also proved efficient in the coupling reaction of aromatic chlorides.

  Figure1

Figure 2 3a

 2 Figure 2

  Figure 4

Table 1

 1


Cooperative effect of carborane and pyridine in the reaction of carboranyl alcohols with SOCl 2 : halogenation versus oxidation

).

Halogenation versus oxidation in these compounds can be interpreted as a competition between nucleophilic addition of Cl -versus proton abstraction at the benzylic position (Schemes 5 and 6). NMR data of the intermediate II clearly show that the benzylic proton is more acidic than that for the starting alcohol 2a (δ = 7.29 ppm compared to 5.11 ppm). This is probably due to the positive charge at the pyridine ring in II. This charge effect (making the benzylic proton more acidic) combined with the bulkiness of the carboranyl fragment hindering the nucleophilic attack of Cl -could explain this unusual oxidation reaction. Chem. 2008, accepted. [5] H. Nakamura, K. Aoyagi, Y. Yamamoto, J. Org. Chem. 1997, 62, 780. When the reaction of 2a with SOCl 2 monitored by NMR, the complete conversion of the alcohol to the intermediate II was observed within 5 min at room temperature. Further transformation according to Scheme 6 was only obtained by heating the reaction medium. These alcohols were obtained in good to excellent yields (Table 1) and fully characterized by spectroscopic methods.

Whereas no intramolecular contacts are found in 1a, there is a clear intramolecular O-H…N hydrogen bond in 2a.

The usual reaction pathway of the halogenation using SOCl

Figure 1 XFigure 2

 12 Figure 1

  [4] V. Terrasson, J.G. Planas, D. Prim, C. Viñas, F. Teixidor, M.E. Light, M.B. Husrthouse, J. Org.

  Scheme 6

  Scheme 5

We thank CICYT (Project MAT2006-05339), Generalitat de Catalunya (2005/SGR/00709), Spanish Government (RyC to J.G.P.), MENRT-France (grant to V.T.), CNRS, Université de Versailles and UK EPSRC for financial support.

Organic chlorides are key compounds in organic synthesis since they serve as intermediates in a wide variety of reactions. [START_REF] Bohlmann | Comprehensive Organic Synthesis[END_REF] These molecules are commonly obtained by the reaction of an alcohol with thionyl chloride, one of the most employed halogenating reagents. [2] With the aim to synthesize new o-carborane derivatives for material science and catalytic applications, [3] we have prepared new carboranyl alcohols and carried out their reactions with thionyl chloride. If alcohols bearing a phenyl substituent gave the expected chlorinated compounds in good yields, those substituted with a pyridine ring surprisingly afforded the ketones as the only products under the same reaction conditions. [4] Following an adaptation to known procedures, [5] we have prepared the series of four new carboranyl methylalcohols bearing a phenyl 1a-b or a pyridine substituent 2a-b (Scheme 1).


Zhuo Chai

Vincent Terrasson

Jean-Philippe Bouillon

Dominique Cahard
email: dominique.cahard@univ-rouen.fr

Chiral Brønsted acid-catalyzed diastereo-and enantioselective synthesis of CF3-substituted aziridines

published or not. The documents may come

Zhuo Chai, Vincent Terrasson, Jean-Philippe Bouillon, Dominique Cahard

Screening of reaction conditions

Using in situ generated CF 3 CHN 2 , [START_REF] Künzi | racemic aziridines using CF 3 CHN 2[END_REF] we tested its reactivity with an imine in situ generated from phenyl glyoxal monohydrate 2a and p-anisidine in the presence of Brønsted acid catalysts (Table 1).

Chiral phosphoric acid 1a (S)-TRIP was found to be an efficient catalyst for this reaction in toluene to give the desired aziridine product 3a in high yield and ee value at a catalyst loading of 10 mol% (Table 1, entry 1).

A series of aryl glyoxal monohydrates 2 were tested in this reaction (Table 2). High yields, excellent product ratios and ee values were obtained, irrespective of the electronic nature and position of the substituents on the benzene ring (Table 2, entries 1-7). In addition, a heteroaromatic substrate 2h also participated in the reaction well (Table 2, entry 8). The absolute configuration of the aziridine cis-3b was determined by Xray crystallographic analysis and the others were assigned by analogy.

Enantiopure aziridines are versatile chiral building blocks that have high potential for further elaboration to a wide range of chiral nitrogencontaining derivatives. 1 The aziridine ring is not only an important reactive intermediate but is also present in many biologically active compounds. [START_REF] Botuha | Heterocycles in Natural Product Synthesis[END_REF] In the context of an explosion of research in organofluorine chemistry due to the matchless properties of fluorinated molecules, trifluoromethylated building blocks are privileged scaffolds for library design and drug discovery. 3 Herein, we report the first catalytic asymmetric synthesis of CF 3 -substituted aziridines that is remarkable for its simplicity, a low catalyst loading, and a very high enantioselectivity. After some experimentation, we found that adding 1a in two batches at a time interval of 12h led to the optimum overall results, which provide an extremely high 417:1 dr ratio for the diastereomeric aziridines and 99% ee for the cis-3a (Table 1, entries 7-8).

Application: synthesis of b-amino acids and peptides

Table 3 Table 2 a Yield of isolated cis-3 products. b estimated by 19 F NMR. c determined by chiral HPLC using OD-H column. d 3+2 mol% of catalyst 1a at a time interval of 16h were used.

a Estimated by 19 F NMR. b yield refers to an inseparable mixture of cis-3i and 6i for entries 1-2; isolated yields for cis-3j:trans-3j:6j, respectively, for entries 3-5. c ees for cis-3:trans-3:6 respectively, determined by chiral HPLC using OD-H column. d a co-solvent PhCH 3 /CH 3 CH 2 CN 2:1 was used.

The scope of the reaction was further explored by using preformed a-imino glyoxilic ester 7 or amide 8 (Table 3).

With a-imino ester 7, cis-triazoline 6i was isolated as the major product with excellent ee (Table 3, entries 1-2). Starting from a-imino amide 8, although a 1:1 mixture of cis-aziridine 3j and cis-triazoline 6j was obtained, the ee of 3j remained excellent (Table 3, entries 3-5).

Chiral free aziridine 9, obtained after removal of the PMP protecting group, was easily converted to diastereomerically pure CF 3 -substituted dipeptide 10. b-CF 3 isocysteine derivative 11 can also be prepared in excellent yield and ee by ring-opening of aziridine 3j with a nucleophilic thiol.

Efforts towards a deeper mechanistic understanding of the current reactions as well as further applications to related reaction systems are underway in our laboratory.

Table 1 a

 1

Scope with aryl glyoxal monohydrates

  4

										Scope with a-imino glyoxilic ester and amide
	Entry	Catalyst (mol%)	Time (h)	Yield b (%)	Product ratio c cis-3a:trans-3a:6	ee d (%)	Entry 7 or 8 (R) 1 d 7 (OEt)	1a (mol%) 10	Product ratio a cis-3:trans-3:6 1.4:1:26	Yield b (%) 82	ee c (%) -/-/95
	1	1a (10)	3	82	18:1:2		97	2 d	7 (OEt)	5	1.2:1:29	42	-/-/96
	2		1a (5)	8	91	39:1:2		97	3	8 (NHBn)	5	7:1:6	45/7/41	98/46/88
	3	1a (2.5)	24	48 e	263:1:4		99	4	8 (NHBn)	1	6:1:6	43/8/46	98/49/88
	4	1b (5)	12	5 e	43:1:8		n.d.	5	8 (NHBn)	0.5	8:1:8	46/6/47	98/7/82
	5		1c (5)	48	10 e	17:1:2		55
	6		5 (10)	16	0	n.d.		n.d.
	7	1a (3+2) f	24	83	185:1:2		98
	8	1a (2.5+2) f	32	75	417:1:4		99
	Entry	Ar		Yield a (%)	Product ratio b cis-3:trans-3:6	ee c (%)
		1	Ph (2a)	75	417:1:4	99
		2	4-BrC 6 H 4 (2b)	82	69:1:2	>99
		3	3-BrC 6 H 4 (2c)	78	95:1:3	98
		4	4-ClC 6 H 4 (2d)	75	140:1:2	>99
		5	3,4-Cl 2 C 6 H 3 (2e)	71	59:1:2	96
		6 d	4-MeC 6 H 4 (2f)	80	227:1:2	>99
		7 d	4-MeOC 6 H 4 (2g)	85	60:1:2	97
		8 d	2-benzofuryl (2h)	79	131:1:3	99

a 2a/anisidine/CF 3 CHN 2 1:1:2, [imine] 0 = 0.05M. b yield of isolated cis-3a. c determined by 19 F NMR. d determined by chiral HPLC using OD-H column. e unreacted imine accounts for most of material balance. f catalyst was added in two batches at a time interval of 12h.