R Mecheri

T Abdelatif

A Irbah

C R A A G -Observatoire D'alger Bp

Bouzareah

Algerie J Alger

G Provost

Berthomieu

New values of gravitational moments J 2 and J 4 deduced from helioseismology

By applying the theory of slowly rotating stars to the Sun, the solar quadrupole and octopole moments J2 and J4 were computed using a solar model obtained from CESAM stellar evolution code (Morel (1997)) combined with a recent model of solar differential rotation deduced from helioseismology (Corbard et al. (2002)). This model takes into account a near-surface radial gradient of rotation which was inferred and quantified from MDI f-modes observations by Corbard and Thompson (2002). The effect of this observational near-surface gradient on the theoretical values of the surface parameters J2, J4 is investigated. The results show that the octopole moment J4 is much more sensitive than the quadrupole moment J2 to the subsurface radial gradient of rotation.

Introduction

Several theoretical determinations of the J 2 and J 4 gravitational moments have been undertaken in case of different solar differential rotation laws : (i) only radius dependence (Goldreich and Schubert, 1968;Paternò, Sofia, and Di Mauro, 1996), (ii) quadratic expansion in colatitude cosine terms (Ulrich andHawkins (1981a and1981b)), (iii) angular velocity distribution with a slowly latitude variation determined by mean of helioseimology technics (Gough (1982)). More recent determinations are those performed by : (i) Armstrong and Kuhn (1999) using a quadratic expansion rotation law with coefficients obtained by fitting higher resolution helioseismic interior rotation data from MDI (Scherrer et al. (1995)), (ii) Godier and Rozelot (1999) and (iii) Roxburgh (2001) using the differential rotation model given by Kosovichev (1996) from BBSO p-modes observations. This model takes into account the presence of a constant near-surface radial gradient based on the assumption that the angular momentum is preserved in the supergranulation layer. The aim of the present work is a contribution to J 2 and J 4 determinations using a new analytical model of solar differential rotation provided by Corbard et al. (2002) which has a latitudinal dependent profile of the near-surface radial gradient of rotation. If we consider the Sun as an axial symmetry distribution of matter in c 2009 Kluwer Academic Publishers. Printed in the Netherlands. Paper-Mecheri.hyper31616.tex;26/11/2009;11:50;p.1 rotation, the outer gravitational field φ out is expressed as :

φ out (r, θ) = - GM ⊙ r 1 - ∞ n=1 R ⊙ r 2n J 2n P 2n (cos θ) (1)
where J 2n are the gravitational moments, P 2n the Legendre polynomials and r, θ respectively the distance from the Sun centre and the angle to the symmetry axis (colatitude).

Since the solar rotation is slow, it induces small perturbations around the spherical equilibrium. These perturbations can be expanded on Legendre polynomial basis. The distribution of the gravitational potential in the Sun can be written :

φ(r, θ) = φ 0 (r) + φ 1 (r, θ) = φ 0 (r) + ∞ n=1 φ 12n (r)P 2n (u) (2)
where u = cosθ.

The gravitational moments J 2n are obtained assuming the continuity of the gravitational potential at the surface :

J 2n = R ⊙ GM ⊙ φ 12n (R ⊙ ) (3)
The perturbed potential is obtained by linearization of the equation of hydrostatic equilibrium and the Poisson equation, leading to :

d 2 φ 12n dr 2 + 2 r dφ 12n dr -(2n(2n + 1) + U V ) φ 12n r 2 = U [(V + 2)B 2n + + r dB 2n dr + 4n + 1 2 +1 -1 (1 -u 2 )P 2n (u)Ω(r, u) 2 du] (4)
where U = 4πρ 0 r 3 /M r , V = dlnρ 0 /dlnr, M r is the mass contained in a sphere of radius r and Ω(r, u) the angular velocity. B 2n is given by:

B 2n (r) = - 1 2n! 4n + 1 2 2n+1 +1 -1 uΩ(r, u) 2 d 2n-1 du 2n-1 ((u 2 -1) 2n )du (5)
Equation ( 3) is integrated with the usual boundary conditions, using U and V provided by a solar model obtained from the CESAM stellar evolution code (Morel (1997)) and a rotation law derived from helioseismology.

Paper-Mecheri.hyper31616.tex; 26/11/2009; 11:50; p.2

Analytical model of solar differential rotation

We consider the recent Corbard et al. (2002) model of solar differential rotation and, for comparison, the Kosovichev one (1996) already used by Roxburgh (2001) and Godier and Rozelot (1999). The Corbard model contains a near-surface radial gradient of rotation inferred from the radial dependence of the MDI f-modes observations (Corbard and Thompson (2002)). Two estimations of this gradient have been derived from different sets of modes leading to two rotation models denoted afterward by (a) and (b). As for Kosovichev's model, the surface rotation is forced to surface plasma observations [START_REF] Snodgrass | ASP Conf. Serf. 27, The Solar Cycle[END_REF].

Figure 1 shows the solar rotation profiles corresponding to these models computed for different latitudes. Kosovichev's model presents a negative constant subsurface radial gradient. The Corbard models have a negative value of the radial gradient at low latitude which is twice smaller than Kosovichev ones. At high latitude, the gradients are positive with larger magnitudes for the Corbard model (b).

We use an analytical expression derived respectively by Corbard et al. (2002) and [START_REF] Dikpati | [END_REF] for the Corbard rotation laws and for the Kosovichev one. We recall hereafter the full set of equations and parameters they give for these rotation laws :

Ω(r, u) = A 1 (r, u) + Ψ tac (r) Ω cz -Ω 0 + a 2 u 2 + a 4 u 4 (6)
where with

A 1 (r, u) = Ω 0 + Ψ cz (r) {α(u)(r -r cz )} + + Ψ s (r) {Ω eq -Ω cz -β(u)(r -R ⊙ ) -α(u)(r -r cz )} (7)
α(u) = Ω eq -Ω cz + β(u)(R ⊙ -r s ) r s -r cz Ω 0
, Ω eq and Ω cz are respectively the constant rotation of the radiative interior zone, the equatorial rate at the surface and at the top r cz of the tachocline localized at r tac . The a 2 and a 4 constants describe the latitudinal differential rotation. β(u) represents the latitudinal dependance of the rotation radial gradient below the surface down to a radius r s . This gradient depends on the latitude through the β 0 , β 3 and β 6 constants by the Equation :

β(u) = β 0 + β 3 u 3 + β 6 u 6 .
The Ψ x function where x stands for tac, cz or s, models the transition between different gradients. An error function centered at r x with width ω x is used for this goal : Ψ x (r) = 0.5 (1 + erf [2(rr x )/ω x ]). All the rotation laws have the following common parameters : Ω 0 = 435nHz, Ω eq = 452.5nHz, Ω cz = 453.5nHz, r tac = 0.69R ⊙ , r cz = 0.71R ⊙ , a 2 = -61nHz, a 4 = -73.5nHz. The parameters which are different for the three laws are given in Table I.

Results and discussion

We present in Table II the computed values of J 2 and J 4 obtained with different solar rotation models described in Section 2 and with an uniform rotation equal to the rotation rate of the solar radiative zone Ω 0 , for comparison. Table III gives also some values of J 2 and J 4 presented by other authors.

Our results show that the differential rotation in the convective zone reduces J 2 value of about 0.8% when the Corbard models are considered and about 0.5% in the case of Kosovichev's model. For this last case, our J 2 determination is larger than the value found by Godier and Rozelot (1999) but in agreement with the one obtained by Roxburgh (2001), both using Kosovichev's model. Our values are also in agreement with those given by Paternò et al. (1996), Pijpers (1998) and Armstrong and Kuhn (1999) (see Table III). All these values deviate from the range obtained by Ulrich andHawkins (1981a and1981b) in the case of the rotation law defined as a simple quadratic expansion. The difference between the subsurface radial gradients induces only a small reduction on J 2 values. It is about 0.25% between Kosovichev's model and Corbard's ones. This difference is however about 0.1% between the two Corbard models.

As expected, the effect of the subsurface radial gradient is more important on J 4 gravitational moment. J 4 absolute values obtained using the models of Corbard III. All these values

Table III. Some computed values of J2 and J4 obtained by other authors. The large value of Gough (1982) is due to an estimation of the internal rotation deduced from earlier helioseismic observations Authors J2(×10 -7 ) J4(×10 -9 ) [START_REF] Ulrich | [END_REF] 1.0 < J2 < 1.5 2.0 < |J4| < 5.0 Gough (1982) 36 - Paternò et al. (1996) 2.22 - Pijpers (1998) 2.18 -Godier and Rozelot (1999) 1.6 -Armstrong and Kuhn (1999) 2.22 -3.84 Roxburgh (2001) 2.206 -4.45 -Mecheri.hyper31616.tex;26/11/2009;11:50;p.5 are consistent with the range given by Ulrich andHawkins (1981a and1981b) except for the (a) Corbard model. Rotation induces a distortion of the solar surface which can be roughly related to J 2 through the following quantity often called oblateness :

Paper

R e -R p R ⊙ ≈ 3 2 J 2 + Ω 2 s R 3 ⊙ 2GM ⊙ (8)
where Ω s is an effective rotation rate. R e , R p and R ⊙ are respectively the equatorial, polar and mean solar radius. This formula is strictly valid for an uniform rotation or for a rotation constant on cylinders. For a solar rotation which presents a complex profile not constant on cylinders, Paternò, Sofia, and Di Mauro (1996) proposed an expression of Ω s derived from the surface rotation Ω(R ⊙ , u). In our case, Ω s will be the same for the three models since they are built so as to have the same surface rotation. Thus, in this rough description, the effect of different subsurface radial gradients of rotation on the oblateness appears through the modification of the J 2 gravitational moment. It is negligible since the main term in Equation ( 8) is the surface rotation term. The value of the oblateness found is 9.1 × 10 -6 . It is in agreement with observations of Lydon and Sofia (1996) and Rozelot and Rösch (1997) but slightly larger than those of Kuhn et al. (1998) and Armstrong and Kuhn (1999). Rozelot, Godier, and Lefebvre (2001) presented new developments taking into account the surface latitudinal differential rotation to link J 2 and J 4 to the solar equatorial and polar radius. To the lowest order, their formula reduces to Equation ( 8) with another definition of Ω s . For our surface rotation, their formula leads to an oblateness value equal to 11.4× 10 -6 . We have estimated that the effects of the second terms are of the order of (4/1000) in the case of Kosovichev's model. New constraints on the oblateness and the shape of the solar surface will hopefully be provided by the future PICARD microsatellite CNES-mission [START_REF] Thuillier | Proc. ISCS 2003 Symposium, Solar Variability as an Input to the Earth's Environment[END_REF]).

In conclusion, the octopole moment J 4 is much more sensitive than the quadrupole moment J 2 to the inclusion of the latitudinal and radial differential rotation in the convective zone and particularly to the subsurface radial gradient of rotation. Indeed, an important subsurface radial gradient at high latitude decreases significantly the value of |J 4 | while it does not affect significantly the J 2 value.

Figure 1 .

 1 Figure 1. Profiles of the solar rotation from 0.55R⊙ to the surface for different latitudes computed each 10 • from the Equator (top) to the Pole (bottom).(1) Model of Kosovichev. (2) Model of Corbard (a). (3) Model of Corbard (b).

  (a) and (b) are respectively about 20% and 7% larger than the one obtained with Kosovichev's model. The (a) Corbard model increases the J 4 absolute value of about 14% compared to the one obtained from the (b) Corbard model. Our |J 4 | value corresponding to Kosovichev's model is in agreement with the one given by Roxburgh (2001) using the same model. However, those obtained from Corbard's models are larger than other values given in Table

Table I .

 I The non common parameter values between the rotation models. The β0, β3 and β6 parameters are given in nHz/R⊙.

	model	ωtac/R⊙ ωcz/R⊙ ωs/R⊙ rs/R⊙	β0	β3	β6
	Kosovichev (1996)	0.1	0	0	0.983	891.5	0	0
	Corbard (a) (2002)	0.05	0.05	0.05	0.97	437	-214	-503
	Corbard (b) (2002)	0.05	0.05	0.05	0.97	437	0	-1445

Table II .

 II The J2 and J4 values corresponding to the different rotation models. Ω0 = 2.733 µrd/s is the rotation in the radiative zone.

	Model of rotation	J2(×10 -7 ) J4(×10 -9 )
	Uniform rotation (Ω0)	2.217	0
	Kosovichev (1996)	2.205	-4.455
	Corbard (a) (2002)	2.201	-5.601
	Corbard (b) (2002)	2.198	-4.805

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Paper-Mecheri.hyper31616.tex; 26/11/2009; 11:50; p.6

Acknowledgements

We thank Thierry Corbard for providing his model of rotation and the referee for his constructive remarks and comments. This work has

been performed with support of the French Foreign Affaire Ministry in the framework of scientific cooperation between France and Algeria (contract 00MDU501)


Etienne Petitprez

François Guérin

Frédéric Guinand

Decentralized Coordination of UAVs Swarm for describing planar shapes

come   L'archive ouverte pluridisciplinaire

Decentralized Coordination of UAVs Swarm for describing planar shapes.

E. Petitprez, F. Guérin and F. Guinand

In this work, we propose a method for positioning, in a decentralized way, many UAVs along any planar shape defined from a reference point C.

The description of the shape uses Fourier's Descriptors (FD) from C in the plan [START_REF] Charles | Fourier descriptors for plane closed curves[END_REF]. Methods based on FDs derived from a shape signature (in general a 1D function) representing 2D areas or boundaries. The function is of the type: 2 , where (x c , y c ) denotes the reference point coordinates, β and angle ranging from 0 to 2π, and d(beta) is the distance between the curve and the reference point for the angle β (see Figure 1). From the harmonics, obtained by a discrete Fourier transformation, the distance expressed on x (North) and y (East) axes can be computed for any value of the β parameter.

d(β) = (x(β) -x c ) 2 + (y(β) -y c )
Knowing their number N , the function and the reference point, UAVs can choose their β angle (one of the 2kπ N for k ∈ {0, N -1}) in a decentralized way by communicating with each other.

From its current position and bearing, drone i can compute a filtered error vector εi of its relative position (direction, distance) compared to the target (C) using the double exponential smoothing method [START_REF] Joseph | Double exponential smoothing: an alternative to kalman filter-based predictive tracking[END_REF]. For reducing this error, we've implemented a control law which consists in regulating to zero the filtered error vector by taking into account its value and its variation and by including a saturation function f (-V if ϵ < D, V if ϵ > D and V ϵ/D otherwise) -D is a breaking distance, and V is the maximum allowed speed). The yaw position control of the UAV (β angle) rests on the low level function already available in the API. For obstacle avoidance, let V i the drone i speed be the subtraction of a repulsive speed V r i to an attractive one V a i . V a i is the attractive effect induced by drone's desired position M (ψ * i ). For coping with reactivity and flexibility constraints of the decentralized network, we decided to use a composition of virtual forces [START_REF] Rezaee | A decentralized cooperative control scheme with obstacle avoidance for a team of mobile robots[END_REF] to ensure collision avoidance. Each UAV adjusts its velocity according to the presence of static or dynamic obstacles in a defined range (see Figure 2). V r i is the repulsive effect applied by neighbor drones j on drone i. When the UAV i crosses the defined protected circular area of UAV j (i.e. d ij is below a threshold Dj ), the drone i is subject to a repulsive effect, homogeneous to a speed, which intensity | ⃗ V ij | changes according to the inter-drone distance d ij . Each UAV computes its distance d ij and bearing angle β ij with its neighbor j with Haversine function using its emitted GPS coordinate in real time via communication network. For the x component of the speed this gives: Our tests were performed on a platform made of hardware-in-the-loop devices reproducing drones' mechanical behavior and companion computers hosting our algorithm (a couple of each for each drone). Several runs were conducted on different shapes, and drones final positions were obtained with less than 10% of the position deviations from the computed shape (see Figure 3).

V x i = V a i (ê x i , V x i , Dx i ) -V r i (d ij , β ij ) = -ėx i and thus: V x i = f (ê x i , Vx , Dx ) -N j=1 | ⃗ V ij | cos (β ij ).

Figure 1 Figure 3 :

 13 Figure 1: Fourier Descriptor Figure 2: Collision avoidance


F Hubert
email: fhubert@etu.univ-poitiers.fr

L Caner

A Meunier

B Lanson

Advances in characterization of the soil clay mineralogy using X-ray diffraction: from decomposition to profile fitting

Structural characterization of soil clay minerals often remains limited despite their key influence on soil properties. In soils, complex clay parageneses result from the coexistence of clay species with contrasting particle sizes and crystal-chemistry and from the profusion of mixed layers with variable compositions. The present study aimed at characterizing the mineralogy and crystal chemistry of the < 2 µm fraction along a profile typical of soils from Western Europe and North America (Neo Luvisol).

X-ray diffraction (XRD) patterns were nterpreted using i) the combination of XRD pattern decomposition and indirect identification from peak positions commonly applied in soil science and ii) the multi-specimen method. This latter approach implies direct XRD profile fitting and has recently led to significant improvements in the structural characterization of clay minerals in diagenetic and hydrothermal environments. In contrast to the usual approach, the multi-specimen method allowed the complete structural characterization of complex clay parageneses encountered in soils together with the quantitative analysis of their mineralogy. Throughout the profile, the clay paragenesis of the studied Neo Luvisol systematically includes discrete smectite, illite and kaolinite in addition to randomly interstratified illite-smectite and chlorite-smectite.

Structural characteristics of the different clay minerals, including the composition of mixed layers, did not vary significantly with depth and are thus indicative of the parent material. The relative proportion of the < 2 µm fraction increased with increasing depth simultaneously with smectite relative proportion. These results are consistent with the leaching process described for Luvisols in the literature.

Introduction

The < 2 µm fraction of soils is commonly dominated by clay minerals which control, to a large extent, important soil chemical and physical properties such as cation exchange capacity and surface area [START_REF] Dixon | Minerals in Soil Environments[END_REF]. In addition, clay minerals record the pedogenetic history of soils (see the review of [START_REF] Wilson | The origin and formation of clay minerals in soils: Past, present and future perspectives[END_REF]. An accurate determination of clay mineralogy and of its changes along the soil profile is thus essential for both purposes. Two main factors impede such a precise identification: first, soil clay parageneses are most often mixtures of clay species with a variety of particle sizes (50 nm -5 µm), and crystal-chemistry. Second, soil clay minerals are often mixed layers with variable compositions [START_REF] Reynolds | Characterization of soil clay minerals: decomposition of Xray diffraction diagrams and high-resolution electron microscopy[END_REF].

Over the last decade, the combined use of DecompXR [START_REF] Lanson | Decomposition of experimental X-ray diffraction profile (profile fitting): A convenient way to study clay minerals[END_REF] and Newmod [START_REF] Reynolds | Characterization of soil clay minerals: decomposition of Xray diffraction diagrams and high-resolution electron microscopy[END_REF] has improved the interpretation of X-ray diffraction (XRD) patterns in soils. DecompXR allows the decomposition of complex diffraction maxima into elementary peaks characterized by their positions, full width at half maximum intensity (FWHM) and intensities. This approach thus reveals the phase heterogeneity of samples and allows quantifying compositional changes within a series of samples, for example in a soil profile. However, the decomposition by itself does not allow the identification of mixed layers that is the determination of the different layer types coexisting within crystallites, of their proportion and stacking sequences. Mixed layer identification is routinely performed from the comparison of experimental peak positions with those calculated, commonly using Newmod, for mixed layers whose composition (nature and proportion of the different layer types) and stacking parameters are optimized. Such a combination of XRD pattern decomposition and Newmod calculations has been successfully applied to samples from diagenetic or hydrothermal geological settings [START_REF] Lanson | Characterisation of the end of smectite-to-illite transformation: Decomposition of x-ray patterns[END_REF]. It has been for soils to i) evaluate the effect of time on soil formation [START_REF] Righi | Characterization and genetic interpretation of clays in an acid brown soil (Dystrochrept) developed in a granitic saprolite[END_REF][START_REF] Righi | Clay stability in clay-dominated soil systems[END_REF][START_REF] Hardy | Mineralogical development of the silt fractions of a Podzoluvisol on loess in the Paris Basin (France)[END_REF][START_REF] Egli | Clay mineral formation in soils of two different chronosequences in the Swiss Alps[END_REF][START_REF] Egli | Clay minerals, oxyhydroxide formation, element leaching and humus development in volcanic soils[END_REF][START_REF] Velde | Evolution of clay minerals in a chronosequence of poldered sediments under the influence of a natural pasture development[END_REF][START_REF] Vingiani | Mixed-layer kaolinite-smectite minerals in a red-black soil sequence from basalt in Sardinia (Italy)[END_REF]Montagne et al., 2008), ii) investigate the role of vegetation cover (Barré et al., 2007a) and of macrofauna [START_REF] Jouquet | Role of the fungus-growing termite Pseudacanthotermes spiniger (Isoptera, Macrotermitinae) in the dynamic of clay and soil organic matter content. An experimental analysis[END_REF] on clay mineralogy,and iii) characterize the interactions between clay minerals and organic matter in in relation to carbon sequestration [START_REF] Fontaine | Stability of organic carbon in deep soil layers controlled by fresh carbon supply[END_REF]. However, this dual procedure allows only an approximate characterization of the mixed layers as the identification relies essentially on peak position without fitting the complete reflection profiles including asymmetries and shoulders. Consistently, profile fitting results in a more reliable identification of mixed layers [START_REF] Drits | Structural and chemical heterogeneity of layer silicates and clay minerals[END_REF]. Fitting simultaneously the profiles of various basal reflections provides additional constraints.

To overcome the intrinsic limitations of the previous approaches, the profile fitting method calculates a complete XRD pattern from a structural model optimized for each clay species present [START_REF] Drits | X-ray Structural Analysis of Mixed-layer Minerals[END_REF][START_REF] Drits | X-ray diffraction by disordered lamellar structures: Theory and applications to microdivided silicates and carbons[END_REF]. Drits et al. (1997a) and Sakharov et al. (1999a,b) further improved the approach as several structural models may fit a given experimental pattern equally well. In the multispecimen method, the optimized structural model should describe all XRD patterns obtained for a given sample following different treatments such as saturation by different interlayer cations, ethylene glycol solvation, heating, etc equally well. The multi-specimen method can be applied to mixed layers with more than two layer types whatever the layer stacking sequences, and there is no a priori limitation to the nature of identified species. It provides also quantitative phase analysis of complex clay parageneses [START_REF] Drits | Structural and chemical heterogeneity of layer silicates and clay minerals[END_REF].

Over the last decade, the multi-specimen method has been widely used to characterize clay mineralogy and its evolution in diagenetic and hydrothermal series (Drits et al., 1997a(Drits et al., , 2002a(Drits et al., , b, 2004[START_REF] Drits | Formation and transformation of mixed-layer minerals by Tertiary intrusives in Cretaceous mudstones, West Greenland[END_REF]Sakharov et al., 1999aSakharov et al., , b, 2004;;[START_REF] Lindgreen | Illite-smectite structural changes during metamorphism in black Cambrian Alum shales from the Baltic area[END_REF]Lindgreen et al., , 2002;;[START_REF] Claret | Clay minerals in the Meuse-Heute Marne underground laboratory (France): Possible influence of organic matter on clay mineral evolution[END_REF][START_REF] Mccarty | Heterogeneous mixed-layer clays from the Cretaceous, Greensand, Isle of Wight, southern England[END_REF][START_REF] Mccarty | Early clay diagenesis in gulf coast sediments: new insights from XRD profile modeling[END_REF][START_REF] Inoue | Illite-smectite mixed-layer minerals in the hydrothermal alteration of volcanic rocks: I. One-dimensional XRD structure analysis and characterization of component layers[END_REF][START_REF] Aplin | Influence of mechanical compaction and clay mineral diagenesis on the microfabric and porescale properties of deep-water Gulf of Mexico mudstones[END_REF][START_REF] Lanson | Diagenetic smectite-to-illite transition in clay-rich sediments: A reappraisal of X-ray diffraction results using the multi-specimen method[END_REF]. Compared with diagenetic and hydrothermal clay pargeneses, soil clay species are poorly crystallized and numerous randomly interstratified mixed layers could coexist. To our knowledge, this method has never been applied to soil samples before the present study which investigates the < 2 µm fraction mineralogy of a Luvisol typical of Western Europe and North America [START_REF] Jamagne | Mineralogy of clay fractions of some soils on loess in northern France[END_REF][START_REF] Velde | Clay minerals in the agricultural surface soils in the Central United States[END_REF]. We aimed to demonstrate that, compared with the common identification approach using decomposition and indirect comparison with calculated patterns, profile fitting provides new insights into soil clay mineralogy allowing a more reliable and more complete identification of clay species and the quantification of their relative proportions. This is essential for the understanding of soil genesis and dynamics. A second aim was to investigate whether, the redistribution of clay species between soil horizons and the limited changes of clay crystal structures were consistent with a leaching process.

Materials and methods

Soil samples

The studied soil is a "Neo Luvisol" according to the World reference base (IUSS working group WRB, 2006). It is developed on loess deposits from the Closeaux Field Experiment, at the Experimental Station of the Institut National de la Recherche Agronomique (INRA -Château de Versailles, France).

On the basis of field observations, five horizons were sampled from the soil profile.

Noticeable marks of hydromorphy were observed in the E1g, E2g, Bt and Bt/C horizons, together with accumulation of clays in the pore system of the Bt/C horizon.

The relative proportion of the < 2 µm fraction steadily increased with increasing depth from 18% in the surface horizon to 27% in the deeper ones (Table 1). In addition, CEC at the soil pH increased with the increasing content of the < 2 µm fraction from 11.2 cmol C kg -1 in Ap to 16.7 cmol C kg -1 in Bt/C. The content of organic carbon decreased from 1.6% in the surface horizon to 0.2% in the Bt/C horizon. Finally, the carbonate content was negligible throughout the soil profile, and the cation exchange complex was predominantly saturated with calcium (Ca) [START_REF] Moni | Stabilisation physique et physico-chimique de la matière organique dans les horizons profonds du sol[END_REF].

Separation of the < 2 µm fraction for X-ray diffraction analysis

No chemical treatments were applied to the raw samples as routine removal of organic matter by using H 2 O 2 or of iron and aluminium oxy-hydroxides by using the dithionitecitrate-bicarbonate protocol [START_REF] Mehra | Iron oxide removal from soils and clay by dithionite-citrate system buffered with sodium bicarbonate[END_REF][START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF]) may alter the clay minerals and more especially mixed layer species [START_REF] Velde | Evolution of clay minerals in a chronosequence of poldered sediments under the influence of a natural pasture development[END_REF].

Samples from each soil horizon were first air-dried and sieved to < 2 mm; 100 g of the sieved sample was then mixed with deionized water and disaggregated by using agitation with glass balls. The < 50 µm fraction was separated next by wet-sieving and dispersed using ultrasonic treatment (20 minutes at 600 W for 400 ml of suspension: [START_REF] Balesdent | The dynamics of carbon in particle-size fractions of soil in a forest-cultivation sequence[END_REF]. The < 2 µm fraction was subsequently isolated from the silt (2-50 µm) by using repeated siphoning of the dispersed material (settling for 18 hours at 20° C and removal of the upper 22 cm). The extracted suspension was centrifuged, and the remaining supernatant was filtered to 0.45 µm and added to the centrifugation 'residue', which was then freeze-dried. The clay minerals were studied in their natural state. Consistent with their natural saturation by Ca, a repeated Ca-saturation test (five repeats) did not reveal any difference between natural and Ca-saturated samples (XRD data not shown).

Oriented mounts of the < 2 µm fraction were prepared by using the filter transfer method (0.2 µm Nucleopore® polycarbonate filters), as recommended by [START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF] for quantitative XRD analysis. Aliquots of 50 mg were deposited on a silicon wafer to avoid scattering from glass. XRD patterns were obtained using a Panalytical X'pert Pro diffractometer equipped with an X'celerator detector (CuKα 1+2 radiation) in the air-dried state (AD) at room humidity (approximately 35%) and after solvation with liquid ethylene glycol (EG). The size of the divergence, two Soller and antiscatter slits were 0.5°, 2.3°, 2.3° and 0.5°, respectively. Diffraction data were recorded in a scanning mode and converted to step patterns (with a step of 0.017°2θ from 2.5 to 35°2θ, using a 200-second counting time per step).

Decomposition of XRD patterns

Decomposition of AD and EG patterns was performed as recommended by [START_REF] Lanson | Decomposition of experimental X-ray diffraction profile (profile fitting): A convenient way to study clay minerals[END_REF] over the 3 -14°2θ range. Over this angular range, the resolution of the Kα 1+2 doublet is low enough to allow using the Fityk 0.8.2 peak fitting software [START_REF] Wojdyr | Fityk 0.8.2 free software[END_REF]. Following background stripping, XRD patterns were fitted with Gaussian elementary curves whose number was steadily increased until a satisfactory fit to the data was obtained. The initial parameters (position and FWHM) of elementary curves were derived from previous studies on similar soil clay parageneses [START_REF] Righi | Clay stability in clay-dominated soil systems[END_REF][START_REF] Pernes-Debuyser | Soil mineralogy evolution in the INRA 42 plots experiment (Versailles, France)[END_REF] and optimized with the Levenburg-Marquardt algorithm.

When compared, the results obtained were identical to those of DecompXR (data not shown).

X-ray profile modelling method

XRD patterns of the five samples were modelled, in both AD and EG states, with the Sybilla© software developed by Chevron™ [START_REF] Aplin | Influence of mechanical compaction and clay mineral diagenesis on the microfabric and porescale properties of deep-water Gulf of Mexico mudstones[END_REF]. This program provides a graphic user interface to the algorithm developed initially by [START_REF] Drits | X-ray Structural Analysis of Mixed-layer Minerals[END_REF] and used recently by Drits et al. (1997a) and Sakharov et al. (1999a, b). It allows the direct comparison between experimental and calculated XRD profiles, the latter being the sum of all elementary contributions which have been identified.

Instrumental and experimental parameters such as horizontal and vertical beam divergence, goniometer radius and slide length were introduced and not further refined.

The sigmastar parameter (σ*) which characterizes the distribution of particle orientation was set for each clay mineral phase as recommended by [START_REF] Rüping | Texturmessungen an Tonmineralen in orientierten Präparaten -Eine kritische Diskussion zur Tonmineralquantifizierung[END_REF]. For all layer types z atomic coordinates proposed by [START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF] were used after modification to fit the layer thickness values used for simulation; thermal motion parameters (B) were also set as proposed by [START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF]. The position and amount of interlayer species (H 2 O and EG molecules in particular) were considered as variable parameters and varied about the values proposed by [START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF] during the fitting process. In bi-hydrated smectite layers (2W), a single plane of H 2 O molecules was assumed to be present on each side of the interlayer mid-plane as proposed by Ferrage et al. (2005a, b). Illite and smectite structural formulae were similar to those proposed by [START_REF] Laird | Chemistry of smectitic and illitic phases in interstratified soil smectite[END_REF] from the ICP-AES elemental analysis of the < 2 µm fraction from similar soils (Table 2).

For each mixed layer, the number, nature, proportion and stacking sequences of the different layer types were considered as adjustable parameters. In the AD state and under room humidity conditions, expandable layers may be dehydrated (S0w: d 001 ~ 1.00 nm), mono-hydrated (S1w: d 001 ~ 1.25 nm), or bi-hydrated states (S2w: d 001 ~ 1.50 nm) (Ferrage et al., 2005b). Illite and S0w layers cannot be differentiated in the AD state, but smectite layers expand following EG solvation to incorporate one or two sheets of EG molecules in their interlayers (S1eg: d 001 ~ 1.30 nm, and S2eg: d 001 ~ 1.68 nm, respectively; Table 2). Finally, the distributions of coherent scattering domain sizes (CSDSs) were assumed to be lognormal and characterized by their mean value (Drits et al., 1997b). The quality of the fit was estimated with the unweighted R parameter [START_REF] Howard | Profile fitting of powder diffraction patterns[END_REF] over the 4 -35°2θ and the 3.5 -35°2θ ranges for AD and EG patterns, respectively, to minimize the influence of the low-angle region where the effect of X-ray scattering becomes significant. The 19 -22°2θ and 26.5 -27.0°2θ ranges were excluded for the calculation of R as they contains peaks other than clay 00l reflections. For practical reasons, optimization was performed using a trial-anderror approach without automatic refinement of the parameters. To ensure the reliability of the model, both AD and EG patterns of a given sample were fitted with a unique set of structural parameters. The relative proportions of the different clay species in these complex parageneses were also optimized with Sybilla. The multi-specimen approach requires that these proportions to be similar in both AD and EG states.

Results

Qualitative description of experimental XRD patterns

XRD patterns obtained on the < 2 µm fraction (AD and EG) of the five soil horizons are shown in Figure 1. All samples contained quartz (0.426 and 0.334 nm peaks), feldspars (0.325 and 0.320 nm) and poorly crystallized goethite (0.418 nm). The clay paragenesis is similar for all horizons including kaolinite (rational series of peaks at 0.716 and 0.358 nm in AD and EG states), illite-mica (rational series of peaks at 1.01, 0.498 and 0.334 nm in AD and EG states). In addition, the presence of broad and irrational peak series whose position shifts between AD and EG treatments suggests the presence of mixed layers containing expandable layers. Specifically, the 1.47 nm peak observed on the AD pattern shifted to approximately 1.75 nm following EG solvation. Such behaviour is characteristic of randomly interstratified illite-smectite [START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF]. The steady intensity increase of the 1.47 nm peak with increasing depth suggests an increasing proportion of this mixed layer from Ap to Bt horizons.

Finally, the presence of a maximum peaking at 0.485 nm, and its behaviour following EG solvation, supports the presence of a mixed layer containing both chlorite and expandable layers.

XRD pattern decomposition results

The number of elementary contributions (6 and 7 in AD and EG states, respectively) necessary to fit the data was remarkably similar for all samples, as are their positions, FWHMs, and relative intensities (Figure 2). This overall similarity supports the hypothesis of a constant composition for all clay minerals along the soil profile. The illite-mica peak at approximately 1.00 nm was fitted by using a broad band at 1.020 nm and a sharp one at 1.000 nm, most probably accounting for a broad CSDS distribution.

Similarly, the kaolinite peak at 0.716 nm was fitted with broad and sharp maxima peaking at 0.730 and 0.716 nm, respectively. The broad contribution at approximately 1.47 nm was fitted also using two elementary contributions. The broad contribution at 1.500 nm (1.550 nm for the Bt/C horizon) sharpens, shifted to 1.750 nm and presents an additional peak at 0.930 nm after EG solvation. The sharp peak at 1.460 nm (AD) broadened and shifted to 1.580 nm after EG solvation.

In their study of a similar soil, [START_REF] Pernes-Debuyser | Soil mineralogy evolution in the INRA 42 plots experiment (Versailles, France)[END_REF] used NEWMOD to identify the clay minerals present in surface samples. These authors attributed the two bands at 1.450 nm (broad) and 1.540 nm (sharp) to two randomly interstratified illitesmectite having similar contents of illite and S2w layers (50:50) but different CSDS distributions (1-4 and 3-6 layers, respectively). The XRD pattern corresponding to this clay paragenesis was calculated using Sybilla and compared with the data (Figure 3) to assess the validity of the identification proposed by [START_REF] Pernes-Debuyser | Soil mineralogy evolution in the INRA 42 plots experiment (Versailles, France)[END_REF]. The profiles of the peaks corresponding to discrete kaolinite and illite were satisfactorily reproduced. The overall profile of the low-angle data, especially that of the EG patterns, was also approximately reproduced. Significant mismatches were, however, observed, especially over the 6 -11, 14 -19 and 26 -35°2θ ranges, that resulted in an overall poor fit (Figure 3; R = 23.6% and 22.7% for AD and EG states, respectively) and therefore refute the identification proposed by [START_REF] Pernes-Debuyser | Soil mineralogy evolution in the INRA 42 plots experiment (Versailles, France)[END_REF]. In particular, the chlorite-expandable mixed layer whose presence was hypothesized from the maximum peaking over the 18 -19°2θ range at 0.485 nm (AD) has a probable contribution over the low-angle region.

Full pattern fitting

To overcome the limitations of an indirect identification illustrated above, XRD patterns recorded on the oriented clay separates preparations of all horizons were all fitted in both AD and EG states. The optimum fit was obtained systematically with randomly interstratified illite-smectite and chlorite-smectite, in addition to discrete smectite, illite and kaolinite as illustrated for the Bt horizon (Figure 4). The structural characteristics of the optimal models are listed in Tables 2 and3, and Table 4 contains the relative proportions of the different contributions. Discrete illite contributed to the three reflections at 1.006, 0.499 and 0.333 nm (AD) and 1.001, 0.501 and 0.333 nm (EG). These reflections were sharp, indicative of a large mean CSDS (18 layers -Table 3).

Two populations of kaolinite having contrasting CSDS (6 and 20 layers on average) were necessary to fit the low-angle asymmetry of the 0.716 and 0.358 nm reflections. At 1.554 nm, the 001 reflection of discrete smectite contributed significantly to the overall intensity of the broad 1.47 nm peak. The 005 reflection (0.305 nm) also accounted for the high-angle tail of the peak at 0.334 nm (AD). Following EG solvation, the first smectite reflection shifted to 1.808 nm accounting for the low-angle asymmetry of the peak at 1.750 nm. The 005 reflection at 0.337 nm contributed to the large 'background' intensity between the 0.358 and 0.334 nm peaks. Discrete smectite has a small mean CSDS (3 layers) to match the width of experimental maxima. The heterogeneous hydration and swelling behaviours (36:64 S1w:S2w ratio in the AD state, and 24:76 S1eg:S2eg ratio after EG salvation: Table 3) also contributes to line broadening. The 003 reflection of smectite has a low intensity compared with that of 001 because of the large content of octahedral iron (1.2 atoms by unit formula:Table 2, [START_REF] Laird | Chemistry of smectitic and illitic phases in interstratified soil smectite[END_REF].

A randomly interstratified illite-smectite with a large illite content (63:37 illite:smectite ratio) was also identified in the clay paragenesis. This mixed layer has a small CSDS (six layers) and its smectite layers exhibited a heterogeneous hydration and swelling behaviour (Table 3). As a result, its first order reflection (at approximately 1.27 nm in the AD state) allowed he high-angle asymmetry of the 1.47 nm peak to be fitted, whereas the 0.503 and 0.322 nm maxima contributed to the low-and high-angle tails of the complex maxima at 0.498 and 0.334 nm, respectively (Figure 4a). Following EG solvation, this randomly interstratified illite-smectite exhibited only weak and poorly-defined modulations over the low-angle region, which make it essentially undetectable using a decomposition approach. This mixed layer thus contributed to the diffracted intensity mostly on the high-angle side of the 0.498 nm peak, and in the complex band at 0.334 nm. A randomly interstratified chlorite-smectite (52:48 chlorite:smectite ratio: Table 3) completed the clay paragenesis accounting in particular for the high angle shoulder of the 0.498 nm peak (AD) and for the sharp maximum of the broad 1.47 nm band (Figure 4a). After EG solvation, this mixed layer contributed mostly to the large 'background' intensity between the 0.358 and 0.334 nm peaks, and to the complex 1.75 nm band.

The same clay paragenesis with discrete kaolinite, illite and smectite, and randomly interstratified illite-smectite and chlorite-smectite was used to fit XRD patterns from all five horizons (Figure 5, Tables 3 and4) with R factor values ranging from 8.7 -12.8% and from 9.3 -12.6% for AD and EG patterns, respectively. The structural characteristics of discrete illite and kaolinite were essentially constant over the entire soil profile. Similarly, discrete smectite was systematically dominated by S2w layers (AD), the relative proportion of which was at a minimum in E1g and E2g horizons at approximately 55%, and increasing to 77% in the Bt/C horizon. Following EG solvation, most smectite layers incorporated two sheets of EG molecules. Consistent with the hydration behaviour, the proportion of S1eg layers was minimal in the E1g horizon (72%) and maximal in Bt/C (94%).

The composition of the two mixed layers was also more or less constant along the soil profile with 63% illite in the illite-smectite and 52% chlorite in the chloritesmectite, except in the most superficial horizon (62% chlorite). In both mixed layers, the hydration behaviour of expandable layers was heterogeneous with 4 -35% of smectite layers having only one sheet of interlayer H 2 O molecules. Following EG solvation, swelling heterogeneity was reduced, especially in the chlorite-smectite (Table 3). In the illite-smectite, swelling heterogeneity was more pronounced with 8 -30% of smectite layers incorporating a single sheet of EG molecules, the proportion of S1eg steadily decreasing with increasing depth.

Relative proportions of the various clay species are listed in Table 4. Discrete illite and kaolinite represent approximately 20% of the < 2 µm fraction each, their proportion being constant throughout the profile. The proportion of discrete smectite increased from the Ap (18%) to the Bt horizon (33%) in which it was the dominant clay species.

At greater depth in the Bt/C horizon, the proportion of discrete smectite decreased to 23%. The randomly interstratified illite-smectite was the dominant clay species throughout the soil profile, except in the Bt horizon, despite its diffuse contribution to the low-angle intensity (Figure 4b). From E2g to Bt horizons, the proportion of this mixed layer decreased from approximately 30 to approximately 25%, increasing again to approximately 30% in the Bt/C horizon. Finally, the chlorite-smectite accounts for 5 -8% of the < 2 µm fraction along the soil profile, without any significant change with depth.

Discussion

In the present work, pattern fitting led to an innovative interpretation of XRD patterns, providing detailed information on the different phases present in the soil horizons, on their structural evolution and on their relative abundances. In the following discussion the fitting approach will first be compared with numerical tools commonly used for the interpretation XRD patterns (DecompXR, Newmod). The results in terms of pedogenesis will then be discussed.

Limitations of the decomposition-XRD calculation approach

The present study allows us to question the combined use of XRD pattern decomposition and indirect identification from elementary peak positions (± FWHM) to describe complex clay parageneses commonly encountered in soils, although it has been widely used for this purpose over the last decade [START_REF] Righi | Clay stability in clay-dominated soil systems[END_REF][START_REF] Reynolds | Characterization of soil clay minerals: decomposition of Xray diffraction diagrams and high-resolution electron microscopy[END_REF][START_REF] Velde | Clay minerals in the agricultural surface soils in the Central United States[END_REF][START_REF] Pernes-Debuyser | Soil mineralogy evolution in the INRA 42 plots experiment (Versailles, France)[END_REF][START_REF] Velde | Evolution of clay minerals in a chronosequence of poldered sediments under the influence of a natural pasture development[END_REF][START_REF] Vingiani | Mixed-layer kaolinite-smectite minerals in a red-black soil sequence from basalt in Sardinia (Italy)[END_REF][START_REF] Jouquet | Impact of subterranean fungusgrowing termites (Isoptera, Macrotermitiane) on chosen soil properties in a West African savanna[END_REF][START_REF] Jouquet | Role of the fungus-growing termite Pseudacanthotermes spiniger (Isoptera, Macrotermitinae) in the dynamic of clay and soil organic matter content. An experimental analysis[END_REF][START_REF] Fontaine | Stability of organic carbon in deep soil layers controlled by fresh carbon supply[END_REF]Barré et al., 2007aBarré et al., , b, 2008a, b;, b;[START_REF] Montagne | Impact of drainage on soil-forming mechanisms in a French Albeluvisol: Input of mineralogical data in mass-balance modelling[END_REF]. In particular, the clay mineralogy deduced from such a data processing (illite, kaolinite and two randomly interstratified illite-smectite, [START_REF] Pernes-Debuyser | Soil mineralogy evolution in the INRA 42 plots experiment (Versailles, France)[END_REF], did not permit the reproduction of XRD data for the samples investigated. Several hypotheses can be proposed to account for this inadequacy.

The first is the specific diffraction fingerprint, without any significant peak in the low-angle region, of the randomly interstratified illite-smectite which is the main clay mineral phase in the soil profile. This mixed layer is characterized by a broad and poorly defined contribution to the diffracted intensity. As a consequence, this major contribution is stripped during the initial background removal. This key drawback of the decomposition approach is especially noteworthy for soil clay minerals, as most of them combine small CSDS and complex interstratification, thus giving rise to weakly modulated XRD patterns.

The second hypothesis, that indirect identification of mixed layers from their peak position is essentially inadequate, is discussed in detail by [START_REF] Lanson | Crystal structure of mixed-layer minerals and their X-ray identification: New insights from X-ray diffraction profile modeling[END_REF]. Specifically, the heterogeneous nature of expandable interlayers hampers the use of simplified peak migration identification techniques based on two-component mixed layers [START_REF] Drits | Mixed-layer minerals[END_REF][START_REF] Drits | Structural and chemical heterogeneity of layer silicates and clay minerals[END_REF]. Such hydration/swelling heterogeneity has been found in most natural samples, whatever their origin and mineralogy (Drits et al., 1997a;Sakharov et al., 1999a;[START_REF] Lindgreen | Illite-smectite structural changes during metamorphism in black Cambrian Alum shales from the Baltic area[END_REF][START_REF] Drits | Structural and chemical heterogeneity of layer silicates and clay minerals[END_REF][START_REF] Mccarty | Heterogeneous mixed-layer clays from the Cretaceous, Greensand, Isle of Wight, southern England[END_REF][START_REF] Inoue | Illite-smectite mixed-layer minerals in the hydrothermal alteration of volcanic rocks: I. One-dimensional XRD structure analysis and characterization of component layers[END_REF]Ferrage et al., 2005b[START_REF] Ferrage | Investigation of dioctahedral smectite hydration properties by modeling of X-ray diffraction profiles: Influence of layer charge and charge location[END_REF]. Again, this drawback is especially important for soils where heterogeneity is expected to be even greater than in other geological settings.

New contributions from XRD profile-fitting for interpreting complex clay mineral assemblages

The overall agreement, both visually (Figure 5) and quantitatively with R values systematically being < 13%, demonstrates the ability of the multi-specimen approach to provide a good quality fit to experimental data obtained on polyphasic soil samples: this is consistent with previous studies in other geological settings (Drits et al., 1997a(Drits et al., , 2002a(Drits et al., , b, 2004[START_REF] Drits | Formation and transformation of mixed-layer minerals by Tertiary intrusives in Cretaceous mudstones, West Greenland[END_REF]Sakharov et al., 1999aSakharov et al., , b, 2004;;[START_REF] Lindgreen | Illite-smectite structural changes during metamorphism in black Cambrian Alum shales from the Baltic area[END_REF][START_REF] Lindgreen | The structure and diagenetic transformation of illite-smectite and chlorite-smectite from North Sea Cretaceous-Tertiary chalk[END_REF][START_REF] Claret | Clay minerals in the Meuse-Heute Marne underground laboratory (France): Possible influence of organic matter on clay mineral evolution[END_REF][START_REF] Mccarty | Heterogeneous mixed-layer clays from the Cretaceous, Greensand, Isle of Wight, southern England[END_REF][START_REF] Mccarty | Early clay diagenesis in gulf coast sediments: new insights from XRD profile modeling[END_REF][START_REF] Inoue | Illite-smectite mixed-layer minerals in the hydrothermal alteration of volcanic rocks: I. One-dimensional XRD structure analysis and characterization of component layers[END_REF][START_REF] Aplin | Influence of mechanical compaction and clay mineral diagenesis on the microfabric and porescale properties of deep-water Gulf of Mexico mudstones[END_REF][START_REF] Lanson | Diagenetic smectite-to-illite transition in clay-rich sediments: A reappraisal of X-ray diffraction results using the multi-specimen method[END_REF]. This approach can thus be used to determine accurate structural characteristics for the phases present in a given sample, as well as their relative proportions. The sensitivity of the approach to structural characteristics and phase heterogeneity has been discussed previously (Drits et al., 1997a(Drits et al., , 2002b[START_REF] Drits | Formation and transformation of mixed-layer minerals by Tertiary intrusives in Cretaceous mudstones, West Greenland[END_REF]Sakharov et al., 1999a;[START_REF] Drits | Structural and chemical heterogeneity of layer silicates and clay minerals[END_REF][START_REF] Lanson | Diagenetic smectite-to-illite transition in clay-rich sediments: A reappraisal of X-ray diffraction results using the multi-specimen method[END_REF]. However, the actual sensitivity of the calculated XRD patterns to key structural characteristics needs to be illustrated. The actual presence of the different contributions is the first of these. In the present work, mixed layers are introduced only if they allowed fitting specific angular ranges without significant overlap with other phases as illustrated in Figure 4. The absence of the small CSDS kaolinite contribution leads, for example, to a significant misfit over the 11 -12°2θ range (Figure 6a). The influence of CSDS is illustrated next. Compared with the optimal fit to the data (Figure 5), increasing the CSDS of discrete smectite from three to five layers leads to evident misfits over the 4 -6°2θ and 29.5 -31.5°2θ ranges, whereas decreasing the CSDS of discrete illite from 18 to 13 layers decreased the resolution of the peak at 17.5°2θ (002 reflection: Figure 6b). Finally, sensitivity of calculated profiles to smectite hydration behaviour may be assessed by considering, for example, that all layers are bi-hydrated in discrete smectite. As a result, the 001 reflection was shifted towards ssmaller angles thus inducing a major misfit over the 4 -6°2θ range (Figure 6c).

The next section focuses on the implications of the original description of clay paragenesis obtained from profile fitting for clay pedogenetic processes and more especially for three major issues.

Clay paragenesis in Luvisols. From XRD results, [START_REF] Jamagne | Mineralogy of clay fractions of some soils on loess in northern France[END_REF] claim that the clay mineralogy is similar in the different horizons of soils formed on loess deposits, even in the case of intense clay illuviation, and indicate that the < 2 µm fraction includes "kaolinite, mica and a complex group of other layer silicates, including smectite and mixed layers of chloritic, micaceous, vermiculitic and smectitic layers in random interstratification". Using XRD profile fitting, the present study confirms the interpretation of [START_REF] Jamagne | Mineralogy of clay fractions of some soils on loess in northern France[END_REF] for discrete clay species with the presence of kaolinite, illite and smectite. It also allows an improved description of the "complex group of other silicates" which includes two randomly interstratified illite-smectite (63:37) and chlorite-smectite (52:48). Direct profile fitting thus confirms that in Luvisols the clay paragenesis is stable along the soil profile as proposed by [START_REF] Jamagne | Mineralogy of clay fractions of some soils on loess in northern France[END_REF].

Structural characteristics of clay species and their development along the profile. Even when looking at a more detailed level, clay mineralogy was remarkably constant along the soil profile. Structural parameters of discrete kaolinite and illite and of illite-smectite and chlorite-smectite phases were similar in the different horizons (Table 3). Some differences were, however, observed at the soil surface. In particular, the chlorite content of the chlorite-smectite increased from 52 to 62% in the topsoil Ap horizon, simultaneously with a decrease of its mean CSDS from nine to seven layers. On the contrary, the mean CSDS of the illite-smectite increases from six to seven layers in the lower horizons to nine layers in the uppermost one (Table 3). The parent material, that is the loess deposit, was thus probably homogeneous. In addition, kaolinite, illite, illitesmectite and chlorite-smectite species did not present significant structural changes along the soil profile compared with discrete smectite. The hydration and swelling (S1w:S2w and S1eg:S2eg ratios, respectively) properties of smectite varied from one horizon to the other, however, without any significant trend with depth. In addition, the relative proportions of S1w and S1eg layers were not strictly correlated, the latter being usually smaller than the former. Except in the Bt/C horizon where smectite was almost fully expanded after EG solvation, the proportion of S1eg layers ranged from 17 to 28% (Table 4). Consistent with our observations, [START_REF] Velde | Clay minerals in the agricultural surface soils in the Central United States[END_REF] reported that approximately one third of expandable layers incorporated a single sheet of EG molecules in the surface horizons of cultivated soils, and thus deduced the presence of a similar proportion of high-charge expandable layers. However, in our case the heterogeneous swelling observed for discrete smectite is possibly induced by sample preparation artefacts. No sample pre-treatments were performed to remove organic matter and iron oxy-hydroxides prior to size fractionation. Such pre-treatments were performed on sample aliquots to extract the < 0.05 µm size fraction. These fractions, which concentrate discrete smectite, were X-rayed following solvation by EG vapour (16 hours at 40°C under vacuum). The results obtained (not shown) showed no difference between Ap and Bt horizons with 100% of S2eg layers in both cases. The intimate mixing of organic matter and/or of iron oxy-hydroxides with clays is thus likely to be responsible for the observed reduced expandability of smectite, and for the observed variation of smectite swelling behaviour along the profile.

Quantitative phase analysis. Direct profile fitting method overcomes the intrinsic limitations of the decomposition approach, which was restricted to peak intensity ratios between similar clay species, and provides reliable estimates of the phase composition for complex clay parageneses (Drits et al., 1997a;[START_REF] Lindgreen | The structure and diagenetic transformation of illite-smectite and chlorite-smectite from North Sea Cretaceous-Tertiary chalk[END_REF][START_REF] Claret | Clay minerals in the Meuse-Heute Marne underground laboratory (France): Possible influence of organic matter on clay mineral evolution[END_REF][START_REF] Mccarty | Early clay diagenesis in gulf coast sediments: new insights from XRD profile modeling[END_REF][START_REF] Lanson | Diagenetic smectite-to-illite transition in clay-rich sediments: A reappraisal of X-ray diffraction results using the multi-specimen method[END_REF]. [START_REF] Jamagne | Mineralogy of clay fractions of some soils on loess in northern France[END_REF] concluded that the relative contents of mica and trioctahedral chlorite increase close to the soil surface as the result of the physical breakdown of coarse particles and/or of the preferential migration of other minerals as reported also in Belgian soils [START_REF] Van Ranst | Mineralogy in silty to loamy soils of central and high Belgium in respect to autochthonous and allochthonous materials[END_REF]. In our work, we show that the relative proportion of discrete smectite increases from 18% (Ap horizon), to approximately 25% (E1g and E2g horizons), and to 33% (Bt horizon -Table 4). This proportion decreases to 25% in the Bt/C horizon. The contribution of discrete smectite increases essentially at the expense of illite-smectite, which dominated the clay paragenesis in all horizons but B. Discrete kaolinite and illite and chloritesmectite were also affected but to a lesser extent because of their smaller abundances. In addition, the increase in the < 2 µm fraction content with increasing depth may further attenuate the impact on these clay species. The present results are thus consistent with the leaching process described for Luvisols, and more especially with undisturbed column leaching experiments performed with the same soil [START_REF] Rousseau | Preferential Transport of Soil Colloidal Particles: Physicochemical Effects on Particle Mobilization[END_REF].

Conclusions

The present study demonstrates that the combined use of XRD pattern decomposition and indirect identification from peak positions does not allow a complete identification of complex clay parageneses such as those commonly encountered in soils. However, when carefully used (see recommendations of [START_REF] Lanson | Decomposition of experimental X-ray diffraction profile (profile fitting): A convenient way to study clay minerals[END_REF], this approach can be a relevant preliminary step in the study of clay mineral evolution in soils formed on homogenous parent materials.

A complete, accurate and quantitative mineralogical characterization of complex clay parageneses requires fitting the data with a pattern calculated for a hypothesized mineral assemblage. Additional constraints can be obtained for a given sample by fitting various XRD patterns obtained after different treatments. Using this multi-specimen approach, structural characteristics and relative proportions of both discrete and mixed layer clays are obtained. The present study demonstrates that, although time-consuming, the multi-specimen approach can be applied to soil samples. The resulting mineralogical characterization of clays can then serve as the basis for studying their individual structural evolution, and that of their relative abundances along the profile.

In particular, it is shown in the present Luvisol profile that the structural characteristics of all clay minerals are essentially constant over the entire profile, thus reflecting the mineralogy of the parent material. As reported in the literature [START_REF] Duchaufour | Entraînement et destruction d'argile dans les horizons éluviaux des sols lessivés[END_REF][START_REF] Jamagne | Contribution à l'étude pédogénétique des formations loessiques du Nord de la France[END_REF][START_REF] Pedro | Two routes in genesis of strongly differentiated acid soils under humid, cool-temperate conditions[END_REF][START_REF] Jamagne | Mineralogy of clay fractions of some soils on loess in northern France[END_REF], pedogenesis ongoing in Luvisols affects, essentially, the vertical distribution of the different clay species as the result of particle migration. Our results indicate that the relative increase of smectite has a major contribution to the overall increase of the < 2 µm fraction with increasing depth. This interpretation of the mineralogical data is in agreement with the leaching process described for Luvisols in the literature and may be valid for other soils formed on loess deposits which are common in North America and Western Europe and used to grow crops. As the proposed approach allows us to gain detailed information on the structural evolution of individual clay species, further research could aim at determining the impact of fertilizers, human activities or plant nutrient uptake on the development of soil minerals. In addition, the complete and quantitative mineralogical characterization allows the comparison of clay parageneses in soils derived from different parent materials. 2 and3, the relative proportions of the different contributions in Table 4. 2 and3, the relative proportions of the different contributions in Table 4.

FIGURE CAPTIONS Figure 1 .

 1 FIGURE CAPTIONS

Figure 2 .

 2 Figure 2. Decomposition of XRD data. The experimental XRD patterns and the best fit

Figure 3 .

 3 Figure 3. Comparison between experimental (grey crosses) and calculated (solid lines)

Figure 4 .

 4 Figure 4. Elementary contributions to the diffracted intensity for the Bt horizon.

Figure 5 .

 5 Figure 5. Comparison between experimental XRD patterns (grey crosses) and

Figure 6 .

 6 Figure 6. Sensitivity of calculated XRD patterns to the mineralogical composition and

Table 1

 1 Main chemical and physical features of the soil profile studied (adapted from[START_REF] Moni | Stabilisation physique et physico-chimique de la matière organique dans les horizons profonds du sol[END_REF]

	Particle size fraction /µm

Table 2

 2 Structural parameters of the different clay layers. S1w: smectite with 1 sheet of interlayer H 2 O molecules; S2w: smectite with 2 sheets of interlayer H 2 O molecules; S1eg: smectite with 1 sheet of interlayer EG molecules; S2eg: smectite with 2 sheets of interlayer EG molecules

	layer type	Layer thickness /nm	Interlayer cation content a	Octahedral iron content a
	discrete illite	1.000	1.5	0.0
	illite in mixed layers	1.000	1.0	0.5
	smectite (S1w) b	1.250	0.5	1.2
	smectite (S2w) b	1.500	0.5	1.2
	smectite (S1eg) b	1.300	0.5	1.2
	smectite (S2eg) b	1.680	0.5	1.2
	chlorite	1.420	-	0.0
	kaolinite	0.716	-	-
	a number of atoms per formula unit

b

Table 3

 3 Composition and structural parameters of clay minerals in the different soil Parameter characterizing the orientation of particles on the X-ray slide CSDS: Coherent scattering domain size expressed in layers a S1w: smectite with 1 sheet of interlayer H 2 O molecules; S2w: smectite with 2 sheets of interlayer H 2 O molecules; S1eg: smectite with 1 sheet of interlayer EG molecules; S2eg: smectite with 2 sheets of interlayer EG molecules; I: illite layers both in discrete illite and in mixed layers

	horizons
	Phases	Horizon	Ap	E1g	E2g	Bt	Bt/C
		σ*	17	17	17	17	17
	illite	CSDS I/S2w a	18 98/2	18 97/3	18 97/3	18 95/5	18 97/3
		I/S2eg a	98/2	97/3	97/3	97/3	97/3
	kaolinite	σ* CSDS	18 20	18 20	18 20	18 20	18 20
	kaolinite	σ* CSDS	18 6	18 6	18 6	18 6	18 6
		σ*	21	21	21	21	21
	smectite	CSDS S1w/S2w a	3 33/67	3 46/54	3 47/53	3 36/64	3 23/77
		S1eg/S2eg a	21/79	28/72	17/83	24/76	6/94
		σ*	17	17	17	17	17
	illite-smectite	CSDS	9	6	6	6	7
	(R0)	I/S1w/S2w a	63/6/31	63/13/24 63/11/26 63/13/24	63/7/30
		I/S1eg/S2eg a 57/13/30	63/7/30	63/3/34	63/8/29	63/3/34
		σ*	17	17	17	17	17
	chlorite-smectite	CSDS	7	9	9	9	9
	(R0)	Ch/S1w/S2w a 62/13/25 52/11/37	52/6/42	52/2/46	52/8/40
		Ch/S1eg/S2eg a 62/0/38	52/0/48	52/6/42	52/0/48	52/0/48
	σ*:

Table 4

 4 Relative proportions (in weight percent) of the different contributions to the 1

	2	diffracted intensity
		Sample		illite	kaolinite (high CSDS)	kaolinite (low CSDS)	smectite	illite-smectite	chlorite-smectite
		Ap	AD EG	20 18	12 9	9 10	18 18	33 38	8 7
		E1g	AD EG	22 21	11 9	9 9	24 27	28 29	6 5
		E2g	AD EG	18 17	11 11	9 8	25 26	31 33	6 5
		Bt	AD EG	18 17	11 10	7 7	33 32	24 26	6 8
		Bt/C	AD EG	21 18	12 11	8 9	23 23	30 32	6 7
	3	CSDS: Coherent scattering domain size
	4	AD: Results obtained on the air-dried preparation
		EG: Results obtained after ethylene glycol solvation

Acknowledgments

Financial support from the ANR ECCO PCBB 'Carbone profond' (ANR-05-ECCO-011-04) program and HydrASA is acknowledged. The authors are grateful to Chevron Energy Technology Company, a division of Chevron U.S.A. Inc., which freely allowed using the Sybilla © software for academic purposes. The authors are especially indebted to Dr. Doug McCarty for its sustained help with Sybilla © . Dr. C. Moni and Professor C. Chenu (BioEMCO, France) kindly provided the soil samples.


Johann Hugon

Towards Adaptive ML Traffic Processing Systems

Keywords: CCS Concepts:, Networks → Network measurement, Network monitoring Traffic analysis, Dynamic configuration, Machine Learning

Machine learning techniques are a common solution used to solve a variety of network management tasks. Often, a network administrator chooses the model to deploy based on offline information, such as model performance and system load. Yet, network traffic is inherently dynamic making it hard to select an optimal model that can work throughout ever changing conditions. In this paper, we make the case that, instead of having to select the optimal candidate model based on offline information, systems should adapt based on the network conditions observed. We present a system design that takes as input a set of candidate models and their features, and adaptively selects the better configuration as a function of the network and system conditions.

INTRODUCTION

Nowadays Machine Learning (ML) techniques have become a common solution used to solve a variety of network management tasks. ML models simplify the identification of complex relationships between network traffic and important events occurring at different network layers. Thus, the networking community has developed ML models to help with traffic analysis tasks like QoE inference, traffic classification, intrusion detection, and more [START_REF] Boutaba | A comprehensive survey on machine learning for networking: evolution, applications and research opportunities[END_REF].

ML inference tasks are commonly identified by a three steps pipeline: the first step involves ingesting raw network traffic, where traffic undergoes multiple operations, including header parsing, flow tracking and reassembly, and more; the second step performs feature extraction, computing statistics and encoding information to prepare for the model; the third and final step inputs the processed features to the ML model (e.g., random forest, neural network) for the final inference. Conventionally, the performance of these pipelines is evaluated at training time based on the quality of the input features and the trained model type. Unfortunately, different factors can impact the actual performance of the model. For example, the inability of a measurement system to cope with the amount of incoming traffic can terminate in packet losses that dramatically impacts the quality of the produced features and the final model performance.

To meet different tradeoffs across model performance and system constraints, different models are available for each task. For example, in the case of video quality inference, Bronzino et al. [START_REF] Bronzino | Traffic refinery: Cost-aware data representation for machine learning on network traffic[END_REF] presented a study of the impact that different feature sets have on the accuracy of video quality inference models as well as on the costs that collecting such features has on the measurement system. However, in most cases, models trained offline in a lab setting provide little to no representation of the system's ability to capture traffic nor the impact that packet loss can have on model performance. For these reasons, the users of these models have to decide a priori on which model might best fit their deployment, configuring their measurement system accordingly [START_REF] Bronzino | Traffic refinery: Cost-aware data representation for machine learning on network traffic[END_REF][START_REF] Wan | Retina: Analyzing 100GbE Traffic on Commodity Hardware[END_REF]. Yet, network traffic is inherently dynamic and varies throughout the day due to continuous shifts in usage, making it hard, if not impossible, to select an optimal configuration that can work throughout these changes. Further, substituting such configurations requires to first observe that the system is not capable of processing the traffic, and then manually change the configuration causing further loss due to reboot times. In this paper, we argue that the best advantage point to understand a system's ability to process traffic and generate the features for a target model is the system itself. Instead selecting the optimal candidate model based on offline information, systems should adapt based on up-to-date information of the traffic observed as well as on the system's ability to extract the requested features for a specific traffic load. Towards this, we present the high level design of a system that takes as input a set of candidate ML models, and the features they require as input, and adaptively selects the better fitting configuration as a function of the network and the system conditions.

USE CASE: VIDEO QUALITY INFERENCE

To demonstrate the impact that the offline choice of a model can have, we focus on the task of video quality inference from encrypted traffic. We partially recreate the experiment from Bronzino et al. [START_REF] Bronzino | Traffic refinery: Cost-aware data representation for machine learning on network traffic[END_REF] and train two candidate machine learning models to infer the resolution of video streaming applications over time. The two models use two different feature sets: the first model employs networklayer features, e.g., packet counters and throughput, while the second model uses application-layer metrics gathered from observing packet patterns generated by video applications, i.e., video segments sizes. We evaluate the performance of the two models in perfect conditions, i.e., with no packet loss, as well as the impact that packet loss can have on the best performing model. From Figure 1 we observe that at no loss the model that uses application layer features does indeed outperform the model that uses network layer features by more than 15%. However, when we introduce packet loss, the performance deteriorates rapidly, and the network-layer based model starts to outperform the other model at around 15% loss.

We then implement the two models in a real system, Retina [START_REF] Wan | Retina: Analyzing 100GbE Traffic on Commodity Hardware[END_REF], and evaluate the ability of the system to extract the required features at varying traffic loads. To emulate realistic traffic, we deploy the system on a testbed with two servers connected by a 100gbps programmable switch. On the second server we deploy TRex [START_REF]TRex, Realistic Traffic Generator[END_REF] injecting an IMIX "SFR" profile, a combination of various traffic templates that we enhance with video traffic, at different rates. In Figure 2 we show the amount of packets per second the system is capable of processing with respect to the injected rate. We observe that, when processing application-layer features, the system starts dropping packets at around 12 Mpps, a 39% lower processing capacity compared to the network-layer features.

These two experiments show that, as traffic loads increase, it might be beneficial to lower-cost configurations and models as a preferred solution to maximize performance. More broadly, they support the argument that it is challenging to train a single model that works in every condition, suggesting the need for an adaptive system, as described in the next section.

DYNAMIC CONFIGURATION

In this section, we propose the high level design of a system that adaptively choses the best ML model to use at any point in time according to the trade-off between model accuracy, system capabilities, a prototype that implements the whole system from the feature extraction components, the ML models, to the monitor that selects features and ML models in real time.

This early work presents several interesting challenges to overcome and future work directions to explore. One key challenge involves expanding the array of feature sets to satisfy the requirements of various machine learning models. Furthermore, exploring more complex profiling metrics beyond the scope of packet loss alone promises to be an interesting avenue of research. With the inclusion of these metrics, our system will be more proficient in extracting the most suitable feature set for the current network context, thus ensuring the choice of the best model.

Fig. 2 .

 2 Fig. 1. F1-score over Loss rate

Network Card

Model Selection

Features extraction Packet Capture

Monitor Renderer Worker Filter

To ML Model Profiler Configuration Fig. 3. Scheme of the system and network load. Starting from a pool of candidate models, and their underlying features to collect, the system comprises three key building blocks, as illustrated in Figure 3. Model Selection. The model selection module has the goal of tracking the system performance and select the best candidate model given the observed environment. The module consists of two parts which create the capabilities for the system to self adapt this configuration without intervention or reboot. The profiler analyzes the performance of the system itself (CPU and memory usage, number of instructions required per feature, etc.). The monitor continuously aggregates information from the profiler as well as statistics from the Packet Capture module (e.g., packets received, packets dropped, etc.). Using this information, the monitor decides whether it is necessary to update the features collected by the system in the likelihood of reaching a bottleneck. Packet Capture. To support high network rates and fast packet processing, the system relies on state-of-the-art packet capture libraries process. Further, the system enables the implementation of packet filters to drop early any unnecessary flow and focus on traffic of interest. Feature Creation. The Feature Creation module is the final step of the packet processing pipeline and it is in charge of transforming raw packets in features to be used by ML models. The module is composed of a set of workers that compute the features selected by the monitor as fast as possible. After processing, the Renderer aggregates the collected features and compute the final representations to be used by the ML models (e.g., averages, min/max, etc.).

In summary, the system consists of three fundamental building blocks, each strategically designed to optimize the tradeoff between model accuracy, system capabilities, and network context. Together, these modules enable our system to seamlessly adapt remaining attuned to the inherent dynamicity of network traffic.

CONCLUSION

In this paper, we have proposed the design of a system that adapts in real time to varying network conditions to select the best features and models for ML-based network management tasks. Such a system can be used to simplify the deployment of ML models in in concrete applications for network administrators and operators to more easily rely on machine learning solutions to drive their networks. Our first implementation shows encouraging early results. We are currently developing