Amine Boukra

Matthieu Masson
email: matthieu.masson@inrae.fr

Corinne Brosse

Mahaut Sourzac

Edith Parlanti

Cécile Miège

Title. Sampling terrigenous diffuse sources in watercourse: influence of land use and hydrological conditions on dissolved organic matter characteristics

Keywords: Dissolved organic matter, non-point sources, land-use, optical fingerprint

This study addresses the sampling of non-point sources of DOM in watercourses

• A combination of land use markers discriminated DOM terrigenous

Introduction

Dissolved organic matter (DOM) is a complex set of organic compounds operationally defined as material obtained after water filtration (commonly ranging from 0.2 to 0.7 µm) [START_REF] Zsolnay | Dissolved organic matter: artefacts, definitions, and functions[END_REF][START_REF] Zark | Universal molecular structures in natural dissolved organic matter[END_REF] with an average molecular size distribution that ranges from <100 Da to >100000 Da [START_REF] Nebbioso | Molecular characterization of dissolved organic matter (DOM): a critical review[END_REF][START_REF] Hawkes | Complexity of dissolved organic matter in the molecular size dimension: insights from coupled size exclusion chromatography electrospray ionisation mass spectrometry[END_REF]. DOM plays a major role in environmental biogeochemistry, particularly as the main driver of terrestrial carbon to the aquatic environment, as a substrate for the growth of microorganisms [START_REF] Bolan | Chapter One -Dissolved Organic Matter: Biogeochemistry, Dynamics, and Environmental Significance in Soils[END_REF][START_REF] Mladenov | Groundwater-surface water interactions and flux of organic matter and nutrients in an urban, Mediterranean stream[END_REF], but also in the fate and bioavailability of pollutants [START_REF] Reuter | Importance of heavy metal-organic matter interactions in natural waters[END_REF][START_REF] Aiken | 1.11 -Dissolved Organic Matter in Aquatic Systems[END_REF]. At the scale of a watershed, DOM inputs to the rivers can originate from a wide range of natural and anthropogenic sources [START_REF] Nebbioso | Molecular characterization of dissolved organic matter (DOM): a critical review[END_REF].

These sources can be either point sources (e.g. wastewater treatment plants and storm overflows) or diffuse discharges (e.g. terrigenous inputs related to land use, underground inputs, autochthonous production; [START_REF] Carstea | In situ fluorescence measurements of dissolved organic matter: A review[END_REF][START_REF] Williams | Human activities cause distinct dissolved organic matter composition across freshwater ecosystems[END_REF].Point discharges of DOM can be easily located and their sampling is often representative of these sources. For example, DOM from wastewater treatment plant discharges, constitutes a mixture of organic molecules including microbial degradation products, surfactants, pharmaceutical products, phytosanitary products (herbicides, fungicides, insecticides) and disinfection by-products [START_REF] Michael-Kordatou | Dissolved effluent organic matter: Characteristics and potential implications in wastewater treatment and reuse applications[END_REF][START_REF] Verkh | Extraction and cleansing of data for a nontargeted analysis of high-resolution mass spectrometry data of wastewater[END_REF].

Diffuse sources of DOM are more difficult to locate and study due to the complexity of geochemical interactions, degradation processes and the uncontrolled meteorological events at the origin of these DOM sources. In the case of terrigenous contributions of diffuse DOM sources, studies have shown that the soil type governs the amount of DOM transferred to the aquatic downstream environment [START_REF] Bolan | Chapter One -Dissolved Organic Matter: Biogeochemistry, Dynamics, and Environmental Significance in Soils[END_REF]. Organic type soils discharge more DOM than mineral type soils. Land use as well as soil biomass influence the composition of DOM transferred to the watercourse [START_REF] Kalbitz | Biodegradation of soil-derived dissolved organic matter as related to its properties[END_REF]. This could be explained by the fact that DOM is considered to be the most active and labile part of soil organic matter [START_REF] Guigue | A comparison of extraction procedures for water-extractable organic matter in soils[END_REF].Low molecular weight labile compounds make up the organic matter in the surface layers of the soil. Their proportion decreases in depth soils giving way to higher fraction of refractory compounds of high molecular weight. In addition, the hydrology of the watershed, or more specifically, the direction of water flow along the soil, determines the type of organic matter transferred to rivers. Indeed, [START_REF] Sanderman | Linking soils and streams: Sources and chemistry of dissolved organic matter in a small coastal watershed[END_REF] demonstrated that vertical flow would favor the transfer of the more refractory denatured organic matter, whereas lateral flow would transfer labile organic matter characteristic of the surface soil layers. However, establishing DOM fingerprints in rivers related to land uses and occupations, driven hydrology, is a complex task. The high reactivity of DOM labile fraction coupled with environmental conditions and the nature of the soils make difficult the establishment of reliable DOM fingerprints. Here we define a DOM fingerprint as a set of physico-chemical markers calculated from one or several analytical techniques (e.g. optical characteristics, molecular size distribution), which are relevant to discriminate a given source. At present, classically used techniques such as UV-Visible spectroscopy and excitation emission matrix (EEM) fluorescence have brought major advances in the study of chromophoric and fluorescent DOM. The application of these spectroscopic techniques has allowed, for example, to differentiate between types of DOM depending on the sources and the state of evolution [START_REF] Li | Utilization of UV-Vis spectroscopy and related data analyses for dissolved organic matter (DOM) studies: A review[END_REF]. Another analytical technique that showed relevance to characterize DOM composition, is the size exclusion chromatography (HPSEC). The principle of HPSEC is based on the separation of molecules according to their size or hydrodynamic volume. Previous studies have shown that HPSEC can be used to determine the distribution of molecular weight for DOM by calculating indicators used to characterize polymers such as average molecular weight (Mw), number average molecular weight (Mn) and polydispersity (p) [START_REF] Huang | Dissolved organic matter characterization in high and low ammonium groundwater of Dongting Plain, central China[END_REF]. Detection by diode arrays and fluorescence (HPSEC/UV-fluorescence) allowed to specifically target absorbing and fluorescent compounds in organic matter, providing further qualitative information on the size continuum of DOM molecules [START_REF] Asmala | Identification of dissolved organic matter size components in freshwater and marine environments[END_REF][START_REF] Brezinski | An overview of the uses of high performance size exclusion chromatography (HPSEC) in the characterization of natural organic matter (NOM) in potable water, and ion-exchange applications[END_REF]. However, the combined information of molecule size and type, provided by HPSEC/UV-fluorescence, could be further explored to propose relevant indicators improving DOM fingerprints. In this context, the aim of this paper was to determine the representativeness of sampling a terrigenous diffuse source of DOM in watercourses. More precisely, we studied the link between soilextracted DOM, characterized by a particular land use, and DOM collected in the soil-adjacent watercourse. A second objective was to improve the study of DOM optical fingerprints by introducing new indicators from size exclusion chromatography HPSEC/UV-fluorescence.

To achieve this, the characteristics of i) DOM extracted from soils defined by distinct land use (forest and vineyard), and ii) DOM from adjacent watercourses collected during high and low water periods were compared. . The starting hypothesis is that during the high water period, there would be a greater contribution of the terrigenous source. This comparison was performed by characterizing DOM properties using a combination of optical analysis techniques including UV-Visible spectrophotometry, EEM fluorescence spectroscopy and HPSEC/UVfluorescence.

Materials and methods

Site description

All sampling areas were located in Ardière-Morcille watershed (152 km 2 ) in eastern France.

The catchment area, in its downstream part, is characterized by vineyard activities representing more than 32 % of total landscape [START_REF] Peyrard | A trench study to assess transfer of pesticides in subsurface lateral flow for a soil with contrasting texture on a sloping vineyard in Beaujolais[END_REF]. Other land uses such as forests (37 %) and pastures (21 %), are also present in the upstream watershed (Figure 1). The region's climate is semi-continental with a mean annual rainfall of 940 mm and episodic snowfalls during winter [START_REF] Gouy | Ardières-Morcille in the Beaujolais, France: A research catchment dedicated to study of the transport and impacts of diffuse agricultural pollution in rivers[END_REF]. The soils are mostly sandy and erodible and the geological characteristics are an altered hercynian crystalline basement of mostly porphyric biotite granite. The watershed is characterized by very steep slopes, ranging between 5 and 30-35 % favoring surface runoff. In addition, numerous and fast hydrological events make the riverbed, rarely dry [START_REF] Rabiet | Transfer of metal(loid)s in a small vineyard catchment: contribution of dissolved and particulate fractions in river for contrasted hydrological conditions[END_REF].

Sampling design and samples preparation before experimentations in laboratory

Water samples were collected manually from rivers, downstream of 10 homogenous subcatchment areas characterized by 5 forest land occupations and 5 vineyard land uses (Figure 1). Sub-catchment land uses were determined based on Corine Land Cover 2018 using Qgis 3.14 software. Sampling was carried out during two campaigns: A first sampling campaign in January 2021 during a period of high water (3.65 and 0.2 m 3 .s -1 respectively for Ardières and Morcille Rivers) and a second sampling campaign in July 2021 during the period of low water (0.65 and 0.03 m 3 .s -1 respectively for Ardières and Morcille Rivers). The flow data was obtained at Villié-Morgon and Beaujeau stations located downstream of the Ardières and Morcille rivers.

The water samples were collected in 250 mL borosilicate glass bottles previously cleaned by an automatic washer at 90°C, then calcined in an oven at 500°C. The samples were filtered in the field using polypropylene syringe and polyvinylidene fluoride (PVDF) filters with a porosity of 0.45 µm. The filtrate was first used to rinse the 250 mL borosilicate glass bottle three times before filling them completely. The samples were then stored in a cooler (at ± 4°C) protected from light during their transport to the laboratory, then stored at 4°C in the dark until analysis. Experimental blanks using ultrapure water (resistivity at 18.2 MΩ.cm) were prepared in laboratory using the same protocol as in the field, in order to identify possible contamination due to bottles, syringes or filters. Soils were sampled in the forest and vineyard sub-catchment areas upstream of water samples (radius of 30 to 50 m) during the high water sampling campaign. Detailed geographic coordinates are available in supplementary material 1. In each site, 20 cm of top soils were taken with an auger; four subsamples were randomly selected to collect approximately 1 kg of soil. Each subsample was placed in a polypropylene bag. Once all 4 subsamples were collected, the bulk sample was mixed in the bag. The 10 soil samples were stored at 4°C protected from light until preparation in the laboratory where the soils were sieved with a 2 mm stainless steel sieve, placed in aluminum trays (40x60 cm) and dried for 96 h at 40 °C in an oven.

To summarize, for each sub-catchment area, one water sample was collected during high water period as well as one soil sample (composite of 4 randomly collected subsamples). During low water periods, an additional water sample was collected.

Dissolved organic matter extracted from soils (soil extracts)

Dissolved organic matter was extracted from soil samples by stirring 20 g (dry weight) of soil in 200 mL of ultrapure water with 10 mM CaCl2 (Supplementary Material 2). Stirring was performed at 180 rotations per minute in a Lovibond thermoregulator cabinet at 20 °C in dark condition. After 6 h of agitation, the samples were centrifuged at 4500 g during 15 min and the supernatant was filtered through 0.45 µm (PVDF filter). An initial 60 mL sample was collected before the incubation experiment.

Incubation experiment

Two inoculums of forest and vineyard soils were prepared 48 h before the incubation experiment. To obtain better microbial diversity, both forest and vineyard inoculums were prepared from, respectively, a mixture of the 5 forest soils and the 5 vineyard soils [START_REF] Kalbitz | Biodegradation of soil-derived dissolved organic matter as related to its properties[END_REF][START_REF] Guigue | A comparison of extraction procedures for water-extractable organic matter in soils[END_REF]. For each inoculum, 5 g of the 5 corresponding soil samples were added to 200 mL of ultrapure water. These preparations were then shaken at 20° for 48h in the dark. A nutrient solution of (NH4)2SO4 and KH2PO4 (C:N:P:S:K molar ratio of <5:1:1:1:1) was also prepared 1h prior to the incubation. The addition of nutrients allows optimizing the activity of the microorganisms during the following incubation.

Incubation of DOM extracted from soils was performed by adding 35 µL of inoculum and 1 mL of nutrient solution to the samples immediately after the soil DOM extraction step [START_REF] Guigue | A comparison of extraction procedures for water-extractable organic matter in soils[END_REF] (Supplementary Material 2). Controls without inoculum nor nutrient solution (inoculum blanks) and controls without soil extracted DOM (extraction blanks) were performed. All samples and controls were incubated at 20°C in the dark, with continuous shaking at 180 rotations per minute during 28 days. The incubation period of 28 days was chosen based on previous work that studied the time required to degrade the labile fraction of DOM from soil samples [START_REF] Guigue | A comparison of extraction procedures for water-extractable organic matter in soils[END_REF]. Sub-samples at 3, 7, and 14 days of incubation were collected to monitor changes in DOM quantity and quality (optical properties).

Analytical strategy

Dissolved organic Carbon

Dissolved organic carbon (DOC) analyses were performed by high temperature catalytic combustion according to the standard NF EN 1484 and using an Analytik Jena multi N/C® 3100 TOC analyzer. The calibration, rinsing, quality controls solutions, as well as samples, were introduced in precombusted (at 500°C during 2 h) glass vials, where they were acidified to pH=1 with hydrochloric acid (HCl 37% RPE). The detection limit was 0.2 mgC.L -1 and the analytical uncertainty was 12%. The accuracy of the analyses (105%) was routinely checked using a certified standard of potassium hydrogen phthalate (5 mg.L -1 , Fluka ® ) different from that used for the calibration (0.2-25 mgL -1 , Sigma-Aldrich ® ).

UV-Visible spectroscopic analysis

UV-Visible spectroscopy analyses were performed using a Shimadzu UV 1900 spectrophotometer with a 1 cm path length quartz cell (Hellma Analytics®). Absorbance spectra were acquired between 200 and 800 nm with a resolution of 1 nm and a scan speed of 0.2 s.nm -1 . A baseline correction was carried out using an ultrapure water blank over the same wavelength range. A series of classical descriptive indicators (SUVA254, absorbance ratios and spectral slopes) were calculated from the generated absorbance spectra (Table 1).

EEM fluorescence spectroscopy and PARAFAC decomposition

Excitation-emission matrix (EEM) fluorescence analyses were performed using an Aqualog (Horiba Scientific) spectrofluorometer in a 1 cm path length quartz cuvette (Hellma Analytics®) thermostated at 20°C. The Aqualog instrument was equipped with a 150 W Xenon arc lamp and excitation wavelengths were scanned using a double-grating monochromator from 240 to 800 nm at 5 nm intervals, while the emission spectra were obtained using a high-gain CCD detector at intervals of approximately 0.58-nm (1-pixel) for wavelengths from 240 to 800 nm. All EEM spectra were corrected for instrumental biases and normalized to the area under the Raman peak of water, at 350 nm excitation, acquired daily. Fluorescence intensities are therefore expressed in Raman units (R.U). In order to avoid inner filter effects, all samples with maximum absorbance > 0.1 were diluted. Raman and Rayleigh scattering peaks were removed by subtracting blank spectrum. The generated spectra were treated using TreatEEM-V1 software developed by Dario Omanović (Ruđer Bošković Institute, Zagreb, Croatia; https://sites.google.com/site/daromasoft/home/treateem). The fluorescence indices HIX (Zsolnay), BIX, FI, YFI (Table 1) were calculated for an excitation wavelength of 250, 310, 370 and 280 nm respectively [START_REF] Heo | A new fluorescence index with a fluorescence excitation-emission matrix for dissolved organic matter (DOM) characterization[END_REF][START_REF] Huguet | Properties of fluorescent dissolved organic matter in the Gironde Estuary[END_REF][START_REF] Mcknight | Spectrofluorometric Characterization of Dissolved Organic Matter for Indication of Precursor Organic Material and Aromaticity[END_REF][START_REF] Zsolnay | Differentiating with fluorescence spectroscopy the sources of dissolved organic matter in soils subjected to drying[END_REF] The multi-way parallel factor analysis (PARAFAC) was applied to a set of 103 EEM spectra (corresponding to 83 soil extracts and 20 water samples collected from the adjacent streams).

The PARAFAC model was run, using the drEEM toolbox under MatLab R2020a, for 4 to 8 components with non-negativity constraints [START_REF] Murphy | Fluorescence spectroscopy and multi-way techniques[END_REF]. Four components were validated based on split-half analysis and compared to previously reported components using the OpenFluor fluorescence database.

Size exclusion chromatography HPSEC/UV-fluorescence

High performance size exclusion chromatography (HPSEC; LC-2030C 3D Plus, Shimadzu) coupled with photodiode array (Deterium D2 Lamp PDA) and fluorescence (RF-20A xs) detectors was used to determine the molecular size distribution of DOM. The injection volume was 10 µL with a flow rate at 0.8 mL.mn -1 of phosphate buffer mobile phase (NaCl, KH2PO4 and K2HPO4). Two columns (Shodex OHpak SB-803 HQ, Shodex OHpak SB-802 HQ) coupled in series were used for the chromatographic separation. The first column covered an exclusion range between 1 kDa and 100 kDa and the second one between 0.2 kDa and 1 kDa. Analytical standards PSS (polysulfonate) were used as references of average molecular weights (0.246, 1. [START_REF] Thieme | Dissolved organic matter characteristics of deciduous and coniferous forests with variable management: different at the source, aligned in the soil[END_REF]4.3,6.8,10,17,32,77 kDa). Other standards were also used to cover a wider range of molecule types, such as nitrates (0.063 kDa), Bovin Serum Albumin BSA (66 kDa) and Polyacrylic Acid PAA standards (1, 2.6 and 3.6 kDa). A calibration curve of molecular weight (from 0.2 -to 77 kDa) according to elution volume was calculated using these analytical standards [START_REF] Brezinski | An overview of the uses of high performance size exclusion chromatography (HPSEC) in the characterization of natural organic matter (NOM) in potable water, and ion-exchange applications[END_REF].

The UV-DAD detector allowed the acquisition of chromatograms on an absorbance range between 200 and 450 nm with an increment of 1.2 nm every 300 ms. Regarding the fluorescence detector, 3 couples of excitation-emission wavelengths (Ex-Em) were retained for all the analyses The fluorescence intensities were measured for the wavelengths corresponding to the humic-like components (315-443 nm), protein-type components (280-330 nm), and tryptophantype components (278-354 nm) were measured every 400 ms.

To optimize the use of the data generated by HPSEC/UV-fluorescence, a Gaussian decomposition was performed. The aim was to decompose the size continuum obtained in each HPSEC chromatogram into distinct Gaussian components (Eq. 1). For this, the toolbox «peakfit.m » (O'Haver, 2020) was applied on MatLab R2020a.

Eq. 1 :

; µ; ; = µ + where nC is the number of Gaussian components, is the residuals which represent the variability not taken into account by the model, is the peak area, µ is the peak position parameter (elution volume), is the peak width and is the proportion of each fitted Gaussian distribution.

The number of detected components was validated using the Bayesian Information Criterion [START_REF] Asmala | Identification of dissolved organic matter size components in freshwater and marine environments[END_REF]. Areas of the identified Gaussian components were summed in order to calculate the total sec absorbance (TSA) from chromatograms obtained with detection at UV 254 nm [START_REF] Asmala | Identification of dissolved organic matter size components in freshwater and marine environments[END_REF]. The total sec fluorescence TSF was calculated from chromatograms obtained with fluorescence detection at three excitation-emission (Ex-Em) wavelengths (nm): Ex: 315-Em: 443, Ex: 280-Em: 330 and Ex: 278-Em: 354. These wavelengths are classically used to characterize DOM properties (Table 1). The calibration curve allowed classifying each Gaussian component in a molecular weight fraction, based on the peak position (elution volume). In this study, three molecular weight fractions were defined as: low molecular weight fraction (LMW) with an average molecular weight < 1 kDa, medium molecular weight fraction (MMW) with an average molecular weight ranging from 1 to 10 kDa, and high molecular weight (HMW) with an average molecular weight >10 kDa. The LMW, MMW and HMW fractions represent the relative percentages of respectively small, medium and large molecules detected at the measured wavelengths.

Mathematical and statistical analyses

Anova analysis coupled with a Tukey test (packages stats and rstatix; R 4.0.

Results

Dissolved organic carbon

Before incubation, dissolved organic carbon (DOC) concentrations (Figure 2.A) in the 5 forest soil extracts ranged from 22.7 to 48.2 mg.L -1 with a mean value of 32.7 ± 9.4 mg.L -1 . For the 5 vineyard soil extracts, DOC concentrations varied between 16.14 and 34.14 mg.L -1 with a mean value of 23.8 ± 6.6 mg.L -1 . These values are consistent with those obtained in previous studies [START_REF] Rinot | Fluorescence spectroscopy: A sensitive tool for identifying land-use and climatic region effects on the characteristics of waterextractable soil organic matter[END_REF]. No significant difference (Tukey test, p > 0.05, n=50) in DOC concentrations was found between forest and vineyard soil extracts before incubation.

The percentage of DOC (Figure 2.B) was calculated for the duration of the experiment (28 days). For forest soil extracts, the percentage of DOC decreased by 67 ± 8 %, with a significant decrease (Tukey test, p < 0.05, n=50)) of 42 ± 9 % within the first three days of incubation. For vineyard soil extracts, the percentage of DOC decreased by 61 ± 3 %, with a significant decrease of 46 ± 5%, again during the first three days of incubation. Previous studies showed DOC losses range from 5 to 93% depending on soil types (forest, pasture, arable) and extraction protocols (pressurized hot-water, water extraction, leaching extraction) [START_REF] Guigue | A comparison of extraction procedures for water-extractable organic matter in soils[END_REF][START_REF] Kalbitz | Biodegradation of soil-derived dissolved organic matter as related to its properties[END_REF].

DOC concentrations of samples collected in streams adjacent to forest soils ranged from 2.2 to 3.0 mg.L -1 during high water periods (Figure 2.A). For these same sites, DOC concentrations were significantly higher (Tukey test, p < 0.05, n=20) ranging between 3.3 mg.L -1 and 4.6 mg.L - 1 during low water periods. In the streams adjacent to vineyard soils, DOC ranged from 3.1 to 4.4 mg.L -1 during high water. Non-significant difference was observed during low water periods with DOC concentrations ranging between 3.5 and 4.6 mg.L -1 . In addition, DOC concentrations were significantly higher in the vineyard stream samples than in the forest stream samples only during high water.

UV-Visible

UV-Visible spectra (Supplementary Material 3) show a classical pattern, i.e. an exponential decrease between 200 and 250nm, followed by a slight decrease between 250 and 400 nm. Then the signal is close to the background for wavelength superior to 400 nm. A decrease in absorption is observed between the soil extracts before and after 28 days of incubation, at wavelengths from 250 to 400 nm, i.e. the range classically used to characterize the chromophoric DOM. SUVA254 (Table 1) increased significantly (Tukey test, p < 0.05, n=50) over the 28-day incubation period of the experiment, from 0.98 ± 0.11 to 2.02 ± 0.12 L.mg -1 cm - 1 for forest soil extracts, and from 1.44 ± 0.45 to 3.02 ± 0.51 L.mg -1 cm -1 for vineyard soil extracts (Figure 3 1) ratios did not vary significantly between the soil extraction and the last day of the experiment (Figure 3.D, E, F).

Regarding samples collected in adjacent streams, no significant difference was observed according to land use. However, the indicator SR showed significant differences between high water and low water sampling periods (Tukey test, p < 0.05, n=20). Indeed, values of SR varied between 0.751 ± 0.0497 to 0.808 ± 0.012 and 0.775 ± 0.027 to 0.833 ± 0.011 for both forest and vineyard adjacent water samples. Previous studies on soil extracts and stream water samples [START_REF] Sanderman | Linking soils and streams: Sources and chemistry of dissolved organic matter in a small coastal watershed[END_REF]Liu et al., 2021;Chen et al., 2021) have reported UV-Visible index values in the same ranges as those presented in this work.

EEM fluorescence spectroscopy

The humification index (HIX; Table 1) showed a significant increasing trend during the first days of incubation (Tukey test, p < 0.05, n=50). These values stabilized for vineyard soil extracts while they decreased for forest soil extracts at the end of incubation (Figure 4.A).

Indeed, the values increased from 3.1 ± 1.0 to 3.7 ± 1.5 for the forest soil extracts and from 2.9 ± 0.4 to 6.6 ± 0.7 for the vineyard soil extracts. Therefore, a significant difference (Tukey test, p < 0.05, n=50) is also observed between the two types of soils at the end of the experiment.

No particular trend was observed for the indicator of biological activity (BIX; For water samples, only HIX showed a significant difference between water collected during high and low water (Tukey test, p< 0.05, n=20). HIX values varied between 8.44 ± 0.88 and 7.28 ± 1.11 for the streams adjacent to the forest, sampled during high and low water periods.

For vineyard streams, it varied between 9.05 ± 0.34 and 7.39 ± 0.53 during the two sampling periods. The other indices BIX, FI and YFI showed no significant differences between forest and vineyard waters, nor between sampling periods. Values of fluorescence indices in this work are consistent with previous studies obtained on forest soils, peat soils, and subsoil extracts [START_REF] Hansen | Optical properties of dissolved organic matter (DOM): Effects of biological and photolytic degradation[END_REF][START_REF] Olshansky | Wet-dry cycles impact DOM retention in subsurface soils[END_REF][START_REF] Zhang | The spectral characteristics and cadmium complexation of soil dissolved organic matter in a wide range of forest lands[END_REF]

PARAFAC modeling

The contour plots of the 4 components determined by PARAFAC analysis are shown in supplementary material 4. Components C1 to C4 were identified from the literature and successfully matched in the OpenFluor database with similarity scores above 0.97. Component C1 showed two excitation maxima, a first one at ≤ 240 nm and a second one with lower intensity at 320 nm with an emission maxima at 420 nm. The component C1 has been described as terrestrial DOM degraded from lignin [START_REF] Peleato | Neural networks for dimensionality reduction of fluorescence spectra and prediction of drinking water disinfection byproducts[END_REF] typical of soils and terrestrial sources in aquatic environments [START_REF] Garcia | Characterisation and reactivity continuum of dissolved organic matter in forested headwater catchments of Andean Patagonia[END_REF][START_REF] Yamashita | Relationships between dissolved black carbon and dissolved organic matter in streams[END_REF]. This component has further been attributed to bioavailable organic matter, microbially derived and/or sensitive to photodegradation [START_REF] Cawley | Characterising the sources and fate of dissolved organic matter in Shark Bay, Australia: a preliminary study using optical properties and stable carbon isotopes[END_REF][START_REF] Eder | Pathways and composition of dissolved organic carbon in a small agricultural catchment during base flow conditions[END_REF]. Component C2 showed an excitation maxima at ≤ 240 and a lower intensity one at 390 nm with a maximum emission intensity at 510 nm. Previous studies have reported the component C2 as an ubiquitous terrestrial material with high molecular weight (MW) and aromatic content [START_REF] Cawley | Characterising the sources and fate of dissolved organic matter in Shark Bay, Australia: a preliminary study using optical properties and stable carbon isotopes[END_REF][START_REF] Wünsch | Quantifying the impact of solid-phase extraction on chromophoric dissolved organic matter composition[END_REF][START_REF] Yamashita | Relationships between dissolved black carbon and dissolved organic matter in streams[END_REF]. It has also been reported as fluorophores derived from higher plants and associated with photochemical [START_REF] Coulson | Small rain events during drought alter sediment dissolved organic carbon leaching and respiration in intermittent stream sediments[END_REF][START_REF] Eder | Pathways and composition of dissolved organic carbon in a small agricultural catchment during base flow conditions[END_REF] or microbial [START_REF] Cory | Fluorescence Spectroscopy Reveals Ubiquitous Presence of Oxidized and Reduced Quinones in Dissolved Organic Matter[END_REF] degradation. Component C3 showed an excitation maximum at 365 nm and an emission at 443 nm. It has been reported to be high MW, aromatic and hydrophobic molecules, corresponding to lignin-like compounds [START_REF] Dainard | Photobleaching of fluorescent dissolved organic matter in Beaufort Sea and North Atlantic Subtropical Gyre[END_REF][START_REF] Derrien | Estimation of different source contributions to sediment organic matter in an agricultural-forested watershed using end member mixing analyses based on stable isotope ratios and fluorescence spectroscopy[END_REF][START_REF] Rinot | Fluorescence spectroscopy: A sensitive tool for identifying land-use and climatic region effects on the characteristics of waterextractable soil organic matter[END_REF]. Other studies reported component C3 as organic matter of plant origin that has undergone little transformation in the soil after production [START_REF] Catalá | Marine dissolved organic matter: a vast and unexplored molecular space[END_REF][START_REF] Retelletti Brogi | In-Depth Assessment of the Effect of Sodium Azide on the Optical Properties of Dissolved Organic Matter[END_REF]. Finally, the component C4 showed an excitation maximum at 280 nm and an emission at 330 nm. Numerous studies have reported this component to be attributed to amino acids, either free or bound to proteins, or to phenolic-type compounds [START_REF] Coble | Characterization of marine and terrestrial DOM in seawater using excitation-emission matrix spectroscopy[END_REF][START_REF] Kida | Origin, distributions, and environmental significance of ubiquitous humic-like fluorophores in Antarctic lakes and streams[END_REF][START_REF] Parlanti | Dissolved organic matter fluorescence spectroscopy as a tool to estimate biological activity in a coastal zone submitted to anthropogenic inputs[END_REF][START_REF] Wauthy | Increasing dominance of terrigenous organic matter in circumpolar freshwaters due to permafrost thaw[END_REF].

Of the four components identified, only component C4 showed a decreasing trend during the incubation experiment (Figure 5). Indeed, for both soil extracts, the maximum fluorescence intensity of the C4 component decreased significantly (Tukey test, p < 0.05, n=50), from 2.6 ± 0.3 ± to 0.8 ± 0.2 for the forest soil extracts and from 1.9 ± 0.7 to 0.5 ± 0.1 for the vineyard soil extracts. On the other hand, all components showed significant differences between streams adjacent to the forest sampled during high and low water periods. In these samples, component C1 varied between 0.62 ± 0.1 and 0.97 ± 0.19 R.U, C2 between 0.34 ± 0.06 and 0.58 ± 0.11 R.U, component C3 between 0.22 ± 0.03 and 0.34 ± 0.06 R.U and component C4 varied between 0.10 ± 0.02 and 0.16 ±0.01 R.U.

Size exclusion chromatography and Gaussian decomposition

The HPSEC/UV-fluorescence chromatograms provided additional information on the size distribution of DOM molecules contained in the samples. The Gaussian decomposition of the chromatograms revealed 6 to 8 fractions, depending on wavelength detection, distributed throughout the chromatogram. The percentage contribution of the LMW fraction (Section 2.5.4), for UV detection at 254 nm (Figure 6.A) and fluorescence at 280-330 and 278-354 nm (Figure 6.C, D), was significantly higher, before incubation, in forest soil extracts compared to vineyard soil extracts (Tukey test, p < 0.05, n=50). At the end of the experiment, the percentage of LMW was different only for UV detection at 254 nm (Tukey test, p < 0.05, n=50). For the adjacent water streams, significant differences were observed on the 280-330 and 278-354 nm fluorescence ranges according to the low vs. high water hydrological regime and this for both soil occupations (Figure 6.C,D). The MMW fraction, which corresponds to all Gaussian components classified between 1 kDa and 10 kDa, showed the least variation. Nevertheless, the percentage of MMW at UV 254 nm were significantly different between the two types of soil extracts at the end of the incubation period (Tukey test, p < 0.05, n=50). The HMW fraction (>

Incubation experiment: from labile to refractory DOM in soil extracts

In the natural environment, the labile fraction of DOM is mainly degraded in the soil before being transported to the adjacent stream. Thus, the incubation experiment was designed to remove a possible labile fraction of DOM in the soil extracts before comparison with DOM from adjacent streams. During the 28-day incubation, most of the DOC mass was lost in the first 3 days for both soils (Figure 2A). The percentage of DOC loss stabilized between 40 and 70 % after 3 days incubation. These results are consistent with those obtained in previous studies investigating the biodegradation of water-extracted DOM from different soil types such as forest, pasture and agricultural soils [START_REF] Guigue | A comparison of extraction procedures for water-extractable organic matter in soils[END_REF][START_REF] Kalbitz | Biodegradation of soil-derived dissolved organic matter as related to its properties[END_REF]. DOC loss ismostly explained by the degradation of labile DOM that is easily assimilated by microorganisms. It is well known that certain organic molecules, such as amino acids or carboxylic acids, are considered as labile while other molecules, such as lignins, are considered more recalcitrant [START_REF] Eilers | Shifts in bacterial community structure associated with inputs of low molecular weight carbon compounds to soil[END_REF]. The variability of the percentage of DOC loss observed in this study (between 40 and 70 %) could be explained by differences in the microorganisms communities contained in the soil samples. Indeed, it has been shown that a greater diversity of microorganisms in soils favors the DOC degradation [START_REF] Raczka | Interactions between microbial diversity and substrate chemistry determine the fate of carbon in soil[END_REF]. Different proportions of labile and recalcitrant DOM pools in the soils could also explain the variability of DOC loss. Thus, soils containing higher levels of labile DOM will be degraded to a greater proportion than soils containing high levels of refractory DOM.

The degradation of labile molecules induced an increase in the average aromaticity content, average size and molecular weight of molecules, as highlighted by the indicators SUVA254, E2.E3 and SR. Previous studies have also shown that degraded organic matter has relatively higher aromaticity content and molecular weight [START_REF] Guarch-Ribot | Hydrological conditions regulate dissolved organic matter quality in an intermittent headwater stream. From drought to storm analysis[END_REF][START_REF] Hansen | Optical properties of dissolved organic matter (DOM): Effects of biological and photolytic degradation[END_REF]. The E3.E4 indicator being inversely correlated to the humification of DOM [START_REF] Claret | Generation of humic and fulvic acid from Callovo-Oxfordian clay under high alkaline conditions[END_REF] can be interpreted with the HIX indicator. The HIX and E3.E4 indicators show that the degree of humification of soil extracts was low at the beginning of incubation, and then increased to stabilize after 3 days of incubation for vineyard soils. For forest soils, a gradual increase was observed throughout the incubation period until 28 days where a significant decrease occurred. The unexpected decrease observed for forest soil extracts at the end of incubation could be explained by the very high values of γ band (280-330 nm); linked with protein-like compounds. The HIX index corresponds to the ratio of areas 435-480 nm and 300-345 nm of the emission spectrum for an excitation at 255 nm, thus a high γ band intensity can make the HIX values vary drastically. The other explanation could come from the humic fraction of forest soils. Indeed, it is a complex fraction consisting of functional groups such as phenols, quinones, methoxyls and carbonyls [START_REF] Maccarthy | The Principles of Humic Substances[END_REF], that are recalcitrant with a slow kinetic of degradation due to its complex chemical nature [START_REF] Marschner | How relevant is recalcitrance for the stabilization of organic matter in soils?[END_REF].

Humification is a process of DOM condensation resulting from several interactions such as plant alteration with partially degraded lignins or the transformation of polyphenols, amino acids and some sugars into quinones under the enzymatic action of microorganisms [START_REF] Stevenson | Humus Chemistry: Genesis, Composition, Reactions, Second Edition[END_REF]. This slow process can sometimes take years.

The BIX index showed a significant variability in forest soil extracts contrary to vineyard soils.

This could be explained by a more contrasted biological activity in forest soil extracts than in vineyard soils. Based on the hypothesis that biological activity is directly related to the diversity of microbial communities, vineyard soil extracts may have less microbial diversity due to intensive soil exploitation allowing an homogenization of the communities present in the soil [START_REF] Jangid | Relative impacts of land-use, management intensity and fertilization upon soil microbial community structure in agricultural systems[END_REF]. Other studies mention the concept of "priming effect", which reflects a greater mineralization of organic matter in soils enriched with fresh litter [START_REF] Derrien | Biodegradation-induced signatures in sediment pore water dissolved organic matter: Implications from artificial sediments composed of two contrasting sources[END_REF].

This could be the case for forest soils which are subject to a contribution of fresh organic matter through vegetation cover. In addition, the significant decrease of the YFI indicator shows a lower contribution of protein-like compounds at the end of the experiment. EEM fluorescence and PARAFAC decomposition bring details on the nature of the degraded molecules along the incubation. allows to affirm that some degraded labile molecules are tryptophan-like with recent biological production [START_REF] Fellman | Fluorescence characteristics and biodegradability of dissolved organic matter in forest and wetland soils from coastal temperate watersheds in southeast Alaska[END_REF]. No significant difference was observed in the evolution of the other components C1, C2 and C3 which are characteristic of the following typical compounds: terrestrial humic-like (plant derived), humiclike matter, commonly found in agricultural catchments and terrestrial high aromatic and hydrophobic macromolecules [START_REF] Derrien | Estimation of different source contributions to sediment organic matter in an agricultural-forested watershed using end member mixing analyses based on stable isotope ratios and fluorescence spectroscopy[END_REF][START_REF] Jørgensen | Global trends in the fluorescence characteristics and distribution of marine dissolved organic matter[END_REF][START_REF] Rinot | Fluorescence spectroscopy: A sensitive tool for identifying land-use and climatic region effects on the characteristics of waterextractable soil organic matter[END_REF].

It has been reported in previous studies that the degraded molecules are generally low molecular weight compounds [START_REF] Fujii | Biodegradation of low molecular weight organic compounds and their contribution to heterotrophic soil respiration in three Japanese forest soils[END_REF][START_REF] Ondrasek | Biogeochemistry of soil organic matter in agroecosystems & environmental implications[END_REF]. However, the size exclusion chromatography showed a decrease in the contribution of low molecular weight molecules LMW< 1k Da, and also high molecular weight macromolecules HMW > 10 kDa at the same time. Based on these results, protein-like content of DOM is likely to be composed of both LMW and HMW fractions. The fraction of medium molecular weight (MMW) compounds, linked to C1, C2 and C3 PRAFAC components (lignin compounds and terrestrial derived DOM), did not vary significantly and seemed to be recalcitrant and not easily degradable.

Evolution of DOM characteristics from soils to adjacent streams

The evolution of soil extracted DOM during the incubation experiment in comparison with the adjacent watercourse DOM is shown in the the principal component analysis (PCA), plotted with the 26 optical indicators calculated from UV-Visible, EEM fluorescence and HPSEC/UVfluorescence (Figure 7). The PCA shows that the optical fingerprints of forest and vineyard soil extracts are more distinct at the end of incubation experiment (82 dats) than before. . This could be explained by the nature and the proportion of labile vs refractory fractions of DOM before and after incubation. This suggests that the labile fraction of DOM is not so different between the two soil types. For all indicators, the evolution of DOM optical fingerprints during the incubation tends towards that of adjacent watercourse (Figure 7). The adjacent stream samples show relatively high contribution of medium weighted molecules MMW and a lower contribution of both low and high molecules of the protein and humic types (LMW and HMW).

This could be explained by the fact that watercourse DOM has already undergone mineralization processes, mainly through microorganisms in top soil layers, before it reaches the adjacent watercourses. Other abiotic ways such as photodegradation and adsorption can influence DOM composition, which can explain the observed differences between samples at the end of incubation and the adjacent watercourse samples. The PCA also showed that water samples taken downstream of the forest soils seem more heterogeneous than downstream of the vineyard soils, whatever the hydrological regime. This heterogeneity could be explained by insitu complex abiotic processes as well as by the difference in vegetation cover in the Ardières-Morcille watershed. Indeed, the forest sources considered in this study are mostly influenced by coniferous forests, but broad-leaved forests and natural grasslands can represent up to 35% of the total sub-catchment areas (calculation based on land use maps, CLC 2018). A previous study highlighted different DOM quality between deciduous and coniferous forests [START_REF] Thieme | Dissolved organic matter characteristics of deciduous and coniferous forests with variable management: different at the source, aligned in the soil[END_REF]. On the contrary, the viticultural sub-catchments are very homogeneous in terms of vegetation cover as they are subject to strict local regulations. The hydrologic regime also seems to have an influence on DOM quality especially for vineyard adjacent watercourses. This could be explained by the contribution of an autochthonous source being more heightened during low water periods. Autochthonous DOM is essentialy produced locally by the microbial activities [START_REF] Münster | Concentrations and fluxes of organic carbon substrates in the aquatic environment[END_REF] and it was demonstrated previously that there is an impact of agriculture on increasing carbon and nutrient inputs to downstream watercourses [START_REF] Williams | Unraveling the role of land use and microbial activity in shaping dissolved organic matter characteristics in stream ecosystems[END_REF].

These nutrient inputs provide energy support for microbial activity which can affect DOM quantity and quality.

How do the fingerprints match between DOM in soil extracts after incubation and that in downstream watercourses during high and low water periods?

As discussed in the previous section, hydrological regime influences the quantity and quality of the DOM in the watercourses. It is therefore more appropriate to look for markers of forest and vineyard soils downstream of the waterways draining these soils considering both high and low water sampling periods. To do this, a linear discriminant analysis (LDA) was applied in two steps. In a first step, the construction of the LDA 1 was conducted with 3 groups: i) a first group, called Forest DOM HW (high water), containing samples of degraded forest soils and adjacent forest streams collected at high water. ii) A second group, called Vineyard DOM HW, which contained samples of degraded vineyard soils with water from adjacent vineyard streams collected at high water, and iii) a third group called low water samples, which contained all the samples from adjacent watercourses taken during low water periods. The purpose of the first LDA (Figure 8.A) was to identify if there was similarities between DOM markers from soil extracts and DOM from the adjacent watercourse during high water period. In a second step, a LDA 2 was carried out by reversing the groups of water samples, thus considering i) a first . Through this supervised cross-sectional analysis, we have highlighted a series of indicators of terrigenous contribution in both high water and low water periods. These results reveal that: (i) there is an influence of land use on the quality of DOM in adjacent streams using selected optical indicators, and (ii) this influence is present as well in periods of high water as in periods of low water. During high water, DOM sampled downstream of forest soils comprise of relatively lower molecular weight compounds with low degrees of humification and higher contribution of protein-type molecules smaller than 1000 Da. On the contrary, the vineyard DOM carries a higher molecular weight, ahigher degree of humification and a lower contribution of small protein-type molecules. During the low water period, DOM sampled downstream of the forest soils has higher aromaticity and molecular weight than the vineyard DOM which contains relatively low molecules. Indeed, vinayard DOM could beimpacted by higher microbial activity [START_REF] Chavarria | Land use influences stream bacterial communities in lowland tropical watersheds[END_REF][START_REF] Williams | Unraveling the role of land use and microbial activity in shaping dissolved organic matter characteristics in stream ecosystems[END_REF]. The differences observed between DOM sampled downstream forest and vineyard regardless the hydrological conditions can be explained by several mechanisms. First, the presence of a biodegraded form of DOM in vineyard soils probably due to the intensive exploitation of the soils and the low rooting networks. Indeed, previous studies reported an higher organic matter oxidation in agricutural soils which are more prone to erosion than forest soils and to an accelerated phenomenon of open-air oxidation in the upper soil layers [START_REF] Graeber | Agriculture has changed the amount and composition of dissolved organic matter in Central European headwater streams[END_REF][START_REF] Shang | Climatic and watershed controls of dissolved organic matter variation in streams across a gradient of agricultural land use[END_REF].Secondly, given the very steep slopes that favore surface runoff in the Ardières-Morcille watershed, the differences observed between high and low water could be explained by a contribution of surface soil organic matter during high water and a contribution of deeper and more degraded soil organic matter during low water period.

It is important to note that DOM fingerprints presented in this study are not generalizable to other watersheds. Considerable differences can be observed from one watershed to another depending on topography, flow direction and soil characteristics. However, the fingerprints of DOM sampled in a stream downstream of a homogeneous watershed while accounting for hydrologic conditions provides a good representation of land use type. This sampling method can be applied to other land use types with different agricultural and livestock types and 1). Indeed, in some soil extract , the SR indicator showed the presence of DOM mostly consisting of low molecular weight compounds, while the HMW TSF 278-354 indicator showed a relatively high contribution of amino-acid type compounds larger than 10 k Da. This result suggests that the SR indicator could be limited to the description of certain types of molecules that exclude acidamine like compounds. Finaly, the indicators from HPSEC/UV-fluoresecence could be use a larger scale like in monitoring studies of agricultural, industrial and urban discharges. The information provided by these indicators would allow better identification of anthropogenic compounds (e.g. pesticides, pharmaceuticals) that are very complicated to detect using classical optical proxies as most of these compounds have almost similar optical properties [START_REF] Hassoun | Total Fluorescence Fingerprinting of Pesticides: A Reliable Approach for Continuous Monitoring of Soils and Waters[END_REF]. Also, the establishment of databases of HPSEC/UV-fluorescence indicators specific to anthropogenic compounds of interest, could facilitate their detection at lower cost than with current techniques using chromatography coupled with mass spectrometry.

The objective of this study was to provide insight into the sampling of terrigenous diffuse sources of DOM directly into streams using relevant land use markers. These markers were identified by comparing DOM from soil extracts with adjacent watercourse DOM, sampled at the outlet of homogenous sub-catchments during low and high water. both the homogeneity of the upstream sub-catchments in terms of land use but also the hydrological conditions. The cross exploitation of the data from these three techniques seems appropriate to establish DOM fingerprints. However, the fingerprints of forest and vineyard diffuse sources studied in this work are not exhaustive contrary to the methodological approach, which can be applicable to other types of diffuse sources. Indeed, application of this approach 609 on a larger scale would provide specific fingerprints for terrigenous diffuse sources in streams.

Figures

  2 software) were used to compare both forest and vineyard soil extracts, the temporal kinetics of the incubation study and also for the comparison between soil extracts and adjacent natural waters for all UV-Vis, EEM fluorescence and HPSEC/UV-fluorescence indicators. Principal component analysis (PCA;package factoextra, R 4.0.2 software) was also used for the comparison of soil extracts vs. natural adjacent waters, and a linear discriminant analysis (LDA; packages MASS and klaR, R 4.0.2 software) for the selection of the most relevant DOM markers of forest and vineyard soil occupations.

group

  Forest DOM LW (low water), which contained the samples of forest soil extracts and forest adjacent watercourses taken during low water. ii) a second group of Vineyard DOM LW with samples from degraded vineyard soils and low water vineyard watercourses; and iii) a third group of high water samples containing all the samples of the adjacent watercourses taken during high water. The second LDA (Figure 8.B) was conducted to determine any similarities between soil extracts and adjacent watercourses during low water periods. Among the 26 optical indicators (UV-Visible, EEM fluorescence and HPSEC/UVfluorescence) considered in this study, 6 indicators were able to correctly classify the samples into Forest DOM HW, Vineyard DOM HW and Low water samples groups (Figure 8). They correspond to one UV-Visible indicator (slope ratio SR), two EEM fluorescence indicators (HIX and PARAFAC component C1) and three HPSEC/UV-fluorescence indicators (LMW-TSA 254, MMW TSF 278-354 and MMW TSF 280-330). The results from LDA 2 also allowed the selection of 6 indicators that classified the samples into Forest DOM LW, Vineyard DOM LW and High water samples groups (Figure 8.B). There were one UV-Visible indicator (SUVA254), three EEM fluorescence indicators (HIX, FI and YFI) and two HPSEC/UVfluorescence indicators (MMW

  pressures. Moreover, given the complexity of DOM composition and reactivity, the combination of optical indicators was essential. The result of the LDA, when calculated with UV-Visible, EEM fluroescence and HPSEC/UV-fluorescence indicators separately, could not provide a good differenciation between forest and vineyard DOM (Supplementary Material 5). At last, indicators from HPSEC/UV-fluorescence proposed in this study, have shown potential as good markers of diffuse sources of DOM in streams as discussed more in depth in the next part 4.4 . 4.4 Relevance of HPSEC/UV-fluorescence indicators to study DOM The HPSEC/UV-fluorescence indicators presented in this study provided additional information regarding classical optical proxies (

  The UV-Visible, EEM fluorescence and HPSEC/UV-fluorescence techniques showed an evolution of DOM extracted from forest and vineyard soils during a 28-day incubation experiment. Indicators calculated from these techniques showed that the evolution of DOM mainly occurred in the three first days of incubation.This resulted in the degradation of high (>10 k Da) and low (<1 k Da) MW protein-like molecules (labile fraction of DOM), leading to an increase of aromaticity and humification mostly observed in medium molecular weight compounds (from 1 to 10 k Da). The labile fraction of DOM did not differ according to the land use.Adjacent stream samples had distinct optical fingerprints influenced mostly by the hydrological regime, as DOM sampled during high water periods showed a large contribution of LMW and HMW than DOM sampled during low water periods. At the end of the incubation study, forest and vineyard soil extract tend to fingerprints of the adjacent watercourse samples. Linear discriminant analysis (LDA) revealed the relevance of 9 indicators to differentiate forest DOM and vineyard DOM fingerprints during high and low water sampling. These results demonstrate that a representative sampling of a diffuse source of DOM in rivers should take into account

Figure 1 .

 1 Figure 1. Map of Ardieres-Morcille catchment howing the location of the water-sampling sites (FP: forest sampling points, VP: vineyard sampling points) and the land-use boundaries (Corine Land Cover CLC 2018). The soil samples were collected upstream the water sampling points.

Figure 2 .

 2 Figure 2. A: Dissolved organic carbon (DOC) concentrations measured i) in soil extracts (forest in dark green and vineyard in dark orange) before incubation (B.I) and after 3, 7, 14 and 28 days of incubation, and ii) in water samples collected from streams adjacent to the forest (in light green) and vineyard (in light orange) soils during high and low water periods. B: Percentage of DOC for soil extracts during the 28 days incubation experiment relative to the DOC concentration measured before incubation.

Figure 3 .

 3 Figure 3. UV-Visible indicators measured i) in soil extracts (forest in dark green and vineyard in dark orange) before incubation (B.I) and after 3, 7, 14 and 28 days of incubation, and ii) in water samples collected from streams adjacent to the forest (in light green) and vineyard (in light orange) soils during high and low water periods. A: SUVA254, B: E2.E3 (abs250/abs365),

Figure 4 .

 4 Figure 4. EEM fluorescence indicators measured i) in soil extracts (forest in dark green and vineyard in dark orange) before incubation (B.I) and after 3, 7, 14 and 28 days of incubation, and ii) in water samples collected from streams adjacent to the forest (in light green) and vineyard (in light orange) soils during high and low water periods. A: humification index HIX, B: biological fluorescence index BIX, C: fluorescence index FI and D: fluorescence index YFI.

Figure 5 .

 5 Figure 5. PARAFAC components C1 (<240(320)-420 nm), C2 (<240(390)-510 nm), C3 (365-443 nm) and C4 (280-330 nm) measured i) in soil extracts (forest in dark green and vineyard in dark orange) before incubation (B.I) and after at 3, 7, 14 and 28 days of incubation, and ii) in water samples collected from streams adjacent to the forest (in light green) and vineyard (in light orange) soils during high and low water periods.

Figure 6 .

 6 Figure 6. Low Molecular Weight (LMW; blue bars), Medium Molecular Weight (MMW; orange bars) and High Molecular Weight (HMW; purple bars) percentage of contribution to: A: Total Sec Absorbance TSA at PDA 254 nm, B: Total Sec Fluorescence TSF at Excitation Emission wavelengths 345-443 nm, C: TSF at fluorescence Excitation Emission wavelengths 280-330 nm, D: TSF at fluorescence Excitation Emission wavelengths 278-354 nm.. Samples plotted are soil extracts before incubation (B.I) and then at 3, 7, 14 and 28 days of incubation as well as for water samples collected from streams adjacent to the forest and vineyard soils during high and low water periods.

Figure 7 .

 7 Figure 7. First factorial plane of the principal component analysis (PCA) performed on data from forest and vineyard soil extracts before incubation (B.I), after 28 days of incubation and their adjacent water stream samples collected during high and low water periods. The variables considered in the PCA are the UV-Visible, EEM fluorescence and HPSEC/UV-fluorescence indicators.

Figure 8 .

 8 Figure 8. A. Linear discriminant analysis (LDA1) calculated with 26 indicators from UV-Visible, EEM fluorescence and HPSEC/UV-fluorescence to discriminate forest and vineyard DOM taken during high water from low water DOM. B. Linear discriminant analysis (LDA2) calculated with the same indicators to discriminate forest and vineyard DOM taken during low water periods from High water DOM.

  Table 1) and the Freshness index (FI; Table 1) during the incubation period (Figure 4.B, C). BIX values ranged from 0.71 ± 0.08 to 0.79 ± 0.08 for forest soil extracts; and from 0.63 ± 0.05 to 0.67 ± 0.02 for

vineyard soil extracts; FI values from 1.40 ± 0.06 to 1.42 ± 0.04 for forest soil extracts; and from 1.31 ± 0.08 to 1.36 ± 0.04 for vineyard soil extracts. The YFI indicator (Table

1

), showed a decrease according to incubation time (Figure

4

.D). This decrease, however, is very limited for both soil extracts during the incubation experiment (YFI values from 0.89 ± 0.27 to 0.71 ± 0.06 and from 0.74 ± 0.04 to 0.61 ± 0.04 respectively for forest and vineyard soil extracts).

Table 1

 1 at 254 nm are poorly aromatic and that the aromatic content of DOM is mostly found in compounds larger than 1 k Da. The correlation matrix (Supplementary Material 6) also shows that the indicator HMW TSF 280-330 is positively correlated with the component PARAFAC C4 associated with protein-like compounds. This suggests that the C4 component is composed of relatively large molecules (> 10 k Da). In the context of this study, this showed that DOM labile pool was also composed of high molecular weight compounds in contrast to what has been reported in previous studies[START_REF] Curtis-Jackson | Characterization of low molecular weight dissolved organic nitrogen by liquid chromatographyelectrospray ionization-mass spectrometry[END_REF] Derrien et al., 2019). Other indicators of HPSEC/UV-fluorescence (e.g. HMW TSF 278-354) point out the limitations of using classic indicators like slope ratio SR indicator (Table

	). For example, the SUVA indicator

Table 1 .

 1 Classical UV-Visible and fluorescence indicators to characterize dissolved organic matter.

	Tables
	Indicator	Calculation		Interpretation		References
	SUVA254	254 ! "#$%&	aromaticity of DOM. Correlated with the	(Weishaar et al., 2003)
	E2.E3	250 ! 365 !	organic molecules size Negatively correlated to	Helms et al., 2008
	E2.E4	254 ! 436 !	Autochthonous terrestrial DOM	versus	Jaffé et al., 2004; Li and Hur, 2017
	E3.E4	300 ! 400 !	Negatively correlated to humification degree	Claret et al., 2003; Li and Hur, 2017
	S1 (275-295 nm)	, + -+ * + : absorption coefficient * + = * +	Negatively correlated to aromatic carbon content	Stedmon et al., 2000 Helms et al., 2008
		at specific wavelength
	S2 (350-400 nm)	.0: wavelength	reference S:
		exponential slope

Acknowledgements

This study was part of the "CHYPSTER" project supported by the French National Research Agency (ANR-21-CE34-0013-01) and "IDESOC" project granted by Zone Atelier Bassin du Rhône (ZABR) and Rhône Méditerranée Corse Water Agency (AERMC). The authors wish to acknowledge Loïc Richard and Alexandra Gruat for their assistance in field sampling, samples preparation and chemical analysis.

for UV detection at 254 nm and fluorescence at 315-443 nm (figure 6B). However, the HMW fraction was higher for 280-330 and 278-354 nm fluorescence detection with a significant difference (Tukey test, p < 0.05, n=50) between forest and vineyard soil extracts before incubation. For adjacent streams, the HMW fraction was also present at very low percentages and no difference was observed between soil occupations nor beteween low and high water regimes.

Credit Author


Francis Balestra

Challenges and solutions for high performance green nanoelectronics devices and materials

published or not. The documents may come

Challenges and solutions for high performance green nanoelectronics devices and materials

Acknowledgements

The author would like to thank all the Sinano Institute Members for their strong involvement in this research area.


Manuel Collet
email: manuel.collet@univ-fcomte.fr

Morvan Ouisse

Massimo Mohamed Ichchou

M Ruzzene

Semi-active optimization of 2D wave's dispersion into mechanical systems by the mean of periodically distributed shunted piezoelectric patches: a new class of adaptive metamaterials

Keywords: Distributed control, 2D Waves Dispersion, Bloch Theorem, Shunted piezoelectric, Mid-Frequency Optimization

may come

Semi-active optimization of 2D wave's dispersion into mechanical systems by the mean of periodically distributed shunted piezoelectric patches: a new class of adaptive metamaterials

INTRODUCTION

Tailoring the dynamical behavior of wave-guide structures can provide an efficient and physically elegant approach for optimizing mechanical components with regards to vibration and acoustic criteria, among others. However, achieving this objective may lead to different outcomes depending on the context of the optimization. In the preliminary stages of a product's development, one mainly needs optimization tools capable of rapidly providing global design directions. Such optimization will also depend on the frequency range of interest. One usually discriminates between the low frequency (LF) range and the medium frequency (MF) range, especially if vibration and noise are considered. However, it should be noted that LF optimization of vibration is more common in the literature than MF optimization. For example, piezoelectric materials and other adaptive and smart systems are employed to improve the vibroacoustic quality of structural components, especially in the LF range [START_REF] Preumont | Vibration control of structures : An introduction[END_REF][START_REF] Nelson | Active Control of Sound[END_REF][START_REF] B A N K Sa N Dy | Smart material structures Modeling Estimation and Control[END_REF] even if ditributed transducers are used. [START_REF] Batra | Multimode vibration suppression with passive twoterminal distributed network incorporating piezoceramic transducers[END_REF][START_REF] Tzou | A study of segmentation of distributed piezoelectric sensors and actuators, part i: Theorical analysis[END_REF] Recently, much effort has been spent on developing new multi-functional structures integrating electro-mechanical systems in order to optimize their vibroacoustic behavior over a larger frequency band of interest. [START_REF] Collet | Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures[END_REF][START_REF] Thorp | Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches[END_REF][START_REF] Beck | Broadband vibration suppression assessment of negative impedance shunts[END_REF][START_REF] Beck | Experimental analysis of a cantilever beam with a shunted piezoelectric periodic array[END_REF][START_REF] Bartoli | Modeling wave propagation in damped waveguides of arbitrary cross-section[END_REF][START_REF] Foda | Vibration suppression of composite laminated beams using distributed piezoelectric patches[END_REF][START_REF] Dawood | Three-dimensional static shape control analysis of composite plates using distributed piezoelectric actuators[END_REF][START_REF] Jiang | Decentralized robust vibration control of smart structures with parameter uncertainties[END_REF][START_REF] Ren | Finite difference based vibration simulation analysis of a segmented distributed piezoelectric structronic plate system[END_REF] However, there is still a lack of studies in the literature for MF optimization of structural vibration. To that end, the focus of this study is to provide a suitable numerical tool for computing wave dispersion in 2D periodic systems incorporating controlling electronics devices. The main final aim is to allow their optimization in order to optimize vibroacoustic diffusion in 2D wave guides. Two numerical approaches can be distinguished for computing that dispersion: the semi-analytical finite element method (SAFE) and the wave finite element (WFE) method. The main disadvantage of the SAFE method is that FE used are not standard so they must be specifically defined for each application. Nevertheless, a large amount of FE has been developed since 1975 to compute dispersion curves of rails, 15 laminated composite plates [START_REF] Mace | Modelling wave propagation in two-dimensional structures using finite element analysis[END_REF][START_REF] Gonella | Analysis of in-plane wave propagation in hexagonal and re-entrant lattices[END_REF] and viscoelastic laminated composite plates. [START_REF] Akrout | Comportement dynamique dterministe et large bande des structures guides[END_REF] To avoid development of specific FE, the WFE method considers the structures as periodic in order to model, with standard FE, a period of the structure. By using the periodic structure theory (PST) introduced by Mead, [START_REF] Mead | A general theory of harmonic wave propagation in linear periodic systems with multiple coupling[END_REF] an eigenvalue problem can be formulated from the stiffness and mass matrices of the FE model to find wave numbers of all the propagating waves. Contrary to SAFE method, the displacement field is now approximated in the direction of propagation. Thus, some numerical issues can arise when the size of FE are too coarse. As recommended by Mace and Manconi, 16 a minimum of six elements per wavelength is a good rule of thumb to ensure a reliable analysis. The WFE method has been successfully used to deal with wave propagation in two dimensional structures. [START_REF] Manconi | The Wave Finite Element Method for 2-dimensional Structures[END_REF][START_REF] Berthaut | Multi-mode wave propagation in ribbed plates : Part i k-space characteristics[END_REF] One of the main problem all these approaches is the difficulty to compute the damped wave numbers in the whole Brillouin domain necessary for optimizing vibroacoustic behavior of smart periodic structures. After recalling the Floquet-Bloch theorems, we introduce a new numerical formulation for computing the multimodal damped wave numbers dispersion in the whole first Brillouin domain of a periodical smart structure made of periodically distributed shunted piezoelectric patches. Based on this wave modeling, optimization of the electrical impedance of the shunted circuit is made in order to decrease group velocity of flexural waves. The obtained optimal impedance is also tested in controlling the HF response of a semi-distributed system.

PIEZO-ELASTO-DYNAMICAL APPLICATION OF THE FLOQUET-BLOCH THEOREM

In this section the application of the celebrated Floquet-Bloch theorem is presented for piezo-elastodynamic problems. Based on the well known results obtained by Floquet 21 in one-dimensional and later rediscovered by Bloch 22 in multidimensional problems, we propose an original application to bi-dimensional piezo-elastodynamical problem leading to very general numerical implementation for computing waves dispersion for periodically smart distributed mechanical systems incorporating electronic components and damping effects. [START_REF] Collet | Numerical tools for semi-active optimization of 2d waves dispersion into mechanical system[END_REF]

The Bloch Theorem

The Bloch theorem gives the form of homogeneous states of Schrödinger equation with periodic potential. This theorem can be considered as a multidimensionnal application of the Floquet theorem. [START_REF] Joannopoulos | Photonic Crystals: Molding the Flow of Light[END_REF] The periodic medium (or potential) properties satisfy M (x + R.m)=M (x), m ∈ Z 3 where R =[ r 1 , r 2 , r 3 ] ∈ R 3×3 is a matrix grouping the three lattice's basis vectors (in 3D). We can also define the primitive cell as a convex polyhedron of R 3 called Ω x . The reciprocal unit cell is denoted by Ω k limited by the reciprocal lattice vector defined by the three vectors g j so that: r i .g j =2 πδ ij (δ i,j the Kronecker index). We note G =[ g 1 , g 2 , g 3 ] the reciprocal lattice matrix in the later. If Ω x is the irreductible primitive cell, Ω k corresponds to the first Brillouin zone of the lattice. One can see [START_REF] Kittel | Introduction to Solid State Physics[END_REF] for details.

The Bloch Theorem stipulates that any functions u(x) ∈ L 2 (R 3 , C n ) can be expressed as

u(x)= Ω k e ikx ũ(x, k)dk (1)
where the Bloch amplitude ũ(x, k)i sΩ x -periodic and has the representations

ũ(x, k)= n∈Z 3 û(k + Gn)e iGn.x , u(x)= |Ω x | (2π) 3 n∈Z 3 u(x + Rn)e ik(x+Rn) (2)
where û(k) stands for the Fourier transform of u(x). One can also demonstrate that the mean value of the Bloch amplitude is the Fourier amplitude of u(x) for the corresponding wave vector: ũ(., k) Ωx = û(k). Using the Bloch theorem to represent the solutions of periodical partial derivative equations implies that all derivatives are shifted by k in the sense given by the used spatial operator.

Based on that theorem one can define the expansion functions v m (x, k), called the Bloch eigen modes, such that they can be used to represent the Bloch amplitudes of any solution of the corresponding partial derivative equation as

ũ(x, k)= m u m (k)v m (x, k)( 3 )
and at the same time diagonalize the partial derivative equations. One notes that the expansion coefficients u m (k) depend on the applied disturbance and also on the induced wave vector (see 26 for details). Let us consider a piezo-elastodynamic problem made of infinite periodic distribution of unitary cell described in figure 1. The harmonic homogeneous dynamical equilibrium of system is driven by the following partial derivative equation :

ρ ẅ(x) -∇σ(x)=0 ∀x ∈ Ω x -∇D(x)=0 ∀x ∈ Ω x (4)
where w(x) ∈ R 3 (Ω x ) is the displacement vector, σ represents the Cauchy stress tensor, ǫ = ∇ sym w = 1 2 (∇w T (x)+w(x)∇ T ) the Green strain tensor, D(x) the electric displacement. The linear constitutive material behavior relationships can be written as

σ = C E (x)ǫ -e T (x)E (5)
D = e(x)ǫ + ε S (x)E (6)
where E = -∇V the electric field vector (V the voltage), C E the elasticity tensor at constant electrical field, e T the piezoelectric coupling tensor and ε S the dielectric permittivity at constant strain. We add to this set of equilibrium equations an output expression

q o = - St D.ndS (7)
allowing the introduction of the charge measurement on the piezoelectric's top electrode and hence the dual counterpart of the imposed electrical Dirichlet boundary condition for applying the shunt impedance operator. The equations above are consistent for each kind of material to the extent that null piezoelectric and permittivity tensors can be used when passive materials are considered. All of these tensors also depend on the spatial location vector x. The piezo-elastodynamic equilibrium can also be written as :

ρω 2 w(x)+∇C∇ sym (w(x)) + ∇e T (x)∇V (x)=0 ∀x ∈ Ω x (8) -∇e(x)∇ sym (w(x)) + ∇ε S (x)∇V (x)=0 ∀x ∈ Ω( 9 )
As the problem is 2D infinitely periodic, only electrostatic boundary conditions have to be considered on each cell:

⎧ ⎨ ⎩ V =0 ∀x ∈ S b V = V o ∀x ∈ S t D.n =0 ∀x ∈ S l (10)
where S b is the grounded bottom electrode of the piezoelectric layer, S t is the top electrode connected to the external shunt and s l the lateral electrode less boundary. The top electrode applied feedback voltage V o depends on the shunt characteristic and on the collected charges q o (7) and can be expressed in the Fourier space by:

V o (iω)=-Z(iω)q o (iω) (11)
By considering a primitive cell of the periodic problem Ω x and by using the Bloch theorem, we can compute the associated Bloch eigenmodes (3) and the dispersion functions by searching the eigen solutions of the homogeneous problem ( 8) and ( 9) as:

u(x)= w(x) V (x) = u n,k (x)e ik.x (12)
with

u n,k (x)= w n,k (x) V n,k (x)
,Ω x periodic functions. By introducing expression (12) in the piezo-elastidynamic equations ( 8), ( 9), one can demonstrate that w n,k (x), V n,k (x)a n dω n (k) are solutions of the generalized eigenvalues problem:

ρω 2 n (k)w n,k (x)+∇C∇ sym (w n,k (x)) + ik {(C∇ sym (w n,k (x))).Φ + ∇(CΞ n,k (x))}-k 2 (CΞ n,k (x)).Φ +∇e T ∇V n,k (x)+ik (∇e T V n,k (x)).Φ +(e T ∇V n,k (x)).Φ -k 2 V n,k (x)(e T Φ).Φ =0 ∀x ∈ Ω x (13)
-∇e∇ sym (w n,k (x)) -ik {∇(eΞ n,k (x)) + (e∇ sym (w n,k (x))).Φ} + k 2 (eΞ n,k (x)).Φ +∇ε S ∇V n,k (x)+ik {(∇ε S V n,k (x)).Φ +(ε S ∇V n,k )(x).Φ}-k 2 (ε S ΦV n,k (x)).Φ =0 ∀x ∈ Ω x (14)
with the associated bounadry conditions :

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ w n,k (x -R.m)=w n,k (x) ∀x ∈ S r m ∈ Z 2 V n,k (x)=0 ∀x ∈ S b V n,k (x)V = -Z(iω)q o n,k ∀x ∈ S t D.n =0 ∀x ∈ S l
where k = k ⎡ ⎣ cos(φ) sin(φ) 0 ⎤ ⎦ = kΦ where φ represent the direction angles into the reciprocal 2D lattice domain and

Ξ n,k (x)= 1 2 (w n,k (x).Φ T +Φ.w T n,k (x)
) the symmetric dyadic tensor or the dyadic product of the displacement w n,k (x) and direction vector Φ. S r are the interface of the cells continuum, and R the matrix grouping the two lattice's basis vectors (in 2D in the considered problem). In the electrical boundary conditions, q t n,k is given by :

q o n,k = St [-e(∇ sym (w n,k (x)) + ik∇eΞ n,k (x)) + ε S (∇V n,k (x)+ikV n,k (x)Φ].ndS ( 15
)
where n is the outpointing unitary normal vector. The proposed formulation is also based on the computation of the Floquet vectors (equation ( 13), ( 14)), instead of computing the Floquet propagators commonly used for elastodynamic applications. Our approach allows to obtain the full 2D waves dispersions functions and to clearly introduce damping and electrical impedance into the piezo-elastodynamic operator. The adopted methodology allows the computation of the complete complex map of the dispersion curves incorporating computation of evanescent waves and allowing the introduction of damping and shunt operator if any.

Weak Formulation and computation of waves dispersion functions in periodical piezo-composite lattice

Let us consider the partial derivative equations ( 13), ( 14) on a unit cell Ω. It stands for a generalized eigenvalue problem leading to compute the dispersion functions ω n (k) and the corresponding Floquet eigenvectors u n,k (x).

For computing the 2D dispersions curves, we need to introduce a suitable weak formulation. If u n,k (x) is a solution of equations ( 13), ( 14), also

∀ wn,k (x) ∈ H 1 (Ω, C 3 )/ wn,k (x -Rm)= wn,k (x) ∀x ∈ S r
and Ṽn,k (x) ∈ H 1 (Ω, C)/ Ṽn,k (x)=0∀x ∈ S b and Ṽn,k (x)=V o ∀x ∈ S t we have :

Ω ρω 2 n (k) wn,k (x)w n,k (x) -(ε n,k (x) -ik Ξn,k (x))C(ε n,k (x)+ikΞ n,k (x)) +(ε n,k (x) -ik Ξn,k (x))e T (∇V n,k (x)+ikV n,k (x)Φ) -(∇ Ṽn,k (x) -ik Ṽn,k (x)Φ)e(ε n,k (x)+ikΞ n,k (x)) +(∇ Ṽn,k (x) -ik Ṽn,k (x)Φ)ε S (∇V n,k (x)+ikV n,k (x)Φ)dΩ - Ṽ t n,k V t n,k Z(iω) =0 (16)
This weak formulation is simply obtained by integrating equation ( 13), ( 14) projected onto any test function ũn,k (x). The boundary integral vanishes as the test functions are chosen so that wn,k (x -Rm)= wn,k (x)o n S r . For a polyhedron cell, each boundary is generally a polyhedral plane sub-domain that can be associated with a parallel opposite one. The symmetry conditions called wn,k (x -Rm)= wn,k (x) explicitly link these associated surfaces.

Numerical Computation of the Bloch's waves

The numerical implementation is obtained by using a standard finite elements method to discretize the weak formulation (16). The assembled matrix equation is given by:

(K(Z(iω n (λ, φ)) + λL(φ, Z(iω n (λ, φ))) -λ 2 H(φ, Z(iω n (λ, φ))) -ω 2 n (λ, φ)M )u n,k (φ)=0, (17)
where λ = ik, M and K(Z(iω n (λ, φ))) are respectively the standard symmetric semi-definite mass and stiffness matrices (the mass matrix is semi definite because elastostatic equation are condensed into the equation), L(φ, Z(iω n (λ, φ))) is a skew-symmetric matrix and H(φ, Z(iω n (λ, φ))) is a symmetric semi-definite positive matrix.

When k and φ are fixed and Z does not depend on ω the system ( 17) is a linear eigen value problem allowing us to compute the dispersion functions ω 2 n (k,φ) and the associated Bloch eigenvector u n,k (φ).

This approach has been widely used for developing homogenization techniques and spectral asymptotic analysis like in the work of. [START_REF] Allaire | Bloch waves homogenization and spectral asymptotic analysis[END_REF] It can also be applied for computing wave's dispersion even if Floquet propagators is preferred for 1D or quasi 1D computation, as indicated in. [START_REF] Ichchou | Guided waves group and energy velocities via finite elements[END_REF][START_REF] Houillon | Wave motion in thin-walled structures[END_REF][START_REF] Mencik | Multi-mode propagation and diffusion in structures through finite elements[END_REF] Nevertheless these approaches have been only developed for undamped mechanical systems that is to say represented by a set of real matrices. In this case, most of the previously published works present techniques based on the mesh of a real k-space (i.e k or λ and φ) inside the first Brillouin zone for obtaining the corresponding frequency dispersion and the associated Floquet vectors. For undamped system only propagative or evanescent waves exist corresponding to a family of eigen solutions purely real or imaginary. Discrimination between each class of waves is easy. If a damped system is considered (K, L, H are complex frequency dependent) or frequency dependence of the electrical shunt impedance is considered, the obtained eigenvalue problem is not quadratic and a complex specific numerical methodology has to be implemented. Furthermore, evanescent part of propagating waves appear as the imaginary part of ω 2 n (λ, Φ). It then becomes very difficult to distinguish the propagative and evanescent waves but also to compute the corresponding physical wave's movements by applying spatial deconvolution.

Another much more suitable possibility for computing damped system, dedicated for time/space deconvolution and for computation of diffusion properties as defined by, [START_REF] Collet | Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures[END_REF][START_REF] Mencik | Multi-mode propagation and diffusion in structures through finite elements[END_REF] is to consider the following generalized eigen value problem:

(K(Z(ω) -ω 2 M + λ n (ω, φ)L(φ, Z(ω)) -λ 2 n (ω, φ)H(φ, Z(ω)))u n (ω, φ)=0. (18)
In this problem, the pulsation ω is a real parameter corresponding to the harmonic frequency. Wave's numbers and Floquet vectors are then computed. An inverse Fourier transformation in the k-space domain can lead us to evaluate the physical wave's displacements and energy diffusion operator when the periodic distribution is connected to another system as in. [START_REF] Collet | Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures[END_REF] Another temporal inverse Fourier transformation can furnish a way to access spatio-temporal response for non-homogeneous initial conditions. As L is skew-symmetric, the obtained eigen values are quadruple (λ, λ, -λ, -λ) collapsing into real or imaginary pairs (or a single zero) when all matrices are real (i.e. for an undamped system). In this case a real pair of eigen values correspond to evanescent modes oriented in two opposite directions on the k-space and imaginary values to two traveling waves propagating in opposite direction.

As previously mentioned, the real part of k = kΦ vector is restricted to stand inside the first Brillouin zone. In the quadratic eigen value problem (18) nothing restricts computation to only find eigen values satisfying this condition. For direction vector Φ orthogonal to the lattice facelets (i.e. for Φ p1 =[ 1 , 0] T and Φ p2 =[ 0 , 1] T in bi-dimensional rectangular cell), the periodical conditions expressed for one dimensional wave guide are still valid: if λ j (ω, Φ p ) is an eigen value associated to w j (ω, Φ p )then∀m ∈ Z 3 , λ + i.Φ T p (G.m) is also an eigen value associated to w j (ω, Φ p )e -i.Φ T p (G.m)x . Thus, for undamped systems, all obtained eigenvalues are periodically distributed in the k-space along its principal directions.

Computation of the group velocity and evanescence criterion

The main aim of this paper is to provide a numerical methodology for optimizing the piezoelectric shunt impedance Z(ω) for controlling energy flow into the periodically distributed piezo-composite structure. For doing this, we need to define a suitable criterion. The waves group velocities indicate how energy is transported into the considered system and allow to distinguish the 'propagative' and 'evanescent' waves. If one Bloch eigen solution (i.e u n (ω, φ),k n (ω)) is considered, the associated group velocity vector 31 is given by :

C g n (ω, φ)=∇ k ω = S e tot = I E tot ( 19
)
where : is the spatial and time average respectivelly on one cell and one period, S is the density of energy flux defined in, [START_REF] Maysenhölder | Körperschall-energie Grundlagen zur Berechnung von Energiedichten und Intensitäten[END_REF] I the mean intensity and e tot , E tot the total piezomechanical energy and its time average on a period (see [START_REF] Maysenhölder | Körperschall-energie Grundlagen zur Berechnung von Energiedichten und Intensitäten[END_REF] for details). In this problem, we only consider mechanical energy transportation as the electrostatic coupling is decentralized and can be condensed as a mechanical interface as proved in [START_REF] Hagood | Damping of structural vibrations with piezoelectric materials and passive electrical networks[END_REF] and generally computed in. [START_REF] Collet | Modal Synthesis and Dynamical Condensation Methods for Accurate Piezoelectric Systems Impedance Computation[END_REF] So we also compute the intensity vector I by :

I n = - ω 2 Re( Ωx C(ε n (x,ω,φ)+ikΞ n (x,ω,φ)).(w * n (x,ω,φ))dΩ/V ol (20)
where . * is the complex conjugate and V ol the domain volume. As the spatio-temporal average of the system Lagragian is null (see [START_REF] Maysenhölder | Körperschall-energie Grundlagen zur Berechnung von Energiedichten und Intensitäten[END_REF] ), the total energy average is approximated by only computing the kinetic energy average:

E tot = 1 2 ( Ωx ρω 2 w n (x,ω,φ).w * n (x,ω,φ)dΩ/V ol (21)
The group velocity vectors C g n (ω, φ) is computed for all wave numbers at each frequency. In order to focus our analysis on only flexural modes (S and SH ones) we introduce an indicator allowing to select them by computing the ratio of kinetic energy average on out of plane displacement as:

Ind(n, ω, φ)= 1 2 ( Ωx ρω 2 wz n (x,ω,φ)wz * n (x,ω,φ)dΩ/V ol E tot ( 22
)
with wz n (x,ω,φ)be i n gt h e( Oz) component of vector w n (x,ω,φ).

Piezoelectric Material

OPTIMISATION OF THE FLEXURAL ENERGY FLOW INSIDE THE SHUNTED PERIODIC PIEZO-COMPOSITE

The considered piezo-composite cell is presented in figure 1. The supporting plate material is standard aluminum with 0.1 % of hysteretic damping ratio and the piezoelectric material characteristics is given in table 1.

The used methodology for optimizing the shunt impedance Z(iω) is based on the minimization of the maximal group velocity collinear to the wave number vector (19) for waves having a ratio of transported flexural kinetic energy (22) greater than 0.8. The used criterion can also be written as:

Crit(Z(iω),φ)=max n/Ind(n,ω,φ)>0.8 (C g n (ω, φ).Φ) (23)
The used numerical optimization of the criteria is based on a multidimensional unconstrained nonlinear minimization (Nelder-Mead).

Case 1 : Z(iω) ∈ C

In a first test, we optimize the criterion by considering any frequency dependent complex impedance. We present in figure 2(a) and 2(b) the obtained real parts and imaginary parts of the wave number kx n (iω)a l o n g (Ox) axis. The red circles mark the dispersions curves for Z = 0 and the blue crossed the optimal dispersion. The corresponding group velocities along (Ox) are presented in figure 3 while the real and imaginary parts of the optimal impedance are plotted in figure 4.

We immediately observe that the optimization of the shunt impedance leads to greatly modify the group velocity of the A o mode in the first part of the spectrum (i.e before the first bending band gap between 22 and 27 kHz). The bending waves also propagate energy with a lower velocity and can even been very low as evanescent waves before 6 kHz. The corresponding real and imaginary parts of the dispersion curves are slightly modified. We notice an increase of the imaginary values indicating an increase of the spatial decay rates. The optimal impedance values are almost real, and correspond to those obtained if a constant negative capacitance is used. The corresponding average value is -150.05 pC.V -1 . Some imaginary parts of the optimal impedance are negative which indicate that the optimization leads to provide energy to the system for controlling mechanical damping effect introduced with hysteretic damping ratios into the model, and, also, obtain a fully conservative system.

Case 2 : Z(iω) ∈ R

As the obtained negative impedance imaginary part does not appear realistic for physical implementation, the second case considers optimization by considering frequency dependent real impedance. We present in figure 5(a) and 5(b) the obtained real parts and imaginary parts of the wave number kx n (iω) along (Ox)a x i s . T h er e d circles mark the dispersions curves for Z = 0 and the blue crossed the optimal dispersion. The corresponding group velocities along (Ox) is presented in figure 6 while the real and imaginary parts of the optimal impedance are plotted in figure 7. We immediately observe that the obtained results are globally similar to those provided by the complete complex optimization presented before, even if the equivalent constant negative capacitance is now -149.88 pC.V -1 . The numerical cost is lower and the optimization faster. In order to study the translation of the wave properties obtained by optimizing the previously described criterion on the dynamical response of a finite dimension system, we apply the optimal impedance on a finite set of shunted piezo-composite cells semi-distributed onto a plate system as described in figure 8. The harmonic response of this system is also computed at different frequency when optimal impedance is connected or not to each patches. We plot in figure 9 the obtained results in term of kinetic energy density.

Validation on a periodically semi-distributed set of adaptive cells

These numerical results clearly show up a strong influence of the modifications of the wave dispersion (i.e on the group velocities) in the standing wave responses plotted in figure 9. We observe at 5 kHz an increase in the dynamic response of the system when optimal shunt is connected. A large part of the system energy remains in its left part where the applied forces is located. The semi-distributed interface also change the system admittance and filter wave diffusion by increasing is reflexibility property. At 22 kHz, the energy diffusion is clearly condensed into the left part of the system with a largely decreased amplitude compared to this obtained with open circuit. The structural dynamical admittance has been decreased by connecting the shunt circuits. Finally, at 60 kHz, the energy is concentrated on the right part of the system between the adaptive interface and the clamped boundary condition. We observe something similar to a wave trap effect. The average value is, one more time, largely decrease by using the shunt circuits.

CONCLUSIONS

This paper presents a numerical procedure able to compute the damped wave's dispersion functions in the whole first Brillouin domain of multi dimensionnal piezo-elastodynamical wave guides. The method was applied for determining the optimal impedance allowing to minimize the group velocities of the flexural waves. Based on this approach, some numerical test on a finite dimension system incorporating a semi-distributed set of shunted piezo-composite cells has been performed. We underline a strong influence of the designed shunt circuits in the dynamical response of the system. Even if the link between the obtained wave properties are not clearly established, we also demonstrated that our developed numerical procedures can be used for optimizing the energy diffusion operator of such adaptive mechanical interface. To do so, additional work has to be done for optimizing the complete interface scattering and for controlling the evanescent waves playing an important role in the finite system dynamical response. The proposed methodology can also be used for studying particular dissipation phenomenon such as those induced by complex shunted piezoelectric patches as proposed by [START_REF] Beck | Broadband vibration suppression assessment of negative impedance shunts[END_REF] and, [START_REF] Casadei | Vibration control of plates featuring periodic arrays of hybrid shunted piezoelectric patches[END_REF] or even foams or complex polymers behaviors. The proposed method furnishes an efficient tool for future optimization of distributed smart cells as proposed in the case of 1D wave guide by.

Figure 1 .

 1 Figure 1. Generic 3D piezocomposite periodic cell

Figure 2 .Figure 3 .4

 23 Figure 2. Real parts (a) and imaginary parts (b) of the wave number kxn(iω)a l o n g( Ox), the red circles mark values obtained for Z = 0 and the blue crossed the optimal ones

Figure 4 .Figure 5 .Figure 6 .1

 456 Figure 4. Real and imaginary parts of the optimal impedance

Figure 7 .

 7 Figure 7. Real and imaginary parts of the optimal impedance

Figure 8 .

 8 Figure 8. 3D piezocomposite periodic semi-distributed Cells

6

 6

Figure 9 .

 9 Figure 9. Kinetic Energy density for different source frequency ((a) 5 kHz,( b )2 2kHz,( c )6 0kHz). On the left with optimal impedance connected to the piezo-patches and on the right with open circuit

Table 1 .

 1 Piezoelectric patch characteristics

	Symbol	Value	Property
	s E 11 = s E 22 = s33 E 11.6 × 10 -12 Pa -1 s E 12 = s E 13 = s E -3.33 × 10 -12 Pa -1 12, 13 and 23 compliance matrix coefficient 11, 22 and 33 compliance matrix coefficients 23 s E 44 = s E 55 = s E 66 45.0 × 10 -11 Pa -1 44, 55 and 66 compliance matrix coefficients
	η	0.1%	Hysteretic Damping ratio
	d 31 = d 32	-6 × 10 -11 C/N	31 and 32 piezoelectric matrix coefficients
	d 33	15.2 × 10 -11 C/N	33 piezoelectric matrix coefficient
	d 24 = d 15	730 × 10 -12 C/N	24 and 15 piezoelectric matrix coefficients
	ρ	7600kg/m 3	Density
	ε T 11 = ε T 22 ε T 33	504.1 ε o C/V/m 270 ε o C/V/m	Dielectric Permittivity Dielectric Permittivity

ACKNOWLEDGMENTS

This work was carried out with a grant of French agency ANR number NT09-617542. We gratefully acknowledge the French ANR and CNRS for supporting this program.