Ignacio Tudela

Veronica Saez

Maria Deseada Esclapez

Pedro Bonete

Hassen Harzali

Fabien Baillon

Jose Gonzalez-Garcia

Olivier Louisnard
email: louisnar@enstimac.fr

Verónica Sáez

María Deseada Esclapez

José González-García

Study of the influence of transducer-electrode and electrode-wall gaps on the acoustic field inside a sonoelectrochemical reactor by FEM simulations

Keywords:

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

Introduction

The synergic combination of electrochemical processes with ultrasound has been an active research in recent years due to its potential use in many different applications [START_REF] González-García | Current topics on sonoelectrochemistry[END_REF]. Many studies are found in the literature referred to its use in environmental remediation as part of hybrid technologies for the degradation of organic pollutants in aqueous media [START_REF] Abramov | Ultrasonic intensification of ozone and electrochemical destruction of 1,3-dinitrobenzene and 2,4-dinitrotoluene[END_REF][START_REF] Oturan | Sonoelectro-Fenton process: a novel hybrid technique for the destruction of organic pollutants in water[END_REF][START_REF] Li | Effect of low frequency ultrasonic irradiation on the sonoelectro-Fenton degradation of cationic red X-GRL[END_REF], but also referred to its use as a non-chemical treatment [START_REF] Joyce | The development and evaluation of electrolysis in conjunction with power ultrasound for the disinfection of bacterial suspension[END_REF] and as its most common application, direct sonoelectrolysis [START_REF] González-García | Sonoelectrochemical synthesis of materials[END_REF].

Sonoelectrochemical processes have been deeply studied by the authors in two different application areas: the sonoelectrodeposition of PbO 2 on various substrates [START_REF] González-García | Electrodeposition of PbO2 on glassy carbon electrodes: influence of ultrasound power[END_REF][START_REF] Sáez | Electrodeposition of PbO2 on glassy carbon electrodes: influence of ultrasound frequency[END_REF][START_REF] Sáez | Lead dioxide film sonoelectrodeposition in acidic media: preparation and performance of stable practical anodes[END_REF] and the sonoelectrochemical removal of organic compounds such as trichloroacetic acid [START_REF] Esclapez | Sonoelectrochemical treatment of water polluted with trichloroacetic acid: from sonovoltammetry to pre-pilot plant scale[END_REF] or perchloroethylene [START_REF] Sáez | 20 kHz sonoelectrochemical degradation of perchloroethylene in sodium sulphate aqueous media: influence of the operational variables in batch mode[END_REF] in water. The latter constitutes an interesting option for environmental remediation, as complete degradation of C-Cl bonds, which are toxic in nature, is achieved [START_REF] Sáez | Sonoelectrochemical degradation of perchloroethylene in water: enhancement of the process by the absence of background electrolyte[END_REF]. However, the high energy consump-tion associated to the application of ultrasound within the reactor and the non-homogeneous distribution of cavitation makes current sonoelectrochemical water treatment industrially unfeasible from an economic point of view. In order to improve the sonication efficiency related to the energy consumption, the optimization of all kinds of sonoreactors must be faced taking into account building materials and geometric design, and also setting an optimum working frequency of the overall sonoelectrochemical system [START_REF] Abdelsalam | A study investigating the sonoelectrochemical degradation of an organic compound employing Fenton's reagent[END_REF]. Therefore, a correct understanding of the acoustic field structure in the reactor is needed, prior to its optimization and scale-up. This consideration would allow us to predict the cavitating zones inside the reactor in order to effectively design large scale reactors [START_REF] Gogate | Sonochemical reactors: important design and scale up considerations with a special emphasis on heterogeneous systems[END_REF] and to control the extent of transient and stable cavitation events [START_REF] Ashokkumar | The detection and control of stable and transient acoustic cavitation bubbles[END_REF].

In the last 15 years, quite a few research groups have tried to model the spatial distribution of the acoustic pressure inside a sonoreactor by numerical methods. Dähnke and Keil developed a 3D model to calculate linear pressure fields in liquids with an inhomogeneous distribution of cavitation bubbles [START_REF] Dähnke | Modeling of three-dimensional linear pressure fields in sonochemical reactors with homogeneous and inhomogeneous density distributions of cavitation bubbles[END_REF]. They compared the results with experimental data, obtaining a good agreement but observing some deviations [START_REF] Dähnke | Modeling of three-dimensional pressure fields in sonochemical reactors with an inhomogeneous density distribution of cavitation bubbles. Comparison of theoretical and experimental results[END_REF]. Liu et al. [START_REF] Liu | Finite element simulation of coupled vibration modes in an ultrasonic cleaning tub: effect of the presence of a washing object[END_REF] used Finite Element Methods (FEM) to simulate coupled vibration modes in an ultrasonic cleaning tub in order to study the effect of the presence of a washing object. They concluded that the acoustic modes depended on the object location, its mechanical restraint conditions and its physical properties (Young modulus and density). More recently, Yasui et al. [START_REF] Yasui | FEM calculation of an acoustic field in a sonochemical reactor[END_REF] simulated a rectangular sonoreactor accounting for vibrations of the vessel wall. They showed the effect of the wall thickness for two frequencies (100 and 140 kHz), employing various attenuation coefficients in order to observe the effect of cavitating bubbles on the acoustic field.

Numerical simulations have also been evaluated by the authors in recent years. An initial approach to the calculation of the acoustic field by FEM techniques was made in order to mechanically characterize a commercial 20 kHz sonoreactor [START_REF] Sáez | Chacterization of a 20 kHz sonoreactor. Part I: analysis of mechanical effects by classical and numerical methods[END_REF], where the liquid boundary in contact with air was treated as infinitely soft and the vessel boundaries were treated as infinitely rigid walls. Further studies, where a first attempt to optimize a sonoreactor was carried out [START_REF] Klíma | Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results[END_REF], focused on the geometry of the reactor (cell dimensions, liquid volume and ultrasonic horn position), treating the cell boundaries as infinitely soft walls. FEM simulations and experimental observations verified that the fast decrease in intensity when increasing distance from the horn could be reversed to an increase due to multiple reflections supported. And more recently, an analysis of the response of an experimental sonoreactor equipped with a cooling jacket excited by a cup-horn transducer was performed [START_REF] Louisnard | FEM simulation of a sono-reactor accounting for vibrations of the boundaries[END_REF]. Simulations were carried out accounting for the vibration of the reactor walls, pointing out the transmission of sound into the cooling jacket. Ultrasound frequency was systematically varied in the range available for the generator, enabling to seek the resonance frequencies of the system, which were characterized by global parameters as functions of frequency.

In this work, we analyzed the effect which may present the distance between the transducer emitter surface and the electrode and the distance between the electrode and the bottom reactor wall in a cylindrical sonoelectrochemical reactor designed by CAD tools. The main goal was to qualitatively estimate the zones where cavitation could take place near resonance frequencies, taking into account two different physical phenomena: the application of ultrasound in the working liquid and the deformation of the reactor walls. For this purpose, the previously developed model accounting for vibrations of the boundaries [START_REF] Louisnard | FEM simulation of a sono-reactor accounting for vibrations of the boundaries[END_REF] was employed to estimate the acoustic field inside a sonoelectrochemical reactor.

The simulated system

The cylindrical reactor simulated is shown in Fig. 1. The reactor is built on polycarbonate (PC) in order to visualize the cavitation fields inside the reactor in further experimental work with luminol. The flange which holds the reactor to the transducer is made of polypropylene (PP) and titanium (Ti) has been considered for the electrode. The horn tip is based on current 20 kHz UIP1000hd transducer [START_REF]UIP1000hd Operating Instructions[END_REF] provided by Hielscher Ultrasonics GmbH.

FEM simulations

Theoretical model

As mentioned before, the acoustic field and the deformation of the reactor walls were calculated by following the simulation strategies exposed in previous works by the authors. Therefore, a short recapitulation of the key equations previously developed is included in the following sections. For deeper discussion on this topic, refer to Ref. [START_REF] Louisnard | FEM simulation of a sono-reactor accounting for vibrations of the boundaries[END_REF].

Linear acoustics in the working liquid

In order to calculate the propagation of sound waves through the liquid the next expression, known as the Helmholtz equation, was considered:

∇ 2 P + ω c l 2 P = 0 ( 1
)
where P is the acoustic pressure, ω is the angular frequency and c l is the sound speed of the liquid. This equation must be supplemented with adequate boundary conditions. First, assuming a horn radiating surface normal displacement of amplitude U 0 , the boundary condition is obtain by imposing the inward acceleration of the liquid as:

1 l ∇P • n = ω 2 U 0 (2)
where l is the density of the liquid. The horn lateral wall is considered as an infinitely rigid boundary, so that the inward liquid acceleration on this boundary is set to zero:

1 l ∇P • n = 0 (3)
Finally, for all interfaces between the liquid and the deformed solid domain (either electrode or the reactor walls), the liquid acceleration must match the solid one, and the boundary condition reads:

∇P • n = l ω 2 U s • n (4)
where U s is the complex amplitude of the displacement field of the solid, which coupled calculation is described in the next section. In those expressions, n is the normal pointing outward the liquid.

Vibrations of the solids

The vibrations of the reactor walls are calculated as in Ref. [START_REF] Louisnard | FEM simulation of a sono-reactor accounting for vibrations of the boundaries[END_REF], using the elasto-dynamic theory, assuming elastic deformation for all materials, neglecting volume forces and assuming monoharmonic vibrations:

-s ω 2 U s = ∇ • = (5) where = = Ev (1 -2v)(1 + v) (Tr = ε) = I + E 1 + v = ε (6) = = 1 2 [ = ∇U s + T = ∇U s ] (7)
where U s is the complex displacement field in the solid, = and = ε are the elastic stress tensor and strain tensor, respectively, s is the solid density, v is the Poisson ratio of the solid, = I is the identity tensor, Tr is the trace operator and E is the Young modulus.

Eq. ( 5) must be supplemented with the following boundary conditions. The solid boundaries in contact with air are assumed free, so that the three components of the stress = • n are ascribed to 0 on such surfaces.

Finally on the interfaces between the liquid and the solid, the stress imposed on the solid is just the normal pressure stress exerted by the liquid, and the condition reads:

= • n = -P • n ( 8
)
where P is the acoustic pressure field in the liquid evaluated on the interface. Again, n is the normal pointing outward the liquid.

It must be noted that Eqs. ( 5) and ( 8) are vectorial. The set of Eqs. ( 4) and ( 8) constitute the correct acoustic-structure interface conditions.

Energy dissipation

In order to account for the energy dissipation by cavitating bubbles, the next energy conservation expression was employed, assuming mono-harmonic waves in steady state:

S sonotrode - 1 2 ℜ(PV * ) • ndS P active = S boundaries - 1 2 ℜ(PV * ) • ndS P bound + V ⟨ diss ⟩dV P diss (9)
where ℜ denotes the real part of a complex number, V is the liquid volume, S is the surface (for both sonotrode and solid boundaries) and V* denotes the complex amplitude of the acoustic velocity field. The first and second terms are respectively the power entering the liquid through the sonotrode radiating surface (P active ) and the power lost through the rest of the liquid boundaries (P bound ). When considering either infinitely soft or rigid boundaries, the second term vanishes (P bound = 0). In our more complex case where S boundaries was the internal wall of the PC reactor, the PP flange and the Ti surface in contact with the liquid, almost the whole external surface of the reactor was in contact with air, and therefore, not being constrained. P bound is still zero for a perfectly elastic vessel formed of external, non-dissipative, unconstrained elastic solid boundaries which do not transmit any wave to the external air. Therefore, we also assumed that P bound = 0 in this study. On the other hand, the third term in Eq. ( 9) represents the power dissipated in the medium (P diss ), where an arbitrary, spatially uniform attenuation coefficient, ˛, was introduced as follows:

⟨ diss ⟩ = ˛|P| 2 l c l (10)

Obtaining of response curves

Among the different scalar quantities representative of the global vibrations of the system (i.e. average acoustic pressure in the liquid, average acoustic energy stored in the solid walls, etc.), we chose to plot the average acoustic energy stored in the liquid domains (E a ) as a function of frequency, according to the following equation:

E a = V 1 4 l |V| 2 + 1 4 |P| 2 l c 2 l dV (11)
where V denotes the real amplitude of the acoustic velocity field.

Resolution procedures

The simulated set-up is represented in Fig. 2, where only one half of a cut plane is shown. The horn tip (d = 40 mm) emitted in the liquid, limited by the PP flange and PC walls of different thickness (4-20 mm). The liquid split in two different domains as the Ti electrode (1 mm thick) was placed in different heights. The liquid was water with properties l = 1000 kg m -3 and c l = 1500 m s -1 . The elastic properties were E = 6.35 GPa, v = 0.48 and s = 898 kg m -3 for the PP flange; E = 2.38 GPa, v = 0.36 and s = 1200 kg m -3 for the PC walls and E = 102.7 GPa, v = 0.34 and s = 4507 kg m -3 for the Ti electrode. The sonotrode had a working frequency range from 19 to 21 kHz, assuming that it would automatically adjust to an optimum frequency where the electric impedance was minimal, with the main oscillation developed along with axis-direction. The emitter surface of the transducer was assumed to vertically vibrate with an amplitude of 25 × 10 -6 m.

Three different configurations were studied (Table 1), which were named referring to the emitter-electrode and electrode-wall gaps as a factor of the wave-length ( = 7.5 cm) for water when the frequency is 20 kHz, the speed of sound is 1500 m s -1 and the density is 1000 kg m -3 .

Eqs. ( 1), ( 5) and ( 9) were numerically solved with COMSOL Multiphysics package, where both linear acoustics and structural mechanics application modes were employed in order to obtain the spatial distribution of the acoustic pressure in the working liquid and the deformation of the reactor walls. Due to the complexity Table 1 Distances between the transducer emitter surface and the electrode and between the electrode and the bottom wall of the reactor for each studied configuration, = 7.5 cm (20 kHz, 1500 m s -1 , 1000 kg m -3 ). of the geometry, the number of calculations needed and the thin mesh required (the mesh consisted of more than 10 5 triangular elements in each studied configuration, with an emphasis on meshing the liquid-solid interface and the Ti electrode domain), we chose the axial 2D mode due to the need of extremely high computer resources in order to carry out the study in the 3D mode. This bidimensional mode enables to obtain much finer meshes, although three-dimensional, non symmetrical modes of the vibrating solid domains (i.e. PC reactor, PP flange and Ti electrode) are not calculated. Nevertheless, non symmetrical modes have no chance to be excited for a purely symmetric motion of the transducer in the frame of linear acoustics. The method used here does not actually compute the eigenmodes of the system, but its response to a harmonic driving at variable frequency. Therefore, simulations with the 3D mode would have yielded the same results for the symmetric configuration studied. The UMFPACK [START_REF] Davis | A column pre-ordering strategy for the unsymmetricpattern multifrontal method[END_REF] solver in parametric mode was employed to obtain the response curves of the system in the working frequency range of the transducer. For this purpose, the frequency was varied by small steps (10 Hz) in the working range of the transducer (19-21 kHz).

Results

Configuration /4-

For the first studied configuration, the response curves shown in Fig. 3 (average acoustic energy stored in the liquid) were obtained for different attenuation coefficients (˛= 0, 1 and 5 m -1 ) in the working frequency range of the transducer. Five resonance peaks were observed when no energy dissipation was considered, which varied or even disappeared when increasing attenuation (Table 2). Those peaks corresponded to global resonances of the whole mechanical system formed by the liquid coupled with the PP flange, the PC reactor and the Ti electrode walls. The amplitude of these global resonance peaks should be infinite when no attenuation is considered, which means that an infinite accumulation of acoustic energy would take place in the whole sonoelectrochemical system. Thus, the finite maxima of the peaks appearing hereinafter for ˛= 0 m -1 are only due to the discretization of the frequency axis.

For ˛= 5 m -1 , peaks II and V presented a higher acoustic energy stored in the liquid by far. Therefore, the spatial distribution of the peak acoustic pressure was analyzed in both cases and is shown in Figs. 4 and5, where dark red regions represent main pressure antinodes and dark blue regions represent main nodes, and the grey line displays the magnified deformed boundary in order to illustrate the coupling between the vibrations of the solid walls and the fluid. For peak II attenuation does not play a great influence in the distribution of the acoustic field, as just a few non-important pressure nodes are affected. However, the spatial distribution of the acoustic pressure at peak V is clearly affected, as a pressure antinode becomes more evident on the emitter surface, and part of the structure of the acoustic field is modified. Still, the main antinode remains on the electrode surface opposite to the reactor bottom wall. Coupling of the deformation of the Ti electrode and the formation of alternated pressure antinodes on both surfaces of the electrode is clearly seen for all the studied attenuation coefficients at peak V. Also, a low-profile antinode stays on the bottom wall surface in the latter case. All these observed features demonstrate that attenuation not only affects the amplitude of the acoustic pressure (see figure captions), but also the structure of the acoustic field.

Configuration /2-3 /4

For the second studied configuration, four resonance peaks were observed (Fig. 6). Peaks II and III disappeared at the highest attenuation factor, while frequency slightly changed for the remaining peaks (Table 3).

If we check the spatial distribution of the peak acoustic pressure for peak I (Fig. 7), we observe that the structure of the acoustic field was slightly modified, with the most noticeable change occurring near the emitter surface (the main antinode came closer to the transducer). However, attenuation strongly affected the structure of the acoustic field for peak IV (Fig. 8), as an antinode on the emitter surface grew in both size and relative pressure amplitude to become the second most important antinode from the peak acoustic pressure point of view. Distribution of nodes and antinodes between the electrode and the wall was completely modified, and as we noted before for peak V in the first configuration, the main antinode remained on the electrode surface. Again, coupling of the vibration of the electrode and the appearance of pressure antinodes on the electrode surfaces is observed, especially at peak V.

Configuration 3 /4-/2

For the last studied configuration, six resonance peaks were observed (Fig. 9). Peaks I, and III disappeared with the highest attenuation factor, while frequency changed for peaks II and V (Table 4). The features of the acoustic field for peak II (Fig. 10) were very similar to those observed for the lowest resonance peak of the previously studied configurations: a main antinode on the emitter surface and few changes on the structure of the acoustic field when attenuation is increased. The same thing occurred for peak VI (Fig. 12) related to the highest resonance peaks from previous configurations: a pressure antinode became more evident on the emitter surface when attenuation increased, but the main antinode remained on the electrode surface. Again, a low-profile antinode formed at the bottom wall of the reactor.

But if we take a look to peak V (Fig. 11), we notice that the acoustic field stayed aside from the other peaks previously commented. When no attenuation was considered, a great, low pressure antinode stayed on the wall surface, while small, high pressure antinodes alternated in both sides of the electrode. No significant antinodes were observed in the upper liquid domain, a very interesting feature in order to avoid cavitation-induced erosion of the sonotrode emitter surface. This situation changed when attenuation was considered (˛= 1 m -1 ), as the great antinodes between the electrode and the reactor wall were almost gone while new antinodes formed between the emitter surface and the electrode.

For the highest attenuation factor, the antinode near the emitter became more evident, but its peak acoustic pressure remained significantly lower than the pressure amplitude near the electrode. Finally, due to the greater distance between the emitter and the electrode in this configuration, it is very easy to see how the deformation of the electrodic domain and the appearance of alternated pressure antinodes and nodes near both surfaces of the electrode are perfectly coupled in all the peaks shown in Figs. 10-12.

Discussion

In order to check which configuration would show a better performance, we compared the response curves for ˛= 5 m -1 (Fig. 13). Higher values were reached for configuration /4-, where peaks II and V were clearly seen. Configuration /2-3/4 could also be inter- esting, while configuration 3/4-/2 (highest transducer-electrode gap) would present the worst performance, from the stored acoustic energy point of view, working at any of its resonance peaks.

However, a high acoustic energy stored in the liquid does not necessary mean that cavitation takes place near the electrode. In order to check this consideration, the peak acoustic pressure on the electrode surface was also analyzed (Table 5 ). As it can be seen, the reactor with the shortest transducer-electrode gap (configuration /4-) would reach the highest pressure amplitude working at peak V, followed by configuration 3/4-/2 at peak IV and configuration /2-3/4 at peak V. Therefore, the configuration with the shortest distance between the emitter and the electrode, working at peak V (Fig. 5), would be the most interesting from a sonoelectro-Fig. 9. Average acoustic energy stored in liquid in configuration 3/4-/2 for various attenuation coefficients: ˛= 0 m -1 (dotted line), ˛= 1 m -1 (dashed line) and ˛= 5 m -1 (solid line). chemical point of view, as pressure antinodes alternating in both sides of the reactor reached higher pressure amplitudes in this case. Consequently, a higher amount of cavitating bubbles would form near the electrode, where mechanical phenomena such as acoustic streaming [START_REF] Klíma | Sonoassisted electrooxidative polymerisation of salicylic acid: role of acoustic streaming and microjetting[END_REF], shock waves [START_REF] Birkin | Cavitation, shock waves and the invasive nature of sonoelectrochemistry[END_REF] and others [START_REF] Klíma | Application of ultrasound in electrochemistry. An overview of mechanisms and design of experimental arrangement[END_REF] would enhance mass-transport there [START_REF] Cooper | Mass transport in sonovoltammetry with evidence of hydrodynamic modulation from ultrasound[END_REF][START_REF] Walton | Sonovoltammetry at platinum electrodes: surface phenomena and mass transport processes[END_REF], also resulting in activation of the electrode surface [START_REF] Compton | Voltammetry in the presence of ultrasound. Sonovoltammetry and surface effects[END_REF]. The existence of a low-profile antinode at the bottom of the reactor would also provide a good location to place the counterelectrode (see file anim 025 100 peak5.gif included as Supplementary data). In addition, if cavitation-induced erosion of the transducer was also considered a key factor in order to chose a reactor design [START_REF] Sutkar | Design aspects of sonochemical reactors: techniques for understanding cavitational activity distribution and effect of operating parameters[END_REF], configuration 3/4-/2 working at peak V (Fig. 11) could be an interesting option from both sonoelectrochemical and emitter erosion points of view. As mentioned before, an antinode near the emitter would form for ˛= 5 m -1 , but its peak acoustic pressure would be significantly lower than the pressure amplitude near the electrode, which is located far enough of the emitter surface (see file anim 075 050 peak5.gif included as Supplementary data).

As a general discussion on the simulations, obtaining the optimum spatial distribution of the acoustic pressure accounting for the vibrations of the solid boundaries by setting a proper working frequency introduces a novel point of view in order to design efficient sonochemical/sonoelectrochemical reactors. Simulation studies generally neglect the deformations of the walls, where solid boundaries are treated as infinitely rigid [START_REF] Sáez | Chacterization of a 20 kHz sonoreactor. Part I: analysis of mechanical effects by classical and numerical methods[END_REF][START_REF] Shao | Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt[END_REF][START_REF] Memoli | The importance of temperature control in the operation of high power ultrasound reactors[END_REF] or soft walls [START_REF] Klíma | Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results[END_REF][START_REF] Vanhille | Nonlinear ultrasonic standing waves: twodimensional simulations in bubbly liquids[END_REF][START_REF] Sutkar | Theoretical prediction of cavitational activity distribution in sonochemical reactors[END_REF][START_REF] Sutkar | Mapping of cavitational activity in high frequency sonochemical reactor[END_REF], or a combination of both [START_REF] Nomura | Analysis of an ultrasonic field attenuated by oscillating cavitation bubbles[END_REF], alleging different considerations in each case. Regarding these apparently controversial hypotheses, the present work shows that vibrations of the solid boundaries could deeply influence the system response in terms of both the spatial distribution of the acoustic pressure and the resonance frequencies of the system. Moreover, the consideration of solid boundaries as infinitely rigid or infinitely soft yields response curves which significantly differ from the ones obtained by properly taking into account the deformation of the solid [START_REF] Louisnard | FEM simulation of a sono-reactor accounting for vibrations of the boundaries[END_REF]. An experimental evidence of the apparently suitable consideration of the solid boundaries as vibrating walls would be the diverse experimental works where the studied solution is not directly irradiated with an ultrasonic transducer (e.g. sonocatalytic degradation of dyes in low-frequency ultrasonic baths [START_REF] Shimizu | Sonocatalytic degradation of methylene blue with TiO2 pellets in water[END_REF][START_REF] Pang | Optimization of sonocatalytic degradation of Rhodamine B in aqueous solution in the presence of TiO2 nanotubes using response surface methodology[END_REF]).

Nevertheless, we must note that even though the main goal of the simulation of the acoustic field inside a sonochemical/sonoelectrochemical reactor is to locate pressure antinodes where cavitation events are expected, the maximum acoustic pressure amplitudes obtained in the simulations included in this work seemed unrealistic, especially when no attenuation was accounted for. This is due to two main reasons: (i) the assumed displacement of the transducer emitter surface (which was defined according to the supplier specifications) and (ii) the need of a more realistic model of attenuation by cavitating bubbles.

Regarding the first reason, some of the works found in the literature define the emitter as an "acoustic pressure source" where the pressure amplitude near the emitter is P 0 [START_REF] Sáez | Chacterization of a 20 kHz sonoreactor. Part I: analysis of mechanical effects by classical and numerical methods[END_REF][START_REF] Klíma | Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results[END_REF][START_REF] Shao | Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt[END_REF][START_REF] Sutkar | Theoretical prediction of cavitational activity distribution in sonochemical reactors[END_REF][START_REF] Sutkar | Mapping of cavitational activity in high frequency sonochemical reactor[END_REF]. In this sense, we tried to take a further step towards a more realistic approach to the matter, as we took the emitter surface displacement provided by the supplier and introduced it as a normal acceleration condition in the emitter boundary, assuming that the sonotrode behaves as an ideal acoustic piston. This displacement may not be exactly what the transducer actually experiences in any specific experimental conditions, but serve as an order of magnitude. In this sense, experimental measurements of the emitter surface displacement (i.e. laser vibrometry [START_REF] Zipser | Laser-scanning vibrometry for ultrasonic transducer development[END_REF]) would help in order to obtain this parameter. Eventually, the complete simulation of the whole system including the ultrasonic transducer (i.e. piezoelectricity, pre-stress, etc.) should be carried out, in order to make a more rigorous approach to the problem. Related to this, some interesting works have been published in recent years where the piezoceramics, countermass and amplifier have been studied with FEM simulations [START_REF] Iula | Finite element threedimensional analysis of the vibrational behaviour of the Langevin-type transducer[END_REF][START_REF] Iula | A high displacement ultrasonic actuator based on a flexural mechanical amplifier[END_REF][START_REF] Gallego-Juárez | Modal interactions in highpower ultrasonic processing transducers[END_REF][START_REF] Cardoni | On the nonlinear dynamics of plate-transducers[END_REF][START_REF] Gallego-Juárez | Power ultrasonic transducers with extensive radiators for industrial processing[END_REF][START_REF] Abdullah | Correct prediction of the vibration behavior of a high power ultrasonic transducer by FEM simulation[END_REF]. Its inclusion in the model employed in this work would enhance the simulations, as vibrations of the horn tip could also be simulated in order to account for the lateral cavitation fields commonly observed during experiments.

Regarding the second reason, the lack of a definitive theory predicting the bubble spatial and size-distribution that would allow the correct calculation of the attenuation factor forced us to treat the latter quantity as a variable, but spatially uniform, parameter in the linear acoustics-based model employed in this work. This treatment allowed us to study how the spatial distribution of the acoustic pressure is affected by energy dissipation, pointing out the existence of an interesting travelling wave component in the propagation of the acoustic field from the emitter surface, even though the simulated geometry was a closed system where reflecting boundaries were defined and classic standing waves would be expected (see files anim 025 100 peak5.gif and anim 075 050 peak5.gif included as Supplementary data in order to visualize the travelling wave component). However, the correct value of a spatially non uniform attenuation factor should be strongly linked to the bubble repartition in the liquid, which in turn depends on the shape of the acoustic field [START_REF] Mettin | Modeling acoustic cavitation with bubble redistribution[END_REF]. Related to this, the long-term objective would be coupling both phenomena in our model to include the main physics of cavitation. This latter point is the most challenging task by far, and recent works by different authors involving non-linear acoustics are showing promising results [START_REF] Vanhille | Nonlinear ultrasonic standing waves: twodimensional simulations in bubbly liquids[END_REF][START_REF] Dubus | On the physical origin of conical bubble structure under an ultrasonic horn[END_REF][START_REF] Louisnard | Nonlinear attenuation of sound waves by inertial cavitation bubbles[END_REF][START_REF] Louisnard | A simple model of ultrasound propagation in a cavitating solid. Part I: Theory, nonlinear attenuation and traveling wave generation[END_REF][START_REF] Louisnard | A simple model of ultrasound propagation in a cavitating solid. Part II: Primary Bjerknes force and bubble structures[END_REF]. Still, linear acoustics presents some intrinsic interest in the conception phase of sonochemical/sonoelectrochemical reactors, because although perturbed by the cavitation bubbles, linear resonance effects can still be visible. This is clearly supported by previous works by the authors [START_REF] Klíma | Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results[END_REF], even though a rough model for solid boundary conditions was employed back then. It may be added that single bubble levitation cells, when used in non-degassed water, still exhibit a clear breathing standing wave with a bubble cloud wandering in the centre. Therefore, linear acoustics, if properly used, remains as a useful tool.

Conclusions

In summary, this work shows how a basic variation of the transducer-electrode and electrode-wall gaps strongly modifies the sonoelectrochemical system response in terms of resonance peaks and structure of the acoustic field. Exciting the sonoelectrochemical system near a resonance frequency enables to reach large peak acoustic pressures and to locate pressure antinodes far from the transducer, in order to avoid cavitation-induced erosion of the emitter surface. However, this latter feature disappears for high attenuation coefficients, as its increase yields the formation and growth of a pressure antinode near the transducer surface. Even so, the election of a proper reactor configuration and working frequency enables to set high pressure antinodes near the electrode, which is very interesting from a sonoelectrochemical point of view. Related to the FEM simulations, the linear acoustics-based model accounting for the vibrations of the solid boundaries used in this work provides interesting results in order to design optimized sonoelectrochemical reactors, as it gives a qualitative idea of the acoustic field inside the reactors, and also provides the approximate location of the resonance frequencies of the system. Nevertheless, the theoretical nature of this work must be remarked, and further developments on the non-linear phenomena involved in the formation of cavitating bubbles and experimental validation are on its way.

Fig. 1 .

 1 Fig. 1. PC cylindrical electrochemical reactor designed for this study.

Fig. 2 .

 2 Fig. 2. Simulated geometry. Only one-half of the reactor is drawn. Modified distances are highlighted in blue. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 3 .

 3 Fig. 3. Average acoustic energy stored in liquid in configuration /4-for various attenuation coefficients: ˛= 0 m -1 (dotted line), ˛= 1 m -1 (dashed line) and ˛= 5 m -1 (solid line).

Fig. 4 .Fig. 5 .

 45 Fig. 4. Spatial distribution of the peak acoustic pressure |P| in the reactor working in configuration /4-near resonance peak II for increasing attenuation coefficients. Dark blue regions represent pressure nodes while dark red regions correspond to pressure antinodes. The color-scales are different for each image. |P|max = 1.96 × 10 5 bar (˛= 0 m -1 ), 4.76 × 10 2 bar (˛= 1 m -1 ) and 1.01 × 10 2 bar (˛= 5 m -1 ). Deformation of the solid boundaries at ωt = n × 2 is magnified. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 6 .

 6 Fig. 6. Average acoustic energy stored in liquid in configuration /2-3/4 for various attenuation coefficients: ˛= 0 m -1 (dotted line), ˛= 1 m -1 (dashed line) and ˛= 5 m -1 (solid line).

Fig. 7 .

 7 Fig. 7. Spatial distribution of the peak acoustic pressure |P| in the reactor working in configuration /2-3/4 near resonance peak I for increasing attenuation coefficients. Dark blue regions represent pressure nodes while dark red regions correspond to pressure antinodes. The color-scales are different for each image. |P|max = 6.50 × 10 3 bar (˛= 0 m -1 ), 3.49 × 10 2 bar (˛= 1 m -1 ) and 8.15 × 10 bar (˛= 5 m -1 ). Deformation of the solid boundaries at ωt = n × 2 is magnified. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 8 .

 8 Fig. 8. Spatial distribution of the peak acoustic pressure |P| in the reactor working in configuration /2-3/4 near resonance peak IV for increasing attenuation coefficients. Dark blue regions represent pressure nodes while dark red regions correspond to pressure antinodes. The color-scales are different for each image. |P|max = 3.84 × 10 3 bar (˛= 0 m -1 ), 4.52 × 10 2 bar (˛= 1 m -1 ) and 1.18 × 10 2 bar (˛= 5 m -1 ). Deformation of the solid boundaries at ωt = n × 2 is magnified. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Spatial distribution of the peak acoustic pressure |P| in the reactor working in configuration 3/4-/2 near resonance peak II for increasing attenuation coefficients. Dark blue regions represent pressure nodes while dark red regions correspond to pressure antinodes. The color-scales are different for each image. |P|max = 3.00 × 10 3 bar (˛= 0 m -1 ), 2.84 × 10 2 bar (˛= 1 m -1 ) and 8.12 × 10 bar (˛= 5 m -1 ). Deformation of the solid boundaries at ωt = n × 2 is magnified. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 12 .

 12 Fig. 12. Spatial distribution of the peak acoustic pressure |P| in the reactor working in configuration 3/4-/2 near resonance peak VI for increasing attenuation coefficients. Dark blue regions represent pressure nodes while dark red regions correspond to pressure antinodes. The color-scales are different for each image. |P|max = 2.77 × 10 3 bar (˛= 0 m -1 ), 3.25 × 10 2 bar (˛= 1 m -1 ) and 1.03 × 10 2 bar (˛= 5 m -1 ). Deformation of the solid boundaries at ωt = n × 2 is magnified. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 13 .

 13 Fig. 13. Comparison of the average acoustic energy stored in liquid for ˛= 5 m -1 : configuration /4-(dotted line), configuration /2-3/4 (dashed line) and configuration 3/4-/2 (solid line).

Table 5

 5 Dimensionless relative peak pressure amplitude near the electrode surface for each resonance peak of all the studied configurations. |P|max = 166.65 bar reached near the electrode for configuration /4-, peak V.

Table 2

 2 Evolution of the resonance frequencies for configuration /4-at various attenuation factors.

	Resonances	˛(m -1 )
		0	1	5
	Peak I (Hz)	19,180	19,180	19,180
	Peak II (Hz)	19,480	19,480	19,500
	Peak III (Hz)	19,930	-	19,970
	Peak IV (Hz)	20,110	20,110	-
	Peak V (Hz)	20,660	20,660	20,670

Table 3

 3 Evolution of the resonance frequencies for configuration /2-3/4 at various attenuation factors.

	Resonances	˛(m -1 )
		0	1	5
	Peak I (Hz)	19,420	19,420	19,460
	Peak II (Hz)	20,070	20,080	-
	Peak III (Hz)	20,190	20,190	-
	Peak IV (Hz)	20,400	20,400	20,420

Table 4

 4 Evolution of the resonance frequencies for configuration 3/4-/2 at various attenuation factors.

	Resonances	˛(m -1 )
		0	1	5
	Peak I (Hz)	19,250	19,250	-
	Peak II (Hz)	19,430	19,430	19,460
	Peak III (Hz)	19,750	19,750	-
	Peak IV (Hz)	20,040	20,040	-
	Peak V (Hz)	20,580	20,580	20,600
	Peak VI (Hz)	20,930	20,930	20,930

Acknowledgments I.T. and J.G.-G. thank the Generalidad Valenciana for its financial support under project ACOMP09/128 and grant FPA/2009/024. I.T. also thanks the Spanish Education Ministry for his research scholarship. O.L. and J.G.-G. thank the Universidad de Alicante and Generalidad Valenciana for their support in scientific exchange missions. M.D.E. thanks Caja de Ahorros del Mediterraneo for her pre-doctoral grant.

Appendix A. Supplementary data Animated files displaying the pressure field for configuration /2-3/4 working at peak V and configuration 3/4-/2 working at peak V.


Caroline Thierry

Jaouher Mahmoudi

Jacques Lamothe

RISK ANALYSIS FOR COOPERATION POLICIES BENEFITS IN REDUCING THE BULLWHIP EFFECT Jaouher MAHMOUDI (a) (b)

Keywords: Information, Simulation, Planning, Capacity, risk assessment

published or not. The documents may come

Risk analysis for cooperation policies benefits in reducing the bullwhip effect in a telecom supply chain

INTRODUCTION

The bullwhip effect, i.e. the amplification of demand variability as one moves up in the supply chain, can be reduced by using cooperation policies (e.g. [START_REF] Moyaux | Multi-Agent cooperationbased on tokens: reduction of the bullwhip effect in a forest supply chain[END_REF][START_REF] Lee | Information Sharing in a Supply Chain[END_REF][START_REF] Xu | Towards better cooperation of the Supply Chain[END_REF]. The purpose of this research is twofold: (1) to propose new cooperation policies based on planning strategies and information sharing strategies (2) to introduce a risk analysis approach in order to evaluate these policies. The system focused on is a one product, four stages supply chain in which capacity decisions must be taken dynamically. The paper is organized as follows: in the next section, we present a literature review, and then we present the system under study in section 3. Section 4 describes the simulation tool that support risk evaluation. Section 5 presents the risk analysis approach which leads us to the validation case and the related data description and characterisation in section 6. And then, in section 7, we focus on the results analysis. A summary, some final remarks and a description of future research conclude the paper.

A LITERATURE REVIEW

The bullwhip phenomenon has been identified and observed in industry for decades. The first academic research into the subject was probably by Forrester (1958). Later, [START_REF] Sterman | Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiment[END_REF][START_REF] Sterman | Business Dynamics[END_REF] offered a more nuanced rationalization of the phenomenon. [START_REF] Lee | Information Distortion in a Supply Chain: The Bullwhip Effect[END_REF] identifies four main causes of bullwhip effect as: demand signal processing, order batching, rationing game and price variation. [START_REF] Fransoo | Measuring the bullwhip effect in the supply chain, Supply Chain Management[END_REF] point out that several bullwhip measures can be used in a given supply chain. One way to do this is by considering the measurements of standard deviations of the upstream and the downstream supply chain demands. Among ways to reduce the Bullwhip effect, supply chain literature and management practice focus on cooperation policies based on information sharing among supply chain members. [START_REF] Lee | Information Sharing in a Supply Chain[END_REF], for instance, report that demand forecast and inventory information sharing is effective in reducing order fluctuations and safety stocks. Aviv ( 2001) using a two-echelon supply chain of a single product compares a policy where the retailer and the supplier develop and employ a joint forecast, to a policy where each party develops and employs its own forecast. [START_REF] Moyaux | Multi-Agent cooperationbased on tokens: reduction of the bullwhip effect in a forest supply chain[END_REF], using a multi-agent system approach, proposes a cooperation technique based on tokens. [START_REF] Xu | Towards better cooperation of the Supply Chain[END_REF] analysed a cooperation scheme where the manufacturer performs the forecasting and ordering activities for both parties, i.e. for the retailer and the manufacturer itself. The impact of certain supply chain characteristicsespecially lead-times and demand correlations between retailers -is also studied (e.g. [START_REF] Aviv | The operational benefits of information sharing and vendor managed inventory (VMI) programs[END_REF] While analysing most of the previous literature, we noticed that the only points-of-view considered in reducing the bullwhip effect were based on information sharing and inventory adjustment approaches and finally on forecasting methods and techniques (e.g. [START_REF] Hanssens | Order forecasts, retail sales, and the marketing mix for consumer durables[END_REF][START_REF] Chen | The impact of exponential smoothing forecasts on the Bullwhip Effect[END_REF][START_REF] Chen | The Bullwhip Effect: Managerial Insights on the Impact of Forecasting and Information on Variability in a Supply Chain[END_REF] Cooperation policies, highlighting planning policies (e.g. policies based on capacity planning strategies) were little studied or ignored (see [START_REF] Småros | Information sharing and collaborative forecasting in retail supply chains[END_REF]. Moreover, for some applications like telecom supply chains, a risk analysis approach is more appropriate than the usual performance evaluation approaches because of the high uncertainty related to this supply chain environment. The goal of this research is to analyse some cooperation policies focusing on: (i) capacity planning strategies (ii) inventory adjustment strategies and (iii) information sharing strategies using a risk analysis approach which is new in such context to the knowledge of the authors. This is done with a dedicated decision support system, based on discrete-eventsimulation.

THE SYSTEM UNDER STUDY

The system under study is a telecom supply chain. Generally, this chain includes 4 categories of actors (see Figure 1.):

• the Global Operator (GO) is responsible for the network coverage deployment and the associated services provided to the customers, • the Original Equipment Manufacturer (OEM) manufactures the different equipment (e.g. hard -drive, printers, monitors, portable phones …),

• the Contract Manufacturer (CM) resells the products it assembles to some partners who incorporated them in their own configurations and put them on the market under their own brand-name, • the SemiConductor Supplier (SCS) manufactures the basic electronic components (chips) used by the CM.

Other characteristics of the telecom supply chain are (see [START_REF] Mahmoudi | Telecom supply chain simulation[END_REF]):

• the uncertainty of the demand: the emergence of new actors in the supply chain, the uncontrolled exchange of information, the difficulties involved in setting up reliable processes of cooperation and collaboration in the chain and the absence of contractual structures binding the actors of the chain, make the demand uncertain.

• instability: the demand is very sensitive to seasonal variation, the vagaries of fashion and national and international events.

• short life cycle products: rapid technological advances drastically reduce product's life cycle. This underlines the need for cooperation policies between the supply chain actors, and shows the convenience of a risk approach for such supply chains operating in a very uncertain environment. These cooperation policies must be centred especially on capacity definition strategy due to the huge investments made to acquire new capacities especially for the semi-conductors suppliers (SCS). Also, they must be centred on stock adjustment strategies and information sharing. In order to implement such cooperation policies, we propose for each actor of the supply chain a four process representation (see Figure 2 The definition of these processes gives the possibility to set up different cooperation policies. In this paper, they result from the combination of: • forecast transmission strategies, more known as collaborative forecasting strategies, • two parameters mainly affect the planning strategies:

-whenever a change of the capacity is proposed, only a ratio of it is accepted: ).

( p -stock cover: ( ).

A SIMULATION TOOL TO SUPPORT RISK EVALUATION

The risk analysis approach adopted in order to evaluate the different cooperation policies described below, is supported by a simulation tool -called LogiRisk-It was developed using Perl Language1 . This simulator is based on discrete-event-simulation modelling approach, and establishes a generic representation of the different planning processes for each actor of the supply chain (see Figure 2.):

• The Sales & Operations Planning (S&OP) Process: details the various decisions which are taken throughout the long term planning. Its most important outputs are the production capacities (see Figure 2.). This process, models (i) the forecast calculation, (ii) the interpretation behaviours the decision-maker exhibits when examining the received forecasts from his customers, (iii) the transmission behaviours when a decision-maker sends his forecasts to his supplier.

If there is no forecasted demand transmission, the S&OP process computes its forecasts internally using the Holt and Winters Smoothing Algorithm. Otherwise, it sums up the forecasts transmitted by the customers.

According to the demand forecasts, workload is computed and smoothed over several time periods.

The resulting workload defines a capacity plan that must be validated by the S&OP manager. This latter has, in this study, a specific behaviour: he compares the proposed capacity plan with the one he validated in the previous S&OP process, and only accepts a given percentage of capacity variation. ) ( p Fig. 2. The generic representation of the supply chain actors' processes.

• The Medium Term Planning (MTP) process computes the estimated production release of final products, the raw materials demand (push strategy) to send to the suppliers, or objective stock levels (pull strategy). As in the S&OP process, the demand forecast are updated either internally or aggregated from the demand forecast information received from the customers.

• The Short Term Planning (STP) and the Release & Inventory Management (R&IM) processes details together the various short term decisions. The STP process takes good account of the actor's own constraints (i.e. breakdowns,…), the calculation of the possible production release and, in cases of a pull strategy, the demand to send to the suppliers. The R&IM process is responsible for taking into account the other actors' constraints (i.e. insufficient delivery,…), the products inventories update, the calculation of the real production release, and, finally, the calculation of the quantities to be delivered to each customer.

Note that these four processes are not made at the same frequency and do not use information (forecasts, production, capacity) aggregated with the same time granularity. Equations that give the details of the model characterising the S&OP, the MTP, the STP and the R&IM processes are given by [START_REF] Mahmoudi | simulation model for customer-supplier cooperation in the telecom supply chain[END_REF].

THE RISK ANALYSIS APPROACH

The cooperation strategies described in section 3 face several possible market scenarios. In the following study the scenarios depend on two uncertain parameters: • a seasonnality growth of the market percentage :

). ( τ• a standard deviation of the normal distribution relating demands and forecasts :

). ( σ

Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts

As a risk oriented approach is chosen, the probability indexes or ranks (subjective probability are used because of the decision-maker's inability to determine objective probabilities) of these scenarios are evaluated according to the decision-makers expertise using a five-rank scale given by the Table 1. For a given cooperation policy and for each scenario two types of criticalities are analysed: (i) a criticality related to the generated costs (C 1 ); and (ii) a criticality related to demand variability amplification (C 2 ).

S&OP S&OP S&OP S&OP

Process Process Process Process Process Process Process Process

The first criticality, C1, is the result of the multiplication of the scenario probability index by the supply chain total cost. This total cost is the sum of: • release costs: the costs of production release, • capacity acquisition costs: the costs associated with the acquisition of new capacities, • stock holding costs: the costs of keeping stocks, • and stock-out costs: the costs of the stock-outs that occur when the supply chain has no finished products to satisfy the market demand.

The second criticality, C2, deals with the demand variability amplification. This indicator is the result of the quotient of the standard deviations associated respectively with the upstream, and the downstream, supply chain demands.

All these indicators are computed along the simulated horizon. This leads us to the definition of the considered policy risk table (see Table 2.). The risk related to the considered cooperation policy in terms of costs is a function characterizing the decision-maker risk assessment criterion.

) ( ies criticalit scenarios f
The risk in terms of demand variability is computed in the same way.

i i i i p x X * = i i i p y Y * = Scenario n p n x n y n X n Y n SC cooperation policy risks f (X 1 , X 2 ,… X n ) f (Y, Y 2 ,… X n )
In this paper is the sum of the criticalities of the different scenarios and measures a mean cost or amplification. Notice that we might have use other functions (e.g. or ) to characterise others risk evaluation methods.

(.) f (.)

) n X f ,..., ) ( min ) ,..., , ( 2 1 i i n X X X X f = ) ( i X max , ( 2 1 i X X f =

THE EXPERIMENTAL VALIDATION

In order to validate the approach, a case study is chosen. It deals with a four stage telecom supply chain with a single product (see Figure 1.) Fig. 3. shape of the market forecast.

The data used in experiments are summarised below:

• Stock covers ( : the evaluated values are 0, 1, 2, 3, 4, 5. These stock covers are expressed in weeks of the forecasted demand estimated or received by and actor. ) p

• Information sharing: two kinds of collaborative forecasting strategies: with and without forecast transmission.

• Market scenarios: The forecast shape of the market is given by Figure 3. Let's note that the market is globally stable. But, the concurrence evolutions and market sharing variations make the demand so fluctuant. Due to this fact, we propose to compute the market demand using a normal distribution centred on the market forecast. Moreover, the shape is coherent with the fact that in December demand has a high seasonality. Therefore, the market demand evolution scenarios result from the combination of the following cases:

-demand ramp-up in December τ : low:10%, average: 50%, high: 100% (calculated relatively to the demand of the other months) -standard deviation σ of the normal distribution relating demands and forecasts:

σ ), ( ( (t) Demand t Forecast Ν =
), where t is an elementary period of simulation. The different values of σ are :

, 0 = σ 10000 = σ 50000 = σ , 100000 = σ , . 250000 = σ
The probability indexes of the market demand evolution scenarios are given in the following table. These indexes are based on the probability assessment scale given in Table 1. The most likely scenario is the one corresponding to an average increase of demand associated with a large standard variation normal distribution. The more we go far from this scenario and the more the probability indexes decrease (i.e. the scenarios become unlikely).

Finally, the simulations were run on a six hundredperiod (week) horizon.

RESULTS AND MANAGERIAL INSIGHTS

Market forecast per week Due to the high combinatorial of experiments, only a summary of risk analysis resulting from the experimental data processing is presented (see Figure 4. to 7.). The method for compiling results is shown for the Figure 4.

For the other curves (Figure 5. to 7.) , the method remains the same. We first consider the case when the capacity constraints are absent (infinite capacity i.e. capacity is considered to be always available in sufficient quantities): Let's consider the stock cover = 0 and suppose that there is no forecast transmission. The criticalities of the different scenarios is given by the table 4.

By considering an objective function as equal to the sum of the criticalities of the different market demand scenarios, we obtain the two surrounded points in the Figure 4.

() f

Table 4 Cooperation policy with infinite capacity no forecast transmission and a stock cover =0. From figure 4, one should retain that: • if there is no forecast transmission, risks of costs and of demand amplification increase with the stock cover.

• in the case of forecasts transmission, production costs and demand amplification are less sensible to the stock cover. Best results are obtained with no stock cover.

With capacity constraints

Now, the capacity constraints are considered and each actor defines his capacity in his S&OP process. Results for different capacity strategies (values of the capacity change acceptance ratio ) are given in figure 5, 6 and 7.

) ( p

From these results, one can see that:

• here also, forecast transmission reduces drastically the risks of demand amplification whatever the capacity strategy. • the stock cover influences the demand amplification only if no forecast are transmitted. • with no forecast transmission and whatever the capacity strategy, a null stock cover does no more give the best cost: a small stock cover (stock cover =1 in Figure 5, Figure 6 and Figure 7) ensures at the same time low production costs and low demand amplification.

• For a stock cover greater than 1, the risk of cost increases linearly in function of the stock cover. • analysing the impact of forecast transmission on the risks of the supply chain total costs, curves are significantly different only for a null stock cover. In this latter case, stock out are frequent and are much better managed in the case of forecast transmission. • influence of the capacity strategy: for a stock cover greater than 1, the risk of the supply chain total cost is smaller for p=75% than for p=50% or 100%. In summary, we retain that, demand forecasts exchange reduces deeply the risks of demand amplification. But this is less effective considering the risks of the supply chain total cost: the reduction appears in a supply chain without in te capacity constraints, but it is not significant if the capacity constraints must be managed. Finally, for each information sharing strategy, simulations suggest values for the capacity change acceptance ratio (p) and for the stock cover (S).

CONCLUSION

We introduced in this paper some cooperation policies which highlight three cooperation dimensions: capacity planning, stock adjustment and information sharing. These cooperation policies were evaluated using a risk analysis approach which is supported by a discreteevent simulation tool developed specifically to implement such approach. A multi-stage telecom supply chain was used for the experimental validation. This policies evaluation allowed us to understand the positive and negative influences of stock covers and information sharing on capacity planning. Future research will keep the three cooperation dimensions presented in the paper but will concentrate on the enrichment of the information sharing dimension through the analysis of the implications of adding other exchanged information such as: the state of inventories of an actor to his supplier and the final demand of the market and its evolution. Moreover, cooperation methodology, based for example on an educational approach, is under study to initiate the discussion between decision-makers involved in setting up some of the retained cooperation policies.

  . and section 4 for more details) that includes: • the Sales & Operations Planning (S&OP) Process, • the Medium Term Planning (MTP) Process, • the Short Term Planning (STP) Process, • and the Release & Inventory Management (R&IM) Process.

  Fig. 1. Telecom Supply chain structure.

•

  Capacity strategy: the analysed strategy consists in accepting only a ratio ( of a proposed change of capacity : p = 50%, p = 75%,p = 100%.

Fig. 4 .

 4 Fig. 4. Cooperation policies without capacity.

  Fig. 5. Cooperation policies with finite capacity and p=50%.

Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Forecasts Capacities Capacities Capacities Capacities Capacities Capacities Capacities Capacities MTP MTP MTP MTPTable 1

 1 Probability assessment scale.

	Estimated launchings Estimated launchings Estimated launchings Estimated launchings Estimated launchings Estimated launchings Estimated launchings Estimated launchings	, stock , stock , stock , stock , stock , stock , stock ,	Index	Subjective estimate	Description
			1	Very unlikely	Very rare event
			2	Improbable	There is indirect evidence
					of event
			3	Moderate	There is direct evidence
					of event
			4	Probable	There is strong direct
					evidence of event
			5	Very probable	Event recurs frequently

stock target target target target target target target target Demand Demand Demand Demand Demand Demand Demand Demand

Stock Stock Stock Stock Stock Stock Stock Stock resource resource resource resource resource resource resource resource Actor Actor Actor Actor Actor Actor Actor Actor

Table 2 A

 2 Risk table of a given cooperation policiy.

	Market	Proba-	Tota	Standar	Criticalit	Criticalit
	scenarios	bility	l	d	y	y C 2
		indexes	Cost	deviatio	C 1
				n
				quotient
	Scenario 1	p 1	x 1	y 1	X 1	Y 1
	Scenario 2	p 2	x 2	y 2	X 2	Y 2
	Scenario i	p i	x i	y

Table 3

 3 Scenarios probability indexes.

	τ /	σ	0 10000	50000	100000	250000
	10%	1 2	3	4	3
	50%	2 3	4	5	4
	100%	1 2	3	4	3

The authors used the object oriented technology concept provided by Perl to design and to develop a prototype of the simulation tool, i.e. LogiRisk.


Isabelle Laffont
email: i-laffont@chu-montpellier.fr

C Jourdan

F Coroian

H Blain

V Carre

E Viollet

I Tavares

C Fattal

A Gelis

F Nouvel

K Bakhti

V Cros

K Patte

L Schifano

M Porte

E Galano

G Dray

M Fouletier

F Rivier

R Morales

P Labauge

W Camu

B Combe

J Morel

J Froger

B Coulet

J Cottalorda

P Kouyoumdjian

O Jonquet

L Landreau

H.-Y Bonnin

O Hantkié

P Nicolas

M Enjalbert

C Leblond

B Soua

P Coignard

D Guiraud

C Azevedo

D Mottet

P Fraisse

E Pastor

J Mercier

R Bourret

J Bousquet

J Pélissier

B Bardy

C Herisson

A Dupeyron

Living Lab MACVIA Handicap

Le Living Lab MACVIA Handicap dans le contexte international, national et régional

Santé publique

La population du Languedoc Roussillon est évaluée à 2,67 millions d'habitants (Insee 2011). Plus de 10 % de la population régionale se trouve en situation de handicap, qu'il soit mental, moteur, psychique, auditif ou visuel [START_REF]La Charte Région Languedoc Roussillon Handicap[END_REF]. Parmi ces personnes handicapées, la prévalence du handicap neurologique et locomoteur est mal connue, mais on sait qu'il figure parmi les toutes premières causes de handicap pour les personnes de moins de 60 ans dans notre pays (figure 1) [START_REF] Palazzo | Respective contribution of chronic conditions to disability in France: results from the National Disability-Health Survey[END_REF]. On estime ainsi qu'il concerne plusieurs dizaines de milliers de personnes de moins de 60 ans en Languedoc Roussillon.

Intégration dans l'EIP on AHA selon les plans d'action

Plan d'action A2 Le LLMH s'intègre dans le plan d'action sur la prévention des chutes (tableau I). Celles-ci concernent plus de 50 % des personnes porteuses d'un handicap neurologique et/ou locomoteur. Leur fréquence dépend de l'étiologie et de la sévérité des déficiences [START_REF] Reynard | Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities[END_REF]. Les actions du LLMH s'intègrent dans une stratégie pluridisciplinaire comprenant la prévention et le traitement des troubles neuro-orthopédiques et des pathologies dégénératives surajoutés, la préconisation et l'adaptation d'aides techniques au déplacement, la préconisation et l'adaptation d'aménagements de l'environnement personnel ou professionnel de la personne handicapée.

Plan d'action A3

Les actions du LLMH en matière de prévention de la malnutrition sont multiples avec, entre autres, la prévention de la dénutrition en lien avec les troubles de déglutition d'origine neurologique ou l'isolement social, la prévention de la surcharge pondérale et de l'obésité pour les personnes handicapées ayant un trouble de la marche ou pour celles se déplaçant en fauteuil.

Plan d'action B3

Le LLMH offre plusieurs exemples de prise en charge intégrée des soins pour les personnes handicapées. Ces prises en charge se structurent à partir de plusieurs établissements de santé qui offrent des bilans ambulatoires en hospitalisation de jour dédiés à ces patients. Ces bilans associent des prestations médicales et paramédicales multidisciplinaires, coordonnées par le médecin de médecine physique et de réadaptation (MPR), des prestations techniques dans le champ de l'aide technique en lien avec des industriels du secteur (exemple des cliniques du positionnement pour les patients en fauteuil), et des prestations médico-sociales dans lesquelles le rôle des associations d'usagers est déterminant.

Glossaire

Plan d'action C2

La logique de vie autonome est centrale dans le LLMH. Elle repose sur les acteurs régionaux : établissements de santé, maisons départementales des personnes handicapées (MDPH), structures médico-sociales, services de soins infirmiers à domicile (SSIAD), service d'accompagnement à la vie sociale (SAVS), professionnels de santé libéraux, conseils généraux, Association de gestion du fond pour l'insertion professionnelle des personnes handicapées (AGEFIPH), Fonds pour l'insertion des personnes handicapées dans la fonction publique (FIPHFP). Plusieurs initiatives régionales en matière de nouvelles technologies illustrent la volonté de notre région de développer les outils technologiques dédiés au maintien à domicile et d'aide à la vie autonome [START_REF] Lebec | High level functions for the intuitive use of an assistive robot[END_REF].

Plan d'action D4

Le LLMH fédère de nombreuses initiatives locales en matière d'aménagements du logement et d'accessibilité permettant un maintien à domicile des personnes handicapées.

Problématique régionale

Notre région offre un cadre exceptionnel à la structuration du Living Lab MACVIA Handicap (figure 2).

Les établissements sanitaires publics ou privés de la région proposent une offre de soins reconnue dans la prise en charge aiguë des maladies neurologiques ou ostéo-articulaires. La très forte implantation régionale de services de médecine physique et de réadaptation à orientation neurologique ou ostéo-articulaire favorise un dynamisme important dans la prise en charge des personnes handicapées : le LR dispose de 2,1 lits et places de soins de suite et de réadaptation pour 1000 habitants, ce qui le place au-dessus de la moyenne nationale à 1,7/1000 habitants. Par ailleurs, le maillage régional en matière de structures médico-sociales accueillant des personnes handicapées de moins de 60 ans est particulièrement dense, avec 4,8 places pour 1000 habitants alors qu'il n'est que de 4,1 au niveau national [12].

Figure 1

Imputabilité des principales classes de maladies sur le handicap en France, en fonction de l'âge des populations, du niveau d'incapacité ressentie, et du niveau de dépendance [START_REF] Palazzo | Respective contribution of chronic conditions to disability in France: results from the National Disability-Health Survey[END_REF] Montpellier La prise en charge globale de la personne handicapée de moins de 60 ans revêt une importance toute particulière en Languedoc Roussillon.

Objectifs

Le LLMH regroupe des initiatives originales destinées à améliorer la prise en charge des personnes handicapées en intégrant des usagers, des acteurs du champ sanitaire, des acteurs du champ médico-social, et des industriels, en lien avec les organismes académiques d'enseignement et de recherche implantés dans la région. L'idée est d'abord de mettre en place des organisations simplifiées permettant le suivi ambulatoire des personnes en situation de handicap et regroupant sur le même site un suivi médical et paramédical, un suivi médico-social, et un accès à des prestations très spécifiques autour des aides techniques. Ce suivi ambulatoire se structure souvent sous la forme de journées de bilan en hospitalisation de jour, sur les CHU de

Activités sociales

Un très grand nombre d'associations à vocation médico-sociale existe dans la région [13]. La déclinaison régionale de la politique nationale de la Caisse nationale de solidarité pour l'autonomie (CNSA) se fait via les MDPH qui sont en liens très étroits avec les établissements sanitaires et médico-sociaux. Le LLMH a pour objectif de renforcer les échanges entre cette kyrielle de correspondants, qu'il s'agisse de structures étatiques ou de structures associatives, afin de simplifier le parcours de vie des personnes handicapées. Le Living Lab du Centre communal d'action sociale (CCAS) de Lattes (L'Etape) est très utile pour présenter les aides techniques aux usagers, en situation écologique.

Associations de patients

De nombreuses associations d'usagers sont impliquées dans les actions du LLMH. Elles constituent un relais d'information important pour les patients/usagers. Elles contribuent à un certain

FIPHFP:

  Fonds pour l'insertion des personnes handicapées dans la fonction publique ; AGEFIPH : Association de gestion du fond pour l'insertion professionnelle des personnes handicapées ; CEDMH : Centre d'évaluation des dispositifs médicaux et du handicap ; CNSA : Caisse nationale de solidarité pour l'autonomie ; DIRECCTE : Direction des entreprises, de la concurrence, de la consommation, du travail et de l'emploi ; EVADIMM : Évaluation du dispositif médical de Montpellier ; IFMK : Institut de formation en massokinésithérapie ; INRS : Institut national de recherche et de sécurité pour la prévention des accidents du travail et des maladies professionnelles ; IFE : Institut de formation en ergothérapie ; INRIA : Institut national de recherche en informatique appliquée ; LIRMM : Laboratoire d'informatique, de robotique et de microélectronique de Montpellier ; SATT : Société d'accélération du transfert de technologies ; Transfert LR : Agence régionale de l'innovation du Languedoc Roussillon.

Le

  Living Lab MACVIA HandicapActivités de soinsLes activités de soins du Living Lab MH reposent avant tout sur des bilans multidisciplinaires ambulatoires du handicap neurologique et locomoteur. Ces activités de bilan sont présentes dans plusieurs établissements sanitaires de la région, comme par exemple le secteur d'hospitalisation de jour du département de MPR du CHU de Montpellier, le centre d'évaluation HADEMOP du département de MPR du CHU de Nîmes, le secteur d'hospitalisation de jour du Centre Propara. Ces structures référentes entretiennent des liens étroits avec les établissements sanitaires et médico-sociaux de la région, mais aussi avec les réseaux de ville qui adressent très volontiers leurs patients pour un bilan complet (Union régionale des professionnels de santé, Montpellier). Elles associent régulièrement les associations d'usagers à la démarche de bilan proposée à ces patients (tableau II). Elles offrent parfois des prestations très spécifiques, comme par exemple les « Cliniques du Positionnement au fauteuil roulant » (CHU de Nîmes, Centre Propara et Institut Marin Saint-Pierre), ou les centres de bilan en vue de la reprise de la conduite automobile (Centre du Grau du Roi, Centre Bouffard-Vercelli, Centre Propara). Enfin, certaines sont dédiées à des pathologies spécifiques comme les maladies neuromusculaires (Centre de référence Grand Sud intégrant le CHRU de Montpellier et le CHU de Nîmes, en lien très fort avec l'Association française des myopathies, AFM), la sclérose latérale amyotrophique (CHRU de Montpellier). . . Ces structures de bilans multidisciplinaires ambulatoires du handicap neurologique et locomoteur sont presque toujours adossées à des équipes de recherche avec lesquelles elles conduisent des projets de recherche sur les déficiences sévères de l'appareil neuro/locomoteur et sur le handicap. Elles sont en relation étroite et souvent contractualisée avec des industriels développant des dispositifs médicaux de rééducation ou de réadaptation (EVADIMM au CHU de Montpellier, CEDMH au CHU de Nîmes, CENROB au Centre Propara).

Figure 2

 2 Figure 2 Localisation géographique des principales structures et groupes de structures impliquées dans le LL MACVIA Handicap

  Caisse nationale de solidarité pour l'autonomie ; INRIA : Institut national de recherche en informatique appliquée ; LIRMM : Laboratoire d'informatique, de robotique et de microélectronique de Montpellier ; SATT : Société d'accélération du transfert de technologies ; Transfert LR : Agence régionale de l'innovation du Languedoc Roussillon. ainsi recensés sur le CHU de Montpellier. Plusieurs reposent sur l'expertise des équipes de MPR dans l'évaluation des dispositifs médicaux dédiés à la compensation des grandes déficiences[START_REF] Laffont | Home trials of a speech synthesizer in severe dysarthria: patterns of use, satisfaction and utility of word prediction[END_REF][START_REF] Laffont | Evaluation of a stair-climbing power wheelchair in 25 people with tetraplegia[END_REF][START_REF] Laffont | Evaluation of a graphic interface to control a robotic grasping arm: a multicenter study[END_REF]. Cette plateforme entretient des liens forts avec son environnement régional : Transfert LR, pôle de compétitivité Eurobiomed, SATT AxLR, conseil régional. . . Le CHU de Nîmes a mis en place le CEDMH, structure de recherche dédiée à l'évaluation des dispositifs médicaux destinés aux personnes en situation de handicap. Son rôle est à la fois le co-développement et l'évaluation clinique de dispositifs médicaux non invasifs destinés à des patients en situation de handicap. Cette structure a permis d'accélérer le transfert de connaissances vers l'autonomie ou le confort de la personne handicapée. Ceci a permis de favoriser les dépôts de co-brevets CHU-industrie et de finaliser des études de qualité comparant l'efficacité de dispositifs existants ou de prototypes reposant sur des critères d'évaluation robustes (indices de pression pour les matelas, étude cinématique pour les guidons de transfert). Ces travaux sont réalisés grâce aux liens forts entre l'École des Mines d'Alès et sa structure d'incubation (Innov'up), les sections génie civil et génie mécanique de l'IUT de Nîmes, la participation de l'Institut national de recherche et de sécurité pour la prévention des accidents du travail et des maladies professionnelles (INRS), du laboratoire M2H d'Euromov et le soutien de la CNSA. Il s'inscrit dans la dynamique locale de la communauté d'agglomération de Nîmes, de la CCI de Nîmes, du plan 2014-2020 de 3S en LR et des actions de la Directe. technologique de l'EMA, créé en 1984, accueille des projets en lien avec les thématiques des laboratoires. L'incubateur a ainsi permis la création d'entreprises dans le domaine du handicap et de la santé, telles que : Le Griot 30 , Cairpol 31 , Bodydens 32 , Ostéorêve 33 . . . Parmi les projets en cours de développement, on peut citer, notamment, les projets S&J Technologies (dispositif médical pour la détection et la prévention de chutes liées à la maladie de Parkinson) et UBIMOV (logiciel de détection de situations potentiellement à risques pour les résidents des EHPAD). Les missions de l'EMA ont développé la pédagogie entrepreneuriale de formation-action avec l'appui d'HEC-Entrepreneur 34 . Les élèves ont réalisé différents services innovants destinés aux personnes en situation de handicap, comme par exemple un déambulateur permettant à des enfants déficients intellectuels de participer aux jeux de leur âge.Les liens avec le tissu industriel régional ou national sont forts et se structurent de façon accélérée depuis une dizaine d'années. Les organismes spécialisés dans le transfert technologique (SATT AxLR, Transfert LR), les incubateurs régionaux et le pôle de compétitivité Eurobiomed facilitent la mise en relation entre industriels et organismes publics, établissements de soin et établissements de formation. Les liens avec l'industrie s'expriment à travers des partenariats de recherche qui vont des phases de Recherche & Développement à l'évaluation clinique en situation de vie. L'exemple de la jeune société NaturalPad est une illustration exemplaire de cette structuration en Living Lab régionale, avec une implantation forte dans les établissements de soin, une incubation au sein d'Euromov et plusieurs projets de recherche en cours sur les jeux vidéo de rééducation.Le concept de Living Lab Santé et Autonomie a été défini par un rapport du ministère de l'Industrie en 2011[START_REF] Picard | Pertinence et valeur du concept de Laboratoire vivant (Living Lab) en santé et économie [Pertinence and value of the Living Lab concept for health care and independent living[END_REF]. Ces initiatives se structurent en Europe à travers des organisations, comme par exemple le réseau ENOLL (The European Network of Living Labs -http://www.openlivinglabs.eu/). Le Living Lab MH répond au cahier des charges proposé par ce réseau avec la particularité d'avoir localement une implication forte des équipes cliniques qui fait parfois défaut dans les Living Lab autonomie-santé. Par ailleurs, il regroupe sur une même région un très grand nombre de structures publiques et privées susceptibles de se structurer dans ce sens en mettant en commun leurs moyens et leurs savoir-faire. d'intérêts : les auteurs déclarent ne pas avoir de conflits d'intérêts en relation avec cet article.

	Enseignement les années 1980 26 pour accompagner la mutation profonde des TABLEAU II Principaux acteurs du Living Lab MACVIA Handicap La thématique du handicap d'origine neurologique et ostéo-arti-entreprises, répondre à leurs nouveaux besoins en créant un
	Activité culaire est au coeur de nombreux enseignements à la faculté de Organisation incubateur technologique pour mettre la créativité de ses élèves	Description de l'activité
	Activité médecine Montpellier-Nîmes : module spécifique d'enseigne-Organisation Recherche Centre Euromov/EA2991 au service de la cause des personnes en situation de handicap.	Description de l'activité Recherche translationnelle : déficiences, plasticité des systèmes
	Soins ment dans le second cycle des études médicales, enseignements CHRU de Montpellier La recherche relève de trois thématiques : les matériaux	Rééducation (MPR) des affections du système nerveux et de sensorimoteurs et rééducation, technologies appliquées à la
	de troisième cycle destinés aux internes futurs spécialistes de (C2MA : Centre des matériaux des Mines d'Alès), l'environne-	l'appareil locomoteur. Bilans fonctionnels complexes ambulatoires du rééducation/réadaptation
	LIRMM/INRIA MPR, diplômes universitaires. Cette thématique est également ment et les risques (LGEI : laboratoire de génie de l'environne-	handicap d'origine neurologique et ostéo-articulaire. Évaluation des Travaux en lien avec des cliniciens sur la robotique d'assistance et/
	fortement représentée dans le cursus des filières paramédicales ment industriel) et les technologies de l'information et de la	dispositifs médicaux (EVADIMM). Centre de référence maladies ou la stimulation électrique fonctionnelle, travaux sur les
	CHU de Nîmes communication (LGI2P : Laboratoire de génie informatique et de rééducation : masso-kinésithérapie, ergothérapie, orthopho-École des Mines d'Alès nie, podo-orthèse, ortho-prothèse. . . Elle imprègne largement les ingénierie de production). enseignements prodigués dans la filière des ingénieurs TIC Santé Dès la création de son laboratoire de mécanique, l'EMA a été	neuromusculaires et sclérose latérale amyotrophique technologies numériques dédiées à la rééducation Rééducation (MPR) des affections du système nerveux, de l'appareil locomoteur, rééducation cardiologique, rééducation vésico-sphinctérienne. Bilans fonctionnels complexes ambulatoires du Projets thématiques « Handicap » portés par des ingénieurs et développés en lien avec les usagers, soutien aux jeunes entreprises, incubateur technologique orienté vers les technologies appliquées au
	ou des Masters Activités physique adaptées de la Nouvelle Uni-sollicitée par de jeunes actifs en situation de handicap, désireux	handicap d'origine neurologique et ostéo-articulaire (HADEMOP). handicap
	Évaluation des dispositifs médicaux (CEDMH). Clinique du positionnement pour patients en fauteuil roulant. Bilans conduite automobile personnes handicapées Rééducation (MPR) pédiatrique. Bilan du handicap moteur et cognitif de l'enfant. Clinique du positionnement pour patients en fauteuil roulant Rééducation (MPR) des patients blessés médullaires. Bilans fonctionnels complexes ambulatoires du handicap d'origine neurologique. Centre d'expertise national en robotique (CENROB). Clinique du positionnement pour patients en fauteuil roulant. Bilans conduite automobile personnes handicapées Rééducation (MPR) des affections du système nerveux et de l'appareil locomoteur. Bilans conduite automobile personnes handicapées Rééducation (MPR) des affections du système nerveux Enseignement aux étudiants en médecine (module transversal « Rééducation-Maladies Chroniques »). Enseignement troisième cycle des études médicales (internes de MPR). Enseignement post-universitaire en lien avec la thématique Handicap. Enseignement de l'Orthophonie Formation des moniteurs en activités physiques adaptées Formation des ergothérapeutes. Animation du congrès national des ergothérapeutes (« Expériences en ergothérapie ») Formation des masseurs kinésithérapeutes Projets thématiques, soutien aux entreprises et incubateur technologique dédié au Handicap Départements Génie Civil/Génie Mécanique. Accompagnement de projets. Incubation de jeunes entreprises Congrès RARE, Congrès des EMPR, Digiworld Summit Recherche prévention santé Recherche en santé et éducation, situations de handicap CHRU de Montpellier et CHU de Nîmes Institut Marin Saint-Pierre Centre Propara Centre B.-Vercelli Centre Bourgès (Oc Santé) UFR médecine Montpellier-Nîmes UFR STAPS Institut de formation en ergothérapie Institut de formation en masso-kinésithérapie École des Mines d'Alès IUT de Nîmes Ingénieurs TIC Santé Congrès thématiques annuels Epsylon/EA4556 Santé SIH/EA4614 Recherche clinique thématique, recherche sur les dispositifs médicaux dédiés à la rééducation et/ou à la compensation/ assistance IFRH Implication forte des acteurs régionaux dans l'Institut fédératif de recherche sur le handicap Labex NUMEV Solutions numériques, matérielles et modélisation pour l'environnement et le vivant : implication forte des acteurs régionaux SATT AxLR Maturation et commercialisation de produits innovants issus de la recherche académique Transfert LR Animation territoriale et accompagnement de projets innovants Eurobiomed Cluster au service du développement des activités innovantes dans le domaine de la santé : soutien aux projets thématiques, liens entre les partenaires institutionnels, académiques et les entreprises I2ML Fondation partenariale de l'université de Nîmes. Accompagnement à l'émergence d'une nouvelle filière économique autour du maintien à domicile Liens avec les sociétés savantes et Formation Liens avec le secteur privé les organismes de recherche Sofmer Les équipes de médecine physique et de réadaptation du Languedoc Roussillon sont très actives au sein de la Sofmer et s'impliquent dans plusieurs actions collectives dans le cadre de la politique scientifique de la Société savante IFRH Deux laboratoires de recherche de la Nouvelle Université de Montpellier sont membres de l'IFRH (EA 4614 et EA 2991), respectivement dans l'axe « Recherches en santé publique et D'autres laboratoires implantés dans la région ont des liens très forts avec les cliniciens sur la thématique des grandes déficien-ces motrices, liens qui s'expriment à travers plusieurs projets de recherche emblématiques sur le sujet : l'équipe DEMAR de l'Institut national de recherche en informatique appliquée (INRIA) sur le développement d'un outil de stimulation élec-trique fonctionnelle du blessé médullaire [26] ou de l'hémiplé-gique [27], le Laboratoire d'informatique, de robotique et de microélectronique de Montpellier (LIRMM) sur le développe-ment des jeux vidéo de rééducation [28], l'École des Mines d'Alès qui travaille avec les équipes de MPR des CHU et le centre EUROMOV sur le développement des interfaces cérébrales dans versité de Montpellier, dans lesquels interviennent de nombreu-ses équipes médicales, dont les équipes de MPR. L'École des Mines d'Alès (EMA) est un exemple éloquent de développement d'un projet pédagogique et de recherche réso-lument tourné vers la personne handicapée. L'EMA a su mettre ses compétences au service des personnes handicapées à travers des projets concrets portés par des étudiants en liens étroits avec les usagers, mais aussi à travers un soutien aux entreprises et la création d'un incubateur technologique orientés vers les technologies appliquées au handicap. Plusieurs congrès thématiques d'envergure nationale ou inter-nationale se déroulent de façon régulière sur le site de Mont-pellier-Nîmes : congrès RARE (rencontres Eurobiomed autour des Maladies rares), congrès des EMPR qui a une vocation affichée de formation professionnelle, Digiword Summit (jour-née DIGIHEALTH), congrès National d'Ergothérapie. . . Recherche Le dynamisme autour de la thématique des grandes déficiences de l'appareil locomoteur et du handicap nourrit de nombreux projets de recherche de dimension nationale ou internationale. Le centre Euromov, dont le coeur est constitué par le laboratoire Movement to Health (M2H) de l'Université de Montpellier, récemment rejoint par l'École des Mines d'Alès, coordonne avec les équipes cliniques des CHU de Nîmes et de Montpellier de nombreux projets de recherche translationnelle en lien avec cette thématique : déficiences motrices dans les suites d'un de vivre en autonomie, et qui demandaient l'amélioration des équipements existants ou le développement de nouveaux produits : un architecte souhaitant un fauteuil de faible encom-brement pour faciliter ses voyages en avion, un agriculteur qui avait besoin d'un fauteuil « tout terrain » pour continuer à exer-cer sa profession, un sportif de haut niveau désireux de conti-nuer sa pratique du ski après son accident. . . Ces réalisations ont été suivies de beaucoup d'autres, plus ambitieuses encore, lorsque l'EMA a disposé d'une plateforme de mécatronique, dotée de moyens d'étude, de conception et de fabrication étendus : adaptation d'une prothèse tibiale pour le handisport, fauteuil tout terrain motorisé, adaptation des commandes d'un kart. . . Avec la généralisation des technologies de l'information et de la communication, les dispositifs d'aide aux personnes en situation de handicap se diversifient et touchent de nouveaux domaines. C'est ainsi que le Laboratoire LGI2P met ses compétences en génie logiciel à contribution dans un projet collaboratif de domotique auto-adaptative pour favoriser un maintien à domi-cile de qualité ; projet est conduit en lien avec l'I2ML 27 et le LIRMM 28 , notamment. . . Le LGI2P collabore également à un programme de recherche consacré au suivi et à la rééducation post-AVC en partenariat avec le centre EUROMOV 29 et l'Université de Maynooth, en Irlande. Enfin, le LGI2P participe au projet AUREVI, porté par l'Institut ARAMAV, faisant appel aux STIC pour lutter contre le handicap visuel. Interactions régionales, nationales et L'incubateur Liens avec l'industrie internationales du Living Lab
	Liens avec les acteurs accident vasculaire cérébral et plasticité des systèmes sen-Région LR sori-moteurs [16-20], plasticité des adaptations posturales dans institutionnels Agence régionale de santé LR la lombalgie chronique [21], troubles de la motricité et réédu-cation par le rythme dans la maladie de Parkinson [22].	sciences humaines et sociales » et dans l'axe « Technologies le champ de la neuro-rééducation [29,30]. Porteur du Projet MacVia-LR Handicap appliquées aux grandes déficiences et au handicap » Le laboratoire Movement to Health (Euromov) et le laboratoire Soutien aux projets thématiques SanteSih (Santé et Éducation, Situation de Handicap) sont des Financement de projets dédiés à la thématique Handicap, labellisation de projets d'Éducation à la Santé dans le champ du membres actifs de l'Institut fédératif de recherche sur le handi-
	La recherche sur les dispositifs médicaux, qui incluent les aides	Handicap cap (http://ifr-handicap.inserm.fr/). Movement to Health par-Déclaration
	CCAS de Lattes : l'Etape techniques de compensation des grandes déficiences et les	Démonstration, essais et préconisation d'aides techniques ticipe à la gouvernance du Laboratoire d'Excellence NUMEV
	CCI de Nîmes technologies de rééducation, est également très active dans	Accompagnement de projets de développement technologique (http://www.lirmm.fr/numev/) en s'impliquant tout particu-
	Municipalités en LR, Nîmes agglomération nombre d'actions d'éducation destinées aux personnes et à leur lièrement dans l'axe « Santé : aide à la personne malade ou Organisations territoriales, soutien aux projets thématiques la région. Elle est structurée à travers des plateformes dédiées
	et Montpellier agglomération entourage, à travers des réunions thématiques ou des journées déficiente » du Labex. sur les deux CHU. Le CHU de Montpellier propose la plateforme
	MDPH Gard et Hérault, CNSA EVADIMM qui offre aux équipes cliniques, aux industriels et aux		Accompagnement des patients et de leurs familles dans leurs projets
	personnel, familial et professionnel École des Mines d'Alès Cap Emploi, AGEFIPH, Association COMETE chercheurs, un guichet unique d'information et d'accompagne-Accompagnement des patients dans leurs démarches de retour Créée en 1843, pour former les cadres de l'industrie minière, ment de projets de recherche sur les dispositifs médicaux. Plus à l'emploi ou de maintien dans l'emploi l'École des Mines d'Alès s'est complètement renouvelée dans de 150 projets de recherche sur les dispositifs médicaux sont

d'information

[START_REF] Laffont | Aging and sequelae of poliomyelitis[END_REF][START_REF] Ribaud | Which physical activities and sports can be recommended to chronic low back pain patients after rehabilitation?[END_REF]

. Elles sont partenaires de certaines organisations sanitaires et contribuent parfois à leur financement. Enfin, elles peuvent être impliquées très en amont lors de la mise en place de projets de recherche, notamment dans le champ des aides techniques où les patients doivent être impliqués tout au long du processus de développement et de validation technologique. Parmi les associations d'usagers impliquées dans le LLMH, on peut citer de façon non exhaustive : APF, AFM, AFTC, GLIP, France AVC, AFSEP, France Parkinson, ALIS, ALARME, GIHP. . . TABLEAU II (Suite). dans l'axe « Aide à la personne malade ou déficiente » Lien avec les associations d'usagers APF, AFM, AFTC, GLIP, France AVC, AFSEP, France Parkinson, ALIS, ALARME, GIHP Implication dans des actions sanitaires, implication dans des projets de recherche cliniques et technologiques, soutien à plusieurs projets thématiques AGEFIPH : Association de gestion du fond pour l'insertion professionnelle des personnes handicapées ; CCAS : Centre communal d'action sociale ; CNSA :

http://www.annales.org/archives/theseAles.html : résumé de la thèse de doctorat en histoire de Cécile Turion, consacrée à l'histoire de l'École des mines d'Alès.

http://www.i2ml.fr : Institut méditerranéen des métiers de la longévité.

http://www.lirmm.fr : Laboratoire d'informatique, de robotique et de microélectronique de Montpellier.

[START_REF] Perrey | Possibilities for examining the neural control of gait in humans with fNIRS[END_REF] http://www.euromov.

eu.[START_REF] Derosière | Towards a near infrared spectroscopy-based estimation of operator attentional state[END_REF] http://www.le-griot.com/ : matériel de facilitation de l'écoute en audiodescription à destination des

malvoyants.[START_REF] Picard | Pertinence et valeur du concept de Laboratoire vivant (Living Lab) en santé et économie [Pertinence and value of the Living Lab concept for health care and independent living[END_REF] http://www.cairpol.com/index.php?lang=fr : systèmes miniatures de surveillance de la qualité de l'air, destinés à l'origine aux

personnes fragiles. 32 http://www.bodysens.com/ : systèmes de monitoring sans fil, utilisés, par exemple

, pour les prématurés. 33 http://www.osteoreve.com/ : matelas anatomique personnalisé.