Amanda J Ross
email: amanda.ross@univ-lyon1.fr

Joseph M Cardon

Data associated with a tellurium absorption atlas 19000 -24000 cm -1

Keywords: Te 2 absorption, Tellurium atlas, Fourier transform spectrum of tellurium dimer, Te 2 reference spectrum

Transmittance and absorbance data in the form of a spectral atlas have been obtained from Fourier transform spectra recorded on a commercial (Bomem DA3) instrument, operated with an external white light source injected through the instrument's 'emission' port. The sample was a sealed, evacuated cell containing a small quantity of 130 Te. This cell was placed in a ceramic furnace maintained close to 620 °C, with tellurium vapour pressures 8-11 Torr. The data are intended as an aid to spectral calibration in the blue-green to violet region. The data relate to work published in

Specifications table

Subject

Molecular Physics

Specific subject area

A spectral atlas; a reference spectrum for calibration extending from blue-green to violet. Raw absorption data (wavenumber, arbitrary intensity)

Type of data

How the data were acquired

Spectra were recorded by Fourier transform interferometry [START_REF] Ross | Te 2 absorption spectrum from 19000 to 24000 cm -1[END_REF], on a Bomem DA3.002 spectrometer operated with with proprietary software (PCDA data acquisition). Light from an external quartz halogen white light source (Osram) running on a stabilized DC power supply (Fontaine) was collimated and passed through a 10 cm sealed evacuated cell, containing a small amount of 130 Te (Ideal Vacuum Products). Interferograms were acquired at nominal apodized resolution of 0.02 to 0.033 cm -1 . To achieve an acceptable signal-to-noise ratio, the spectrum was recorded in several pieces using combinations of optical filters, averaging between 200 (above 500 nm) and 600 scans (in the violet, where emission from the lamp was much weaker) in each piece.

Description of data collection

The tellurium cell was maintained at temperatures between 600 and 645 °C in a temperature-stabilised furnace [START_REF]PID Plug and Play Heater Control System from Ideal Vacuum[END_REF] ΔT ± 7°C, to provide strong absorption without saturation. External filters limited spectral extent, and a broadband glass filter (CS 4-97 or 5-61) in the FTS sample compartment removed residual HeNe contributions. Recording times were about 5 hours per piece of spectrum.

Data source location

•

Value of the data

• These data provide a convenient secondary spectral calibration standard for Doppler-limited applications in the blue/violet spectrum. They offer a convenient alternative to a printed atlas published in 1980 by Luc and Cariou [START_REF] Luc | Atlas du spectre d'absorption de la molécule de tellure[END_REF].

• High-resolution spectroscopists working with tunable lasers can benefit from these data, particularly if working without a high-performance wavemeter.

• Part or all of the transmittance/absorbance files can be imported to any graphical software to enable direct comparison with calibration traces to establish an absolute wavenumber scale. The isotopically enriched tellurium source used here is commercially available, it is compact and convenient for secondary calibration. The file Raw_transmission_spectrum_extending to_UV.zip is a transmission spectrum extending beyond the range of the 'official' atlas. It was recorded with the quartz uv beamsplitter. The intensity axis is arbitrary. Note that this spectrum extends beyond the 24000 cm -1 limit indicated in the title. There is no check on calibration above 23720 cm -1 .

The file Te2_overviewFig.pdf provides a graphical abstract.

Experimental design, materials and methods

The experimental set-up used to record absorption spectra of tellurium dimer is illustrated schematically in Figure 1. L1, L2 and L3 are convex lenses with focal lengths 4, 6 and 4 cm respectively, chosen to adapt to the f/4 aperture of the FT interferometer and to the physical diameter of the tellurium cell. The combination of the external and internal optical filters is intended to limit the spectral range to about 2000 cm -1 , so that interferogram fringes (recorded on a silicon avalanche photodiode from Hamamatsu) were adapted to the dynamic range of the analog-to-digital converter, and so that the number of interferogram points remained below the PC-memory-imposed maximum of 10 6 . We aimed for 50% filling of the analog-to-digital converter at zero-path-difference by adjusting the current/voltage input to the external white light. The internal filter was a blue-green or blue band-pass filter, serving to remove stray HeNe light and attenuate the long-wavelength emission from the white-light source. We placed a Corning glass (cs 4-97, 5-56 or 5-61) filter inside the instrument sample compartment, in front of the detector. A variety of external filters were used. A series of narrow bandpass interference filters would have been ideal, but were available only centred at 520 and 460 nm. To cover the desired spectral region, we used combinations of an interferential low-pass filter, either λ < 450 or λ < 500 nm from Corion Inc. whose optical response is conveniently tuned by changing angle of incidence, and high-pass filters (Corning cs 3-73 or Corion λ > 450 nm). The tilt in figure 1 was actually close to 45° for the shortest wavelength region recorded with λ < 450 (Corion LS450) and Corning 5-61 filters). The absorption spectra generated in Bomem GRAMS format were adjusted so that their wavenumber scale matched reference data from other sources [START_REF] Gillaspy | Absolute wavelength determinations in molecular tellurium -new reference lines for precision laser spectroscopy[END_REF][START_REF] Scholl | Absolute wavenumber measurements in 130 Te 2 : reference lines spanning the 420[END_REF][6]. A wavenumber-dependent correction was necessary, attaining 0.03 cm -1 at 23000 cm -1 . The pieces were then concatenated (see Figure 2), averaging the regions of overlap using wave arithmetic software provided by IGOR-Pro 6 [START_REF] Pro | Scientific graphic and data analysis software for scientists and engineers[END_REF]. The percentile and boxcar smoothing algorithms in IGOR-Pro were used to generate the baseline contour required to generate transmittance and absorbance traces. Transmittance was calculated from Transmission/Baseline, and Absorbance as log 10 (1/Transmission). The results were exported using a cubic spline interpolation to generate Ascii files with evenly-spaced wavenumber points (a short extract is given in Table 1) covering the blue-green to violet region of the optical spectrum. The short wavelength end of the transmittance data is truncated at 24015 cm -1 , indicating the range for which we have confidence in the wavenumber scale. The fourth file available for download, Raw_transmission_spectrum_extending to_UV.zip contains only two columns, and provides the complete transmission curve for the last section of the spectrum, without truncation.

  Figure (experimental setup) Figure (overview of raw spectra) Tables Processed wavenumber, transmittance and absorbance data.

Figure 1 .

 1 Figure 1.Diagram of the optical arrangement used to record the spectra. L1, L2 and L3 are convex lenses with focal lengths 4, 6 and 4 cm respectively, chosen to match the f/4 aperture of the FT interferometer and the physical diameter of the tellurium cell. The external filter is drawn tilted; we used combinations of interferential high-and low-pass filters from Corion Inc; their optical response can be (and was) tuned by changing the angle of incidence.

Figure 2 1

 21 Figure 2Overview of the composite transmission spectrum recorded with the visible beamsplitter, the contour being imposed by selections of optical filters. The continuous trace above (red) represents the baseline used to generate a transmittance spectrum.

Figure 1 :

 1 Figure 1 : Schematic diagram of the experimental setup

Figure 2 .

 2 Figure 2. Overview of the composite transmission spectrum recorded with the visible beamsplitter, the contour being imposed by selections of optical filters. The continuous trace above (red) represents the baseline used to generate a transmittance spectrum.

Table 1 .

 1 Extract from the data file Atlas_green.txt, illustrating our data format. Column 1 is wavenumber in cm -1 . Column 2 gives the transmittance (= transmission/baseline), and column 3 absorbance (=log10 (1/transmittance)). The range and details of optical filters for each section of the atlas are given in the section 'Data Description'.

	___________________________________________
	Wavenumber, cm	-1 Transmittance	Absorbance
	___________________________________________
	18850.000	0.7677	0.1148
	18850.002	0.7699	0.1136
	18850.004	0.7713	0.1128
	18850.006	0.7724	0.1122
	18850.008	0.7739	0.1113
	18850.010	0.7766	0.1098
	18850.012	0.7812	0.1072
	18850.014	0.7879	0.1035
	18850.016	0.7962	0.0990
	18850.018	0.8051	0.0941
	18850.020	0.8136	0.0896
	18850.022	0.8207	0.0858
	18850.024	0.8257	0.0832
	…..
	___________________________________________

Acknowledgments

The authors acknowledge the support of Ideal Vacuum Products LLC for this work, and wish to thank Professor D. Clouthier and Dr T. Smith for their helpful remarks and suggestions. This research did not receive any specific grant from funding agencies in the public, commercial, or notfor-profit sectors.

Declaration of interests

✓ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests. Although there is no obvious competing interest, we indicate that Joseph M. Cardon is an employee of Ideal Vacuum Products, a company that commercializes the tellurium reference cell and temperature-controlled furnace cited in the paper.

Ethics statements

The authors confirm that this paper is original work, adhering to the ethics principles of Data in Brief.

CRediT author statement

Amanda Ross: Investigation, Data curation, Writing-Original draft preparation; Reviewing and Editing. Joseph Cardon : Methodology; Resources; Writing-Reviewing and Editing.


Emmanuel Bernuau
email: emmanuel.bernuau@agroparistech.fr

Thibaut Viné

Denis Flick

Bertrand Broyart

SENSITIVITY ANALYSIS OF A HEAT AND MASS TRANSFER MODEL APPLIED TO CONTACT HEATING OF SLICED POTATOES

Keywords: Sensitivity analysis, heat and mass transfer modelling, contact heating

While much work has been devoted to thermal convection and radiation, studies concerning the modelling of contact heating of food products remain rare in the literature. To deal with this, a 2D model based on a moving boiling-front approach was developed to deal with the case of contact heating of sliced potatoes (with or without oil below the product). This model allowed a better understanding of limiting phenomena during contact heating as well as the determination of contact heat transfer coefficient between the product and the heating surface. In view of the relatively large number of model parameters, a sensitivity analysis was realised in parallel of the validation of the model coupling Morris method and Sobol sensitivity analysis. This analysis allowed to significantly reduce the number of unknown parameters of the model by drawing up a list of parameters having a lesser influence on the measured values used for validation and whose values could therefore be fixed by considering bibliographical data.

INTRODUCTION

While much literature is devoted to the study of convective and radiative heat transfer during heating of food products, studies concerning contact heat transfer are rare. That seems surprising given the facts that (i) contact heat transfer is the major mode of heat transfer for unit operations such as grilling in industrial or out-ofhome catering applications or pan-frying in domestic applications and that (ii) this mode of heat transfer (where food products which can be considered thermal insulators are exposed to very high heating flux) is expected to lead to drastic product quality changes particularly in the zone of the product close to the heating surface. [START_REF] Haak | Effec of pan-frying in different culinary fats on the fa y ac d prof le of pork[END_REF]Boskou et al. 2007;[START_REF] Flaskerud | Effec s of cook ng ec n ques on fa y ac d and oxyl p n content of farmed rainbow trout (Oncorhynchus mykiss)[END_REF].

In this context, mechanistic modelling of heat and mass transfer phenomena occurring during contact heating seems to be an attractive approach to improve our understanding of couplings between elementary transfer phenomena, to identify limiting phenomena and to determine rational strategies in order to improve the sensory and nutritional qualities of products heated by contact.

A key step in the modelling approach to be developed is to determine as precisely as possible the value of the contact heat transfer coefficient between the product to be heated and the heating surface, bearing in mind that (i) this coefficient can vary drastically during cooking due to the high reactivity of food products during heat treatments and that (ii) its direct and non invasive experimental measurement is very delicate [START_REF] Viné | Exper men al and numer cal s udy of ea and mass ransfer dur ng con ac ea ng of sl ced po a oes[END_REF]. Its indirect determination by identification using a mathematical model of transfer phenomena is therefore unavoidable. The accuracy of the identified value of the transfer coefficient by contact is therefore closely linked to the accuracy of the model used to describe the heat and mass transfer phenomena within the heated product and in particular at the interface between the product and the heating surface. Recent experimental works [START_REF] Cernela | Exper men al s udy of heat and mass transfer phenomena during the contact heating of sol d food models[END_REF][START_REF] Viné | Exper men al and numer cal s udy of ea and mass ransfer dur ng con ac ea ng of sl ced po a oes[END_REF]) has demonstrated that it is necessary when describing the transfer phenomena of concern to take into account a strong coupling between heat transfer and (possibly intense) evaporation of water exuding from the product at its lower surface. Only three authors have proposed models that take this coupling into account (Ou and Mittal 2006;[START_REF] Dhall | Transport in deformable food materials: a poromechanics approach[END_REF][START_REF] Feyissa | Modell ng of coupled ea and mass ransfer dur ng a con ac bak ng process[END_REF]. This was done: (i) by describing the drying of the product lower surface using a formalism specific to convective drying although the existence of a boundary layer relative to mass transfer is questionable in the interfacial zone (Ou and Mittal 2006;[START_REF] Dhall | Transport in deformable food materials: a poromechanics approach[END_REF] or (ii) by considering the rate of liquid water removed from the product and the rate of water vapour generated at the interface both equal to the rate of evaporation [START_REF] Feyissa | Modell ng of coupled ea and mass ransfer dur ng a con ac bak ng process[END_REF]. In these works, water evaporation is also considered in the whole product. To describe it, Ou and Mittal (2006) and [START_REF] Feyissa | Modell ng of coupled ea and mass ransfer dur ng a con ac bak ng process[END_REF] assumed that liquid water was in equilibrium with water vapour in the product whereas [START_REF] Dhall | Transport in deformable food materials: a poromechanics approach[END_REF] opted for a non-equilibrium formulation.

In [START_REF] Viné | Exper men al and numer cal s udy of ea and mass ransfer dur ng con ac ea ng of sl ced po a oes[END_REF], a 2D mathematical model based on a moving boiling-front approach was developed and validated. This model aimed at reaching a better understanding of all coupled heat and mass transfer phenomena during the contact heating of solid food product (case of sliced potato). Given the large number of parameters involved in the development of the model (fine description of the transfers in the product and at the interface between the product and the heating surface), particular care was taken in the calibration phase of the unknown parameters of the model. To this end, a global sensitivity analysis of the measured variables to the unknown parameters was carried out by combining Morris method and Sobol sensitivity analysis and is presented in this paper. This is part of a current trend to streamline the process of identifying the unknown parameters of a model. In the case of transfer models applied to food products (often heavily parameterized), the recent works of [START_REF] Dimov | Monte Carlo algorithms for evaluating Sobol' sensitivity indices[END_REF][START_REF] Feyissa | Uncer a n y and sens v y analys s: ma ema cal model of coupled ea and mass ransfer for a con ac bak ng process[END_REF] and [START_REF] Rabeler | Modell ng of food processes under uncertainty: Mechanistic 3D model of c cken mea roas ng[END_REF], for example, are noteworthy.

The paper is organized as follows. In Section I, the mathematical model is recalled. In Section II, the sensitivity analysis is performed and the results are presented. In Section III, the results and the methodology are discussed. Finally, a conclusion sums up the main results of the paper.

MAIN PART

Nomenclature

I) Mathematical Model

A moving boiling-front approach is chosen to describe coupled heat and mass transfer phenomena during contact heating of sliced potatoes. In a first heating stage and due to the very high contact flux exchanged with the heating surface, the temperature of the lower surface of the product is expected to increase rapidly to reach the boiling temperature of water at atmospheric pressure (100°C). At this point, a second stage of heating occurs and a boiling front at 100°C and atmospheric pressure is formed on this surface and propagates towards the interior of the product during the remaining time of the heating. This front divides the product in two zones: (i) a so called crust below the boiling front where the concentration of liquid water can be assumed negligible and where the temperature can be higher than 100°C and (ii) a so called moist region above the boiling front. To simplify the mathematical formulation of the transfer phenomena, further assumptions were made:

(1) Given the geometry of the potato sample, heat and mass flux are expressed in 2D cylindrical system of coordinates.

(2) In the moist region, the product is constituted by dry matter and liquid water whereas in the crust region, the product is only constituted by dry matter and water vapour (produced at the boiling front)

(3) Given the low thickness and the high porosity of the crust, the resistance to water vapour transfer in this zone is assumed negligible.

(4) Heat transfer in the crust is considered to occur in quasi-steady-state regime since the energy consumed by the crust to raise its temperature is very small compared to the energy consumed by water evaporation at the position of the boiling front. According to this assumption, the temperature profile in the crust is assumed linear. The heat flux through it is calculated using a global thermal resistance adding the resistance induced by thermal conduction within the crust and the thermal contact resistance (5) The shrinkages of the porous solid network constituting the crust and of the rest of the moist product are assumed negligible

Stage 1: Initial heating stage During initial heating, heat and water transfers in the moist region of the product are described using the following conservation equations:

where refers to the total enthalpy by unit-mass of dry matter and is calculated according to:

At the upper and lateral surfaces of the disk of product, the product is in contact with ambient air and some convective heating and drying occurs described according to the boundary conditions:

where the influence of and on values of water activity needs the values of two parameters and to be determined (see Tab. 1) and where the values of (on lateral and upper surfaces) and corresponding values of were calculated using the Nusselt correlations for free convection in flat and cylindrical geometries at the upper and lateral surfaces respectively. During this stage, the drying of the produc 's lo er surface s assumed negl g ble. A e same interface, the heat flux transferred to the product by the heating surface is given by the boundary condition:

Note that the contact heat transfer coefficient is supposed to be constant throughout the process. This hypothesis, made in [START_REF] Viné | Exper men al and numer cal s udy of ea and mass ransfer dur ng con ac ea ng of sl ced po a oes[END_REF], has consequences on the sensitivity analysis that will be discussed in Section III.

Stage 2: Formation and propagation of a boiling front

Governing equations in the moist region and boundary conditions at the upper and lateral surface are identical for both stages. Considering assumptions made previously, no boundary condition is required for the crust layer formed below the product. Considering the definition of the boiling front, the boundary condition for heat transfer at this boiling front (lower surface of the moist region of the product) is:

The water diffusion from the moist region to the boiling front is neglected in comparison with the local evaporation rate due to boiling. The liquid water of the crust being assumed equal to zero, the advance of the boiling front is hence used to calculate the instantaneous water loss at this location:

The boundary condition for the heat balance is used to calculate the local velocity of the boiling front within the product. This local velocity is assumed to be only on the z-axis but depends on the radial position. It is calculated according to: where is the conductive heat flux in the moist region at this location and is the conductive heat flux through the crust calculated by using an thermal resistance globalising the thermal contact resistance between the product and the heating surface and the crust thermal resistance :

II) Sensitivity Analysis

The model developed in Section I has been validated in [START_REF] Viné | Exper men al and numer cal s udy of ea and mass ransfer dur ng con ac ea ng of sl ced po a oes[END_REF] with experimental data. In this section, a sensitivity analysis of this model is performed. The aim of this section is twofold. The first goal consists in checking that the relative influence of the parameters appearing in the equations established in Section I is as expected from physical considerations. In particular, it is expected that the contact transfer coefficient h ct plays a key role in the model of heat and mass transfer previously presented; it should therefore naturally be very sensitive. The second objective is to split the parameters appearing in the equations in two subsets. On the first hand, those which need to be determined carefully in order to ensure the predictive ability of the model and on which all the effort should be focused. The precise determination of these so called "cr cal parame ers" can ence be carr ed n ree different ways: by off-line experimental measurements, analysis of data found in the literature or calibration during the validation process, keeping in mind that the number of parameters to be calibrated must be as low as possible for this procedure to be successful. On the other hand, those which value can be selected with less accuracy without any notable deterioration of the predictive ability of the model. This allows to select the latter parameters from the literature or from correlations while keeping satisfactory predictions from the model.

The list of parameters involved in the model developed in Section I is summarized in Table 1, together with their unit and the a priori probability distribution selected to performed the sensitivity analysis. For each of the 15 parameters, the distribution has been selected according to physical sense. Normal distributions have been chosen when a given value, or values close to it, were supposed to be much more likely than distant values, whereas uniform distributions have been taken when only a range of values was presupposed.

Table 1: To better understand and describe the complex interactions between the parameters, multiple outputs were selected corresponding to experimental measurements. They are summarized in Table 2. Five physical quantities are listed: three temperatures and two mass flux densities (one at the bottom surface and one for the lateral and upper surfaces of the product). Each of these quantities are observed at 4 instants, leading to a total of 20 outputs. In practice, apart from the three temperatures, only the total mass loss is measured. However, the mass flux has been split into bottom flux and lateral and upper flux because they represent different physical mechanism: boiling and convective drying, respectively.

Quantity

Unit Instants

The mathematical model described in Section I is simulated using Comsol Multiphysics (version 5.3). Each simulation takes between 1 and 10 minutes, depending on the selected precision. Given the high number of parameters involved, the following methodology has been adopted in order to achieve the sensitivity analysis in a reasonable time. First, the Morris's elementary effects screening method (Morris 1991) is applied, using the R function morris from the sensitivity library (with , which leads to 480 model calls). This method is not as precise as other methods can be, but in return is not too computationally demanding. Using this method first is a way to simplify the analysis by first detecting the parameters which have a negligible influence on the selected outputs and hence do not need to be investigated further. An excerpt of the results is presented in Figures 1 and2. In Figures 1 and2, the x-axis represents the overall first order effect of a parameter, while the y-axis represents interaction or nonlinear effects of a parameter. Hence, a parameter situated on the bottom left corner of the graph has a weak influence on the output, that is, is weakly sensitive. As can be seen, several parameters are clustered in the bottom left corner, leaving only, when considering the outputs and the parameters , , and as sensitive for these outputs. This visual analysis is performed for each of the twenty outputs; keeping only the parameters which never cluster on the bottom left corner, we end up with , , , , and as the only remaining parameters.

The next step consists in computing the Sobol indices [START_REF] Sobol | Sensitivity analysis for non-linear ma ema cal model[END_REF][START_REF] Martinez | Analyse de sensibilité globale par décomposition de la var ance[END_REF] for the six remaining parameters, using the R function sobolmartinez from the sensitivity library (with , which leads to 1600 model calls). The results for the the outputs and are presented in Figures 3 and4. For each of the six remaining parameters, the main and total effects are estimated together with a 95% confidence interval, this confidence interval being estimated by a bootstrap method with 100 replicates. Remark first that, given that the indices are only numerically approximated, the main effects often appear to be greater than the total effect; however, in view of the confidence intervals (omitted here), the values seem consistent. Remark also that the different effects do not add up to 1 as they should, again due to numerical errors, but again this discrepancy is acceptable given the confidence intervals.

The results of the sensitivity analysis are summed up in Tab. 3. For each quantity and each time, the sensitive parameters are listed in descending order or importance. To summarize only has an influence on at 100 s and 300 s;

only has an influence on at 600 s and 900 s;

only has an influence on at 900 s; the three other parameters have an influence on almost every output and at any time, with the influence of decreasing when time goes on, while the influence of is increasing when times goes on. The three most sensitive parameters are therefore , and ; is sensitive only on the initial times for only one observed quantity and and are weakly or not sensitive at all, depending on the considered output.

III) Discussion

From the results of the sensitivity analysis, it is first important to notice that the parameter is among the most sensitive parameters of the model. This was expected given the physical significance of this parameter. Another result concerning is that its influence decreases with time. This implies that, in order to accurately estimate this parameter, it is important to get as much experimental data as possible during the first minutes of the heating.

The second consequence of the sensitivity analysis is that and are of very sensitive throughout the heating. Although this was expected from the physical meaning of these parameters, it turns out that they are crucial to the modeling of heat and mass transport phenomena and are even sometimes more important than . This highlights the need for a meticulous determination of these two parameters for a good understanding of the heating process. For the determination of for instance, an experimental characterization of its structure at microscopic scale and the determination of the influence of this structure upon heat and mass transfer phenomena could be a great help.

The third takeaway is that is sensitive for at initial times. This shows the need for a careful determination of its value. Indeed, even though is only a fraction of the total mass flux density, even a small discrepancy in the value of could lead to a non-negligible error in the energy balance and hence a degradation of the predictions of the model.

The fourth takeaway is that the other parameters are either weakly or almost not sensitive taking into account the outputs considered (cf. Tab. 2). This justifies taking references values in the literature for these parameters and not spending too much time in experimental estimations, which would be almost useless for the predictive abilities of the model. For instance, it is well known that the initial water content of the potato slice may vary depending on the variety and/or on the storage conditions and duration. However, given that the parameter is almost not sensitive, there is no need to determine it with a high precision for each experimental trial.

Although the methodology adopted here allows to better understand the system and the relative influence of the parameters, it also has some limitations. First, the a priori probability distributions taken for the parameters and presented in Table 1 are somehow arbitrary. They have been selected considering the underlying physical meaning, but the exact bounds (for uniform distributions) or the mean value and standard deviation (for normal distributions) could have been selected differently. For instance, the prior distribution on was taken as uniform between the conductivity of air and the conductivity of lipids. This choice reflects the incertitude on the structure and composition of the crust. Similarly, the bounds on the prior distribution of were selected considering the values found in the literature (Viné et al., 2019). These values were found in fact to vary in a very wide range even for similar food products. This reflects that the determination of the value of this parameter is always very delicate either (i) by direct experimental measurement or (ii) by comparison between measured and predicted data using a model. Indeed, the value determined by this latter method often incorporates misunderstanding or misdescription of the mechanisms occurring during contact heat transfer. Furthermore, it is worth noting that a different choice of the distributions could lead to different results for the sensitivity. However, studying the sensitivity of a parameter outside of its typical variation range is not physically relevant. The distributions have been selected to be representative of the expected possible range of the parameters and therefore the obtained results can reasonably be taken as representative enough.

Another limitation of the method appears after applying the Morris method, when selecting the parameters which will be kept for the computation of the Sobol indices and those which will be left. This step has been performed graphically, keeping in mind the contradictory needs of (i) reducing the number of parameters to get exploitable results, and (ii) not eliminating parameters that could end up being sensitive and therefore important. However, when looking at the values of the Sobol indices, it turns out that only a few parameters account for nearly all the variations of all the considered outputs. Hence it seems unlikely that a very sensitive parameter was left behind after the Morris method.

The third limitation of the methodology is the initial choice of the set of parameters to study. Indeed, the only considered parameters are those appearing explicitly in the model equations and other factors could be considered. Some might have an even bigger impact on the process than , or as for instance the exact geometry of the potato slice, the sharpness of the cut for the product in particular at its lower surface or the heating surface covering. However, these factors are easily controlled in experimental setups, which limits the interest of studying their relative effect on the outputs.

The fourth limitation consists in the interpretation of the sensitivity of . Indeed, as stated above, this parameter was supposed to be constant. However, in reality, is not constant and its variations reflects the drastic changes of structure in the contact surface. Therefore, the value of is an average value throughout the process and the analysis of its decreasing sensitivity refers to the decreasing sensitivity of this average value.

Last, but not least, given that the Sobol indices represent percentages of the outputs, when comparing the effect of a given parameter on a given quantity at different instants, it is worth noting that the percentages do not refer to the same absolute value. For instance, the temperature of the product is increasing and thus it is possible that a parameter is responsible of the same amount of variation in degrees at different times, meaning its relative influence is decreasing, and thus we see its Sobol indices is decreasing as well. This remark does not contradict the interpretation of the effects of the parameters but it is important to keep in mind that these interpretations consider only the relative influence on the outputs.

CONCLUSION

In this paper, a sensitivity analysis of a heat and mass transfer model for the contact heating of potato slices has been performed. It has shown that a large number of the parameters appearing in the model equations are weakly or almost not sensitive for a number of outputs representing the evolution process. Only three parameters have been shown to be very sensitive, namely the thermal conductivities of the crust and the moist product , as well as the contact heat transfer coefficient . This has in turn consequences, as the need to get meticulous estimations of these parameters on one hand and the lack of interest of a precise estimation of the other considered parameters on the other hand. The sensitivity analysis performed on this model has shown useful in understanding the relative importance of the parameters. In future works, different approaches for estimating the sensitivity which reduce the sampling required may be tried, as in [START_REF] Bhonsale | Global Sensitivity Analysis of a Spray Drying Process[END_REF]

  List of the Parameters of the Model, their Unit and a

Figure 1 :Figure 2 :

 12 Figure 1: Results of the Morris Method for the Bottom Mass Flux Density at 100 s

Figure 3 :Figure 4 :

 34 Figure 3: Estimation of the Sobol Indices for the Bottom Mass Flux Density at 100 s

Table 2 :

 2 List of the Outputs of the Model, with the corresponding Physical Quantity, Unit and Instant Considered

Table 3 :

 3 List of the Sensitive Parameters for each Output of the Model, in Descending Order of Importance

	100 s	300 s	600 s	900 s
			,	,
			,
				,
			,	,


Akiebe Humphrey Ahworegba

Christophe Estay

Myropi Garri

Institutional duality incidence on subsidiaries: configuration, differentiation and avoidance strategies

Keywords: Subsidiaries, Configuration, Differentiation, Avoidance, Operational legitimacy, Institutional duality

Purpose-To illustrate how threats of institutional duality (ID) incidence subsidiaries confront are converted to opportunities, by conceptualizing how subsidiaries attain operational legitimacy at both their headquarters (HQ) and host-countries. Design/methodology/approach-Using a systematic literature review, we build on institutional theories by analyzing ID literature along its structure, main processes, and outcomes. We configure frameworks of both HQ control systems and host-countries' institutional threats, showing how subsidiaries contingently navigate across them using configuration, differentiation, and avoidance strategies. Findings-Our findings show that "foresighted" subsidiaries attain operational legitimacy through configuration, differentiation, and avoidance of threats incidental to ID, by strategizing along certain formal and informal institutional variables including legal, socio-cultural, and technical factors. Originality/value-We propose "structural configuration of ID incidence" and "subsidiary path to legitimacy" frameworks. The former configures how the interaction between HQ and hostcountries' variables constitute ID incidence threats. The latter highlights how "foresighted" subsidiaries use configuration, differentiation, and avoidance strategies to attain operational legitimacy.

Introduction

Multinational corporations' (MNCs) subsidiaries face threats arising from institutional duality (ID) incidence. ID incidence threats refer to isomorphic (double) pulls or pressures [START_REF] Dimaggio | The iron cage revisited: institutional isomorphism and collective rationality in organizational fields[END_REF]) that concurrently arise from the subsidiaries' headquarters (HQ) and the hostcountry [START_REF] Kostova | Adoption of an organizational practice by subsidiaries of multinational corporations: institutional and relational effects[END_REF][START_REF] Hillman | The determinants of MNE subsidiaries' political strategies: evidence of institutional duality[END_REF]. The interplay between environmental and organizational variables in MNCs illustrates the framework in which MNCs operate [START_REF] Sundaram | The environment and internal organization of multinational enterprises[END_REF]. Subsidiaries align with the host-country's context to avoid isomorphic pressures, without eroding the context of their homeland. They use resource commitment, personal relationships, political accommodation, and organizational credibility to improve cooperation with the host-institutions [START_REF] Luo | Toward a cooperative view of MNC-host government relations: Building blocks and performance implications[END_REF]. Even in local illegitimate institutional contexts, firms develop exploitation and exploration strategies to survive and remain competitive [START_REF] Ramirez | Ambidexterity strategies in illegitimate institutional contexts: the role of informal institutions[END_REF]. Subsidiaries must fulfill a dissimilar set of stakeholders' expectations from the ones stemming from their HQs [START_REF] Kim | Stakeholder influence, institutional duality, and CSR involvement of MNC subsidiaries[END_REF]. Undoubtedly, companies cannot completely please all audiences [START_REF] Suchman | Managing legitimacy: strategic and institutional approaches[END_REF]. Subsidiaries from institutionally mature markets [START_REF] Child | The role of contextual combinations in the globalization of Chinese firms[END_REF] behaviorally avoid ID incidence by setting a "model" which those from emerging markets usually adapt [START_REF] Edwards | Multinational companies and the diffusion of employment practices from outside the country-of-origin: explaining variation across firms[END_REF]. This includes, re-contextualization or contexts harmonization [START_REF] Mu | Foreign subsidiaries' learning from local environments: an empirical test[END_REF][START_REF] Gertsen | Recontextualization of the corporate values of a Danish MNC in a subsidiary in Bangalore[END_REF], practices diffusion [START_REF] Edwards | Multinational companies and the diffusion of employment practices from outside the country-of-origin: explaining variation across firms[END_REF], market opportunities integration and strategy renewals [START_REF] Gupta | Knowledge flows and the structure of control within multinational corporations[END_REF][START_REF] Chang | Control in multinational corporations (MNCs): the case of Korean manufacturing subsidiaries[END_REF][START_REF] Collinson | The regional nature of Japanese multinational business[END_REF]. Subsidiaries from emerging markets generally lack sufficient insights to tackle environmental and institutional changes [START_REF] Yaprak | Emerging market multinationals' role in facilitating developed country multinationals' regional expansion: a critical review of the literature and Turkish MNC examples[END_REF]. They draw on the strength of institutions in developed countries to overcome weaknesses in their home countries [START_REF] Bandeira-De-Mello | Unpacking the ambidexterity implementation process in the internationalization of emerging market multinationals[END_REF][START_REF] Edwards | Mapping the impact of home-and hostcountry institutions on human resource management in emerging market multinational companies: a conceptual framework[END_REF]. This research aims to derive conceptual frameworks to describe subsidiary's strategic ID incidence avoidance to gain operational legitimacy. Research has not clarified how subsidiaries configure, differentiate and avoid ID incidence threats to attain operational legitimacy.

To understand the contextual issues that drive subsidiary operational legitimacy between HQ and host-environment, the following research question (RQ) arises: RQ: How can a subsidiary configure, differentiate and avoid institutional variations stemming from the HQ and the host-environment to attain operational legitimacy?

To answer this question, we systematically review literature on ID incidence on MNC subsidiaries.

Then, we create frameworks to help subsidiaries face ID threats.

Findings clarify how subsidiaries adapt to turbulent environment in their host-countries through strategy renewals, either they originate from developed or from emerging markets. Findings show how subsidiaries achieve operational legitimacy using configuration, differentiation and avoidance of the variables causing the ID incidence.

Our frameworks advance the existing knowledge on ID incidence. They help subsidiaries operating in developed and emerging markets to avoid institutional threats by understanding better how their behavior is shaped by their external environments.

The rest of the paper is organized as follows: After discussing the theoretical underpinning of the research, we explain our research design. Then, we present our findings and discussion, implications, future research agenda and conclusion.

Literature Review

Operational legitimacy indicates subsidiary's compliance with institutional standards at the HQ and the host-country, including formal and informal regulations, control processes, norms, and value systems [START_REF] Nell | Strictly limited choice or agency? Institutional duality, legitimacy, and subsidiaries' political strategies[END_REF][START_REF] Li | The dual effects of home country institutions on the internationalization of private firms in emerging markets: Evidence from China[END_REF][START_REF] Samdanis | The Duality of an atypical leader in diversity management: the legitimization and delegitimization of diversity beliefs in organizations[END_REF]. There are two research streams in this area. The first refers to institutional conflicts driving subsidiaries to realign strategies with their HQ and host-country (e.g., [START_REF] Jaeger | The transfer of organizational culture overseas: an approach to control in the multinational corporation[END_REF][START_REF] Westney | Institutionalization theory and the multinational corporation[END_REF][START_REF] Hoffman | Generic strategies for subsidiaries of multinational corporations[END_REF][START_REF] Edwards | Mapping the impact of home-and hostcountry institutions on human resource management in emerging market multinational companies: a conceptual framework[END_REF]. [START_REF] Oliver | Strategic responses to institutional processes[END_REF] seminar work describes companies' strategic responses to institutional processes, which vary from passive conformity to proactive manipulation, depending on specific institutional factors. [START_REF] Pache | When worlds collide: the internal dynamics of organizational responses[END_REF] develop this work reckoning the intraorganisational political processes. They showcase how the management of conflicts between internal groups either leads to the transformation of conflicts into opportunities for institutional agency, or to organizational paralysis. The second stream describes how subsidiaries face rigid domestic and cultural laws stemming from the protocols of regional economic blocs (e.g., [START_REF] Chen | Convergence in human resource systems: a comparison of locally-owned and MNC subsidiaries in Taiwan[END_REF][START_REF] Fenton-O'creevy | Human resource management in US subsidiaries in Europe and Australia: centralisation or autonomy?[END_REF][START_REF] Samdanis | The Duality of an atypical leader in diversity management: the legitimization and delegitimization of diversity beliefs in organizations[END_REF]. In both cases, subsidiaries strive to attain operational legitimacy [START_REF] Peng | Bringing institutions into strategy teaching[END_REF] at the HQs and host-environment, by conforming, selecting or manipulating environmental structures [START_REF] Suchman | Managing legitimacy: strategic and institutional approaches[END_REF].

However, how subsidiaries strive to concurrently gain operational legitimacy at their global corporation and host-country environment is unclear [START_REF] Pant | How do subsidiaries confront institutional duality? Identity claims at Hindustan Lever 1961-2009[END_REF]2017). There are variations of ID pressures stemming from different local contexts (LC), as LC appears to have a stronger "pull" on subsidiary. Despite legitimacy being hard to manipulate and self-sustain, firms establish and strengthen operational legitimacy [START_REF] Peng | Bringing institutions into strategy teaching[END_REF] through institutional configuration, differentiation and avoidance strategies.

Institutional configuration allows subsidiaries to differentiate and avoid pressures stemming from their host-countries and HQs. It is a collective structural process moderated by "constraints, incentives, and resources provided by formal and informal institutions" (Stephan et al. 2015, p.309). Such institutions "are more or less compatible" (p.309). "More or less" institutional compatibility indicates institutional differences. Institutional configuration and differentiation are interdependent, but differentiation helps MNCs to segment institutional pressures between hostcountries [START_REF] Edwards | Multinational companies in cross-national context: integration, differentiation and the interactions between MNCs and nation states", Introduction to a Special Issue of the ILRReview[END_REF]. Firms avoid institutional pressures by exploiting "existing loopholes in regulations and long tradition of lax rule enforcement" (Jaehrling and Méhaut, 2012, p.8).

Moreover, MNCs use institutional configuration to differentiate their operations in the hostcountry while maintaining central control at the HQ [START_REF] Lawrence | Organization and Environment[END_REF]. They use configuration to align host-country traits and corporate identities [START_REF] Kostova | Transnational transfer of strategic organizational practices: a contextual Perspective[END_REF], as different host-country environments lead to different levels of institutions and configuration strategies [START_REF] Acemoglu | Asymmetric growth and institutions in an interdependent world[END_REF]. Diverse levels of institutional configurations increase the chances of local partnerships in MNC activities which reduce environmental turbulence [START_REF] Vazquez-Barquero | Endogenous development and institutions: challenges for local development initiatives[END_REF]. For instance, Philips and Dutch Electronics configure generic strategies to suit local contexts [START_REF] Hoffman | Generic strategies for subsidiaries of multinational corporations[END_REF]. MNCs in Central and Eastern European (CEE) countries experienced a reversed context that transformed the structure of these countries, after 1991 [START_REF] Festing | Path-dependent evolution of compensation systems in Central and Eastern Europe: a case study of multinational corporation subsidiaries in the Czech Republic, Poland and Hungary[END_REF]. MNCs in emerging markets use social investment schemes [START_REF] Nwankwo | Social investment through community enterprise: the case of multinational corporations involvement in the development of Nigerian water resources[END_REF], while MNCs in the Baltic Sea encourage local participation, to achieve operational legitimacy [START_REF] Ritvala | MNCs and local cross-sector partnerships: The case of a Smarter Baltic Sea[END_REF].

MNCs also avoid ID threats by creating projects promoting the host-country's economic advancement (Quesada-Vázquez and Rodríguez-Cohard, 2019) to close the "institutional distance" between the home and host-countries [START_REF] Kostova | Transnational transfer of strategic organizational practices: a contextual Perspective[END_REF]. Chinese MNCs seek investment in environments that resemble their home country [START_REF] Deng | The internationalization of Chinese firms: a critical review and future research[END_REF]. Russian MNCs prefer international partnerships because globalization influences them more than their home context [START_REF] Panibratov | Obtaining international results through partnerships: evidence from Russian MNEs in the IT sector[END_REF]. Western MNCs are also keen about the structure of Russian business context [START_REF] Koveshnikov | A framework of successful organizational practices in Western multinational companies operating in Russia[END_REF]. Aligning contextual practices is an ID threats avoidance strategy that leads to operational legitimacy. Research has not clarified how subsidiaries configure, differentiate and avoid ID incidence threats to attain operational legitimacy. In this paper, we are exploring in how subsidiaries configure, differentiate and avoid institutional variations stemming from the HQ and the host-environment to attain operational legitimacy.

Methodology

Following guidelines of methodological rigor [START_REF] Tranfield | Towards a methodology for developing evidenceinformed management knowledge by means of systematic review[END_REF] and aiming to consolidate the literature across the domain, we conducted a systematic literature review [START_REF] Torgerson | Systematic reviews[END_REF] on the ID incidence on subsidiaries. This approach's advantage is its enriched rigor. Systematic reviews minimize bias, and provide answers to specific research questions, using specific filtering criteria [START_REF] Tranfield | Towards a methodology for developing evidenceinformed management knowledge by means of systematic review[END_REF]. They are reproducible, objective, transparent, unbiased and rigorous [START_REF] Boell | On being "systematic" in literature reviews in IS[END_REF].

We served these goals by providing an audit of the selection and review process that can be potentially replicated [START_REF] Tranfield | Towards a methodology for developing evidenceinformed management knowledge by means of systematic review[END_REF]. We conducted an exhaustive literature search in two databases, Science Direct (SD) and Google Scholar (GS). Science Direct, a "scholarly" database, indexes articles with certain journals being included, while Google Scholar scans different webpages for scholarly material, with less care going into the journals that publish these articles.

The combination of the two brings out results that adequately cover the subject area. We used the terms ""institutional duality" and subsidiary" (SD:49, GS:1010), "subsidiary and "institutional configuration"" (SD:92, GS:1340), "subsidiary and "institutional differentiation"" (SD:12, GS:581), "subsidiary and institutional avoidance"" (SD:4, GS:78), "subsidiary and operational legitimacy"" (SD:3,GS:87). To account for the terminological heterogeneity in the field, we also looked for the ""local context" and "host-pressures"" (SD:0, GS:3), ""host-environment" and headquarters" (SD:194, GS:2410). These terms were chosen based on relevance to our research question, giving us more than 5,800 results. These papers were examined in three steps. First, we scanned through the results and we downloaded the papers that had a title relevant to the topic, and were published by a business and management journal. This reduced the number of papers to around 400. Second, we excluded duplicates and database artefacts, such as calls for special issues or brochures. This step left us with 124 papers. Third, we went through the abstracts and eliminated the ones that didn't fit the research focus; e.g. the search identified papers that referred to public policies and tax evasion, which were excluded. This final filtering left us with 74 articles, covering the period 1967-2020.

We read the full text of these 74 articles and used thematic analysis [START_REF] Braun | Using thematic analysis in psychology[END_REF] to answer our research question. Looking at papers describing the strategic responses of subsidiaries facing ID threats and seeking legitimacy, we coded these responses to tables, using one table for each theme and sub-theme. The main themes and subthemes were predetermined in order to provide answers to our research question, while a few new emerged while coding. Results are presented in Table I. This research is guided by institutional theories. We chose these theories as they aptly form the "duality" in the "institutions'" construct, and to strengthen the dominance of ID in international business (IB) debate since the era of [START_REF] Lawrence | Organization and Environment[END_REF] [START_REF] Ahworegba | The dilemma of institutional duality and multinational firms 1967-2017: Implications and future research[END_REF]. We followed through these theories against our selected methodological contexts (configuration, differentiation, and avoidance), and used them to structure the shape of variables moderating subsidiaries behavior at both HQ and host-countries. In fact, we categorized the strategic responses of subsidiaries to ID incidence into three strategic processes-themes, i.e. configuration, differentiation and avoidance of the variables causing the ID incidence. We methodologically defined these contexts as follows: First, "configuration" is the structuring of institutional settings to improve subsidiary's adaptation to foreign regulatory regimes [START_REF] Stephan | Institutions and social entrepreneurship: the role of institutional voids, institutional support, and institutional configurations[END_REF].

"Differentiation" is identifying variables or threats of ID incidence with a view to avoiding them. This helped us to segment different institutional conflicts for avoidance [START_REF] Edwards | Multinational companies in cross-national context: integration, differentiation and the interactions between MNCs and nation states", Introduction to a Special Issue of the ILRReview[END_REF].

"Avoidance" is the process of minimizing the threats of ID incidence to gain operational legitimacy. It is a calculated way of bypassing institutional constituents through local and international regulatory experience, regulatory loopholes exploitation, and contextual adaptation [START_REF] Jaehrling | Varieties of institutional avoidance: employers' strategies in low-waged service sector occupations in France and Germany[END_REF].We identified specific ID incidence threats, and the strategies used to be avoided. Variables relating to HQ pressures including structural alignment and integration of organizational sub-units place a burden on subsidiaries which reduces performance [START_REF] Birkinshaw | Configurations of strategy and structure in subsidiaries of multinational corporations[END_REF][START_REF] Qu | The impact of integration and responsiveness on MNC subsidiaries' market orientation[END_REF]. LC pressures such as cultural complexity, norms, beliefs, regulations, moderate subsidiaries response to both the host-environment and HQ pressures [START_REF] Tempel | Subsidiary responses to institutional duality: collective representation practices of US multinationals in Britain and Germany[END_REF][START_REF] Hoffman | International franchise expansion: the role of institutions and transaction costs[END_REF]. We configured both sets of variables and argued that subsidiaries that continually renew their strategies can avoid or minimize ID threats, while recognizing that subsidiaries are shaped by the identified variables constituting ID incidence. Table I specifies the structure of the literature, the conceptual process, and outcomes of ID incidence. Our methodology which anchors on the "structure" of ID literature, its "main processes" and "outcomes" helped us to "configure" the underlining institutional theories streamlining this paper.

Table I divides the literature into "prior research" and "topical issues". At "prior research", we identified two basic streams in ID literature: "institutional duality conflicts" and "protocols of regional blocs". Subsidiaries strive to "configure" them to achieve operational legitimacy. "This research" reveals what is new in the field. Then, we focused on the exploration of topical issues to understand the contextual issues that drive subsidiary operational legitimacy between HQ and host-environment, and to monitor the processes companies use to strategize to achieve operational legitimacy. At "topical issues", we focused on strategies of "configuration", "differentiation" and "avoidance" as paths to operational legitimacy, through two conceptual frameworks: "structural configuration of ID incidence" and "subsidiary path to legitimacy".

huge dilemma for the subsidiaries [START_REF] Westney | Institutionalization theory and the multinational corporation[END_REF] since they are barriers to the enterprise's global expansion [START_REF] Chen | Convergence in human resource systems: a comparison of locally-owned and MNC subsidiaries in Taiwan[END_REF]. Regional development agencies, especially in Asia and CEE countries [START_REF] Odrobina | Structural barriers to research and development activities in emerging markets: the case of Poland, the Czech Republic, Slovakia and Hungary[END_REF], are promoting better operating policies for subsidiaries located in their regions (Quesada-Vazquez and Rodriguez-Cohard, 2019). These countries have allowed their indigenous enterprises to expand globally [START_REF] Deng | The internationalization of Chinese firms: a critical review and future research[END_REF][START_REF] Panibratov | Obtaining international results through partnerships: evidence from Russian MNEs in the IT sector[END_REF]. They have also opened-up their domestic business landscapes for foreign enterprises [START_REF] Festing | Path-dependent evolution of compensation systems in Central and Eastern Europe: a case study of multinational corporation subsidiaries in the Czech Republic, Poland and Hungary[END_REF]). This regional policy improvement results from the pressure of international harmonization processes [START_REF] Chen | Convergence in human resource systems: a comparison of locally-owned and MNC subsidiaries in Taiwan[END_REF].

Subsidiaries face ID incidence threats in any location. They need to understand the structures and components of their external institutions to differentiate and avoid pressures arising from them [START_REF] Child | The role of contextual combinations in the globalization of Chinese firms[END_REF], as institutions set business rules [START_REF] Yang | Dealing with institutional distances in international marketing channels: governance strategies that engender legitimacy and efficiency[END_REF]. ID threats exacerbate in times of environmental turbulence. Environmental turbulence is described as the rapid, unpredictable change of the external environment [START_REF] Dess | Dimensions of organizational task environments[END_REF]. Environmental dynamism refers to changes in technology, consumer preferences, demand conditions, laws and regulations; driving the emergence of opportunities and threats for companies [START_REF] Jansen | Exploratory innovation, exploitative innovation, and performance: Effects of organizational antecedents and environmental moderators[END_REF].

Firms have to be agile to respond to these changes [START_REF] Jansen | Exploratory innovation, exploitative innovation, and performance: Effects of organizational antecedents and environmental moderators[END_REF]. Global turbulence inhibits subsidiaries to understand the institutions' structure, to obtain legitimacy by reconciling global and local norms [START_REF] Ahworegba | The dilemma of institutional duality and multinational firms 1967-2017: Implications and future research[END_REF][START_REF] Edwards | Mapping the impact of home-and hostcountry institutions on human resource management in emerging market multinational companies: a conceptual framework[END_REF]. Consequently, subsidiaries develop institutional fields serving as maintenance control centers for the requirements of operational legitimacy [START_REF] Samdanis | The Duality of an atypical leader in diversity management: the legitimization and delegitimization of diversity beliefs in organizations[END_REF]. Global turbulence challenges the subsidiaries to continually renew strategies to cope with ID incidence. Subsidiaries need to understand specific variations of ID to "contingently" or "contextually" configure conflicting governance policies at

Home-Country

Environmental Turbulence [START_REF] Almeida | Subsidiaries and knowledge creation: the influence of the MNC and host-country on innovation[END_REF][START_REF] Meyer | Multinational enterprises and local contexts: the opportunities and challenges of multiple embeddedness[END_REF]. The LC sets operating standards for subsidiaries thereby compelling them to maintain governance policy balances between their HQs and host-countries [START_REF] Westney | Institutionalization theory and the multinational corporation[END_REF][START_REF] Meyer | Multinational enterprises and local contexts: the opportunities and challenges of multiple embeddedness[END_REF][START_REF] Schweizer | Headquarters-subsidiary relationships during dramatic strategic changesthe local implementation of a global merger between MNCs in India[END_REF]. The pressures of "nonmarket agents" and HQs alignment of its units concurrently stem from hostenvironment and the MNC organization, meeting at the "location" of the LC [START_REF] Meyer | Multinational enterprises and local contexts: the opportunities and challenges of multiple embeddedness[END_REF], and constituting ID incidence "threats" for subsidiaries [START_REF] Kostova | Adoption of an organizational practice by subsidiaries of multinational corporations: institutional and relational effects[END_REF][START_REF] Hillman | The determinants of MNE subsidiaries' political strategies: evidence of institutional duality[END_REF][START_REF] Tempel | Subsidiary responses to institutional duality: collective representation practices of US multinationals in Britain and Germany[END_REF]. However, such threats can be avoided by extending the structural configuration of ID incidence model through differentiation process.

Host-Country

Differentiation and avoidance of ID incidence

Multiple authority, causing ID, affects the decision making of the MNC in areas like entry mode, configuration of activities, control mechanisms and competitive strategies [START_REF] Sundaram | The environment and internal organization of multinational enterprises[END_REF]. But institutional differentiation and avoidance strategies strengthen subsidiaries against ID incidence. Subsidiaries that avoid ID threats are "foresighted" because they possess superior strategies to configure and differentiate institutional conflicts in the host-country to gain legitimacy [START_REF] Ahworegba | Embedded opportunities and conflict of subsidiary initiatives[END_REF]. [START_REF] Stephan | Institutions and social entrepreneurship: the role of institutional voids, institutional support, and institutional configurations[END_REF] argue from a survey of 26 countries including Spain, South Africa, China, US, UK, and France, that advancing entrepreneurship in IB requires superior differentiation and avoidance of conflicting institutions through strategic configuration. For their part, [START_REF] Edwards | Multinational companies in cross-national context: integration, differentiation and the interactions between MNCs and nation states", Introduction to a Special Issue of the ILRReview[END_REF] find from US subsidiaries in Canada, Ireland, Spain, and the UK that, differentiation across countries helps to integrate subsidiaries into the MNC worldwide network. While subsidiaries in liberal markets including Ireland and Canada shared characteristic and high degree of dependence on HQ in US, those in a lesser liberal economy such as Spain were cautious of distinctive institutional differences in configuring avoidance strategies. Thus, institutional avoidance strategy enhances IB's sustainability in the host country.

Moreover, "foresighted" subsidiaries master the threats of ID variations and refocus them as opportunities for growth. They engage in strategy renewals through continuous "configuration" of their activities, to concurrently fit into both HQ's structural control processes and LC protocols.

They showcase in-depth experience of non-market factors in the host-country such as local norms and traditional beliefs. Jaehrling and Méhaut (2012, p. 21) conclude that through in-depth host country experience, companies in France and Germany were able to avoid institutional conflicts to attain operational legitimacy. However, while examples of avoidance strategies can be found in both France and Germany, the two countries display differences regarding the varieties and combinations of institutions. For instance, institutional differentiation led to a higher use of "outsourcing" of operations in Germany than in France. In any case, companies in the two countries strategically key into institutional change by technical and socio-cultural avoidance of labor regulation, through obvious loopholes therein, thereby legally "undercutting established employment standards". Table II shows subsidiary's path to obtaining operational legitimacy wherever they operate. Table II shows how "foresighted" subsidiaries contextually configure institutional changes between HQ and LC to attain operational legitimacy. This configuration enables differentiation of ID variables into categories, preparing for their avoidance. Operational legitimacy acquisition process flows from configuration to differentiation, to avoidance. This is the process used to avoid ID incidence by converting its threats to opportunities to attain operational legitimacy in the hostcountry and at the HQs.

Previous research explores how subsidiaries balance pressures at the host and HQ's environments to achieve operational legitimacy [START_REF] Jaeger | The transfer of organizational culture overseas: an approach to control in the multinational corporation[END_REF][START_REF] Westney | Institutionalization theory and the multinational corporation[END_REF][START_REF] Hoffman | Generic strategies for subsidiaries of multinational corporations[END_REF][START_REF] Chen | Convergence in human resource systems: a comparison of locally-owned and MNC subsidiaries in Taiwan[END_REF][START_REF] Edwards | Mapping the impact of home-and hostcountry institutions on human resource management in emerging market multinational companies: a conceptual framework[END_REF][START_REF] Fenton-O'creevy | Human resource management in US subsidiaries in Europe and Australia: centralisation or autonomy?[END_REF]Ahworegba and Colovic, 2018;[START_REF] Samdanis | The Duality of an atypical leader in diversity management: the legitimization and delegitimization of diversity beliefs in organizations[END_REF]. The strategic responses to institutional processes vary from passive conformity to proactive manipulation, depending on the institutional environment [START_REF] Oliver | Strategic responses to institutional processes[END_REF]. The diversity of legitimacy dynamics creates pressures on managers to strategically maneuver within their environments [START_REF] Suchman | Managing legitimacy: strategic and institutional approaches[END_REF]. Conformity to the host-environment signals deviation from the norms and expectations of the HQ [START_REF] Peng | Bringing institutions into strategy teaching[END_REF], requiring sophisticated organizational responses. Organizational responses are affected by intraorganizational processes, showcasing how the conflicts' management between the HQ and the subsidiary creates opportunities for institutional agency and strategic choice [START_REF] Pache | When worlds collide: the internal dynamics of organizational responses[END_REF]. Strategies like conformity, selection, manipulation, have been proposed as possible pathways to gain internal and external legitimacy [START_REF] Suchman | Managing legitimacy: strategic and institutional approaches[END_REF]. Previously, institutionalists show that companies in uncertain environments seek comprehensibility and taken-for-grantedness via mimetic isomorphism [START_REF] Suchman | Managing legitimacy: strategic and institutional approaches[END_REF]. They even use exploration and exploitation strategies to manage ID incidence and to achieve operational legitimacy [START_REF] Ramirez | Ambidexterity strategies in illegitimate institutional contexts: the role of informal institutions[END_REF], along with resources commitment, personal relations, and political accommodation [START_REF] Luo | Toward a cooperative view of MNC-host government relations: Building blocks and performance implications[END_REF]. In this paper, we adopt a process approach to demonstrate how subsidiaries convert ID incidence threats to opportunities, to gain operational legitimacy, through the configuration, differentiation, and avoidance pathways. Configuration refers to subsidiaries' initiatives to strategize for institutional change between the HQ and the local context. This requires the detailed mapping of the institutional characteristics of the local context, of their origins and causal factors, and of the links between them (differentiation). Avoidance can take place afterwards, through strategy renewals for the concurrent management of the identified institutional local framework and the alignment with HQ policies, leading to the achievement of operational legitimacy.

Managerial Implications

Managers should know that subsidiaries can behaviorally turn ID threats, including HQ control policies and host-country's institutional requirements, to opportunities, to achieve operational legitimacy. The configuration processes of ID incidental threats, is passing through the differentiation and avoidance processes.

The variables constituting ID threats include differences between HQ's and host-country's policies, such as control of MNC network of subsidiaries by the HQ, protocols of regional blocs, host-country's formal and informal regulations. The differentiation process prepares for ID incidence avoidance. It is composed by specific actions including drawing-up a context-specific matrix, tracing the origin of each ID variable in its context, clarifying HQ and host-country policies, and listing the causal factors of each variable.

During the ID incidence avoidance process, managers should attempt to legally, socio-culturally and technically avoid ID threats through application of in-depth experience in local and international regulatory dynamics, exploitation of regulatory loopholes, contextual adaptation, promotion of the host-economy through social investment, and pursuit of a high level of autonomy from the HQ. Operational legitimacy is gained by subsidiaries embracing institutional change, which translates into closing of institutional gaps across countries.

Subsidiaries which configure and differentiate the ID incidence variables, effectively avoid its threats, and gain operational legitimacy. These insights will help subsidiaries' managers and other stakeholders to respond more "contextually" to ID incidence and harmonize the HQ's integration processes, while tilting toward the LC, including cultural and traditional beliefs, norms and value systems, as well as formal regulatory institutions.

Avenues for future research

Our paper shows how "foresighted subsidiaries" understand dual institutions, configure ID incidence's threats to opportunities, and avoid conflict of interests, to gain operational legitimacy.

However, the concept "foresighted subsidiaries" including their features needs further exploration. Do the threats of ID incidence make subsidiaries more strategic? Are the strategies used by subsidiaries to convert threats of ID incidence to opportunities context-specific? Our approach is limited by the fact that HQ configuration process depends on MNC's country of origin. Hostcountry's non-market variables differ between emerging and developed markets, and from one country to another. Future research can address these limitations for better moderation of ID incidence by LC.

Concluding remarks

"Foresighted" subsidiaries behaviorally configure, differentiate, and convert ID incidental threats to opportunities through avoidance. Prior research concentrated on how subsidiaries strive to concurrently gain legitimacy at the HQs and host-environment. However, a gap exists in converting ID incidence's threats to opportunities to gain legitimacy. We contribute to existing literature by filling this gap as well as advancing subsidiaries' foresights in ID incidence, through our "structural configuration of ID incidence" and "subsidiary path to legitimacy" frameworks.

The first configures how the interaction between HQ and host-countries' variables constitute ID incidence threats. The second highlights how "foresighted" subsidiaries use configuration, differentiation, and avoidance strategies to attain operational legitimacy. Subsidiaries can use these frameworks to convert ID incidence's threats to opportunities to gain operational legitimacy.

  environment's pressures; moderating subsidiaries response to both host and HQ/home institutions) Dual external pressures on subsidiaries: (Non-market agents-culture, norms, beliefs, rules and regulations, HQ controls) Source: The authors their host-locations and HQs. Figure I is a configuration of specific variations of ID incidence subsidiaries confront, illustrating the moderating role of the environmental turbulence.

Figure I :

 I Figure I: Structural configuration of ID incidence

Table I : Conceptual focus Literature structure Main processes Outcomes Prior research:

 I

	Basic streams	Institutional duality conflicts	Subsidiary striving for operational legitimacy
		Protocols of regional blocs	Subsidiary striving for operational legitimacy
	"This research"	Framework of variables of institutional	Subsidiary absolves ID incidence and achieves
		influence on subsidiaries	legitimacy through tilting toward the LC by
			configuration of threats to opportunities, through
			differentiation and avoidance as well as
			harmonization of HQ practices
	Topical issues:
	Dual institutions	Striking a balance between HQ and LC	Strategizing to achieve legitimacy
	Mature institutions	Setting IB standards	Diffusion and harmonization of contexts,
			integrating local opportunities, strategy renewals,
			emerging markets MNCs coping developed
			markets.
	LC and HQs	Institutional duality incidence
			LC center of IB interrelationships by moderating
			subsidiary response to institutional interactions
			between HQs and host-country

Table II : Subsidiary path to legitimacy

 II

		Configuration zone		Differentiation zone		Avoidance Zone	Legitimacy zone
		(Structural evolution)		(Process 1)		(Process 2)	(Outcome)
			■	Drawing up a context-	■	Legal, social and technical mapping of
				specific matrix		ID threats through institutional loopholes
			■	Tracing the origin of		and closing cultural gaps by adaptation.
				each ID variable	■	In-depth experience of non-market
	■	Subsidiary strategizing for	■	Clarifying HQ and host-		activities in the host-country
		institutional change		country's policies	■	Extracting benefits of configured and	■	Subsidiary attains operational
		between HQ and host-	■	Showing contextual		differentiated variables	legitimacy
		country (LC)		origin;	■	Conversion of ID threats to opportunities	o	Harmony with HQ and
			■	Listing causal factors of		for growth in the host-country	LC
				each variable	■	Subsidiary strategy renewals and
			Formal and informal		concurrently fitting into HQ and LC
			regulations, norms and		policy initiatives
			beliefs, developed and mature	■	HQ consenting unlimited autonomy to
			institutions, country versus		subsidiary on local decision making
			country	■	Autonomously tilting towards the LC to
						gain legitimacy at both ends
		Source: The authors

Results and Discussion

Configuration, processes, and outcomes of ID incidence

Subsidiaries face ID pressures wherever they operate. What counts is their ability to configure patterns in the host-environment. Subsidiaries configure institutional pressures in a "contingent manner" (Negandhi and Reimann,1972;[START_REF] Scott | Organizations: rational, natural, and open systems[END_REF], since the processes and outcomes of their configuration strategies depend on how they perceive institutions [START_REF] Birkinshaw | Knowledge as a contingency variable: do the characteristics of knowledge predict organization structure?[END_REF][START_REF] Harzing | The relative impact of country of origin and universal contingencies on internationalization strategies and corporate control in multinational enterprises: worldwide and European perspectives[END_REF][START_REF] Kim | The global integration of business functions: a study of multinational businesses in integrated global industries[END_REF]. For instance, subsidiaries contingently pursue independent strategies when MNC goals don't fit into the host-environment (Devinney et al., 2002), because aligning with the host-environment allows them to avoid institutional pressures [START_REF] Kang | Understanding diverging isomorphic pressures on foreign subsidiary managers: a contingency model[END_REF][START_REF] Kang | Institutional forces and environmental management strategy: moderating effects of environmental orientation and innovation capability[END_REF].

Subsidiaries behave similarly when exposed to comparable institutions [START_REF] Van Grinsven | Translating management concepts: towards a typology of alternative approaches[END_REF]. Comparing Germany and Britain to USA, Britain is considered institutionally similar to USA because of the common IB practices in the two countries [START_REF] Tempel | Subsidiary responses to institutional duality: collective representation practices of US multinationals in Britain and Germany[END_REF]. However, US subsidiaries in both Britain and Germany strive to close legal or socio-cultural gaps to avoid threats deriving from institutional distances [START_REF] Yang | Dealing with institutional distances in international marketing channels: governance strategies that engender legitimacy and efficiency[END_REF][START_REF] Hamprecht | Subsidiary initiatives in the institutional environment[END_REF][START_REF] Nell | Strictly limited choice or agency? Institutional duality, legitimacy, and subsidiaries' political strategies[END_REF]Samdanis and Özbilgin, 2020). Local institutional structures intensify HQ's control over subsidiaries [START_REF] Kim | The global integration of business functions: a study of multinational businesses in integrated global industries[END_REF][START_REF] Marin | Innovativeness of MNC subsidiaries in Brazil: the effects of global and local integration[END_REF][START_REF] Mcgaughey | Institutions, entrepreneurship and co-evolution in international business[END_REF].

These HQs controls include a mixture of organizational structure and host-environment knowledge [START_REF] Birkinshaw | Knowledge as a contingency variable: do the characteristics of knowledge predict organization structure?[END_REF][START_REF] Collinson | The regional nature of Japanese multinational business[END_REF]. HQ control targeting avoidance of institutional conflicts led US subsidiaries in Europe and Australia, to resist pressures from institutional constituents, such as labor unions [START_REF] Fenton-O'creevy | Human resource management in US subsidiaries in Europe and Australia: centralisation or autonomy?[END_REF].

Subsidiaries responses to host-environments drive institutional conflicts [START_REF] Kang | Understanding diverging isomorphic pressures on foreign subsidiary managers: a contingency model[END_REF][START_REF] Schweizer | Headquarters-subsidiary relationships during dramatic strategic changesthe local implementation of a global merger between MNCs in India[END_REF]. These conflicts, arising from both HQs and the host-environment, present a