Chungpyo Hong
email: hong@mech.kagoshima-u.ac.jp

Yutaka Asako
email: y.asako@utm.my

Gian Luca Morini
email: gianluca.morini3@unibo.it

Danish Rehman
email: danish.rehman2@unibo.it

International Journal of Heat and Mass Transfer

Keywords: average friction factor, turbulent, gas flow, micro-tube, flow choking

published or not. The documents may come

Data reduction of average friction factor of gas flow through adiabatic micro-channels

INTRODUCTION

The pressure loss (drop or difference) determined by a friction factor between two points is one of the significant factors to design micro piping lines for MEMS (Micro Electro Mechanical System). Since the experimental work by Wu and Little [START_REF] Wu | Measurement of friction factors for the flow of gases in very fine channels used for micro miniature Joule-Thompson refrigerators[END_REF] who obtained the average friction factors using pressure difference between the inlet and the outlet of gases in micro-channels, many experimental and numerical studies on friction factor in a micro-channel have been undertaken. The friction factor for gases with large variations in the physical properties flowing through channels was obtained under the assumption of isothermal flow by most of the researchers, e.g. Turner et al. [START_REF] Turner | Experimental investigation of gas flow in microchannel[END_REF], Asako et al. [START_REF] Asako | Effect of Compressibility on Gaseous Flows in a Micro-Tube[END_REF], Tang et al. [START_REF] Tang | Experiment study of compressibility, roughness and rarefaction influences on microchannel flow[END_REF], Lorenzini et al. [START_REF] Lorenzini | Laminar, transitional and turbulent friction foator for gas flows in smooth and rough microtubes[END_REF],

Yang et al. [START_REF] Yang | Heat transfer and friction characteristics of air flow in microtubes[END_REF] and Hong et al. [START_REF] Hong | Experimental investigations of laminar, transitional and turbulent gas flow in micro-channels[END_REF] due to the measurement limitation of gas temperature flowing through a channel. The literature is surveyed in the article by Kawashima and Asako [START_REF] Kawashima | Data Reduction of Friction Factor of Compressible Flow in Microchannels[END_REF].

However, in the case of micro-channel gas flow at high speed, a large expansion occurs near the outlet and the pressure gradient along the length is not constant with a significant increase near the outlet. This results in flow acceleration and a decease in gas temperature.

Therefore the friction factor of micro-channel gas flow should be obtained with measuring both the pressure and temperature. In actual situation, micro-channel gas flow does not stay isothermal and shows a strong decrease in temperature near the outlet for adiabatic walls.

Recently, Kawashima and Asako [START_REF] Kawashima | Data Reduction of Friction Factor of Compressible Flow in Microchannels[END_REF] found that the gas temperature can be determined by the pressure under the assumption of one dimensional flow in an adiabatic channel (Fanno flow) to obtain the friction factor considering the effect of a decrease in gas temperature.

3 This is the motivation of the present study. In this paper an equation is proposed to calculate the average friction factors between relatively distant points considering the effect of a decrease in gas temperature.

DERIVATION OF AVERAGE FANNING FRICTION FACTOR FOR ADIABATIC WALL

The four multiples of the Fanning friction factor for an adiabatic wall (Fanno flow) is defined by [START_REF] Kawashima | Data Reduction of Friction Factor of Compressible Flow in Microchannels[END_REF]

      -       -       = = x T T D x p RT u Dp x p p D u f d d 2 d d 2 d d 2 2 1 4 2 2 2 w f    (1)
The pressures at the ports that are located adjacently are measured to obtain a semi-local friction factor. In such a case the change in temperature between two ports is small. Therefore, the temperature which appears in the second term in the right hand side of Eq. ( 1) can be treated as constant. Integrating Eq. ( 1) with the average of the temperatures at two pressure ports,

2 2 1 T T T + =
where T1 and T2 are the temperatures at the pressure ports 1 and 2, the following equation is obtained.

( )

( )         + + - + - - = - =   2 1 2 2 1 2 2 2 1 2 1 1 2 f 1 2 f ln 2 2 ln 2 d 1 2 1 T T G T T R p p p p x x D x f x x f x x  (2)
The temperature in Eq. ( 2) can be determined solving the following quadratic equation obtained by total temperature balance between given two points (inlet and x) [START_REF] Kawashima | Data Reduction of Friction Factor of Compressible Flow in Microchannels[END_REF].

0 2 2 p 2 in in 2 2 p 2 2 in 2 in =         + - + c u T T T p c R u   ( 3
)
where p is the pressure at the pressure port. The temperature is determined by

2 p 2 2 in 2 in p 2 in in 2 p 2 2 in 2 in 2 2 2 2 4 1 1 p c R u c u T p c R u T              +   + + - = (4)
where the inlet values of velocity, density and temperature are obtained with isentropic process between the inlet and the stagnation under the assumption of ideal gas. Kawashima and Asako [START_REF] Kawashima | Measurement of quasi-local friction factor of gas flow in a microtube[END_REF] measured three local pressures near the outlet of a PEEK (polyether ether ketone) micro-tube with D = 514.4 m and L = 50 mm and obtained semi-local friction factors between two pressure ports that are located adjacently using Eqs. ( 2) and (4).

Hong et al. [START_REF] Hong | Flow characteristics of gaseous flow through a microtube discharged into the atmosphere[END_REF] also measured three local pressures near the outlet of a glass micro-tube with D = 397 m and L = 120 mm to obtain semi-local friction factors between two adjacently located pressure ports. The effect of a decrease in gas temperature between two pressure ports is relatively small since the distances between two pressure ports are less than 0.1L. However in the case that two locations are not close such as the inlet and the outlet, T in the second term of Eq. ( 1) can not be considered as a constant. It should be integrated between x1 and x2. Therefore, in the present study, the focus is to obtain the friction factor between two relatively distant points. The above T (Eq. ( 4)) is a function of p. The average Fanning friction factor integrating Eq. ( 1) between x1 and x2 is

            -         -         - = - =     2 1 2 1 2 1 2 1 d 2 d 2 d 2 d 1 2 2 1 2 f 1 2 ave f, x x x x x x x x T T p RT u p p p x x D x f x x f  ( )                             + - + + + + + + + -                  +  - + - - = 2 2 1 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 2 2 p 2 in in 2 in 2 in 2 1 2 1 1 2 2 1 2 2 2 1 2 2 B p p B p p B p p B p p ln B p p c u T R u T T ln p p ln x x D  (5)
where

        +   = p 2 in in p 2 2 in 2 in 2 2 2 4 c u T c R u B   (6)
Therefore, the average Fanning friction factor between x1 and x2 can be obtained from Eq. ( 5).

Eq. ( 5) will also help piping design where pressure loss determination between relatively distant points is done using average friction factors. At least the inlet temperature, the inlet pressure, the mass flow rate and the outlet pressure are required to obtain the average friction factor from Eq. ( 2) or Eq. ( 5). These raw data are not shown in the literature. We asked Professor Tang [START_REF] Tang | Experiment study of compressibility, roughness and rarefaction influences on microchannel flow[END_REF] and Professor Yang [START_REF] Yang | Heat transfer and friction characteristics of air flow in microtubes[END_REF] to show us the raw data but they failed to find the data since they were collected long time ago. Then, the experiments and numerical calculations for nitrogen gas flowing through a stainless steel microtube (D = 867 m, L = 200mm and Ra = 0.48 m) whose inner surface is relatively smooth were carried out for data reduction. The average Fanning friction factors between the inlet and the outlet, ff, ave were obtained under the assumption of Fanno flow from Eq. ( 5) with both the experimentally measured and numerically calculated data. For both of them, the micro-tube outlet pressure is assumed to be at atmospheric pressure for the micro-tube gas flow discharged into the atmosphere. Detailed description of the experimental setup and the numerical methodology are documented in the previous studies [13 and 14] and will not be given.

EXPERIMENTAL AND NUMERICAL ESTIMATIONS OF AVERAGE FANNING FRICTION FACTOR

The experimentally and numerically obtained ff, ave is plotted in Fig. 1

        + - = D k f Re f 72 . 3 51 . 2 log 2 1 s f f (7)
where ks is equivalent sand grain surface roughness. In order to employ the above Colebrook-White equation obtained with ks, of the stainless steel micro-tube, the ks is assumed to be 1Ra. Due to the steep decrease in gas static temperature near the outlet from gas expansion, T in the second term of Eq. ( 1) can not be treated as a constant. Therefore, the values of  f f obtained from Eq. ( 2) deviate from those of ff, ave obtained from Eq. ( 5) at Re > 10000 for Fig. 2 as the gas velocity and bulk temperature differences between the inlet and the outlet are large.

The values obtained by the

In the range of Re > 23000, they deviate greatly from those of ff, ave obtained from Eq. ( 5) since the assumption of pout = patm is not valid with flow choking. When the flow is choked, the gas velocity and bulk temperature at a specific cross section inside a tube remain unchanged, and the outlet pressure is higher than the back pressure (atmospheric pressure) with an increase in Reynolds number. However, the outlet bulk temperature obtained under the assumption of pout = patm does not remain unchanged and rather decreases. Therefore the arithmetic average bulk temperature decreases and  f f increases at Re > 23000.

Both experimental and numerical values of ff, ave obtained from Eq. ( 5) are in excellent agreement with Blasius equation even though the outlet flow is under-expanded with flow choking and the outlet pressure is higher than the atmospheric pressure in the range of Re > 23000. The measure of under-expansion at the outlet is relatively small in this tube. And the relatively larger pressure difference between the inlet and the outlet is not significantly affected by under-expansion at the outlet.

In the case of the high speed gas flow in an adiabatic tube, the gas temperature decreases in the tube. This results in viscosity change. In order to account for the variation of the viscosity, the viscosity which is evaluated at the average of the inlet and the outlet temperatures, is used to calculate the Reynolds number. The average friction factor ff, ave obtained from Eq. ( 5) vs the Reynolds number based on the average temperature is also plotted Fig. 1. Then the obtained uncertainty of the friction factor is represented in the figure. The uncertainty of the pressure measured by the pressure transducer ( Krone KDM30, 0~1 MPa) is 2.5 kPa (0.25 % F.S.). In the lower Re range, the uncertainty of the friction factor is slightly higher compared to the uncertainty of the friction factor in the higher Re range. The corresponding uncertainty of the friction factor obtained in the range of 2590  Re  43204 is less than 0.0095 and more than 0.0002. In the same Reynolds number, the uncertainty of the friction factor obtained by Eq. ( 2) and Eq. ( 5) is also the same. The average friction factor ff, ave vs the Reynolds number based on the average temperature is slightly higher than the average friction factor ff, ave vs the Reynolds number based on the stagnation temperature, since the Reynolds number based on the average 8 temperature is larger than the Reynolds number based on the stagnation temperature. As a result of that, the average friction factor ff, ave vs the Reynolds number based on the average temperature is in very close agreement with Blasius equation. Eq. ( 5)

 at average temp.

Exp. Eq. ( 2)

Eq. ( 5)

 at stagnation temp. (

Stainless

/ f f, Eq.

(

) 5
p in / p out Fig. 3 Tin / Tout and ff, Eq. (2) / ff. Eq. ( 5) as a function of the pressure ratio

In the present experiment, the pressure and temperature in the chamber at the upstream section of the micro-tube were measured. The measured pressure and temperature can be considered as the stagnation values, since the gas velocity in the chamber is very low. The temperature and pressure at the inlet of the micro-tube are obtained with an isentropic process between the inlet and the stagnation under the assumption of ideal gas. Also the pressure loss at the tube entrance is considered. The square edged type is assumed for the entrance configuration.

The outlet pressure is assumed to be at atmospheric pressure since the gas at the outlet is discharged into the atmosphere. The outlet temperature of the thermally insulated micro-tube can be obtained by solving Eq. ( 4) since the outlet pressure is assumed to be at atmospheric pressure. As a result of that, the correlation between the temperature ratios at two points (the inlet and the outlet) and their corresponding pressure ratios were obtained. The temperature ratio, T1/T2 is plotted in Fig. 3 as a function of its pressure ratio. The ratio of the friction factors obtained by Eq. ( 2) and Eq. ( 5), ff, Eq. (2) / ff. Eq. ( 5) is also plotted in the figure. T1/T2 and ff, Eq. (2) / ff.

Eq. ( 5) increase with an increase in the pressure ratio. T1/T2 is 10 % higher than isothermal value at pin/pout=3 and ff, Eq. ( 2) is 5 % higher than ff. Eq. ( 5) at pin/pout=3. Therefore, Eq. ( 5) should be used instead of Eq. ( 2) when the pressure ratio pin/pout is greater than 3 if the 5% difference is allowed.

CONCLUSION

The average Fanning friction factor between two relatively distant points is derived with the temperature determined by the pressure measured at a location to estimate friction factor between the inlet and outlet for gas flow through adiabatic micro-channels. The following conclusions were reached.

(1) The experimental and numerical Fanning friction factors obtained from Eq (5) in the turbulent flow regime are in excellent agreement

(2) Both experimental and numerical average friction factor ff, ave obtained from Eq. ( 5) nearly coincide with Blasius equation even though the outlet flow is under-expanded with flow choking.

(3) The average friction factor ff, ave vs the Reynolds number based on the average temperature is in very close agreement with Blasius equation.

NOMENCLATURE

  as a function of Reynolds number. The  f f obtained from Eq. (2) is also plotted in the figure. The viscosity, which is evaluated at the stagnation temperature by using REFPROP[START_REF]NIST Reference Fluid Thermodynamic and Transport Properties -REFPROP[END_REF] is used to calculate the Reynolds number. The solid line and dotted line in the figures represent the values obtained by the theoretical formula (f = 64/Re) and f = 0.3164/Re 0.25 (Blasius equation) for incompressible flow theory, respectively. Since the effect of inner surface roughness on micro-tube flows is relatively large compared with conventional tube flows, the inner surface roughness of microtubes used for the experiment were measured. In order to measure the roughness of the inner surface of the tube, a part of the micro-tube is cut. The arithmetic mean heights of the surface of the micro-tubes were measured with a 3D laser scanning confocal microscope for profilometry (Keyence, VK-X260). The arithmetic mean height of the stainless steel micro-tube used in this study was 0.448 m. The value of the inner relative surface roughness of the micro-tubes was 5.1710 -4 . Therefore the inner surface of the micro-tube used in this study is considered to be smooth. For reference, the following Colebrook-White equation (Eq. 7)[START_REF] White | Fluid Mechanics[END_REF] calculating the friction factor of turbulent flow in a rough pipe is plotted in the figure with the red dotted line.

  Colebrook-White equation nearly coincide with Blasius equation within Re = 20000. And in the range of Re > 20000, it deviates from Blasius equation. Mach numbers obtained using the measured local pressures at three locations near the micro-tube outlet are plotted in Fig. 2 as a function of Reynolds number. The values of Mach number increase with increasing Reynolds number and level off in the range Re > 23000 since the flow is choked.

Fig. 1

 1 Fig.1 Fanning friction factor as a function of Re

Table 1

 1 Experimental results on average friction factors for turbulent gas flow in micro-tubes

		D (m) Gas	Re	Micro-tube	Average friction factor
					Outer surface
	Choi et al.	3.0 ~ 81.2 N2	20 ~ 18000 Silica tube	Isothermal flow
	(1991) [11]				Not clear	lower than Blasisu eq.
	Yu et al.	52 ~ 191 N2	250 ~ 20000 Silica tube	Isothermal flow
	(1995) [12]				Nearly adiabatic	lower than Blasisu eq.
	Tang et al.	55 ~ 201 N2	28 ~ 6200 Fused silica tube	Isothermal flow
	(2007) [4]				Not covered	lower than Blasisu eq.
	Yang et al.	86, 308,	Air 150 ~18800 Stainless steel tube	Isothermal flow
	(2012) [6]	920			Inserted in	higher than Blasius eq.
					a vacuum chamber

There are a few literature which investigate friction factors of turbulent gas flow through micro-tubes as tabulated in Table

1

. The most average friction factors between the micro-tube inlet and outlet are obtained under the assumption of isothermal flow and the obtained average friction factors are lower than the Blasius equation. Only the exception is friction factors obtained by Yang et al.

[START_REF] Yang | Heat transfer and friction characteristics of air flow in microtubes[END_REF]

.


S Timorian

S De Rosa

F Franco

M Ouisse

N Bouhaddi

WAVE AND FINITE ELEMENT ANALYSIS OF QUASI PERIODIC 2D PHONONIC SUPER-CELL CRYSTALS

Phononic Crystals (PCs) are artificial materials with extensive application in the aerospace and aeronautical industries since they introduce frequency stop-bands (frequency ranges where wave cannot freely propagates). In this investigation 2D periodic and quasi-periodic pattern: instead of strictly repeating a pattern, a certain degree of irregularity is introduced. Quasi-periodic PCs in this paper are defined as assemblies of two different elements in two direction by using Thue-Morse and semi-Sierpinski carpet which results in asymmetry in both directions. Numerical studies on periodic and quasi-periodic lattices are performed. The spectral analysis in periodic waveguide is validated with the dispersion diagram of a reference model and vibration transmission of the lattices are studied. The wave characteristics in quasi-periodic super-cell configuration increases the wide of band-gaps about 22% compared to the reference model. Nevertheless, the associated level of vibration in the forced response of quasi-periodic lattices are predicted.

INTRODUCTION

The very first findings of PCs dates back to Sir Lord Isaac Newton who imagined that sound waves propagated through air in the same way that an elastic wave would propagate along a lattice of point masses connected by springs with an elastic force constant. Recent literature study shows theoretical, numerical and experimental works based on vibration reduction and acoustic transmission loss of small and large scale elastic structures using 2D PCs. The existence of band-gaps in PCs was predicted theoretically by [START_REF] Manvir | Acoustic band structure of periodic elastic composites[END_REF]. There are two types of band-gap mechanism: the first one is Bragg scattering, this type of band-gaps can be shaped by the elastic wave reflection during the incidence with the scatterer of the neighbouring element which operates as a perfect non-absorbing mirror. The second one is local resonances mechanism that can provide a low frequency band-gap due to the coupling of two oscillators, say, the frequency is not dictated by the spacing of the periodic arrays but by the frequency of the local oscillator. This property could be an asset in plenty of applications, from vibration filtering to acoustic shielding and from seismology to the dynamic behaviour of space stations. In this investigation quasi-periodic 2D PCs is considered for passive broad band-gaps analysis. The PCs which is embedded in a super-cell is composed of a periodic combination proposed by [START_REF] Sun | Band gap and experimental study in phononic crystals with super-cell structure[END_REF]. The model is optimised by introducing a small degree of irregularity by using Thue-Morse and semi-Sierpinski carpet. The proposed model has same mass as in the reference [START_REF] Sun | Band gap and experimental study in phononic crystals with super-cell structure[END_REF], but with different filling rates of resonator and different cylindrical radius. Dispersion analysis of infinite PCs and forced response of finite panels are analysed. The content of this paper is structured as follows: in section 2 quasi-periodic lexicon is presented. Section 3 introduces results of the infinite super-cells and finite forced response. Closing section brings the conclusion of this study.

QUASI-PERIODIC LEXICON

The quasi-periodic model is defined by a small degree of irregularity in the PCs super-cells and finite panels [START_REF] Timorian | Spectral analysis and structural response of periodic and quasi-periodic beams[END_REF]. Two unit cells are modelled for wave finite element analysis, beside that two finite periodic and one quasi-periodic panels are modelled for forced response analysis shown in Fig. 1 2

.1 Thue-morse sequence

The Thue-Morse sequence is based on binary arrays. Starting from a 1D example, the sequence can be derived by a function s from the set of binary sequences to itself by replacing every A in a 1D sequence with AB and every B with BA [START_REF] Berstel | Combinatorics on words: Christoffel words and repetitions in words[END_REF]:

s(x, y) = s(x)s(y) (1)
Eq.1 defines a map s for all strings x, y. Defining the Thue-Morse morphism s(A) = AB, leads to the relations for increasing the quasi-periodicity pattern in one direction. The associated sequence starts with A then AB, ABBA, ABBABAAB, and so on, [START_REF] Allouche | The ubiquitous prouhet-thue-morse sequence[END_REF].

Semi-Sierpinski carpet PCs

Sierpinski carpet has a technique of subdividing a shape into 9 smaller copies of itself by removing one copy from the middle, and continuing recursively for the rest of copies [START_REF] Martin | Analysis on the sierpinski carpet[END_REF]. In the present model Semi-Sierpinski carpet is used to create PCs with local resonators.

Super-cell

The super-cell is made of 25 cells including square matrices with circular scatters, in which 9 of the circles of these square unit cells are filled with metal scatters and the rest are hollow air holes all around the super-cell. Cell-A and cell-B are designed in two different cases. In case 1 (quasiperiodic 1) the Thue-Morse sequence is applied by considering cell-A (r = 5 mm), cell-B (r = 3 mm), cell-C (r = 5.5 mm), and cell-D (r = 2.5 mm). The 9 middle cells are associated to Semi-Sierpinski carpet model and the other circles with the air holes follows Thue-Morse sequence (Fig. 1). The semi-Sierpinski carpet model is adapted to the variation of volume fraction of resonance material by reducing the inclusion (45 steel) of cell-A and at the same time increasing the inclusion (45 steel) of cell-B, using different circular radius in order to keep the same mass as the reference model. On the contrary, case 2 (quasi-periodic 2) deals with a super-lattice of cell-A and cell-B (r = 4 mm) as in the reference model but the position of coordinate of the circles in the entire lattice is changed with only two combined elements, using Thue-Morse sequence. For instance the coordinate of the constant cell-B is at base position p( i, j), in this method unit cell-A is displaced to ρ(2 i, -2 j). In this case cell-A and B is replicated by Thue-morse sequence in two directions (Fig. 1). Material properties are introduced in the Tab. 1

RESULTS OF THE INFINITE SUPER-CELLS AND FINITE FORCED RESPONSE

The dispersion diagram of the super cell quasi-periodic 1 in Fig. 2 In periodic pattern a total of four super-cells exist, whereas for the quasi-periodic panel 2 periodic super cells and 2 quasi-periodic super cells are combined (Fig. 3). Forced response of the panels are computed by applying fixed constraint boundary conditions in the upper and lower sides of the panels (Fig. 3) and a unit boundary load is applied with the frequency range of 0 -300 Hz with a bandwidth of 1 Hz. The vibration transmission is observed as T L = 20log(a 1 /a 2 ). The response of finite panels give four types of band-gaps (BG1, BG2, BG3, and BG4), in BG1 the response is the same almost for periodic B and quasi-periodic cases. It is the largest one for both cases but possesses a localised mode in the last part of the attenuation level. In BG2 the band-gap is very narrow, and it is only in periodic 2, while BG3 is narrower compared to BG2 and it is in periodic 2 and quasi-periodic case. BG4 is almost two times of BG3 and it is in quasi-periodic with a great fall and partially it could be seen in periodic 2 too. In conclusion periodic B has more band-gaps following quasi-periodic case.

2 OFigure 1 :Figure 2 .

 212 Figure 1: From the right, quasi-periodic 1 and quasi-periodic 2 configurations are graphically presented, in the left, first Brillouin zone reduced by all symmetries in the point group of the lattice Material type Modulus of elasticity (Pa) Poissons Ratio Density (kg • m -3 ) Matrix (vulcanized rubber) 21.06 × 10 10 0.26 7780 Scatter (45 steel) 1 × 10 6 0.47 1300

Figure 3 .

 3 Figure 3. Vibration transmission of two types of periodic and one quasi-periodic panel

ACKNOWLEDGEMENTS

The work is carried out in the framework of the VIPER project (VIbroacoustic of PERiodic media). The project has received funding from the European Union's Horizon 2020 research and innovation program under Marie Curie grant agreement No 675441 and EUR EIPHI (ANR 17-EURE-0002) project.


S Timorian

S De Rosa

F Franco

M Ouisse

N Bouhaddi

and Vibroacoustics Sevilla (Spain) FIRST LITERATURE REVIEW FOR THE ANALYSIS OF QUASI-PERIODICITY VARIABILITY EFFECTS AND MODELING STRATEGIES

Quasi periodicity and variability effects on structures are spread in all the engineering branches. The inherent research works are carried out with both numerical and experimental activities. A more specific goal is the analysis of the influence of such effects on the vibroacoustic response. The modern tools for investigating the most significant impacts of imperfections and irregularities on the vibrational and acoustical response of a given structure are codes based on combination of wave and finite element, spectral finite elements, transfer matrix methods and the adoption of stochastic variables. In view of the foreseen work inside the VIPER project, this paper refers to the analysis of the most recent literature and possible initial strategy.

INTRODUCTION

"Quasi-periodicity is the property of a system that displays irregular periodicity. Periodic behaviour is defined as recurring at regular space and time intervals. Quasi-periodic behaviour is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurements": this simple definition is taken from Wikipedia.

It precisely points to the core of the problem. In fact, an increasing literature is appearing on methods for the analysis of a given system by replicating only its elemental cell in space directions and time scale, thus simulating conditions of perfect periodicity. How to simulate systems, if perfect periodic conditions are violated, is still to be analysed together with their influence.

This paper belongs to the VIPER project (http://viper.ec-lyon.fr.) which is fully centred on the vibroacoustic of periodic media. For the periodic structures, the definitions of the effect of quasiperiodicity is to be investigated in order to understand the physics, how this can be modelled and what are the effects of the final design. In fact, it will be important to analyse if and how the presence of imperfections or irregularities, on quasi-periodic bases, can have a significant impact on the vibro-acoustic responses of given components.

It is expected and already shown that the effects on micro-scale can influence the performance on macro-scale: the engineering design can receive important information if more light is shed in this link. Several effects are known in literature (the Anderson localization is one of the most famous) but some insights are now necessary in order to improve the simulations of these kind of problems; to move to prototypes which can demonstrate on experimental basis the achievement of increased vibroacoustic performances (structural damping and/or acoustic transmission loss).

LITERATURE REVIEW

Quasi periodic structures are scattered from those identical cells which has a periodic form in the assembly of a piece of element in the structures. The analysis could be done by the presence of imperfection or irregularity which have a significant impact on the vibrational and acoustic behaviour.

The difference between imperfection or irregularity in a quasi-periodic sequence has to be defined: the importance of this step should not be underestimated.

In [START_REF] Ham | A finite element method enriched for wave propagation problems[END_REF], an enriched finite element method is presented to solve various wave propagations. However, the standard finite element method is not very effective for utilising the solution of the wave propagation problems [START_REF] Harari | A survey of finite element methods for time-harmonic acoustics[END_REF]. The errors introduced in this method have been identified and analysed and they are due to the fact the wave propagation analysis is based on piecewise polynomial approximation: the accuracy of the numerical solution becomes rapidly worse with increasing wave number.

Ref. [START_REF] Cotoni | A statistical energy analysis subsystem formulation using finite element and periodic structure theory[END_REF] and [START_REF] Manconi | Modelling wave propagation in two dimensional structures using finite element analysis[END_REF] are a good example of how the use of periodicity and the Wave and Finite Element can be real enhancements of the predictive quality.

An extension of WFEM is presented in [START_REF] Errico | Application of the Wave Finite Element Approach to the Structural Frequency Response[END_REF]: the actual status of the wave and finite element method has been identified as a best approach for the vibroacoustic analysis over periodic structures. The numerical method has been carried out via Bloch's theorem and imposing periodicity conditions to a single cell which represents a repetitive part of the whole structure. The results show a promising agreement between Wave and Finite Element Method (WFEM) and Classical Finite Element Method (CFEM). Experimental testing and validating comparisons on stiffened cylinders are ongoing at Pasta-Lab.

It has to be remembered that the prototype under research and investigation is a structural component that has characteristics which periodically repeat in one or more directions. In general, a generic structure obtained as an assemble of identical elements, called cells, which can be considered as periodic structures. The modelling of a short section of the waveguide is expressed by supposing time harmonic motion, the equation of motion is implied by discrete coordinates, relating nodal degrees of freedom 𝑞 and force 𝑓 of the undamped section:

(𝐾 -𝜔 2 𝑀)𝑞 = 𝑓 (1)
where 𝐾 and 𝑀 are the stiffness and mass finite element matrices, [START_REF] Manconi | Modelling wave propagation in two dimensional structures using finite element analysis[END_REF][START_REF] Errico | Application of the Wave Finite Element Approach to the Structural Frequency Response[END_REF][START_REF] Moser | Modeling elastic wave propagation in waveguides with the finite element method[END_REF][START_REF] Mencik | Multi-mode propagation and diffusion in structures through finite elements[END_REF][START_REF] Collet | Floquet-bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems[END_REF]. The analysis of periodic systems is thus well undertaken through WFEM. The analysis of transmission and diffusion at joints between waveguides as well as the damped periodical waveguides were investigated in several research works, [START_REF] Mencik | Multi-mode propagation and diffusion in structures through finite elements[END_REF][START_REF] Collet | Floquet-bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems[END_REF].

In [START_REF] Doutres | Impact of the irregular microgeometry of polyurethane foam on the macroscopic acoustic behavior predicted by a unit-cell model[END_REF][START_REF] Ouisse | On the sensitivity analysis of porous materials models[END_REF][START_REF] Petrone | Numerical and experimental investigations on the acoustic power radiated by Aluminum Foam Sandwich panels[END_REF], the first models to take into account the irregularities are presented: they are very recent and represent useful investigations to guide the next required steps.

At the moment, the approach adopted in [START_REF] Cotoni | A statistical energy analysis subsystem formulation using finite element and periodic structure theory[END_REF] seems the most promising for reproducing the forced response of periodic structures in presence of quasi-periodicity and variability effects. The flexibility of getting the K and M matrices from standard finite element codes and the definition of an external post-processing code appears as the most viable procedure even in view of the expected variations to be included for simulating the quasi-periodicity.

STRATEGY

The envisaged steps for facing a such complicated problem are the following:

A. definition of the quasi-periodicity; B. analysis of the nature and sizes of the causes altering the perfect periodicity; C. definition of the required 1. mathematical, 2. numerical and 3. experimental tools.

They are all challenging. In Fig. 1 a sketch of the possible problems/configurations is reported: the perfect periodic system (a) can be altered to get a (b) quasi periodic system in terms of shapes, junctions, sizes, materials, manufacturing issues, etc.; what does quasi mean?

These effects could be evaluated adding each of them on a predictive environment: this will lead to development of a new class of codes expected to be based on a combination of wave and finite element, spectral finite element, transfer matrix methods and the adoption of stochastic variables, if needed. It has to be considered also the possibility to use non-deterministic (possibilistic) algebras as those associated to the fuzzy-logic or the interval algebra.

In literature, it is already shown that a sandwich panel, optimized versus the vibroacoustic performance, with added random properties of the core can exhibit stop-band characteristics in some frequency ranges. Therefore, the analysis of these quasi-periodicity effects is much closer to the engineering application than many others trying to simulate real structures with 3D models with huge computational costs.

  (a). Periodic System, (b). Quasi-Periodic System Figure 1: Sketches of the periodic and quasi-periodic distribution of repeated cells.

ACKNOWLEDGEMENTS

This paper containing the preliminary work carried out in the framework of the VIPER project (VIbroacoustic of PERiodic media). This project has received funding from the European Union's Horizon 2020 research and innovation program under Marie Curie grant agreement No 675441 and it has financed the PhD programme of the 1st author.


Fang Ling

Vincent Goossaert

Actors, Spaces, and Norms in Chinese Transnational Religious Networks: A Case Study of Wenzhou Migrants in France

Gregor Benton has listed six trends of Chinese migration in Europe from early 19th century to the 1950s (Breton 2011:62-64). However, their number was too small to be noticed by the host societies

Introduction

The Chinese diaspora has a long tradition dating back to the nineteenth century and earlier. After China lifted migration restrictions and reopened its gates at the end of the 1970s, the increased flow of Chinese migrants has considerably changed the social landscapes of both their host countries and China itself, while attracting increasing scholarly attention, both Chinese and Western. Scholars analyze this phenomenon from social, historical, educational and political angles and are constructing a panorama of Chinese migrants in the world [START_REF] Kuhn | Chinese Among Others: Emigration in Modern Times[END_REF][START_REF] Hsu | Dreaming of Gold, Dreaming of Home: Transnationalism and Migration Between the United States and South China, 1882-1943[END_REF][START_REF] Xiaoli | Erzhan hou de Dongnanya huaren de haiwai yimin 二戰後東南 亞華人的海外移民[END_REF][START_REF] Lau-Clayton | British Chinese Families: Parenting, Relationships and Childhoods[END_REF][START_REF] Benton | Chinese Migrants and Internationalism: Forgotten histories, 1917-1945[END_REF]. Most of previous studies focused on Chinese communities in America [START_REF] Hsiang-Shui | Chinatown No More: Changing Patterns of Chinese Organizations in Queens (Niuyue huanghou qu xin huaqiao de shehui jiegou 紐約皇后區新華僑的社會結 構)[END_REF][START_REF] Young | Alien Nation: Chinese Migration in the Americas from the Coolie Era through World War II[END_REF][START_REF] Mcclain | Search of Equality: The Chinese Struggle against Discrimination in Nineteenth-Century America[END_REF][START_REF] Zhou | Contemporary Chinese America: Immigration, Ethnicity, and Community Transformation[END_REF] and those in Southeast Asia [START_REF] Freedman | Her Majesty's Stationery Office[END_REF][START_REF] Yih-Yuan | An Immigrant Town:Life in an Qverseas Chinese Community in Southern Malaya (Yige yizhi de shichen: Malaiya huaren shizhen shenghuo de diaocha yanjiu 一個移殖 的市鎮:馬來亞華人市鎮生活的調查研究)[END_REF]Zeng Ling and Zhuang Yingzhang 2000;[START_REF] Alip | The Chinese in Manila[END_REF] where have the largest overseas Chinese communities and their history is among the longest in the oversea Chinese societies. Comparatively speaking, the presence of Chinese migrants in Europe is a recent phenomenon 2 . Only a few exploratory researches can be found on this issue (Breton 2011;[START_REF] Pang | Chineseness' and diversity: an exploratory analysis of second generation Chinese identity in Belgium[END_REF][START_REF] Baldassar | Chinese Migration to Europe: Prato, Italy, and Beyond[END_REF][START_REF] Sanfilippo | Chinese Migration and Economic Relations with Europe[END_REF].

One key aspect of the Chinese diaspora is their religious practices. The religious groups that they organized play a major role in reorganization of the oversea Chinese community and reassertion of their identity vis-à-vis the host country. In recent years, the relationship between globalization and transnational religious networks has drawn growing attention. Thomas Jansen, Thoralf Klein and Christian Meyer's edited volume analyzes the Chinese-Western encounter and the global dimension in Chinese history from social-political perspectives [START_REF] Jansen | Globalization and the Making of Religious Modernity in China: Transnational Religions, Local Agents[END_REF]. That book, however, does not deal with overseas Chinese migrants' religion. For Chinese migrants in Southeast Asia, previous research has highlighted the role of ancestor worship in the reconstruction of migrant identity and the creation of relationships with their native places [START_REF] Hongli | Fujian tongxiang de tongxing zuzhi yu haiwai huaren: Shishi Caishi zongzu ji qi zongqin zuzhi de ge'an yanjiu 福建僑鄉的同姓組織與海外華 人:石獅蔡氏宗族及其宗親組織的個案研究[END_REF][START_REF] Ling | Zushen chongbai Dongnanya huaren yu zujidi wenhua niudai zhi jiangou yi Xinjiapo penglaisi de liuge xingshimiao weili 祖神崇拜:東南亞華 人與祖籍地文化紐帶之建構-以新加坡蓬萊寺的六個姓氏廟為例[END_REF]. As for Chinese migrants in Western countries, most scholarship has centered on Christian communities. Some studies suggest Christianity produces visible and invisible spaces for networks of Chinese Christian migrants in a global-local context (Huang Yuqin and Hsiao I-hsin 2015); others associate network-building with contemporary capitalism and view Chinese transnationalism as a form of modernity [START_REF] Ong | Ungrounded Empires: The Cultural Politics of Modern Chinese Transnationalism[END_REF]. Scholars examine the successful global expansion of Taiwanese Buddhist organizations such as Foguangshan 佛光山 and Tzu Chi Foundation (Ciji gongde hui 慈濟). Their studies converge on two points: first, the globalization of Chinese religious groups, to a great extent, was driven by the growth of Chinese migrants. Second, those Buddhist organizations resort to a trust system to construct their networks [START_REF] Chandler | Globalizing Chinese Culture, Localizing Buddhist Teachings: the Internationalization of Foguangshan[END_REF][START_REF] Huang | Buddhism and its Trust Networks between Taiwan, Malaysia, and the United States[END_REF].

Wenzhou natives represent an integral component of the migration patterns described above, and have made their presence felt worldwide since the 1980s. Their religious practices largely contribute to the construction of their transnational network. This paper aims to analyze the mechanisms of Wenzhou migrants' religious networks through three vectors: Where (places of worship on which religious networks anchor), Who (actors who build and use religious networks), and What (religious knowledge and norms which are imported into communities through religious networks). The author suggests Chinese temples and churches represent a public place for Chinese migrants where they continue to practice their usual religion, even if sometimes most like in a substitutional way, and relive their collective memory. Overseas Chinese communities are thereby related to mainland China and other Chinese cultural countries or regions and are constructing a transnational network. In this network, some groups aim at exporting their value system to spread their influence worldwide and some other groups seek to import a value system for a better internal organization and establishing a hierarchy. The "push and pull" effect makes possible the circulation of religious knowledge and norms which help to structure religious organizations founded by Chinese migrants and create an institutionalized authority for the new elites emerging from new communities.

Historical Context

Wenzhou has a long history of migration. Situated at the border between Zhejiang Province and Fujian Province, migrants from north China, north Zhejiang and south Fujian came settle down in Wenzhou and brought cultural diversity which has created different local identities.

People come in and people come out. Short of agricultural land, Wenzhou has been home to countless emigrants, especially during the modern era. Whether driven by the poverty that ravaged Wenzhou during the 1950s and 1960s, or attracted by the profit of the market economy from the 1990s, Wenzhou natives travel extensively to try their luck. Wherever they go, they perpetuate Wenzhou traditions by building their own communities governed by autonomous regulations. Zhejiang Village in the immediate suburbs of Beijing is a prime example [START_REF] Xiang | Transcending Boundaries. Zhejiangcun : The Story of a Migrant Village in Beijing[END_REF].

The displacement of Wenzhou natives is hardly limited to the interior of China; they cross borders all over the world. France, alongside Italy [START_REF] Baldassar | Chinese Migration to Europe: Prato, Italy, and Beyond[END_REF], Spain, the Netherlands and the United States, is one of their favorite destinations.

The first generation of Wenzhou migrants arrived in France at the beginning of the 20 th century,3 being mainly itinerant merchants from Qingtian. 4 They are said to have gotten rich by selling objects made of Qingtian stone from throughout the Wenzhou region, especially villages bordering on Qingtian such as Yuhu. Those Eldorado rumors and some Qingtian migrants' "coming back home in glory" (yijin huanxiang 衣錦還鄉) conspicuous consumption have stimulated their countrymen to follow in their footsteps and go abroad as China opened its doors toward the end of the 1970s (Li Minghuan 1999:85-86). Several hometowns of overseas Chinese such as Yuhu Village in Wencheng County, Li'ao Village in Rui'an County and Chashan Village in Ouhai District, were created in this way and inhabitants of these villages moved to France in a domino effect. Migrants from Qidu, a village close to Wenzhou harbor, also settled in France. The first generation of Qidu migrants worked as sailors on foreign boats, and this was how they spread around America and Europe.

Due to their frequently being illegal migrants, Wenzhou natives have tended to rely on their families, clans or community networks to get to France en masse, especially before Europe was hit by the financial crisis in 2008. Today, France has between 234,000 and 252,000 Wenzhou migrants, probably the biggest Chinese community in France, although this estimate, made on the basis of the INSEE (the National Institute of Statistics and Economic Studies) data, remains hypothetical (Lucchini 2012:267). The first Wenzhou migrants settled mainly in the 3rd arrondissement 5 in Paris; as time has passed, they are increasingly residing in the Belleville quarter stretching over the 10 th , 11 th , 19 th and 20 th arrondissements and in the department of Seine-Saint-Denis, in particular in the commune of Aubervilliers where the first textile import-export platform is developed with China and other parts of Europe [START_REF] Ji | Territoires migratoires et lieux religieux : cartes des religions des Chinois en Île-de-France[END_REF].

Wenzhou migrants in France mainly work in catering, import-export commerce, and garment-making. Benefiting from a mutual aid system and hard work, most migrants manage to earn a living and even build wealth. Their good performance in the economic realm directly shapes their religious activities. Believing in the principle of do ut des, or "a favor for a favor", Wenzhou religious practitioners never hesitate when it comes to making donations to their groups and enabling them to enhance their economic dynamics. Thus we can observe that during the 1990s the number of Chinese religious groups grew rapidly thanks to believers' donations, a period corresponding to the rising tide of Wenzhou migrants. The economic dynamics of these groups also allows them to propose different activities to their members and keep their independence vis-à-vis other groups. At the same time, control over the money can become a controversial issue sparking increasing internal conflicts results followed by schisms in religious groups (Pan Junliang 2017: 287).

Apart from Wenzhou people in France, there are also Asian migrants from Indochina, generally referred to as "boat people". Many are Chinese descendants and speak Cantonese or/and Chaozhou dialect. They arrived in France around the 1970s, just before the Wenzhou migration tide, to flee from communist persecution. Many live in the 13 th arrondissement, which is called by some Parisians "China Town". From the 1990s, a lot of Dongbei people 6 were driven out by mass unemployment in the region and journeyed to France to try their luck (Li [START_REF] Peilin | La réinsertion professionnelle des « xiagang »: Une enquête dans la province du Liaoning met en évidence l'importance de stages de formation[END_REF][START_REF] Lévy | Entre contraintes et interstices, l'évolution des projets migratoires dans l'espace transnational Une ethnographie des migrants de Chine du Nord à Paris[END_REF]. In recent years, the origins of Chinese migrants coming to France have become increasingly varied, encompassing every corner of China. Without developed community networks like migrants from Wenzhou or Indochina, these new arrivals face considerable difficulties in finding a place in the labor markets for Chinese migrants.

Wenzhou Religious Networks

As Xiang Biao described in his book on Zhejiang Village in Beijing, the functioning of the Wenzhou community is based on interpersonal relationships (guanxi 關係) and 5 Arrondissements is French administrative division that roughly corresponds to a with district. 6 The Dongbei region refers to China's northeast which consists of the three provinces of Liaoning, Jilin and Heilongjiang. Its industrial sector was once powerful, but suffered huge losses in the liberalization and privatization of China's economy after 1990s.

economic dynamics that have developed on the basis of mutual trust (Xiang Biao 2005:2-12,448-489). Indeed, the Wenzhou community in France was created thanks to such interpersonal relationships. As soon as migrants arrived, they were welcomed by relatives who had already settled. It is also thanks to them that these newcomers could find work in the community without difficulty. In family or clan networks, trust is built on bloods bond, but it is not the same when it comes to community or transcommunity networks, although it is often through a close relative or compatriot that a person joins such networks, which then develop due to frequentation, exchange and conviviality. Religious groups are one such platform on which members can build their interpersonal relationships. However, the case of Chinese religious groups in France barely fall into the category of NGOs that Robert Weller and other scholars have explored [START_REF] Weller | Civil Life, Globalization, and Political Change in Asia: Organizing between family and state[END_REF]. Their activities are limited to their community and they have little interaction with local society. Thus they do not represent a substitution or a composition to a civil society. Those groups try to adapt themselves to the political frame, both French and Chinese, but show little, at least not in an obvious way, interest in terms of political claims. They should rather be examined inside the migrants' community and be seen as a form of self-regulation based on a structuring value, such as territory or lineage.

Wenzhou religious groups in France can be roughly divided into two categories: Christian groups and non-Christian groups. In the first category, the earliest Chinese Christian church in France, Eglise évangélique des Chinois à Paris (Jidujiao Bali huaqiao jiaohui 基督教巴黎華僑教會), was created in 1972 and frequented by believers of different origins: Taiwanese, Hong Kongese, overseas Chinese from Indochina and Wenzhou natives. It also was the mother-church of many Chinese churches in France founded by former members who preferred to worship in their own communities. This was the case for the biggest Wenzhou Protestant church, Eglise protestante chinoise de Paris (Jidujiao Bali Wenzhou jiaohui 基督教巴黎溫州教會), which was founded in 1992 and is situated today in the Wenzhou people's most crowded quarter. From then on, the number of Wenzhou Protestant churches has multiplied and now there are nine. These churches are different from each another at certain levels. The Église protestante des Chinois de la Chine du Sud en France (Jidujiao Bali juhuichu 基督徒巴黎聚會處) belongs to Watchman Nee's "Little Flock" tradition (Lian Xi 2010:155-178) and has a particular structure, and organization, as well as its own network, with little cooperation with other Chinese churches in France. The leader of Eglise évangélique (Jidujiao Bali fuyin jiaohui 基 督教巴黎福音教會) comes from a "Little Flock" church, which is why this church keeps some features of this tradition. Another particularity of Eglise évangélique is that almost all its members come from the same church of Qidu village, with common origin making it function like a transplanted church. The Eglise du Renouveau chrétien à Paris (Jidujiao Bali fuxing jiaohui 基督教巴黎復興教會) is a Pentecostal-like church and belongs to an international organization based in Hong Kong, the Revival Christian Church. Nevertheless, it remains independent at economic and operational levels. The Eglise protestante évangélique chinoise de France (Faguo huaren Jidujiao jiuentang 法國華 人基督教救恩堂) was created by a charismatic pastor, Yu Dubing 余督兵, who is famous in Wenzhou. A graduate of Nanjing Union Theological Seminary, he had taken over the presidency of the Yueqing Christian Council before moving to France, and his church has closer relationships with some big Protestant organizations in China. In spite of their particular features and even conflicts (Pan Junliang 2017: 292-293), most of them have set up a common network in order to work together by training young believers and evangelization.

The second category mainly encompasses Buddhist and religious groups professing to be related to Buddhism. The first such associations were created by Taiwanese or Hong Kongese international organizations that were trying to expand their influence among overseas Chinese, such as Foguangshan (Jones 1999:189-198). However, this was not only due to the initiative of these organizations but also that of some overseas believers who needed Buddhist ritual specialists for their daily worship. In the beginning, such believers would contact Buddhist monks from their native regions, but such local temples lacked both international expansion plans and well-organized networks of monks, and could not meet overseas believers' needs. These believers then turned to more institutionalized organizations. On the other hand, Foguangshan's monks move around the world by invitation or conference tours they have organized, which enable them to meet overseas believers and set up plans for creating local temples. Other Taiwanese Buddhist organizations have used similar strategies to try to take root in overseas Chinese communities. For example, Zhongtai Temple (Zhonagtai shan 中台山) has created a branch in Rome with the help of local Wenzhou believers in 2012. Recently, another well-known Chinese Buddhist organization, Longquan Temple (Longquan si 龍 泉寺), whose leader, the monk Xuecheng 學誠, is the president of the Buddhist Association of China, has adopted a similar strategy and created its first overseas branch in Utrecht, Holland, in 2015. Drawn by the reputation and organizational activities of Foguangshan, many rich Wenzhou merchants have joined its French branch, and one of them has taken the presidency of its secular twin: the Buddha's Light International Association in France (Foguanghui 佛光會).

Redemptive societies and other new religious movements rarely benefit from such large-scale financial support from overseas Chinese, since there is a natural tendency to try and maintain the community from within. Their overseas expansion mainly relies on members' personal migration plans. After the members of these groups move to France, they first set up family altars at the homes of believers with sufficient space for staging regular rituals. As their numbers grow, they present to the central committee a petition for building a temple. Once the petition is approved, the information will be announced in a regular meeting and a fund-raising drive launched. In this way, two Yiguandao 一貫 道 branches, namely Miaofa fotang 妙法佛堂 from Taiwan and Linguang fotang 霖光佛 堂 from Hong Kong, a branch from the Zhenfo zong 真佛宗 and a branch from the Guanyin famen 觀音法門 were founded. These groups usually present themselves as "Buddhist Halls" (fotang 佛堂) and are regarded as such by Wenzhou believers, who would go there to worship Buddha and Bodhisattvas when no Chinese Buddhist temples had been established. However, once believers realize the differences between these groups and Buddhist ones, and more Buddhist temples are built, many end up leaving redemptive societies and new religious movements, or just show up occasionally. Today these groups remain more prevalent among Cantonese or Chaozhounese speaking dominated groups.

Belonging to a religious group does not prevent a believer from joining one or several others. The more networks one joins, the more sources one can draw on, be they economic, social or political. Many Wenzhou believers are not limited to one group, a phenomenon particularly common among non-Christian believers who frequent different places of worship following the principle of accumulation as applied to divine protection and good karma. Thus we often see the same Wenzhou believers circulating among Wenzhou Buddhist temples, a pagoda presided over by Cambodian nuns, a Vietnamese Buddhist temple and other Buddhist-related groups. Through these peregrinations, Wenzhou believers multiply their social networks and increase their potential capacity to mobilize the resources.

Among Christians, the affiliation of a believer to one church is more visible. Even though splitting off is not a singular phenomenon, a believer who leaves his/her original church to join another one will be considered inappropriate. Following the same logic, the accumulation of religious networks is also realized at the group level rather than at the individual level, for example when a church joins an international Protestant organization or establishes cooperation with another Church, with the decision of the leaders of a church having much more influence on the extension of networks. It would not be surprising to see a hierarchy created and leading authority established more often in an institutionalized group.

The networks created around religious groups provide essential daily life resources to Wenzhou believers, who share information about housing, jobs, current events in France and news from China. The latter information is particularly valuable for migrants, since they have left their native land and are deprived of parts of their interpersonal networks. Undoubtedly, Wenzhou believers have other networks such as family networks to benefit from common resources, and these networks and religious network overlap to some extent. The affiliation of a believer to a religious group is also a reaffirmation or a recreation of his/her identity as a Qidu, a Wenzhou, or a Chinese. However, religious networks allow them to go beyond their clans and communities to reach resources provided by non-Wenzhou Chinese migrants. Considering that Indochinese and Hong Kongese migrants were followed by Wenzhou people, especially in the economic sector, their experience is precious for later migrants. At the same time, the social networks on which religious groups are based do not necessarily coincide with ethnic networks [START_REF] Nagata | Christianity among Transnational Chinese: Religious versus (Sub)ethnic Affiliation[END_REF], but can represent a complementary component. Such networks enable Wenzhou people to not only renew their bonds with China, but also establish connections with Taiwan, Hong Kong, and Western countries where a Chinese community is present through actions such as training programs, common worship meetings and pilgrimage.

On the other hand, certain religious groups clearly bear their community's marks and tend to be quasi-exclusive. Even some Protestant churches which are supposed to be proselyte show a big difference between their enthusiastic evangelization discourse and their relative lack of action, preferring instead to operate in a relatively closed fashion. The choice of preaching language is a key strategy to define the difference between "us" and "them" and keep the group's solidarity. Another name of Eglise protestante chinoise de Paris, the church of Wenzhou dialect (Wenzhouyu jiaohui 溫州語教會), shows that church's position. Identity becomes a more pressing issue when the second and third generations take over the organization of the church and French identity also needs to be taken into consideration. All in all, people, capital, and information circulate in religious networks that help Wenzhou migrants not only rebuild their identity and adapt to new circumstances, but also to maintain continuous vitality of their communities.

Where: Places of Worship as Anchorages

In Wenzhou, as well as abroad, places of worship represent anchorages from which networks can be established or further consolidated. This is in large part because these sites embody community values and stand for a social dimension. It is in these places of worship that collective memories are revitalized and that new elites strive to exert their influence. It is also through them that institutions, whether official or not, approach a community.

Communal Temples in Wenzhou

In Wenzhou, as in most of the villages of China, community life was previously structured around the worship of local deities. Today, even if other social forms are introduced and the organization of local communities can vary, the symbolic side of their cults remains strong. The birthday ceremony of a local deity often takes the form of an economic or cultural holiday, and is a highly dynamic moment. Moreover, it is on such occasions that communal and individual identities are reaffirmed, and the common values of a community emphasized. The most popular deities in Li'ao, the most important hometown of Wenzhou migrants in France, are Lord Yang (Yang fuye 楊府爺) (Lin [START_REF] Yixiu | La diaspora chinoiseen France : immigration, activités socio-économiques, pratiques socio-culturelle[END_REF] and Chen Shisi furen 陳十四夫人, also known as Lady Linshui (Linshui furen 臨水夫人) (Baptander 2008). The former's temple is situated at the top of the Baiyan hill. A procession in his name is carried out on his birthday annually in the hillside. Three temples are dedicated to the latter with regular plays performed on different religious occasions. It is noteworthy that all these temples have been rebuilt or renovated mainly thanks to overseas the donations of Li'ao migrants.

The interaction between deities follows a conventional procedure of vows (xuyuan 許願) and thanksgiving in case the wish is granted (huanyuan 還願), and can be divided into two stages. In the case of migrants, before departure they go to temples to ask for protection from the gods, since the clandestine road of migration is dangerous and life abroad full of challenges. In order to prevent unpredictable events, they need the advice of a deity. One example is a temple dedicated to Guanyin in Li'ao, reputed to provide effective answers from Guanyin through a dream given to the believer, represents an irreplaceable starting point for future migrants. They spend the night there in the hope of having a dream that gives them a favorable response. There are other temples, including those with divinatory sticks (qianshi 籤詩) deemed effective, which also attract the attendance of future migrants. As for those men and women who are attached to a deity via a ritual form of adoption, they go to see that deity's medium7 . Often believers make a vow concerning their security or their future abroad in the presence of a deity and communicate with the deity via a medium. After the migrant's departure, it is the turn of their families to take care of the remaining rituals; they go to temples to consult the situation of migrants en route. Once believers arrive in France safe and sound, their families will give thanks in return: gifts, big candles, incense sticks or plates of offerings expressing the gratefulness they had promised.

In subsequent years, once the status of migrants has been regularized and they can find time to return to Wenzhou, they are supposed to go to the temples they first worshipped at to present offerings of gratitude in person, thereby completing a series of ritual communications with the gods. The boom of building temples from the 1980s onwards in the migrant centers in Wenzhou would not have been possible without the donations of overseas Wenzhou migrants (Mayfair [START_REF] Yang | Wenzhou moshi zongde liyi jingji "溫州模式中的禮儀經濟[END_REF]. Indeed, in some temples, donations from Wenzhou migrants in Europe constitute more than 70% of construction funds. It is also noteworthy that the bonds between overseas Wenzhou migrants and their hometowns fall into the system of gift and counter-gift. That is one reason why, besides real estate (Zhang Zhicheng 1998:415-416), they have mainly invested in the construction of temples plus the bridges and roads that lead to them.

Even if Wenzhou migrants reside in France, they still maintain their links to local deities in Wenzhou. When they have problems, they ask their families to go to consult these deities. If the responses of the gods involve religious talismans or traditional herbal medicines, their friends or relatives will take care to bring them back from China. Family and friends thus become intermediaries between local deities and a migrant in such a way that the individual, the family, the clan and local society are integrated into an over-arching structure and are united around a common value, one that centers on deity worship. The bonds between a migrant and his family, and between a migrant and the gods, are not weakened because of geographical separation. On the contrary, migration reinforces the relationships of gift and counter-gift between migrants and their families, as well as between migrants and local deities. The end result is that migrants are more indebted to them than ever, and therefore obliged to maintain close ties to both family and local society.

The Fahua Buddhist Temple

At the same time, however, the religious lives of Wenzhou migrants depend not only on links between Wenzhou and France; they also create new places of worship in France like the Fahua Buddhist Temple, which was founded in 2000 by Wenzhou believers. While other Chinese (or Indochinese) migrants created guild halls (huiguan 會 館) or set up sacred sites dedicated to their local deities, Wenzhou believers chose to build their main place of worship as a Buddhist temple. One reason may be that, in modern China, Buddhism has served as a protective umbrella for communal cults accused of fraud or "superstition" (mixin 迷信), although Buddhism itself has at times also participated in attacks on local cults. Buddhism also provided a means for communal cults to be integrated into the system of official religions and eventually escape repression. In Wenzhou, temples to local deities are often referred to as "Buddhist halls" (fotang 佛堂), and their deities called "Buddhas" (Fo 佛). Thus these communal cults are nominally identified with Buddhism. At the same time, Buddhism, a religion of Indian origin, has become a state-approved symbol of religion in China today, with Chinese government discourse presenting Buddhism not only as a source of social stability but also a leading example of the sinicization of a foreign religion, at times even trying to export it to the West. Therefore, it hardly seems surprising that the Wenzhou elites who led the effort to build the Fahua Temple were in contact with and received approval of the Chinese authorities (see below)

The Fahua Temple is officially the center of cultural activities belonging to the Association of Chinese Residing in France (Faguo huaqiao huaren hui 法國華僑華人會, henceforth ACRF), the largest association created by Wenzhou merchants. Today, a Taiwanese Buddhist nun runs the temple and presides over rituals. Believers come chiefly on the first and fifteenth day of each lunar month, as well as mammoth annual festivals such as for the dead and for the Chinese New Year. On New Year's Eve, thousands of believers rush to the temple to burn incense, write their names in a protective lamp (literally "lamp of light" or guangmingdeng 光明燈), or simply eat a bowl of porridge that is supposed to bring good fortune. Wenzhou migrants represent the great majority of believers, and they seek to practice their tradition in a Buddhist setting.

In Wenzhou, it is not uncommon for popular practices to be housed in a Buddhist temple. This is because local forms of Buddhism present themselves as an alternative, even a competitor, for religious functions normally performed by Daoist priests, spirit mediums, and other ritual specialists. Accordingly, one often sees statues of local deities enshrined in a Buddhist temple.

It is in this tradition that the Fahua Temple operates. Its Guanyin Hall is clearly a prime space for Wenzhou migrants in France because of the presence of divinatory tools. Often, after saluting Buddha in the main hall, believers head straight for this one. When a migrant leaves Wenzhou and sets out, and his family in Wenzhou goes to a temple to seek protection and consult his/her situation en route by divination, his/her family in France does the same in the Fahua Temple. They also follow the same procedure of vow-promise and thanksgiving once the migrant has arrived in France.

Apart from the divine answers the Guanyin Hall can provide, the Fahua Temple also responds to other religious needs of its believers, including the "lamps of light" mentioned above being lit provide protection to those who write their names. As for worshippers who want to accumulate good karma, they have to participate in regular rituals. In this functional structure, the Taiwanese nun Ciqing 慈青, plays an essential role. She presides not only at the great annual ceremonies, but is also invited to do geomancy, preside over funeral rituals, and consecrate statues of the deity that believers wish to worship in their homes. Some followers bring their children or grandchildren to the temple and ask the nun to become their master. One striking aspect of such practice is that in Wenzhou this is called "eating rice" (dafanchi 打飯吃), and it is often a spirit medium who plays the role of godfather (or more often godmother). If a child often falls ill and if, according to the result of a divinatory consultation, he/she is advised to "eat rice" from a deity, he/she will be brought to a religious specialist (often a medium) to become an adoptive child of the deity that the medium embodies. The most popular godmother deity in Wenzhou is Fourteenth Lady Chen. Once this has been done, then the child comes regularly to take a bushel of the rice, which is eaten after mixing with rice at home. In the Fahua Temple, whereas the medium is replaced by the Taiwanese nun and the appellation of godmother is replaced by that of master, the function and practice remain remarkably similar.

As a sacred site for Wenzhou migrants in France, the Fahua Temple represents a public space for believers. They meet here on the occasion of regular rituals and communicate information. The Fahua Temple is often the starting point of fundraising to build a temple in China. Through it, migrants are connected as a community to their native land.

Who: Actors

When Wenzhou migrants took the initiative of building a temple, leaders of the ACRF attempted to assume control over this endeavor. They first sought advice from the Chinese Embassy in France, which advised them to create rather a Buddhist temple than a temple dedicated to the local deities of Wenzhou. Therefore, it is clear that the Chinese state exerted some influence over the founding of the Fahua Temple. Moreover, during the consecration of the statues of Buddha and Bodhisattvas, senior officials from the Office of Religious Affairs of China and the Chinese Embassy in France accompanied monks from a prominent Chinese Buddhist temple in attendance. Thus, it seems that, by opting for a Buddhist temple, the leaders of the ACRF chose to embrace a larger Chinese identity as well as that of Wenzhou. This identity corresponds to the leadership's ambitions, since they wish to represent not only Wenzhou migrants but also the entire Chinese community in France. As a result, they seek the support of provincial or even national bodies in China, and to obtain more benefits from these relations. One of the founders of the Fahua Temple, Lin Debiao 林德標, for example, came to France from Li'ao in 1966. He is always keeping a close relationship with his hometown where he donated money to built roads, schools and temples. Lin Debiao took over the presidency of the ACRF in 2005. Soon after, he organized a meeting with the head of Overseas Chinese Affairs Office in China and considered bridging the relationship between China government and Chinese community in France his vocation.

In China, the construction of a temple is often initiated by local elites, and this was is also the case for the Fahua Temple. Nevertheless, Chinese elites in France are no longer the gentry of the past who had studied under the Confucian education system. Instead, many have peasant origins, and were among the first Wenzhou migrants in France. They thus climbed the social ladder by virtue of their seniority and economic prowess, not education. These rich merchants seek to play the same intermediary role between a local community and the state as the gentry used to do during temple construction projects, promoting the temple to the state and taking advantage of the presence of official representatives to increase both the temple's prestige as well as their own symbolic capital. Although the temple is in France, their founders applied to the Chinese state, not the French state, because of their conviction that it is with the former that their status as "elites" will be more valued.

In the case of the Fahua Temple, the Chinese government promoted an institutionalized religion in order to have a channel allowing it to contact and possibly exert its influence over a community. This channel is all the more important when the Chinese government no longer has administrative control over overseas Chinese communities. Rich merchants, on the other hand, in order to gain the support of the Chinese government, have accepted a Buddhist framework for their religious organization, although popular practices are tolerated in the temple as well. These elites also take advantage of the construction of the Fahua Temple to present themselves as representatives of the Chinese community in France, thereby trying to curry more favor from the Chinese government.

While the ACRF is in charge of the economic management of the Fahua Temple, the organization of its religious life is entrusted to the Taiwanese nun who plays an indispensable role. Drawing on links to seminaries and large Buddhist organizations in Taiwan, she has established not only a series of regular rituals to cadence the practices of believers who come to worship the Buddha and Bodhisattvas or practice divination, but has also introduced them to Buddhist theories and practices while creating a system of organization by attributing functions to active members, establishing a hierarchy among believers, and creating rules that regulate the management of the temple. The traditional practices of Wenzhou believers have gradually been integrated into an institutionalized framework with the application of the religious norms brought by the Taiwanese nun without believers losing their Wenzhou identity.

The Fahua Temple case study also merits comparison with Wenzhou migrant Christianity. Processes of institutionalization have been shaping Wenzhou Protestant churches in France in recent years, albeit with somewhat different actors. Most such churches originally lacked a pastor or preacher, something that can be traced to their roots in Wenzhou, where they often organized around a group of lay leaders. During the initial phases of their development in France, Wenzhou churches more or less retained this practice of laymen management. As time progressed, however, Wenzhou churches in France established contact with Protestant churches in Taiwan, Hong Kong, the United States and other western countries. The latter had developed for a long time, and often possessed an institutionalized structure around a pastor as the prime source of authority. These organizations forged international networks through the establishment of branches or cooperation with local churches, while also sending missionaries to help Chinese Protestant migrants to found their own groups or to teach them how to organize their churches. Through such activities, these churches worked to guide Chinese Protestant migrants (including from Wenzhou) as to their religious norms, whether pertaining to the organization of a church or the training of its leaders.

At the same time, some leaders of Wenzhou Protestant churches in France, such as Lin Fuchun 林福春 of Eglise Evangelique Chinoise de France (Jidujiao Faguo huaren jiaohui 基 督 教 法 國 華 人 教 會 ), worked to institutionalize their groups and join international networks of Chinese Protestants. Lin Fuchun was born in Qingtian and moved to France in 1970s. She was converted to Protestantism in 1983 through her husband's family. She was one of the founders of Eglise protestante chinoise de Paris and was in charge of the training of young members. She later left to create her own church, seeking to build a more institutionalized organization. The creation of the branch of the GETS Theological Seminary in Paris in 2004 and that of the International Chinese Biblical Seminary in Spain in 2008 gave these leaders the opportunity to train themselves in theology and church organization. Moreover, at the end of their studies, they could obtain theological and pastoral authority. When these new graduates were ordained pastors or preachers at ceremonies presided over by pastors from Taiwanese, Hong Kong or American Protestant groups, they were henceforth integrated into the international networks of Chinese Protestants. The application of the religious norms proposed by international Chinese Protestant groups encourages the creation of a common network among such churches in France, with the joint worship of some 20 Chinese Protestant groups on January 1, 2015 reflecting a trend towards deeper cooperation. This unprecedented event occurred at the initiative of a group of Protestant churches, many of whose members are of Wenzhou origin. They are very active in organizing trans-church meetings and inviting internationally recognized pastors or preachers to come preach in France.

The profile of Wenzhou Protestants elites also tends to be different from that of the Buddhist elites described above. While the former are also successful merchants, they tend to be younger and better educated. Practicing a deterritorialized religion, they are less attached to their native hometowns and less likely to pursue a Chinese identity. That is the reason why they have approached international Protestant groups and integrated their religious norms into their own groups. By adopting these religious norms, they seek to embody religious authority and rise through the hierarchy of the community.

What: Religious Norms and Structuring

As Julia Huang points out in her article, people travel in the age of globalization and transnationalism [START_REF] Huang | What Travels? Notes on a Globalizing Buddhist Movement from Taiwan[END_REF]. But that is not all. People also travel with material possessions such as money and immaterial possession such as ideas. The circulation of people then goes together with the diffusion of knowledge and norms often from a space where they are developed to another where they are underdeveloped and needed. That is why in the case of religious practices of Chinese migrants in France, Taiwan, Hong Kong and America play the role of the centre of exportation of religious norms. In these countries or regions, without strict state regulation and tight control over religious activities, non-official religious organizations have established their theoretical and practice system and aim for a world expansion against the backdrop of globalization. Among those organizations, Foguangshan and Tzu Chi (Yao Yu-Shuang 2012) have had a great deal of success with global expansion. From 1980s to the present day, Foguangshan and Tzu Chi have founded many overseas branches worldwide [START_REF] Huang | Buddhism and its Trust Networks between Taiwan, Malaysia, and the United States[END_REF][START_REF] Chandler | Globalizing Chinese Culture, Localizing Buddhist Teachings: the Internationalization of Foguangshan[END_REF], including France. Their headquarters in Taiwan oversees every local branch and makes sure coherent organization of local branches' activities. Especially Foguangshan, a Sangha-oriented organization supplemented by a layperson society, the Buddha's Light International Association, regularly sends monks to local temples and manages to generally implement the same religious norms.

However, not only organizations, but also individual actors can convey religious knowledge and norms through contact with others. The Taiwanese nun Ciqing of Fahua Temple was converted to Buddhism and became nun during college. Later, she followed Buddhist education in Fagushan 法鼓山. At the same time, she frequented different Buddhist temples, both big and small and is familiar with their internal organization. When master Ciqing arrived in Fahua temple and began to charge its organization, she also brought what she had learnt and seen in Taiwanese Buddhist temples.

The nun Ciqing created a volunteer group composed by the most active believers to whom she assigns administrative tasks. They are organized in tandem on daily duties such as overseeing temple, cleaning and ensuring daily offerings. Meanwhile, master Ciqing taught them some simple rituals and use of musical instruments that volunteers may carry out the Sunday ritual in her absence and she also arranged volunteers to work in a group of four for regular rituals. By transmitting religious knowledge, the nun Ciqing delegates to volunteers an authority that places them on the top of ordinary believers, particularly on ritual occasions. Not only believers, but also members of ACRF, considered as leaders of Fahua Temple are integrated into the system of rotation. Every week, five members are expected to come to oversee the temple.

Besides the Sunday ritual and those on the first and fifth days of every month, the birthday of Guanyin, Dizang and Buddha's are celebrated. The Chinese New Year and the Ghost Festival are considered as two biggest events at the Fahua Temple. On these occasions, three Taiwanese monks are invited to preside a seven-day ritual.

Furthermore, master Ciqing has also organized pilgrimage-like trips for some active believers, often members of volunteers group, and bought them to Taiwan where they followed a short term training of meditation, recitation and other Buddhist teachings in several Buddhist organizations, especially that of Fagushan. When returning from pilgrimage, these volunteers share their experience and the religious knowledge that they have learnt with other believers and in return gain a kind of prestige. Thereafter, they are expected to lead ordinary believers in regular rituals.

For Protestant organizations, we find a globalization pattern quite different from that of their Buddhist counterparts. Like Buddhism, Taiwanese, Hong Kongese and American protestant organizations have exerted a great influence in Chinese churches in France. Chinese Overseas Christian Mission, Chinese Coordination Centre of World Evangelism and Evangelical Formosan Church have helped Chinese Protestants in France to create their own churches and paved the way for further development of local Protestantism. Nevertheless, except for two churches, the True Jesus Church and the Evangelical Mission and Seminary International, none of these Protestant organizations seem to have sought to construct a transnational network by founding local branches worldwide. Instead, they choose to send their missionaries to carry out evangelization work in countries where a Chinese community is settled and train local Chinese Protestants who then became their spokesperson.

The most significant and visible work that these transnational Protestant organizations have achieved is the foundation of two Chinese seminaries, the GETS Theological Seminary in Paris and the International Chinese Biblical Seminary in Europe in Spain, as I have showed above. The creation of the GETS Theological Seminary would not be possible without the initiative and efforts of the pastor Zhou Shuhui and the support of her institution, Evangelical Formosan Church while we attribute the foundation of the International Chinese Biblical Seminary to a charismatic Taiwanese Protestant, Wu Yong, who had created several missionary organizations. Meanwhile, these two seminaries maintain a close cooperation thanks to their founders' network with others Taiwanese seminaries, such as Taiwan Theological College and Seminary, China Evangelical Seminary, LOGOS Evangelical Seminary in Taiwan, Christ's Disciples Training Seminary and Chinese Christian Church Mission Association which provide them with experienced teachers and administrative staff. The GETS Theological Seminary has also joined the Asia Theological Association and received the official certificate of accreditation from ATA.

Based on the general pattern of Taiwanese seminary, these two Chinese seminaries in Europe offer various degree programs. The International Chinese Biblical Seminary in Europe is principally dedicated to pastoral training whereas the GETS Theological Seminary is more developed and complete and offers both research-oriented degrees such as Master of Arts in Christian Studies, Bachelor and Master of Theology and Doctor of Philosophy, and ministry-oriented degrees such as Diploma of Pastoral Studies.

The creation of these Chinese Protestant seminaries represents a win-win game for both Chinese Protestants leaders in France and Taiwanese transnational Protestant organizations. On the one hand, thanks to the development of Internet, it is increasingly easier to find information on Protestantism. The old type of authority, often based on seniority, is facing challenge. The training that these seminaries offered enables Chinese Protestants leaders in France to gain, by the end of their program, a kind of theological authority generally acknowledged in the Protestant world. At the same time, the training allows them to integrate themselves into the general Protestant hierarchy once they are ordained as pastors. On the other hand, Taiwanese transnational Protestant organizations do not need to risk creating a pricey and unsuccessful overseas branch. By offering pastoral training, they manage to attract new Protestant elites and can henceforth exert an indirect influence through their graduates. When those graduates use the religious norms that they have learnt in seminary to structure their own churches, they share the same value system with ones who taught them, which reinforces the relationship between local Chinese churches in France and Taiwanese transnational organizations. Certain local graduates such as Lin Fuchun from Eglise Evagelique Chinoise de France have even been integrated into the management of the GETS Theological Seminary. Their churches thus became knots in the global network of these Taiwanese Protestant organizations.

Conclusion

With the increased flow of Chinese migrants in Western countries, an unprecedented major social phenomenon is emerging. If we choose to view a network as consisting of a set of actors and nodes along with a set of ties of a specified type that link them [START_REF] Borgatti | On Network Theory[END_REF]Halgin 2011:1169), then the circulation of capital, people, knowledge, texts and norms situate China and Chinese communities residing abroad in a religious continuum, regardless of whether it concerns a practitioner or place of worship (Yang Fenggang 2002:130). Situated in this continuum, overseas Chinese migrants like those from Wenzhou continue to preserve as well as reinvent their traditions, but also need to reorganize their community to adapt themselves to new circumstances. They abide by a traditional system of values or adopt a new one. A variety of actors are engaged in this process including states or their agents, international organizations, as well as moral or religious authorities.

Whereas China always represents political appeal for traditional territorial organizations such as guild halls, overseas religious groups generally turn to Taiwan, Hong Kong or America to learn religious norms. Some groups are even exporting to China religious norms that they have learnt, because few religious organizations are able to develop a fully institutional form under strict governmental control. Furthermore, most of religious organizations are content with their local development and barely have the intention of spreading outside China. It is also possible that they hesitate to do so to avoid catching the government's attention. Only organizations with certain official backing are expanding to the overseas, which is in line with the Chinese government's project to export ideology. When a Wenzhou migrant in Netherlands, Hu Zhiguang 胡 志光, asked Longquan Temple to send monks for regular residence in the temple that he, with the support of other Chinese migrants in Netherlands, built in Utrecht, the abbot of Longquan Temple and president of the Buddhist Association of China responded favorably to Hu's request. The first overseas branch of Longquan Temple, the Longquan Great Compassion Temple (Longquan dabeisi 龍泉大悲寺) was thus founded in 2015 with monks Xuecheng sent in charge of the daily organization of the temple. However, if we take a close look at evangelization strategy and the organization form of Longquan dabei Temple, we see they are, at least partly, inspired by Taiwanese Buddhist transnational organizations, especially Foguangshan.

The predominant place of Taiwan in exporting religious norms makes that island a "sacred site" for Chinese migrants in France. Leaders or active members of Buddhist groups, Protestant churches and Redemptive Societies such as Yiguandao and Mile dadao 彌勒大道 all regularly make pilgrimage to Taiwan to follow advanced training. In Tzu Chi, for instance, this kind of training gives participants a feeling of being part of an elite. When they return to France, they are expected to transmit the knowledge that they have learnt and lead the daily ritual. Thereby active members work their way up through the hierarchy in the group. Meanwhile, the pilgrimage to Taiwan enables participants to learn the fundamental value of their group: charisma of the founder, the history of the group and their headquarter.

But the religious adherence does not eclipse ethnic identification. Members of Chinese religious organizations in France, both Buddhism and Protestantism, are almost purely Chinese. Thus, Chinese identity remains the most encompassing label to attract followers and transnational organizations often play this ethnic card because it is the main channel through which they can approach their communities as a whole.

In short, the shaping of a migrant community is directed towards both native place identity as well as transnational institutionalization, blending the intervention of external forces such as the state and major international organizations, as well as internal forces such as the agendas of elites and average worshippers. All of these actors seek to impose standards that are favorable to them in terms of exerting influence. It is in this game of competing strengths that the community finds its way of development.

For more on the history of Chinese immigrants in France, see Yu-Sion Live 1991; Ma Li 2012. For studies on Wenzhou immigrants in France, see[START_REF] Poisson | Franchir les frontières : le cas des Chinois du Zhejiang en diaspora[END_REF][START_REF] Guerassimoff | The New Chinese Migrants in France[END_REF]

Before 1963, when it became a county of Lishui, Qingtian had been for its entire history part of Wenzhou. Many of Qingtian people understand and speak Wenzhou dialect.

For studies on Wenzhou mediums, see[START_REF] Yang | Shamanism and Spirit Possession in Chinese Modernity: Some Preliminary Reflections on a Gendered Religiosity of the Body[END_REF]

1 This paper is result of the research project "La