Jean Noel Capdevielle

Fabrice Cohen

Barbara Szabelska

Jacek Szabelski

The primary energy estimation of inclined giant EAS

Determination of the primary energy by surface arrays (like AGASA) through estimators (instead of total size), taken as densities at 600 m from the shower axis, needs a special procedure for inclined cascades when the maximum is close to the array (less than 2-3 radiation lengths above). According to the cascade theory and the simulations with the CORSIKA code above 10 EeV the exponential function used for ¢¡ ¤£ ¦¥ §¥ ©¨c onversion from inclined to vertical showers is no longer valid. As follows from simulations at energies near to 100 EeV, the density at 600 m for zenith angles 25-35 exceeds by 10% the vertical density, whereas it was assumed to be 30% lower in the previous treatments. Such treatments generate an artificial increase in the estimation of the primary cosmic ray energy. The primary spectrum reconstructed by an appropriate procedure for inclined showers confirms GZK prediction and eliminates the divergence between measurements at ultra-high energies.

I. INTRODUCTION

An important discrepancy in the determination of the primary energy spectrum above 10 eV was underlined in 2001 [1] between the data of HiRes collected by the atmospheric fluorescence and the data accumulated by the very large surface array of AGASA. The results of HiRes based on the registration of the longitudinal development exhibited a tendency in agreement with GZK prediction. This tendency is confirmed by the recent compilation of HiRes 1, 2 and HiRes stereo [2]. Last year we pointed out [START_REF] Capdevielle | Proc. 29£ ¥¤ ICRC[END_REF], [START_REF] Capdevielle | [END_REF] that the primary energy in the surface array was mainly overestimated by reason of an inappropriate conversion of the energy estimation, i.e. the density, "! $# to the vertical density % % & (' &) §# , for giant inclined showers. Recently, the group of AGASA has reduced the intensity of ultra-high energy [5] and a new calibration of the raw data is in progress in the direction of a more complete reduction. We review here the problem of energy estimation for inclined showers taking into account the results of our simulations. A general method suitable for the scientific problems related to the absorption versus zenith angle above 10 0 eV is proposed.

II. APPROACH OF THE PRIMARY ENERGY FROM THE SIZE

1

IN AKENO

The arrangement of scintillators in original Akeno air shower experiment [6] was covered over an approximate area of 1 km2 and was characterized by a general spacing of 120 m. The configuration of detectors was reduced to 30 m in 3 regions, each of area (3 ' 54 63 ' # m2 . The configuration of 1 km2 included a total of 156 scintillators with 1 m2 area to measure the differential size spectrum 7 8 1 # at 920 gcm9 @2 and to derive the primary flux 7 8 (A # up to B §' C 0D FE D eV. The lateral distribution of charged particles used in Akeno [6] for very large shower is the sum of one pair of NKG functions and the size 1 is derived from the densities by integration over the area.

The size is then converted to the primary energy for (B ¦' HG 1 G B ¦' I ) following [6]:

P A (Q FR S# 8T VU XW 3 54 YB §' 0`4 a 1 B §' ¢b E W (1)
We have verified that this relation applied for vertical showers coincides with the results of CORSIKA [START_REF] Heck | FZK. The CORSIKA Air Shower Simulation Program[END_REF] (version 6.16, proton primaries, QGSJET model [START_REF] Kalmykov | [END_REF]) within c &d around B ¦' ¢ 0D

eV [9].

In the case of inclined showers, an average attenuation length can be expressed by e gf = 204 gcm9 @2 for a zenith angle ! G ih &p ) and the relation between inclined and vertical size for the same primary particle energy can be written as:

1 "! $# 8T 1 (' # q4 6Q sr ut a wv (x v x # e f b (2) with x yT x © § © "! $# and x = 920 gcm9 2 . This attenuation length is also in agreement with the longitudinal development calculated with CORSIKA [10], [9]. After correction for the dispersion in zenith angle determination, the fluxes plotted in Fig. 1 have been obtained and expressed by a power law:

7 8 (A # 8T V 4 a A A b 9 @ W (3)
This method was applied to events with energy up to p B §' ¢ D eV.

III. APPROACH OF THE PRIMARY COSMIC RAY SPECTRUM FROM THE DENSITIES IN GIANT SURFACE ARRAYS

A. Charged particle densities and scintillator arrays

The 20 km2 array (Array 20) which was constructed before the AGASA experiment, consisted of 19 detectors (individual area of the detector 2.25 m2 ), separated by about 1 km from each other. The array involved 4 detectors inside the 1 km2 area of Akeno. The registration of giant EAS with very large distances between the detectors gives statistically more chances to record low densities at large distance from the core. Furthermore, the detectors inside about 2 Moliere radii from the axis are usually saturated. The Particle Data Group (PDG) estimates that 1% only of the cascade energy lies outside a cylinder of 3.5 Moliere radii [11]. A direct access to the total size 1 from the densities becomes hopeless and a common procedure, the conversion of the density near 600 m from the axis, was introduced as a preliminary energy estimator [START_REF] Hillas | Proc.12£ ¦¤ ICRC[END_REF]. This method is very sensitive to axis localization accuracy, as the lateral distribution is decreasing rapidly with distance [START_REF] Capdevielle | [END_REF]. In such context, the lateral distribution for the Array 20 has been selected as follows [START_REF] Nagano | [END_REF]:

¡ £¢ # T 1 ¥¤ f §¦ 9 ©¨ 0B ¦ # 9 ©9 B ¢ c ' ' I' ! 9 E ` (4)
( ¤ f being a normalization constant). This analytic description with a fixed value " = 1.2, without reference to the age parameter is used to determine the shower axis and to interpolate the value of the density at 600 m. In contrast to the size conversion in Array 1, the scintillator response in terms of density # is here converted to the primary energy following:

P A 2 ¤Q §R $# T c uW ' B §' %$ 4 &# # E W (5)
This energy estimation takes into account the relation between # and ¡ (' I' ' # following calibrations with the arrays of Haverah Park and Yakutsk [START_REF] Dai | [END_REF]. The quantity # £¢ # can be related to the electron and muon densities [14] following: T B IW B and from comparison of scintillator densities to spark chamber densities as 1 B (¢ # 5T B W B . This last value was underestimated at large distances and a value of 1.4 has to be taken at 600 m from the axis [14]. From a set of 40 vertical showers simulated with CORSIKA (proton primaries, GHEISHA option) at 10 D eV, we obtain at 600 m the average electron and muon densities of 3.3 and 1.2 respectively. The value 1 ) (¢ # qT iB W C has been obtained from the muon densities recorded for A ) RD B SF TH at 600 m distance by the muon detectors contained in Array 20. Taking into account the energy thresholds for electrons and muons in CORSIKA (1.5 and 300 MeV respectively), we have inserted in formula 6 f and ) for 600 m, attributing to 1 ) (' ' I' # a value 1.4 (given by our muon energy spectrum from CORSIKA [9]). This conversion by formula 6 in those conditions appears to overestimate the primary energy by about 20%, even if we select the FLUKA or UrQMD options of CORSIKA [9], [START_REF] Drescher | Proc. 28£ ¦¤ ICRC, Tsukuba[END_REF], which are more favourable than the GHEISHA option. The average electron and muon densities from CORSIKA return here via relation (5) A T B W c ' B §' C 0D eV, respectively B IW B §3 B §' C 0D eV for Fluka, instead of the primary energy A T B §' C 0D eV set in our simulation. In other words, we received from our simulation (CORSIKA, option UrQMD) an average density # = 6.0 from equation (6) involving the average electron and muon densities calculated, when # % % = 5.0 was expected according to the conversion of Array 20; this minimal overestimation of the primary energy by about 20% remains approximately constant up to B §' &2 eV by reason of the quasi- linear dependence of # on # % .

# £¢ # T ¡ f £¢ # ¡ 0) (¢ # 21 ) £¢ # #

B. Energy estimators for giant EAS

In place of the size spectrum, the # % % differential spectrum in Array 20 is obtained taking an attenuation length e g % in parallel to e f in Array 1 following:

# w % % & ! $# T P# w C (' # q4 6Q sr ut a wv (x v x # e % % b W (7)
A constant value e = 500 gcm9 @2 was assumed according to the best fit value on the zenith angle distribution for constant # % % adjusted by the simulations [START_REF] Dai | [END_REF] for different e % . This conversion used in the Akeno 20 array [START_REF] Nagano | [END_REF] was considered as valid up to ¦ © ! $# T B IW h . The determination of the attenuation curve of # % % by the method of "equal intensity cuts", including experimental data recorded for showers with larger zenith angles (up to 60) ), demonstrated later significant deviations for ¦ © ! $# U B IW h . An improved and more general conversion (valid also for § © "! $# §U B W h was inferred by fitting the attenuation of # % up to § © "! $# T iB W ¡ [17] represented by: 8) with e 2 = 594¢ 2 D 9 ¤£ gcm9 2 .

# "! $# 8T P# ' # 4 Q sr ut a wv x e ¦ © "! $# v B ©# v x e 2 ¦ ¦ ! $# v B ¦# 2 b (
This relation 8 was finally used in the treatment of AGASA data with e = 500 gcm9 2 [18], introducing minor changes for § © "! $# ¦¥ B W h .

IV. # "! $# VERSUS # % (' &# WITH CORSIKA ABOVE B §' & EV A. Simulations
Simulations with CORSIKA code have been performed for gammas, protons and iron nuclei as primary particles for 6 energies and in most cases for 8 different zenith angles. The observation level corresponded to the Auger experiment. 40 EAS have been simulated for each combination of primary particle, energy and zenith angle [10]. From simulations we have obtained the total number of particles in EAS at observation level

1 ¨ § © §
as a function of zenith angle ! for gammas (energy above 2 MeV), electrons-positrons, and muons.

§ © ¤ §

was estimated in the CORSIKA program using fits to longitudinal development. We used these estimations present in results of simulations. Presented here values are average numbers from 40 EAS.

In the Fig. 2 we present 1 § © § ( ¢ 9 only) as a function of ¦ ¦ ! $# for each primary particle type. The energies of primary particles are indicated. The dashed line is proportional to AGASA conversion of particle density at 600 m from zenith angle ! to the corresponding value for vertical shower (formula 7).

B. Fit with distorted gaussian function

We have pointed out [START_REF] Capdevielle | Proc. 29£ ¥¤ ICRC[END_REF] AGASA would be obtained with a model of modest multiplicity such as HDPM). For a model with large multiplicity, such as QGSJET2, the same maximum is near 3 electron radiation lengths above AGASA and the total discrepancy is slightly reduced but still appreciable (Fig. 3). This typical behavior can be described analytically by the so called distorted gaussian Total number of particles ( ) in EAS versus ! #" %$ '& )( for primary photon, proton and iron. Primary energies are indicated. The broken line is Akeno formula 2 for 0 1$ '& )( with normalization to 0 1$ 32 4( = 10 5 6 . function: where:

7 8 # T i4 6Q sr ut a 1 C v @9 c v B h c 1 ¢# 9 2 B ' @9 £ B c h 1
8 wT ¦ © ! $# , 9 T 8 v ¥ 8 U # $# &% , % w2 T ¨¥ 8 (2 U v ¥ 8 U 2 T ¨¥ 8 v ¥ 8 U # £ U '# &% £ skewness 1 5T ¨¥ 8 v ¥ 8 U # A U '# (% A kurtosis
Values of parameters in formula 9 for different energies are summarized in the Table I for the interaction models with low multiplicity and in the Table II for interaction models with high multiplicity.

The depths of the experimental array taken in the calculations are respectively 860 gcm9 @2 for AUGER and 920 gcm9 2

for AGASA. The dependence shown in the Fig. 3 is a general consequence of the electromagnetic cascade theory. This can be illustrated easily, at least quantitatively by the behavior of NKG curves just after maximum for U B , as shown a long time ago [START_REF] Cocconi | Cosmic Rays[END_REF].

Even if the total size decreases, for small densities, at about 2 Moliere radii from axis for showers of B §' GeV recorded, for instance at Chacaltaya, the density will increase with zenith angle before decreasing above U I' C) . In our simulation with CORSIKA, in spite of the limits of validity of cascade theory (we are dealing with distances of about 7 Moliere radii), those comparable consequences result from the effect of the multiple Coulomb scattering as decribed in EGS and implemented in CORSIKA.

V. INDUCED DIVERGENCE IN THE PRIMARY SPECTRUM

We have simulated several groups of two millions of EAS above B ¦' & D eV with an A 59 £ spectrum and examined the reconstruction following the procedure used by AGASA. Both primary energy and zenith angle are generated. The vertical density at 600 m from the axis is first sampled from the distribution derived from our CORSIKA data bank. This density is transformed to density # "! $# by interpolation on the primary energy in relation 9. This density is then converted to # w % % C (' &# following the treatment of AGASA through the formula 8 from zenith angle ! to the corresponding value for vertical shower (formula 8). In the last step, the primary energy A (in eV) is recovered with the conversion of AGASA [5]:

A T B W 3 4' B §' 0 4 a # w % % & (' &# B §' I' b E 2 (10)
For both configurations of Fig. 3, the divergence at ultra high energy introduced artificially in the primary spectrum can be ascertained (Fig. 4) In both parts of the Fig. 4 we present the same results on the reconstructed spectrum: in the upper part differential intensity multiplied by A £ and in the lower part differential intensity. In both cases a cut off at B §' &2 eV has been introduced in the II), those proportions are slightly reduced, respectively to 36% and 44%. Despite the suppression of the energy generation above 100 EeV, the simulation shows that the treatment of AGASA artificially generates events up to 200 EeV. With additive fluctuations (uncertainty in axis localisation, fluctuations of detector's responses...), we have ascertained that this bias at ultra high energy could even increase. An extended simulation of 200 million showers without upper energy cut off confirmed those features as shown in the Fig. 5. Turning to a more actual generation procedure, we have selected the spectrum described by 3 power laws introduced by Bergman [START_REF] Bergman | Proc. 28£ ¦¤ ICRC, Tsukuba[END_REF]; the results of the Monte Carlo generation are displayed on the lower part of Fig. 5 and they reflect a discrepancy exhibiting several similarities with the experimental polemics between AGASA and HiRes. and red triangles show AGASA spectrum [2]. Lower histogram is the CR energy spectrum generated from 4E distribution without energy cut off with 1000 events above 10 5 eV and normalized to HiRes spectrum at 10 5 eV. Upper histogram was obtained from events generated assuming isotropy (& 0 ¡ 2 ) and AGASA method: eq. 5, top Figure 3 and Table I.

Lower part: Bergman's [START_REF] Bergman | Proc. 28£ ¦¤ ICRC, Tsukuba[END_REF] spectrum with 3 power laws (grey band) was used for generation limited to 1000 events above 10 5 eV. Normalization to Bergman's spectrum was applied to lower histogram. Upper histogram was obtained using AGASA method.

Again, in the 3 parts of this spectrum (3 power laws with an exponent iT U ¢W B ¦c c ¢W C 4' p W respectively for ¡ £¢ ¥¤ w (A # G B GC ¢W h G B ¦3 ¢W 3 and D B ¦3 ¢W 3 ), the energy overestimation is also generated in a proportion similar to the discrepancy between AGASA and HiRes in Fig. 1.

VI. DISCUSSION

A. Earliest discrepancies between Akeno and AGASA

The intensity excess by a factor 1.5 of the primary spectrum obtained with Array 20 in the overlapping region when compared to Akeno (the corresponding points are plotted in Fig. 1, together with the best fit following the adjustment [START_REF] Nagano | [END_REF]) was immediately explained by the different methods used for the primary energy reconstruction in each array. A discrepancy by a factor 1.15 in the primary energy derived from equation 5 instead of equation 1 was pointed out and considered as in agreement with the energy determination via # in the experiments of Haverah Park and Yakutsk. Those ambiguities have been treated later [18] in terms of systematic errors on detectors response versus zenith angle, seasonal variance and other complex problems related to the shower selection and the collecting area. The more recent values reported by AGASA [START_REF] Takeda | ), 28£ ¦¤ ICRC[END_REF] are closer to the values of Akeno than the values of Array 20 (Fig. 1); the intensities of AGASA remain, however, larger than for Array 1 in the overlapping energy region and exhibit a general excess by 30% when compared to HiRes Stereo data.

B. Attenuation length for the energy estimator

From our simulation data, we have derived the values of the attenuation length e for different zenith angles (Fig. 2); for small inclinations ! G U I' &) the values of the attenuation length concerning proton primaries are quite more important than the average value e % % 5T p ' I' gcm9 2 used in AGASA.

When the primary energy is increasing, the depth of the maximum becomes more and more close in altitude to the arrays, such as AUGER or AGASA: the conversion of inclined densities to # w % (' &# according to equation 8 becomes poorly appropriate as the cascade is far from a stable absorption phase, especially for proton primaries. In the depth interval of about 5 radiation units following the maximum, we can summarize the absorption process as follows:

¦ the total size 1 is decreasing slowly versus the atmospheric depth x ¦ the age parameter increases in parallel from 1.0 up to 1.2 ¦ the lateral distribution around 600 m from the axis becomes flatter [9] The increase of the flattening of the density distribution turns to a systematic overestimation (via relation 8) of the vertical density which influences the primary energy. The shower recorded might be classified in bins of larger energy.

The values of e q % derived from lines presented in the Fig. 6 will increase for energies lower than c B ¦' u 0 eV (at higher energy there is no more classical exponential absorption). The experimental points in the Fig. 6 suggest indeed at the highest energy the suppression of the absorption with a maximum of # % against ! resulting from the method of the constant intensity cuts. The overestimation of the primary energy from the densities converted by formula 8, using 500 gcm9 2 instead of 2000 gcm9 @2 in the overlapping region for ! T c ' C) is about 10%. The adaptation of the conversion of the densities of inclined showers, the ambiguities on the scintillator response and the relation 8 can probably explain the discrepancies of 30% between HiRes and AGASA (Fig. 1) for energies below c B ¦' & eV.

Above U ¢W p B §' C eV a clear divergence in the discrepancies between AGASA and HiRes Stereo appears rising from 150%

to above 300% at ' B §' C eV. This may come again from the lateral distribution becoming flatter more rapidly than the reduction of the total size: the net result is that the densities (at 600 m) are 5-10% larger in the bin ! T c ' ) v U ' ) than the vertical density when the atmospheric depth separating the array and the shower maximum becomes lower than 3 cascade units. Additionally the inaccuracy of position of shower axis determination can contribute here [START_REF] Capdevielle | [END_REF] as the relation 4 is constant in the central part (" is fixed to 1.2), with consequences on the estimator # .

C. Influence of the primary composition

Relation of the # w % estimator versus zenith angle in the neighbourhood of the maximum is complex and depends also on the primary composition. In the for the water Cerenkov tanks. The conversion to the primary energy for scintillators is then comparable for protons and heavy primaries only near U I' C) ; the relation 8 provides an inappropriate description for the absorption generating an energy overestimation for protons in the band B §' u) -h ' ) and a constant overestimation up to U I' C) for iron primaries.

On the contrary the error on the localizations of the estimators at 800 m or 1000 m do not change the situation for a heavy primary component; (' &# and 9 ¥ f (' # are increasing similarly, by 26% and 30% respectively at each distance, when passing from proton to iron. (Those values are obtained from the respective densities at axis distances of 800 m and 1000 m).

Furthermore, for iron, s and 9 f do not depend on ! up to U I' ) .

In the case of protons, the maximal enhancement near U I' ¢)

appears reduced at 800 m from the axis (11% for both s and 9 f instead of 26% at 1000 m). For giant showers and detectors separation by 1000 m or more, the accuracy on the density interpolation might be improved (a larger number of detectors hit are located at distances lower than 800 m) and there could be some advantages to move the estimator at 800 m.

D. How to amend AGASA data?

It is difficult to trace back the characteristics of the showers used to build the primary spectrum presented by AGASA. An experimental zenith angle distribution is needed after correction of all possible bias. At ultra high energy, due to the low statistics and corrections being still in progress, it is not available. To illustrate an approach of rescaling the data, we have generated a primary spectrum following one analytic description commonly used by the group of AGASA [18]: the differential spectrum is approximated by two power laws, as in equation 3 with a first exponent T U ¢W c for A G B ¦' & eV and a second exponent 2 T c ¢W U at larger energies (Fig. 7). For each primary energy generated, the vertical density is derived via relation 10; the angle ! is then generated randomly inside h &p ) (we underline that this step is a pure assumption neglecting the registration conditions and non adapted to the low statistics of events at ultra high energy).

The corresponding # "! $# is then derived by relation 8 with a statistic weight "! $# taking into account the size of the elementary solid angle. The assumed correct energy (obtained via relation 9) is then sorted in the adequate energy bin. The corrections near to B ¦' &2 eV would reach a factor of reduction by 7-10, if we consider a large number of showers in each energy bin converted by our procedure. This procedure is not valid for a limited number of showers and the experimental data must be sorted again in the convenient bins of energy and zenith angle event per event. Such work can be performed correctly only with the raw data of the experimentators.

Revision is now in progress by AGASA group [5] going along formula 8, as previously suggested by us [START_REF] Capdevielle | Proc. 29£ ¥¤ ICRC[END_REF], [START_REF] Capdevielle | [END_REF]. Half of the events above 100 EeV have been already rejected [5] and the present intensities look more close to the measurements of HiRes.

A very speculative solution to the problem is shown in the Fig. 8. AGASA energy spectrum from the Fig. 1 has been repositioned bin by bin according to the factors obtained from the Fig. 7. The oversimplifications of the procedure could make dubious the claim of a quantitative correction of AGASA spectrum and we exhibit hereafter a simple tendency of the reduction expected. Conserving in mind the limits and weak points of the statistical treatment, we observe, however, a reasonable and encouraging tendency...

VII. CONCLUSION

An impressive data of high quality has been collected in AGASA. Further simulations with CORSIKA, even with fastened versions (hybrid Monte carlo and analytic codes) to estimate more carefully the array response with a huge statistics, completed by simulations with GEANT for the scintillator response and carried in close contact with the experiment, may help to clarify in detail the discrepancies between the surface arrays and the fluorescence observatories. The present approach points out a better consistency between the spectra obtained by classical size measurements and HiRes Stereo measurements, but also the possibility to amend the AGASA spectrum by an adequate procedure determining the primary energy of inclined showers. This tendency favours the GZK prediction and after a suitable correction of AGASA data, a general convergence towards the GZK prediction can be expected. New estimations of the attenuation length by the classical approach of the constant intensity cuts method (applied on larger statistics at UHE in AGASA) and also on the hybrid showers in AUGER will be useful to improve definitely the energy calibration of giant surface arrays.

We note also that a heavy composition will reduce the problems of inclined showers in AGASA, but will still be in conflict with the fluctuations of 3 ¢¡ measured with the Fly's Eye [START_REF] Sokolsky | [END_REF], [30].

Fig. 1 .

 1 Fig. 1. Differential primary spectrum for Array 1 (Akeno), Array 20, AGASA and HiRes Stereo experiments. Array 1 or Akeno (full squares) concerns the data of the 1 km array before 1992. Array 20 (open squares) concerns the earliest data of the 20 km array. AGASA (full triangles) is the data of the 100 km array in 2003 and HiRes Stereo labels the Stereo data in 2003 (open triangles). Also shown are the fitted spectra, for Akeno (full line) and Array 20 (dashed line). For the clarity of the graph, the error bars are not plotted for AGASA data.

  from the total data simulated above B §' eV, an important change of the behavior of # "! $# versus § © "! $# . Instead of the classical decrease of the absorption regime of relation 8, the density increases progressively in function of the primary energy versus ¦ ¦ ! $# reaching a maximum between B §' v c ' C) and then decreases with zenith angle as shown in Fig. 3 for primary protons for A T B §' I p u B §' §B §' & p u B §' & §B §' C % GeV. Such situation in the case of AUGER corresponds to a maximum depth of the longitudinal development at about one electron radiation length (for A T B §' & GeV) above the experimental array (a similar situation in

  Fig.2. Total number of particles ( ) in EAS versus ! #" %$ '& )( for primary photon, proton and iron. Primary energies are indicated. The broken line is Akeno formula 2 for 0 1$ '& )( with normalization to 0 1$ 32 4( = 10 5 6 .

Fig. 4 .

 4 Fig. 4. Differential energy spectrum generated as 4E for &! 2 C showers (on lower histogram with dotted line) and reconstructed respectively for interaction models of high multiplicity and low multiplicity. The upper histogram (dashed line) corresponds to theTable I (solid line), associated to the Table II is in the middle.

Fig. 5 .

 5 Fig.5. Upper part: black circles are HiRes-2 Monocular energy spectrum[2] and red triangles show AGASA spectrum[2]. Lower histogram is the CR

Fig. 6 .

 6 Fig. 6. Attenuation length of § C 6 6 for & 2 ©¨ 2 compared to the earliest measurements (method of constant intensity cuts) and description of AGASA [17].

Fig. 7 .

 7 Fig. 7. Upper part: Intensity multiplied by 4E generated for AGASA spectrum fitted with 2 power laws (dotted line) and amended (solid line). Lower part: Differential spectra in the same conditions. Statistics obtained from the simulation of ! 2 C showers. The solid lines are obtained with the assumptions of Table I

Fig. 8 .

 8 Fig.8. Differential primary spectra for Akeno, Array 20, HiRes as in Fig.1with a conjectural position of AGASA points. The conversion of AGASA points is rather one of the possible tendencies than a precise correction by reason of the oversimplified and speculative treatment, as indicted in the text.

  9 BA b

	1 1.2 600 (Θ)/S 600 (0)
	S
	0.8
	0.6
	0.4
	0.2
	1	1.1	1.2	1.3	1.4	1.5
						secΘ
	1 1.2 600 (Θ)/S 600 (0)
	S
	0.8
	0.6
	0.4
	0.2
	1	1.1	1.2	1.3	1.4	1.5
						secΘ
	Fig. 3. Relative dependence	¡ £¢ ¥¤ ¥¤ ¦ ¨ § © § ¡ ¢ ¥¤ ¤ § © § versus ! " %$ & )( for protons of primary
	6 2 5 6 "! respectively for interaction models of high multiplicity (lower part) and low energy 2 "! 2 2 5 6 2 5 5 GeV (from bottom to top) 6
	multiplicity (upper part)
						(9)

TABLE I TABLE OF COEFFICIENTS

 IOF ) , 0 21 43 , 5 , ! AND 6 VERSUS ENERGY FOR LOW MULTIPLICITY MODEL AT AGASA LEVEL OR FOR HIGH MULTIPLICITY MODEL AND AUGER LEVEL

	6 (eV)	)	0 71 83	5	!	6
	10 6	1.1	1.159	0.339	0.143 ! 10 89	0.832 ! 10 5
	5 ! 105	1.06	1.146	0.341	0.244 ! 10 89	0.158
	105	1.032	1.090	0.345	0.300 ! 10 4@	0.104
	5 ! 105 BA	1.011	1.029	0.384	0.242 ! 10 4C	0.191 ! 10
	105 BA	1.0	0.998	0.368	0.179 ! 10 89	0.203 ! 10 5

TABLE II TABLE OF COEFFICIENTS

 IIOF ) , 0 71 D3 , 5 , ! AND 6 VERSUS ENERGY FOR HIGH MULTIPLICITY MODEL AT AGASA LEVEL

	6 (eV)	)	0 71 D3	5	!	6
	10 6	1.0	1.155	0.310	0.214 ! 10 8E	0.550
	5 ! 105	1.0	1.109	0.312	0.278 ! 10 8C	0.968
	105	1.0	1.029	0.337	0.764 ! 10 8@	0.337
	5 ! 105 BA	1.0	1.012	0.339	0.119 ! 10	0.341
	105 BA	1.0	1.016	0.310	0.323 ! 10 5	0.963

  Table III we have reported the relative dependence on zenith angle at B §' C2 eV for! $# = # w C ! $# /# w % % & (' &# and 9 f "! $# = f ! $# / f ' #in the case of water Cerenkov tanks, like in Haverah Park or AUGER, for vertical muon equivalents ( f "! $# is the average density of vertical muons equivalent recorded at the distance considered, here 600 m).

TABLE III RELATIVE

 III DEPENDENCE OF ESTIMATORS AT 600 M ON ZENITH ANGLE FOR PROTON AND IRON PRIMARIES AT 2 6 6 EV. THE RATIO TO THE VERTICAL DENSITIES ARE TABULATED FOR SCINTILLATORS (! $ & )( ) AND WATER CERENKOV DETECTORS ( ¢¡ ¤£ ¦¥ $ '& )( ) For iron primaries, the situation is more stable but the average excess in vertical density, # % (' &# or f (' &# , is respectively 26% and 30% as compared to vertical protons: this discrepancy decreases when ! increases with similar values of the estimators at U ' &) for scintillators and at h &p )

	&	2	2	§ 2	¨2	2
	! $ & )( , p	1.05	1.08 1.17	1.0	0.65
	! 4$ '& )( , Fe	1.01	1.01 0.94	0.80	0.47
	¢¡ ¤£ ¦¥ @$ '& )( , p	1.06	1.09 1.13	1.02	0.70
	¡ ©£ ¥ $ & )( , Fe	1.01	1.01 0.97	0.83	0.53
	From our Monte Carlo calculation, we found the maximal
	increase of the # % % densities near U I' &) for protons, equal to
	17% for scintillators and 12.6 % for water Cerenkov tanks
	(those proportions are average quantities for groups of 40
	showers). This can be the origin of an overestimation of the
	primary energy in comparable proportions.


Juan Durango
email: juan.durango@ensat.fr

; Mehdi

Laurence Mauriceᶜ

Emilie Lerigouleurᵇ

Nicolas Maestripieri

Arnaud Elgerᵃ

Heterogeneous Data Mining for a Semi-Quantitative Risk Assessment of Oil Contamination from Multiple-Sources in The Ecuadorian Amazon

Results & Discussion

Materials & Methods

Perspectives

1A

2A

In Ecuador oil activities began in 1964 under no environmental policy implementation in one of the most biodiverse biomes in the world. In 1993, communities of the Amazon claimed tons of millions of barrels have been unartfully dropped to the environment. Lack or non-regulated standards for industry, resulted in an infamous heretofore-unresolved litigation upon Texaco (now Chevron) by local population. Pollutant emissions have caused environmental degradation and diseases to populations [START_REF] Buccina | Accounting for the environmental impacts of Texaco's operations in Ecuador: Chevron's contingent environmental liability disclosures. Account Forum San Sebastián M, Hurtig AK[END_REF], San Sebastián and Hurtig 2005, Center for Economic and Social Rights 1994). Three periods of oil activity management in the Northeastern Ecuadorian Amazon can be differentiated [START_REF] Juteau | Environment, oil and political vulnerability in the Ecuadorian Amazon: Towards new forms of energy governance?[END_REF] We aim to set the framework for quantifying the emissions at source to air, soil and water. The spatial statistical analysis of these data will allow identifying patterns for a spatially-explicit model of risk.

• GIS data and inventories of potential polluting infrastructures due to spilling and infiltration (i.e. drill cuttings pits, oil wells, flare stacks and pipes) for more than 45 years, were obtained from different Ecuadorian institutions. These data were grouped together and expressed in terms of density for each watershed.

• Programa de Reparación Ambiental y Social (PRAS) from Ecuador, provided historical oil spills data from environmental impact assessments. Threshold of variable " noil wells" resulting in n-"oil spills volume" is analyzed with regression analysis. Occurrences/quantity of oil spills vs. time is plotted for different parishes to compare practices in T1, T2 and T3.

Introduction

  1A) The Northeastern Ecuadorian Amazon (NEA) located in Eastern Ecuador close to the borders of Colombia and Peru. 2A) The NEA with parishes studied: Green Polygon= Dayuma (DA), Orange = Joya de Los Sachas (JS), Grey= Shushufindi and Limoncocha (SH), Dark Blue = Part of Cuyabeno Reserve (CU), Light Brown = Pacayacu (PA), Light Blue = Nueva Loja (NL). In grey lines and pink color filled is shown the watershed network.

  ): • T1 (1972-1991): Foreign Texaco and state CEPE (Ecuadorian Petroleum Ecuadorian Corporation) engaged in oil activities. • T2 (1992-2001): State managed Petro-Ecuador has taken over the oil activities. • T3 (2001-2014): After decreed of the hydrocarbon oil activity regulations.

B

  ) Oil infrastructure density and population occur in same areas. JS and SH are the most threatened due to the amount of oil wells drilled. DA and PA oil wells reach higher numbers with time. C) People settle along roads built for developing oil extraction. Contamination differs geographically, JS and DA account for highest volume spilled registered from 1995 to 2006. D) Lower occurrences of oil spills during T1 challenges people claims of environmental contamination at this period. Data is missing from 1990 to 1994, which may be explained by switch in managerial operators, and T3 suggests an improvement of management activities through time. However, uncertainty of data seems to be high due to lack of disclosure in management practices. E) Total oil infrastructure density may indicate that at least 5 watersheds are at highest risk ( 1.29-3.11 #/sq.km) between cumulative oil contamination and number of oil wells is observed (r²=0.96). Two thresholds at 450 & 600 oil wells plead for the implementation of two sub-models. Future investigation should focus on prospective analysis and spatial analysis, considering probabilities of occurrences at each individual oil well at each watershed within the NEA. Heavy metals such as V and Ni could be estimated from crude oil characteristics (e.g. API gravity index). Upper streams aspects, data harmonization and building indicators is a next step. To solve problems with uncertainty, selecting areas with spatially homogenous distribution of oil spills to extrapolate to other areas from periods with better disclosure of oil spills records should be done. These findings could help defining key parameters to improve data and indicators measured by PRAS (e.g. substance spilled) to facilitate future decision-making processes for environment and population protection in the NEA.

Acknowledgements


Mosnier Emilie

Caron Mélanie

Grard Gilda

Liégeois Florian

Olivia Faucher

Leroy Eric

Rouet François

High mortality rate and aetiologies of central nervous system infections among HIV-1-infected patients from Gabon

Objective

In sub-Saharan Africa, data on acute central nervous system (CNS) infections observed in HIV-1infected subjects are very scarce. The goal of this study, conducted in Gabon (Central Africa), was to assess the mortality rate and aetiologies of CNS infections among HIV-1-infected subjects, receiving or not highly active antiretroviral therapy (HAART).

Methods

From November 2009 to April 2010, a prospective case series study was conducted in two Gabonese cities. Standardized clinical, laboratory and imaging data were collected among HIV-1infected subjects presenting an acute febrile neurological impairment.

Results

Of 22 cases (woman, 54%; median age, 43 years), all but three patients were untreated with HAART. A high proportion (60%) of subjects ignored their HIV serostatus before their neurological impairment. The main clinical presentation was encephalitis (80%). Among the patients who could be clinically followed-up (n=20), 10 (50%) died in a median time of 11 days. All of them were untreated with HAART. Aetiological causes were found in 12 patients as follows: toxoplasmosis (n=5), tuberculosis (n=3), bacterial infection (n=2), Cryptococcus neoformans (n=1), and neurospyhilis (n=1). CMV DNA was detected in plasma from six (27%) patients, combined with a HSV DNA positive result for three of them, and a HHV-6 DNA positive result for one.

Conclusion

Our study revealed that, among late-presenting, severely immunosupressed HIV-1-infected adults, mostly untreated with HAART, acute neurological infections constitute a frequent and severe (mortality of ~50%) clinical entity, with a broad spectrum of aetiologies. It makes their diagnosis difficult to implement in resource-limited settings such as Gabon.

Introduction

By the end of 2010, around 5.0 million people were receiving highly active antiretroviral therapy (HAART) in sub-Saharan Africa. These promising results underline that nearly two thirds of people needing HAART failed to access to medical care and/or were unaware of their HIV serostatus, and consequently remained not treated [START_REF] Robertson | NeuroAIDS in Africa[END_REF]. In this context, HIV-1-related opportunistic infections (OIs), such as those affecting the central nervous system (CNS), still continue to occur among HIV-1infected persons.

However, data are very scarce about CNS infections in Africa since infrastructure, access to neurological expertise, diagnostic capabilities (notably molecular techniques) and imaging facilities are quite limited, in comparison with developed countries [START_REF] Holmes | Review of human immunodeficiency virus type 1-related opportunistic infections in sub-Saharan Africa[END_REF]. Whereas there is a potential role for HIV subtype differences in varying neuropathogenicity [START_REF] Sacktor | HIV subtype D is associated with dementia, compared with subtype A, in immunosuppressed individuals at risk of cognitive impairment in Kampala, Uganda[END_REF], paired plasma/CSF HIV-1 RNA concentrations were rarely measured in Africa [START_REF] Morris | High human immunodeficiency virus type 1 RNA load in the cerebrospinal fluid from patients with lymphocytic meningitis[END_REF][START_REF] Christo | Factors influencing cerebrospinal fluid and plasma HIV-1 RNA detection rate in patients with and without opportunistic neurological disease during the HAART era[END_REF]. For instance, in Gabon (Central Africa) where a high HIV-1 adult prevalence (~7%) and a wide HIV-1 genetic diversity have been previously described [START_REF] Mintsa-Ndong | High HIV Type 1 prevalence and wide genetic diversity with dominance of recombinant strains but low level of antiretroviral drug-resistance mutations in untreated patients in northeast Gabon, Central Africa[END_REF], the relationship between HIV-1 and neurological signs remains largely unknown.

The main objective of the present study was to assess mortality and aetiologies of acute febrile neurological manifestations observed in patients at different stages of HIV infection, and receiving or not HAART.

Methods

Between November 2009 and April 2010, our study prospectively recruited 22 HIV-1-infected adults admitted to three distinct public Gabonese hospitals from two cities (Libreville, the capital city, and Franceville) for suspected neurological disease. The study was approved by the Gabonese Ethics Committee, and consent was obtained from patients or accompanying relatives. Acute CNS infections were suspected with a fever or history of fever, and at least one of the following sign: reduced level of consciousness (Glasgow coma score <14); severe headache; neck stiffness; focal neurological signs; or convulsions. Patients with slide-positive cerebral malaria were not included in this study.

Patients underwent a full neurologic examination at the time of admission by a trained physician.

They were clinically followed-up until day seven, 21 after admission and at the end of hospitalisation. At lumbar puncture, CSF was taken for cell count and differential protein, glucose, gram stain, specific research of Cryptococcus and bacterial culture. Blood was taken for toxoplasmosis and syphilis serology when possible. HIV serology was performed for subjects who ignored their HIV serostatus. Data were collected from each subject included gender, age, use of HAART and CD4 + lymphocyte T-cell counts (when available). HIV-1 RNA viral load (VL) measurements were done on paired CSF and plasma samples, by using the LTR-based real-time PCR Generic HIV Viral Load assay (Biocentric, Bandol, France) [START_REF] Rouet | Impact of HIV-1 genetic diversity on plasma HIV-1 RNA Quantification: usefulness of the Agence Nationale de Recherches sur le SIDA second-generation long terminal repeat-based real-time reverse transcriptase polymerase chain reaction test[END_REF] with a low detection limit of 300 copies/ml. Spearman correlation coefficients were calculated to determine the relationship between HIV-1 RNA concentrations in CSF vs. plasma specimens.

The diagnosis of "probable central nervous tuberculosis" was done on the basis of a high level of

proteins and a low level of glucose in CSF associated with CT pulmonary scan findings (miliary) and/or results of adenopathy biopsy. A good recovery under specific treatment was also considered for this diagnosis. The diagnosis of "probable cerebral toxoplasmosis" was done on the basis of CT scan findings associated with a good response under specific treatment.

Finally, qualitative home-made real-time PCR assays were performed in CSF and blood for herpesviruses infections (including cytomegalovirus [CMV], herpes simplex virus [HSV], varicellazoster virus [VZV] and human herpesvirus type-6 [HHV-6]), enterovirus, influenzae A virus, measles virus, mump virus and arboviruses (Rift valley fever, chikungunya, dengue and West Nile).

Results

Clinical presentation and aetiology spectrum

As shown in Table 1, a total of 22 patients were enrolled during our studied period. Their median age was 43 years (range, 27-68). Women were predominant (54.5%). A high proportion (~60%) of patients ignored their HIV status before their neurological impairment. The majority (73%) of patients were at advanced WHO clinical stages III or IV. All patients but three were untreated with HAART. The main clinical presentation was encephalitis (80%). Altered mental status was the main neurological manifestation with a median Glasgow coma score of 13 during admission. Focal neurological involvement was found in 50% and seizure in 18%. Among the patients who could be clinically followed-up (n=20), 10 (50%) died in a median time of 11 days. All of them were untreated with HAART.

A specific aetiology was identified in 12 patients whereas it remained unknown in 10 individuals (Table 1). The identified aetiologies of acute neurological manifestations in our population were as

Biological results

As summarized in Table 2, the most common laboratory abnormality was an increase of proteinorachia in CSF (defined by a proteinorachia > 0.5g/l). The two patients who had bacterial CNS infections showed a significant increase of their leucocyte counts in CSF. The median CD4 + Tcell count (n=12) was 78/mm 3 (range, 7-494). All patients except two had CSF HIV RNA VL values higher in plasma than in CSF. The median plasma and CSF HIV viral load was 5.34 and 3.65 log 10 copies/ml, respectively. A significant correlation was obtained between CSF and plasma HIV-1 RNA levels (R=0.675, p<0.001).

By using real time PCR assays, CMV (n=6), HSV (n=3), and HHV-6 (n=1) DNA were detected in sera samples. Among these, three co-infections HSV/CMV and one co-infection HHV-6/CMV were obtained. Finally, one patient (subject #2) exhibited a positive result for both HSV and HHV-6 in his CSF sample.

Discussion

In sub-Saharan Africa, although behavioural prevention and HAART access efforts continue [START_REF] Farmer | Community-based approaches to HIV treatment in resource-poor settings[END_REF], opportunistic infections, including those affecting CNS, remain a major public health problem. Our study, conducted in Gabon, revealed that, among late-presenting, severely immunosupressed HIV-1infected adults, mostly untreated with HAART, acute neurological symptoms constitute a frequent and severe (mortality of ~50%) clinical entity. Further, in our studied population, ~60% of patients ignored their HIV status before their neurological impairment, strongly suggesting that neurological manifestations constituted the initial AIDS-defining illness.

It is well established that HAART significantly improves immune function and decreases HIV RNA levels [START_REF] Beaudrap | Incidence and determinants of new AIDS-defining illnesses after HAART initiation in a Senegalese cohort[END_REF][START_REF] Laurent | The Senegalese government's highly active antiretroviral therapy initiative: an 18-month follow-up study[END_REF]. Consequently, the incidence of OIs has dramatically decreased, notably in developed countries where HAART coverage is much higher than in developing countries [START_REF] Moore | Natural history of HIV infection in the era of combination antiretroviral therapy[END_REF]. Unfortunately, in many African countries, such as in Gabon, HAART coverage is still insufficient (~50% in Gabon) [START_REF]Epidemiological Fact Sheet on HIV and AIDS[END_REF]. In addition, OIs in these areas continue to occur, particularly in untreated subjects, ignoring their HIV serostatus. In sub-Saharan Africa, efforts to implement prophylaxis for HIVrelated OIs are still important in preventing associated morbidity and mortality [START_REF] Holmes | Review of human immunodeficiency virus type 1-related opportunistic infections in sub-Saharan Africa[END_REF].

In our study, even if we found a correlation between CSF and plasma HIV-1 RNA levels, most of untreated patients showed higher HIV RNA levels in the plasma, suggesting that the CSF viruses may be mostly originated from plasma by diffusion across the blood-brain barrier. However, higher CSF VL values were observed for two patients without HAART, suggesting that the source might be in few cases the CNS itself, by a HIV self-replication within the brain. The clinical usefulness of HIV-1 RNA quantification in the CSF of patients with acute neurological diseases, or the effect of opportunistic diseases on CSF HIV-1 RNA levels remains controversial [START_REF] Christo | Factors influencing cerebrospinal fluid and plasma HIV-1 RNA detection rate in patients with and without opportunistic neurological disease during the HAART era[END_REF]. Prospective studies are further required to elucidate the clinical consequences of HIV RNA levels in CSF among patients with or without acute neurological infections.

In our resource-constrained setting, we were able to identify aetiological causes for about 50% of neurological HIV-related OIs. Toxoplasmosis and TB were the most frequent causes of febrile central neurological infection, which is consistent with results obtained in other African countries among HIV-1-infected subjects [START_REF] Karstaedt | The bacteriology of pulmonary tuberculosis in a population with high human immunodeficiency virus seroprevalence[END_REF][START_REF] Modi | Management of HIV-associated focal brain lesions in developing countries[END_REF][START_REF] Bhigjee | Intracranial mass lesions in HIV-positive patients--the KwaZulu/Natal experience. Neuroscience AIDS Research Group[END_REF]. Besides toxoplasmosis and TB, we were also able to identify other causes (such as bacterial infections, Cryptococcus, neurosyphilis), illustrating the large spectrum of aetiologies in HIV-1-infected individuals showing acute CNS signs.

Finally, we were able to detect Herpesviridae viruses in the plasma compartment of some patients.

More precisely, CMV DNA was detected in six individuals, either alone (n=2) or associated with the presence of HSV (n=3) or HHV-6 (n=1) DNA. In one patient, HSV was also detected in the CSF compartment. As previously described by other researchers [START_REF] Berrington | Clinical correlates of herpes simplex virus viremia among hospitalized adults[END_REF][START_REF] Limaye | Cytomegalovirus reactivation in critically ill immunocompetent patients[END_REF][START_REF] Skolnik | Bidirectional interactions between human immunodeficiency virus type 1 and cytomegalovirus[END_REF][START_REF] Spector | Cytomegalovirus (CMV) DNA load is an independent predictor of CMV disease and survival in advanced AIDS[END_REF][START_REF] Steininger | Cytomegalovirus disease in the era of highly active antiretroviral therapy (HAART)[END_REF], CMV and HSV reactivations may occur in HIV-infected patients, mostly when they are not treated with HAART. However, their neurological significations remain largely unknown.

Our study has several limitations. The sample size was relatively small and cerebral imaging was not available for all patients. We did not perform PCR assays for tuberculosis, toxoplasmosis, and JC virus which may explain why we found a high proportion of unknown aetiological causes for neurological signs. However, based on our preliminary results, our group has decided to initiate a large-scale evaluation of neurological OIs observed in HIV-positive Gabonese subjects in order to define more precisely their prevalence rates and aetiologies.

In conclusion, our results strongly suggest the need to continue endeavours for providing HIV testing and counselling, to further increase HAART coverage in Gabon (which is around ~50% in

  follows: (i) cerebral toxoplasmosis (n=5); these five patients presented focal neurological signs, seizure or confusion, CT scans were characterized by multiple lesions, associated with contrast enhancement; (ii) multifocal tuberculosis (TB) (n=3); these three individuals showed cerebral involvement associated with miliary or multiple tuberculosis lymphadenitis. All presented clinical signs of meningeal irritation; (iii) bacterial CNS infection (n=2); it included a meningo-encephalitis due to Streptococcus B and one case of multiple brain abscesses; (iv) cryptococcal infection (n=1); this patient had a positive cryptoccal antigen test in CSF and the cerebral CT scan disclosed a mass lesion non-enhanced in cerebellum, probably correlated with a cryptoccoma; and (v) neurosyphilis (n=1).

  2010), and to use the new World Health Organization 2010 criterion (CD4≤350/mm 3 ) for earlier treatment initiation. Providing regimens containing ARVs with high CSF penetration should also reduce CSF HIV-1 VL in the CNS and decrease morbidity and mortality by preventing or attenuating acute HIV-1-associated neurological signs. Due to the broad spectrum of aetiologies, the diagnosis of CNS OIs remains difficult in resource-limited settings, such as Gabon.


J Giordano
email: jerome.giordano@polytech.univ-mrs.fr

J D Parisse

L Biamino

J Devesvre

P Perrier

Experimental and numerical study of weak shock waves transmissions through mini-tubes

Keywords: numbers: 47.61.-k, 47.40.-x, 47.11.Df

The aim of this paper is to present an original experimental technique to study weak shock wave in a mini-tube. Thus, we have designed an apparatus, which can be connected to any classical shock tube, in order to characterise high speed flows induced by the shock wave transmission in minitubes. We have proposed appropriated measurements based on high speed strioscopy coupled with pressure sensors. Two mini-tube diameters are considered: 1.020 ±0.010 mm and 0.480 ±0.010 mm.

We have realized preliminary experimental and numerical campaigns with an incident shock wave Mach number at 1.12 ±0.01 . The generation of a micro-shock wave was observable in the two minitubes. For the smallest mini-tube, we have found an attenuation of the strength of the shock wave with a decrease of 1.8% of the Mach number.

The recent researches in the fluids mechanics of micro-systems let us foresee the advances that may allow the miniaturization of micro-valves, micro-nozzles or micro-pumps [START_REF] Laser | A review of micropumps[END_REF]. In this micro-devices the ratio between lateral surfaces and volume could be extremely greater than in macro devices and, as consequence, increases the energy exchanges. If we focus on the domain of the micro-flows of gas, many studies have been proposed by the scientific community since the last two decades [START_REF] Sun | Shock propagation in narrow channel[END_REF][START_REF] Brouillette | Shock waves at microscales[END_REF][START_REF] O'hare | Near-wall e↵ects in rarefied gas micro flows: some modern hydrodynamics approaches[END_REF]. Previous studies were carried in our team to treat microfluidic flows with low velocity regime. The aim of these studies was to characterize the gas/wall interactions through the slip velocity (in the slip regime) and the estimation of accommodation coe cients from hydrodynamics to free molecular regime (Knudsen Number [0.001, 50]) [START_REF] Ewart | Mass flow rate measurements in microchannel, from hydrodynamic to near free molecular regimes[END_REF][START_REF] Ewart | Tangential momentum accomodation in microtube[END_REF]. Moreover, these studies have allowed us to develop experimental techniques to deal with micro-flows at low speed [START_REF] Ewart | Mass flow rate measurements in gas micro flows[END_REF]. However, the applications in high speed regime are numerous, for example in micro-wave rotors where shock waves are e ciently used to transfer energy [START_REF] Iancu | Design and fabrication of microchannel test rig for ultre-micro wave rotors[END_REF]. Nevertheless, the shock propagation in micro channel is not yet well studied and need to be better understood to increase micro-sytems e ciency. Even if we can note recent analytical modelization study, such as Mirshekari and Brouillette's one [START_REF] Mirshekari | One-dimensional model for microscale shock tube flow[END_REF], there is an important lack of experiments dealing with the high speed flows, with or without shock wave. To our knowledge, the only working device devoted to the high speed gaseous flows in micro-channels is that developed by Udagawa, Garen and their co-workers in [START_REF] Udagawa | Interferometric detection of dispersed shock waves in small scale diaphragm-less shock tube of 1mm diameter[END_REF]11].

Their apparatus is based on the use of a quickly deformable opening valve which initially separates the micro channel from the high pressure chamber. In previous studies, we have numerically investigated the possibility to transmit a shock wave into a micro-channel [12].

In this work, several simulations have been realized to consider the influence of the microchannel dimensions. Besides, we have designed an original apparatus based on the use of a generic micro-valve to generate micro-shock waves [13]. However, before building this whole device, we have decided to use our classical shock tubes facilities in order to study weaker micro-shock waves and to bring additional validations for our code carbur [14] to deal with microfluidics phenomena. Thus, the present paper is dedicated to the presentation of the new experimental technique and the results we have obtained both experimentally and numerically. First of all, we describe how we have adapted a mini-tube to our classical shock tube T 80 [15] and what types of measures have been done. Then, we present the results of experiments and simulations and we conclude and give the main perspectives of this work.

As the simplest device to generate shock wave is a shock tube, our idea is to connect a mini-tube to the end of a classical shock tube. A shock tube allows to study compressible flows with a good repeatability and with an easy control of the shock strength. With this principle, one can deal with the shock wave transmission and high speed flow generation in a micro-system. In this context, we use our T 80 facility with a high speed shadowgraph video recording diagnostic. We use mirrors with a diameter equals to 0.3 m and a focale length of 3 m. The video is recorded with the digital camera fastcam SA1 of Photron (San Diego -USA). All the experiments were made with Air, and because the mini-tube makes a connection between the shock tube and the ambient Air, the pressure P 1 was atmospheric pressure 1 ±0.01 .10 5 P a and the temperature was the ambient temperature 300 ±2 K. In these conditions, the maximum of incident shock strength we can reach with our facility is equal to M s = 1.5 ±0.01 . One can note that is smaller than shock wave strength expected by the other device we have designed in [13]. Mini-tubes overall dimensions are given by the figure 1.

The mini-tubes are realized with commercial micro-syringes. We only keep the cylindrical glass tube of the micro-syringes, cut at the required dimensions. The main dimensions of mini-tubes are: for mini-tube 1, its length is equal to 81.24 ±0.05 mm and its diameter was measured at 1.020 ±0.010 mm. For the mini-tube 2, its length is equal to 46.44 ±0.05 mm and its diameter measured at 0.480 ±0.010 mm. As the figure 1 shows, the system was designed for an easy adaption of the di↵erent mini-tubes. The support is made in plexiglass and fixed to the shock tube ending. The fluid flow characterization is carried through two types of measurement. First of all, the macro-tube T 80 is instrumented with several pressure sensors, regularly positioned along the tube. These sensors allow us to know the celerity of the incident shock wave. To obtain an estimation of the shock wave celerity in the mini-tube, another sensor is placed out of the device, right in front of the mini-tube (Fig. 1). Indeed, we cannot use classical pressure sensors along the wall of the mini-tube, as it is done in the macro-tube, without major flow disturbances. Nevertheless, the information given by this pressure sensor takes into account the sum phenomena which occurred in the mini-tube.

Thus, this measure is relevant to give a validation for our simulations. A second measure is provided with a high speed shadowgraph digital video recording. The recording rate is fixed at 90000 fps and we visualize the space near the mini-tube ending. These pictures are useful to identify the shock structures generated forward the mini-tube outlet and to determine the velocity of these shock wave structures. One can note that we have also realized experiments without the pressure sensor positioned in front of the mini-tube in order to study the free jet structures. We use our numerical code carbur [13] to simulate the compressible air fluid flows. This code is based on a second order discretization, in time and in space, of the Navier-Stokes' equations with a finite volume method. Convective fluxes are estimated through the solution of a Riemann's problem at each cell interface with an exact solver, whereas di↵usive ones are obtained with a finite di↵erences method. The walls are supposed as adiabatic with no velocity slip. The geometry is decomposed into 100000 cells densely distributed close to walls : 1.10 5 m. In the two mini-tubes, 100 cells are used in the radial direction to describe correctly the velocity distribution.

For the two mini-tubes, we have realized a first campaign of simulations and experiments with an incident Shock wave Mach number at ⇡ 1.12 ±0.01 . In these first simulations, the flow was supposed as laminar. With these flow conditions, the Knudsen's number is lower than 7. 10 5 in the mini-tube 1 and lower than 1.4 10 4 in the mini-tube 2. As a consequence, the flow is in the continuous regime and the Navier-Stokes approach is fully relevant. These values of the Knudsen's number are small because we have chosen to work with high levels of pressure. So, we do not have to take into account rarefaction e↵ects as it was done by Brouillette [START_REF] Brouillette | Shock waves at microscales[END_REF], Zeitoun and Burtschell [16]. The Reynold's number, calculated with the mean velocity, is close to 4400 along the mini-tube 1 and close to 2500 along the mini-tube 2. To quantify the influence of the turbulence on the transmitted shock wave into mini-tube 1, others simulations have been made with the Spalart-Allmaras turbulence model [17]. We found that the velocity of the transmitted shock wave is about 407 m.s 1 in laminar assumption and about 408 m.s 1 in turbulent one. This 1 m.s 1 of deviation can be neglected compared to 10 m.s 1 of the speed increase of the shock wave observed in this mini-tube 1. These results confirm that, in these experiment conditions, the turbulent e↵ects have no significant influence on the transmitted shock wave velocity. Therefore, we think that turbulence e↵ects can be neglected in our study of transmitted shock wave modifications by the micro-scales e↵ects, even if the Reynolds number is close to 5000.

In the figure 2, one can see the time sequence of typical experimental Schlieren, pictures at every 22.22 ±0.1 µs, observed when the transmitted shock wave and the flow get out the mini-tube. These pictures give an overview of the fluid flow generated downstream the minitube and allow us to identify a discontinuity followed by a jet stream with vortex structures.

The figure 3 represents the main discontinuities and interactions of the fluid flow in a space time diagram (mini-tube 1 and incident shock wave at Mach 1.12 ±0.01 ). The lines are the iso-contour of the fluid flow temperature given by the simulations, whereas experimental points are provided by the di↵erent pressure sensors and the high speed camera. Each pressure sensors give one measure of pressure at one location per experiment, nevertheless we have plotted on the figure 3 the pressure measures from four experimental runs. For these di↵erent runs, variations of initial conditions are observed (ambient temperature and pressure, etc.) which induce a low variation of the fluid flow properties, particularly the Mach number of the incident shock wave. On the figure 3, the results of one simulation are plotted. The fluid flow conditions of this simulation correspond to one experimental run whose measures are represented by the points (triangle for the pressure measure and square for the optic ones) filled with white. The other pressure measurements from the three other runs are filled with grey. One can note that experiments and simulation are in good agreement and, as a consequence, that simulations seem to describe correctly the main physics phenomena. The repeatability is correct as the pressure measures show, but should be improved in the future.

Moreover, the experimental and numerical results attest that a shock wave is transmitted into the two mini-tubes. This transmitted shock wave is transmitted again into the air at rest at the mini-tube ending. The secondly transmitted wave is a blast wave with a celerity equals to the sound one. Following the acoustic wave, a stream flow is observable. The mean velocity of this jet is close to 110 m.s 1 for the mini-tube 1 (less than 5 m.s 1 of deviation between experiments and simulations). For the second mini-tube, this velocity is close to 105 m.s 1 with less than 5 m.s 1 of deviation between numerical and experimental results.

One can also make an important remark: the pressure sensor does not detect the acoustic wave but the jet stream. This is explained by the low pressure gradient observable across the acoustic wave which is estimated by simulation at less than 500 P a. The pressure sensor cannot detect this pressure jump due to its own detection limit around 5000 P a. Besides, we have estimated the Mach number of transmitted shock wave for each mini-tube. For the mini-tube 1 (diameter equal to 1.020 ±0.010 mm), the transmitted shock wave Mach number is close to 1.15 ±0.01 (mean estimated along 80 ⇥ diameters), which represents an increasing of ⇡ 2.5%. For the second mini-tube (diameter equal to 0.480 ±0.010 mm), we note a decrease of the transmitted shock wave Mach number of ⇡ 1.8% (Mach equals to ⇡ 1.10 ±0.01 , mean estimated along 80 ⇥ diameters). So, these results seem to confirm the micro-scale influences on the shock wave strength previously observed by Parisse et al. in [12]: the decrease of the mini-tube diameter induces a the diminution of the shock wave celerity. What is remarkable is that, in spite of the section changing between the macro-tube and mini-ones which should lead to the increasing of the shock wave strength [18], we observe in the mini-tube 2 a weaker shock wave. This shock wave attenuation e↵ect is explained by the growth of the boundary layer, which at these scales quickly modifies the idealized wave system and the flow variables. For the mini-tube 1, an attenuation should be visible for a greater length than 80 ⇥ diameters.

To check the viability of our device to study higher incident shock wave Mach numbers, we have realized one run at Mach ⇡ 1.5 ±0.01 . The pictures (a) and (b) of the figure 4 show the comparison of a numerical and experimental schlieren for the flow generated upstream the mini-tube 1. On this figure, we can identify the acoustic radiations induced by the vortex structure of the jet. The frequency of acoustic wave emission is about 165 KHz. An estimation of the mechanical eigen-frequencies of the apparatus (software CATIA, Dassault System, Vélizy-Villacoublay -France) shows that the mechanical vibrations are not coupled with the vortex shedding and acoustic wave emission. Even if simulation and experiment are in relatively good agreement for the early times, for this stronger shock wave, the turbulence has to take into account for describe the jet-stream development. Indeed, as we can see in the picture (c) of the figure 4, the jet-stream becomes shortly fully turbulent. We can see that our experimental apparatus could be used to characterize the behaviour of high speed micro-jets. The knowledge of these micro-jets should be useful for the safety of high pressurized tanks. Indeed, a micro leak could have the same structures as the micro-jet observed with our experiments.

In conclusion, we have designed and built an original device to study micro-compressiblefluid flows. This experimental apparatus could be easily adapted in a classical shock tube, as we have done. We have realized first campaigns of experiments to try to transmit an incident Shock Wave at Mach 1.12 ±0.01 into two mini-tubes. In a same time, we have simulated these experiments with our code carbur and, after di↵erent comparisons, we have found a good agreement between the two approaches. Thus, we have seen, in all the cases treated in this study, that a shock wave was transmitted into the mini-channel. For the smallest minitube, we have found an attenuation of the strength of the shock wave with a decrease of 1.8% of the Mach number. To our knowledge, the measure of this shock attenuation for these scales (475 µm for mini-tube 2) and for these pressure level (P 1 = 1 ±0.01 .10 5 P a) has not been provided experimentally before. Thus, these first results are promising, and more experiments for di↵erent shock wave strengths should be realized to confirm these primary conclusions. Moreover, di↵erent perspectives could be considered. On the one hand, we could decrease the initial pressure in the mini-tube to study rarefaction e↵ects. On the other hand, we could also use di↵erent gases, like Helium/Air or Helium/Argon, to reach higher shock wave Mach number and as a consequence higher compression e↵ects. Besides, combustion phenomena could be also investigated for example by using mixture of H 2 and O 2 gases.