Ana Espinosa

Mathieu Bugnet

Guillaume Radtke

Sophie Neveu

Gianluigi A Botton

Claire Wilhelm
email: claire.wilhelm@univ-paris-diderot.fr.

Ali Abou-Hassan
email: ali.abou_hassan@upmc.fr

Can magneto-plasmonic nanohybrids efficiently combine photothermia with magnetic hyperthermia?

Multifunctional hybrid-design nanomaterials appears to be a promising route to meet current therapeutics needs required for efficient cancer treatment. Herein, two efficient heat nanogenerators were combined into a multifunctional single nanohybrid (a multi-core iron oxide nanoparticle optimized for magnetic hyperthermia, and a gold branched shell with tunable plasmonic properties in the NIR region, for photothermal therapy) which impressively enhanced heat generation, in suspension or in vivo in tumours, opening up exciting new therapeutic perspectives.

Nanomedicine has emerged as a rapidly developing field to face current diagnostics and therapeutics challenges.

1 On the one hand, nanoparticles can be activated by a physical stimulus only once it has reached its target, thus preventing damaging effects on healthy bystander tissues, and on the other hand, several functions can be incorporated within a single nanostructure, to provide a synergic efficiency by merging multiple therapeutic modalities. 2 One promising remotely activated nano-therapy is based on the ability of some nanoparticles to generate heat under external stimulus. 3 Currently, gold (plasmonic) and iron oxide (magnetic) nanoparticles are the prime candidates for the development of such thermo-therapy. Optical excitation of plasmonic nanoparticles by an infrared laser causes localized heating that can destroy surrounding cancer cells (photothermia). 4 In the case of magnetic nanoparticles, application of a high-frequency alternating magnetic field excites the fluctuations of the magnetic moment, the resulting magnetic energy being released and dissipated as heat (magnetic hyperthermia). In both cases, the size and shape of the nanoparticles are crucial. 5 Indeed, gold nanoparticles such as gold nanoshells, 6 nanostars, 7 and nanorods 8 are often preferred due to their strong absorption cross sections. Furthermore, the possibility of engineering their shapes results in surface plasmon resonances in the near infra-red (NIR) region, where light absorption by biological tissues is minimal (650-900 nm). 9 For magnetic nanoparticles, finetuning the shape, magnetization and anisotropy is necessary to enhance the heat-generating capacity. New generation of magnetic cubic, 10 cooperative multicores, 11 or core-shell nanostructures 12 have recently reached unprecedented heating capacities. Nanoscale combination of materials with magnetic and plasmonic properties has drawn particular interest these past few years.

13

Several novel developments and recent reports in magnetoplasmonic multifunctional platforms have demonstrated a synergistic potential resulting from the association of both materials. 14 For example iron oxide core nanoparticles with a gold shell have been synthesized to enable molecular optical and magnetic resonance imaging (MRI) in combination with gold photothermal therapy of cancer cells.

14a Nano-transducers with a superparamagnetic iron oxide core embedded in a silica and a gold nanoshell have been studied in magnetic targeting and MRI detection imaging of brain tumors associated with photothermal ablation treatment provided by the gold nanoshell.

14g These recent developments in magneto-plasmonics have thus mainly focused on the use of iron oxide cores for MRI, magnetic manipulation and targeting, while gold layers were integrated to provide optical response of the hybrids for imaging or photothermal heating.

Combining efficiently the magnetic hyperthermia potential of iron oxide cores and the plasmonic photothermal effects of gold layers remains, however, an open challenge. Moreover, beside the bimodality in hyperthermia which could be brought by the combination of both materials in one single nanostructure, magneto-plasmonic nanohybrids allow to guarantee a similar biodistribution of iron oxide and gold in tissues, 15 a rich surface chemistry for conjugation due to gold, compared to the iron oxide core alone, 16 and finally a protective shield against the degradation of magnetic cores is brought by the gold shell. 17 Up to date, magneto-plasmonic hybrids efficient for both magnetic hyperthermia and plasmonic photothermia are rare, 18 and mapping of plasmons at the nanoscale, on an iron oxide core, is still unmet. Herein, we propose an efficient class of magneto-plasmonic nanoparticles (MagPlasNPs), which combine high thermal capabilities for both magnetic hyperthermia and photothermia at low excitations doses. We selected two high-performance heat nano-generators, a multi-core iron oxide nanoparticle for the magnetic part and a gold-branched nanostructure for the plasmonic part. Combined elemental and surface plasmon mapping performed at the nanoscale on single nanohybrids allowed for an unprecended assessment of plasmons on an iron oxide core, and the combination Please do not adjust margins Please do not adjust margins of magnetic and plasmonic properties in the single nanohybrids impressively enhanced heat generation, in suspension or in vivo in tumours. The synthesis of MagPlasNPs was carried out using a seed-mediated growth approach as illustrated in Fig. 1a (see experimental section in Supplementary Information (SI) for full details). Maghemite multi-core shape nanoparticles (MagNPs) (average diameter 30 ± 4 nm from TEM, see Fig. S1) were synthetized as cores for the magneto-plasmonic hybrids and they were prepared via the polyol process. 20 Afterward, their surface was functionalized with citrate anions which guaranteed for the seeding step a high colloidal stability in ammonia solution (ζ = -80 mV at pH = 10) and efficient attraction of [Au(NH 3 ) 4 ] 3+ that was reduced in the following step into Au seeds with NaBH 4 .

21

The resulting magnetic nanoparticles decorated with Au seeds (MagNP-seeds) were then redispersed in ethanol in presence of polyvinylpyrolidone (PVP) to enable the growth of spiked or multibranched gold shells during the step in presence of dimethylformamide (DMF), PVP and AuCl 4 -(see experimental section in SI for more details). 22 Transmission electron microscopy Scanning transmission electron microscopy (STEM) was also employed to obtain the chemical images of the different magnetoplasmonic nanohybrids at the seed stage (MagNP-seeds), and after their growth under different synthesis conditions to final MagPlasNPs. In each case, high-angle annular dark field (HAADF) images are shown together with the chemical maps recorded simultaneously using electron energy loss spectroscopy (EELS) in Fig. 1 (see also Fig. S2 andS3). As the intensity scattered by an atom in HAADF roughly scales as Z 1.7 where Z is the atomic number, 23 the Au seeds formed after the seeding step appear much brighter than the maghemite cores. The Fe, O and Au elemental maps shown together in Fig. 1b confirm this chemical contrast and the desired complex architecture. Also, the attachment of Au seeds to the surface of MagNPs resulted in the appearance of a plasmonic shoulder at λ  530 nm originally absent in the spectrum of MagNPs (Fig. 1f). This result is expected for discrete gold clusters on iron oxide cores, 24 and is in agreement with the observed brown colour of the MagNP-seeds in ethanol. After the growth step, depending on the ratio of HAuCl 4 to MagNPs available during the growth, we observed different organizations and thicknesses of the Au shells. For a final ratio of Au/Fe = 1.13 ± 0.04 (MagPlasNP-1, Fig. 1c) the size of the seeds increased from ∼ 4 nm to ∼ 10 nm in diameter. Moreover, individual quasi-spherical gold nanoparticles homogeneously distributed on the surface of maghemite cores with an interparticle distance of 10 to 15 nm can be observed. For the MagPlasNP-2, characterized by a Au/Fe = 3.1 ± 0.7 ratio, a gold shell of thickness reaching 15 to 20 nm around the maghemite cores is observed, forming a discontinuous thick shell as highlighted in the HAADF image and corresponding chemical maps in Fig. 1d. Moreover, the anisotropic shape of the gold particles forming the shell is more pronounced and spikes are observed. Finally, for the MagPlasNP-3, characterized by a Au/Fe = 4.7 ± 0.9 ratio, the gold shell thickness increased to more than 20 nm, so that maghemite cores can barely be detected in the core due to the very efficient coverage of the gold shell (Fig. 1e). As the concentration of HAuCl 4 in the growth step increased, the interparticle space still present at the maghemite surface for MagNP-seeds and MagPlasNP-1 disappeared completely in MagPlasNP-2 and MagPlasNP-3, in favor of a continuous spiky shell formed by merging gold nanoparticles of larger sizes. These results are in excellent agreement with conventional TEM observations (Fig. S1) and with the results obtained by UV-Vis-NIR spectroscopy (Fig. 1f). Indeed the suspension became blue and the resonance, red-shifted indicating growth and merging of Au seeds into spiky shells. Such shift was reported by other groups after growth of Au shells on magnetite iron oxide cores.

2a, 25 Beside the optical properties in the NIR, the superparamagnetic behavior of the iron oxide core remains unmodified by the gold shell (Fig. S4). Finally, the mean hydrodynamic diameters of all NPs were measured by dynamic light scattering (DLS, Fig. S5) and by recording their Brownian motions (Nanosight, Fig. S6). It increased from MagNPs to MagPlasNP-3, and was found higher than the TEM measurements due to the hydration of the multi-layered PVA, 26 but never exceeding 200 nm, revealing the absence of any aggregation. The colloidal stability of the MagNPs and MagPlasNPs after dispersion in physiological media (phosphate buffer solution (PBS), fetal bovine serum (FBS) and plasma) was also checked using DLS (Fig. S7). While citrated MagNPs quickly destabilized, MagPlasNPs showed a remarkable | 3

Please do not adjust margins Please do not adjust margins stability evidencing the role of the PVP coating.The plasmonic response of isolated MagPlasNP-2 hybrids was then investigated at the nanoscale using STEM-EELS (Fig. 2). The EELS map shown in Fig. 2b, corresponding to the integrated intensity in the 1.4-2.4 eV energy range highlights a localized surface plasmon resonance around the nanohybrid. The raw spectra displayed in Fig. 2c correspond to different positions of the electron beam around the nanohybrid as indicated in the sketch in the inset. A broad surface plasmon resonance is consistently observed at ~ 2.0 +/-0.2 eV (λ ∼ 620 nm). Slight shifts of the surface plasmon resonance, such as the one observed in position C, can be assigned to the local variations of the shape of the Au nanocrystals forming the shell. The different assemblies of nanohybrids observed display a sizeable dispersion in their surface plasmon resonance energies, ranging from the visible (λ ∼ 560 nm) to the near infrared (λ ∼ 855 nm) regions, as well as in the number of distinguishable modes (see also Fig. S8 andS9). These results, obtained on single or multi-maghemite core nanostructures, establish an unambiguous relation between their nanoscale and macroscopic optical properties. Indeed, the typical optical response of an isolated MagPlasNP-2 nanostructure consists primarily in a surface resonance at about 620 nm, confirming accurately the UV-Vis-NIR spectroscopy observations shown in Fig. 1f. Furthermore, intrinsic size and shape inhomogeneities combined with the formation of anisotropic agglomerates of multi-core nanostructures lead to slight energy shifts of the surface plasmon, and even to the appearance of multiple modes explaining the sizeable energy broadening of the resonance observed in the macroscopic measurements.

Magneto-plasmonic nanohybrids were then subjected to magnetic and laser stimulations. First, all nanohybrids were dispersed at [Fe] =7 mM in water, and exposed to i) magnetic hyperthermia (MHT) at magnetic field of 900 kHz and 25 mT, (ii) 680-nm NIR laser at a power density of 0.3 W/cm 2 (PLASM), and (iii) combined magnetic field and laser at the exact same conditions (MHT+PLASM) (Figs. 3a and3b). In the first case (MHT only), the same temperature elevation of 6°C was observed for all samples, corresponding to a heating power (specific absorption rate (SAR) expressed in W/g of iron) at 634 ± 76 W/g, in the range of the highest SAR yet reported. This excellent magneto-thermal efficiency is brought by the multicore assembly which decreases the surface disorder and enhances the magnetic susceptibility, thus potentiating thermal losses.

11

During laser exposure at 0.3 W/cm², the temperature elevation was tuned by the nanohybrid design, increasing from 2°C for MagNPs, to 6°C for MagPlasNP-1 and 11°C for MagPlasNP-2 and 3. The combination of both magnetic and laser exposures (MHT+PLASM) led to a remarkable accumulation effect, reaching 14°C elevation for MagPlasNP-1, and up to 18-19°C for MagPlasNP-2 and 3 (see also the cumulative effect for a 808 nm-laser excitation in Fig. S10, and the influence of laser power density, from 0.1 to 0.5 W/cm 2 in Fig. S11). Second, the MagPlasNP-2 heat generation potential was investigated as function of the concentration ([Fe] = 3.5, 7, 15, 30 and 60 mM) (Figs. 3c-d), using a magnetic coil ensuring biosafety for future clinical application (110 kHz, 25 mT). The magnetic heating was proportional to the concentration, corresponding to a heating power of 170 ± 30 W/g (consistent with the decrease in frequency to 110 kHz). The 680 nm laser was used at the same low power (0.3 W/cm²), evidencing a saturation of the heating capacity with concentration. In the magneto-plasmonic mode, the resulting thermal efficiency increased with the concentration, and therapeutic temperature elevations over 17°C were achieved in very short times (100 s, see Fig. S12 for the temperature profiles) for concentrations in the [Fe] = 30-60 mM range. The combined heating was finally tested in a mouse animal model (Fig. 3e) in order to evaluate its workability in vivo. Before injecting in animals, we determined that the nanohybrids were biocompatible and effective for tumour cell capture (Fig. S13). This biocompatibility, confirms the long-standing and safe record of PVP coating in biomedical/pharmaceutical applications. [START_REF] Robinson | PVP: A Critical Review of the Kinetics and Toxicology of Polyvinylpyrrolidone (Povidone)[END_REF] The thermal window to achieve tumor ablation corresponds to 45-48°C temperature range. For subcutaneous tumor (initial temperatures around 28°C), it means a temperature elevation of 17-20°C. For a tumor volume of about 150 mm 3 , we thus chose to inject intratumorally 50 µl-suspension of MagPlasNP-2, at [Fe] = 150 mM (expected final intratumoral concentration in the 50 mM range, corresponding to a potential 18-20°C temperature elevation). The collateral tumor was non-injected and considered as control. Both magnetic induction and laser irradiation alone showed an efficient and rapid thermal performance with a 9-10°C temperature increase, while no temperature increase was observed in noninjected tumor. Under the two stimulations, the heating was definitely cumulative, with an increase of almost 20°C, reached within 2 min. Moreover, the heating performance was still high after 3 days (80% of heating maintained), indicating lasting effectiveness (Fig. S14). Histological sections were examined for a tumor excised after injection, revealing nanohybrids-rich zones around the tumor corona that diffusely penetrate to deeper tissues (Fig. S15), confirmed as well by TEM observations (Fig. S16) close and far to the injection spot. Nevertheless, the tumoral localization of the nanohybrids was sufficient to afford global heating in macroscopic zones, even 2 days after injection (see Fig. S14). Finally, a preliminary follow-up of the tumor growth was performed after the combined treatment, revealing a promising therapeutic tumor regression during the 5 following days, in comparison with the control tumors (Fig. S17).

Please do not adjust margins

Please do not adjust margins

Conclusions

To summarize, we have demonstrated that an adequate magnetoplasmonic design can efficiently combine photothermia with magnetic hyperthermia into an efficient bimodal thermo-therapy. The proposed stable and biocompatible magneto-plasmonic nanohybrids were composed of an iron oxide multi-core optimized for high efficiency in magnetic hyperthermia, and a gold shell with tunable plasmonic properties in the NIR region. We provided nanoscale characterization by mapping for the first time the plasmon around a magnetic oxide core, connecting unambiguously the optical response of single, isolated nanostructures with that of large assemblies. We then demonstrated the versatility of the system in generating heat through a remarkable cumulative effect when both magnetic and plasmonic modalities were applied simultaneously and showed that heating efficiency was maintained in in vivo conditions. The tumor temperature can then rapidly reach 48°C, condition for therapeutic tumor ablation, with dose injected 10 times lower than for classical magnetic hyperthermia treatment.

Fig. 1

 1 Fig. 1 (a) The seeding-growth process used for the synthesis of the magneto-plasmonic nanoparticles (MagPlasNP) of different ratio Au/Fe: MagPlasNP-1 (Au/Fe = 1.13 ± 0.04), MagPlasNP-2 (Au/Fe = 3.1 ± 0.7) and MagPlasNP-3 (Au/Fe = 4.7 ± 0.9). (b-e) STEM-EELS analysis of nanohybrids. HAADF image, EELS Fe elemental map (green), EELS O elemental map (blue), EELS Au elemental map (red) and overlaid elemental maps are shown for (b) MagNP-seeds, (c) MagPlasNP-1, (d) MagPlasNP-2, and (e) MagPlasNP-3. (f) Vis-NIR absorption spectra of the different structures. PVP: polyvinylpyrolidone; DMF: dimethylformamide.

  images (TEM) are shown in Fig. S1 for MagNP-seeds, with average diameter, d ≈ 39 ± 4 nm, MagPlasNP-1, d ≈ 47 ± 6 nm, MagPlasNP-2, d ≈ 53 ± 7 nm and MagPlasNP-3, d ≈ 63 ± 11 nm.

Fig. 2

 2 Fig. 2 Surface plasmon resonance of a single nanohybrid MagPlasNP-2. (a) High-angle annular dark field (HAADF) image and electron energy loss spectroscopy (EELS) elemental maps of a single nanohybrid (MagPlasNP-2), confirming the presence of an iron oxide core of ∼ 30 nm in diameter covered with a ∼ 20 nm thick discontinuous Au shell. (b) Surface plasmon resonance map (smoothed) corresponding to the 1.4-2.4 eV energy range. The contour of the nanohybrid is superimposed to the map. (c) EELS corresponding to four different beam positions around the nanohybrid. A single broad resonance is observed at ∼ 2.0 eV (λ  620nm) is observed. Raw data are shown.

Fig. 3

 3 Fig. 3 Heating efficiency of the nanohybrids. (a,b): Tunability of the heat generation with the nanohybrids design. All NPs were dispersed at the same concentration [Fe] = 7 mM. The magnetic coil used delivered a (900 kHz, 25 mT) magnetic field. 680 nm laser was used at 0.3 W/cm². (a): Typical infrared images after 5 min heating of magneto-plasmonic nanoparticles (MagPlasNP-1 and MagPlasNP-2) under magnetic hyperthermia (MHT), laser irradiation (PLASM) and the combination of both modalities (MHT + PLASM) (100 µl sample in 500 µl eppendorf (8 mm-diameter) placed within the coil). (b): Average temperature elevation recorded for magnetic (MagNPs) and magneto-plasmonic nanoparticles (MagPlasNP-1, MagPlasNP-2 and MagPlasNP-3) under the three different heating protocols (c,d): Tunability of the heat generation with the nanohybrids (MagPlasNP-2) concentration. MHT was now performed in conditions of biosafety (magnetic coil at 110 kHz frequency). Same laser settings were used (680 nm, 0.3 W/cm²). (c): Typical infrared images after 5 min heating for MagPlasNP-2 at [Fe] = 15 and 60 mM (100 µl sample in a home-made 8 mm tube containing a cylindrical hole of 3x3x5 mm to be filed with the solution). (d): Average temperature elevations recorded in all conditions. The magnetic heating (MHT) increases linearly with the concentration, while the laser efficiency (PLASM) saturates at high concentrations. As a result, the magneto-plasmonic heating (MHT+PLASM) mostly follows the magnetic-related variation with concentration. (e): In vivo hyperthermia performance. A solution of [Fe] = 150 mM of MagPlasNP-2 is injected into the tumour (T+). (Left): typical infrared thermal imaging pictures after 5 min heating under MHT alone (110 kHz, 25 mT), PLASM alone (680 nm, 0.3 W/cm 2 ) and bimodal MHT+PLASM (same parameters). (Right) Typical temperature elevation profiles of the injected (T+) and non-injected tumours (T-, control tumour) as a function of time for the three treatments.

29 A. E. acknowledges support from the European Commission under a Marie Curie Intra-European project FP7-PEOPLE-2013-IEF-626471. G.R. acknowledges Institut de Physique (INP) of Centre National de la Recherche Scientifique (CNRS) for partial financial through a PICS. G. A. B. is grateful to the Natural Sciences and Engineering Research Council (NSERC), Canada, for a Discovery grant partially supporting this work. The STEM and EELS work was carried at the Canadian Centre for Electron Microscopy, a national facility supported by NSERC, the Canada Foundation for Innovation and McMaster University. A. A. H acknowledges N. Menguy (IMPMC lab, UPMC) for discussions. We thank A. Djemat from Buffon Animalery for animal care and housing.


Patrice Meunier

Peter Huck

Clément Nobili

Emmanuel Villermaux

Experimental measurement of the Melnikov function

We study the transport properties of a genuine two-dimensional flow with a large mean velocity perturbed periodically in time by means of an original experimental technique. The flow, generated by the co-rotation of two cylinders is both stratified with a linear density gradient using salted water, and viscous in order to prevent Ekman pumping and centrifugal instabilities. Thus, the mean flow contains a hyperbolic point with a homoclinic streamline, which we perturb periodically by an extra oscillation. A blob of scalar injected close to the stagnation point contracts on the stable manifold, and stretches in the unstable direction. The distance between the stable and the unstable manifolds is measured as the distance between the maximum and the minimum of the dye undulating pattern, and is recorded as a function of the perturbation frequency. This distance, also called the Melnikov function, presents a maximum when the residence time of a fluid particle in the mean flow is about half a perturbation period. This resonance criterion is recovered with good quantitative agreement by the theoretical prediction of the Melnikov function computed for this flow.

I. INTRODUCTION

Scalar mixing is a key point for numerous natural and man-made operations, spanning a broad range of length scales from microns [START_REF] Stroock | Chaotic mixer for microchannels[END_REF][START_REF] Villermaux | Bridging kinematics and concentration content in a chaotic micromixer[END_REF] to geophysical scales [START_REF] Wiggins | The dynamical systems approach to Lagrangian transport in oceanic flows[END_REF] . In the atmosphere, fluxes of moisture, temperature and chemical components are governed by mixing. Scalars can be trapped in atmospheric vortices, thus representing barriers for transport [START_REF] Joseph | Relation between kinematic boundaries, stirring, and barriers for the antarctic polar vortex[END_REF][START_REF] Haynes | Effective diffusivity as a diagnostic of atmospheric transport: 1. stratosphere[END_REF][START_REF] Koh | Lobe dynamics applied to barotropic Rossby-wave breaking[END_REF][START_REF] Provenzale | Transport by coherent barotropic vortices[END_REF] . For example, strong polar vortices form above each pole during winters, and maintain low temperatures and low ozone concentrations. However, it was observed that these polar vortices may split, as happened in 2002 on the Antarctic polar vortex [START_REF] Shepherd | The antarctic vortex splitting event[END_REF] , creating undulating stretched structures leading to fast mixing [START_REF] Lekien | The computation of finite-time lyapunov exponents on unstructured meshes and for non-Euclidean manifolds[END_REF] . The dynamics in this instance was governed by the presence of a hyperbolic point with a homoclinic manifold i.e. whose streamline reconnects on itself. This object, which consists of a weak unsteady flow added to a hyperbolic point flow, has been long ago identified as a paradigm in chaotic advection [START_REF] Ottino | The Kinematics of Mixing: Stretching, Chaos, and Transport[END_REF][START_REF] Rom-Kedar | An analytical study of transport, mixing and chaos in an unsteady vortical flow[END_REF][START_REF] Beigie | A global study of enhanced stretching and diffusion in cahotic tangles[END_REF] , but despite its fame has never been the subject of laboratory study. The goal of the present study is to reproduce experimentally this type of flow and to analyse it with available theories, namely Melnikov theory.

The dynamics homoclinic and heteroclinic manifolds has been widely studied in dynamical systems theory [START_REF] Guckenheimer | Non-Linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[END_REF][START_REF] Wiggins | Introduction to Applied Nonlinear Dynamical Systems and Chaos[END_REF] . Indeed, the stability of these trajectories with respect to external perturbations is of critical importance in the transition to chaotic behaviors. This problem is often studied as an hamiltonian time-invariant system perturbed by a small time-periodic flow. The homoclinic (or heteroclinic) trajectory splits into a stable and an unstable manifold whose separation distance can be predicted at first order by a simple integral called the Melnikov function [START_REF] Guckenheimer | Non-Linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[END_REF] . This theory was then applied in fluid dynamics [START_REF] Rom-Kedar | An analytical study of transport, mixing and chaos in an unsteady vortical flow[END_REF] in the case of two counter-rotating point vortices in order to predict the transport of scalar across the homoclinic trajectory. It is a very interesting result since this slow transport across the separatrix is usually the limiting process of the long-range transport in chaotic mixing [START_REF] Solomon | Resonant flights and transient superdiffusion in a timeperiodic, two-dimensional flow[END_REF] . This powerful technique was used for numerical and theoretical studies of various flows [START_REF] Camassa | Chaotic advection in a Rayleigh-Benard flow[END_REF][START_REF] Samelson | Fluid exchange across a meandering jet[END_REF][START_REF] Gence | Efficient stirring in planar, time-periodic laminar flows[END_REF][START_REF] Ngan | Chaotic mixing and transport in rossby-wave critical layers[END_REF][START_REF] Del Castillo-Negrete | Asymmetric transport and non-gaussian statistics of passive scalars in vortices in shear[END_REF][START_REF] Rom-Kedar | Universal properties of chaotic transport in the presence of diffusion[END_REF] . Such a mechanism was proven to be responsible for large asymmetries in the dye visualisations of vortex breakdown [START_REF] Brons | The influence of imperfections on the flow structure of steady vortex breakdown bubbles[END_REF][START_REF] Brons | Dye visualization near a three-dimensional stagnation point: application to the vortex breakdown bubble[END_REF] and lead to strong transport from inside to outside the vortex breakdown bubble [START_REF] Lopez | Axisymmetric vortex breakdown. part 3 onset of periodic flow and chaotic advection[END_REF][START_REF] Meunier | Mixing in a vortex breakdown flow[END_REF] . However, this technique has never been used to quantitatively predict the transport of a real experimental flow except once [START_REF] Meunier | Mixing in a vortex breakdown flow[END_REF] , where it was found to be an order of magnitude too large. Early experimental studies have focused on two-dimensional (2D) flows which would oscillate temporally between two states [START_REF] Chien | Laminar mixing and chaotic mixing in several cavity flows[END_REF][START_REF] Chaiken | Experimental study of lagrangian turbulence in stokes flow[END_REF][START_REF] Ottino | Morphological structures produced by mixing in chaotic flows[END_REF][START_REF] Swanson | A comparative computational and experimental study of chaotic mixing of viscous fluids[END_REF][START_REF] Janat | Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows[END_REF] , and showed that the Poincaré sections 31 could distinguish the zones of high (chaotic) dispersion from the zones where the particles were trapped (KAM tori and periodic orbits). Solomon and Gollub (1988) [START_REF] Solomon | Chaotic particle transport in time-dependent Rayleigh-Bénard convection[END_REF] also showed that a periodic oscillation of the flow would enhance the advection of a passive scalar in Rayleigh-Benard convection rolls. But all these flows were obtained in a very viscous fluid where Ekman pumping on the boundaries might have introduced an additional three-dimensional (3D) motion.

In order to keep the flow two-dimensional, experimentalists have tried to confine the flow in a thin layer of electrolyte forced electromagnetically [START_REF] Solomon | Role of lobes in chaotic mixing of miscible and immiscible impurities[END_REF][START_REF] Rothstein | Persistent patterns in transient chaotic fluid mixing[END_REF][START_REF] Williams | Mixing of a passive scalar in magnetically forced twodimensional turbulence[END_REF][START_REF] Voth | Mixing rates and symmetry breaking in twodimensional chaotic flow[END_REF][START_REF] Rossi | Electromagnetically controlled multi-scale flows[END_REF][START_REF] Figueroa | Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions[END_REF] . But the flow would still be subject to a 3D Ekman pumping at large amplitudes [START_REF] Kelley | Onset of three-dimensionality in electromagnetically driven thin-layer flows[END_REF] (although reduced thanks to the stratification of the electrolyte [START_REF] Paret | Are flows electromagnetically forced in thin stratified layers two dimensional?[END_REF] ), leading to a complete and quicker mixing [START_REF] Solomon | Uniform resonant chaotic mixing in fluid flows[END_REF] . The idea of using a stratified flow has been used in the case of a vortex 42 which increased by a factor ten the lifetime of the vortex. However, stratified flows are also subject to 3D instabilities at large Reynolds numbers. This paper presents a new experimental technique which allows the motions to remain exactly 2D over a very long time.

The paper is organized as follows: after presenting the experimental set-up in section II, the flow is analyzed in detail in section III before the Melnikov function is measured in section IV. Conclusions follow in section V.

II. FORMULATION OF THE PROBLEM

A. Periodic perturbation of a homoclinic point

The goal is to study the Melnikov theory in a real experiment by creating a flow with a homoclinic point under the influence of a periodic perturbation. This is done by rotating at the angular velocity ω 0 = 0.5 -2 rad/s two cylinders of radius R 0 = 2 cm separated by a distance D = 11.3 cm between their axes (see Fig. 1). This creates a hyperbolic point at the middle between the cylinders whose streamlines surround each cylinder. This mean 2D incompressible (i.e. Hamiltonian viewed from dynamical systems) flow is perturbed periodically by a third cylinder of radius R 1 = 3 cm which oscillates in translation at the frequency ω 1 = 0.3 -2 rad/s with an amplitude A. This flow is contained in a Plexiglas tank of dimensions 40 × 40 × 16 cm 3 to allow visualisations from the side and from the top.

All lengths are counted in units of the distance D between the rotating cylinders. This defines a first non-dimensional parameter r 0 = R 0 /D = 0.177, which is small. As a consequence, the flow close to each rotating cylinder is similar to a point vortex flow (decaying as 1/r) with a circulation Γ = 2πR 2 0 ω 0 . This circulation Γ is used to define the timescale D 2 /Γ. The two main non-dimensional parameters are thus the non-dimensional frequency and amplitude of the forcing

ω = ω 1 Γ/D 2 and = A D . (1)
The flow also depends on the ratio r 1 = R 1 /D = 0.265 which is kept constant in this study. The Reynolds number Re = Γ/ν = 125 -500 (ν being the fluid kinematic viscosity) has no impact on the flow.

B. 2D or not 2D?

That is the question of any experimentalist trying to study a 2D flow in our 3D world. Several attempts have been made by studying a thin electrolyte layer electromagnetically forced or by using a soap film. In the first case, the friction from the bottom damps the flow and eventually enables vertical Ekman pumping at large Reynolds number. In the second v 0 = -∂Ψ 0 /∂x (dashed line, 2) along the homoclinic streamline. Symbols (•,2) correspond to experimental data obtained by PIV measurements whereas solid and dashed lines correspond the theoretical prediction of Eq. ( 2) without (thick lines) and with (thin lines) the correction given by Eq. (3) induced by the oscillating cylinder. Here, ω = 2.47, = 0.35 and Re = 125.

case, the variation of the thickness of the soap film creates some divergence in the flow as in a compressible 2D flow. Both set-ups are thus not ideal to create a 2D incompressible flow.

In a previous study [START_REF] Meunier | Van Hove singularities in Probability Density Functions of scalars[END_REF] , we had used a stable density gradient to prevent any vertical velocity. Indeed, imposing a continuous linear variation of the density with the altitude allowed to study the mixing properties of a solitary vortex which remained 2D during a few hundred revolutions. We used the same set-up in this study, but we increased the viscosity of the fluid to prevent a 3D centrifugal instability to appear. For this purpose, we added to the water 10% by volume of UCON TM oil 43 whose viscosity ν Ucon is about 10 4 that of water at 20 • Celsius, in order to increase the fluid viscosity by a factor about 10. This allowed to decrease the Reynolds number below the threshold of the centrifugal instability while allowing to stratify the water by adding salt.

The continuous stratification is obtained using the double bucket method. The solution of water and UCON TM oil is split in two small buckets and 5% salt is added in one bucket. The salt-free solution is slowly injected at the bottom (under a 10 cm diameter disk) while the salted solution is continuously added to the salt-free solution (through a pipe connecting the two buckets). If the two buckets have the same area, the final fluid is stratified with a density varying linearly from the salted solution (at the bottom) to the salt-free solution (at the top). This stable density gradient could be used during two weeks for about a hundred experiments. The density gradient introduces an additional non-dimensional parameter, defined by the Froude number F = ω 0 /N ∼ 0.25 -1, where N = -(g/ρ)(∂ρ/∂z) is the buoyancy (Brunt-Väisälä) frequency. However, this parameter has no influence on the final results.

C. Measurement techniques

We used two different methods to study the velocity and the stirring properties of this flow. First, small reflecting particles were added into the fluid and illuminated by a hor-izontal laser sheet from a continuous Argon laser. Correlating two images separated by 0.3 seconds using a homemade Particle Image Velocimetry (PIV) algorithm [START_REF] Meunier | Analysis and optimization of the error caused by high velocity gradients in PIV[END_REF] permitted to get instantaneous velocity fields. Second, a small drop of dye (Fluoresceine) was injected at the altitude of the laser sheet close to the hyperbolic point. The dye stretches into a thin filament as it reaches the hyperbolic point. The filament is then advected around the rotating cylinder and thus reveals the unstable manifold of the homoclinic point. The characteristics of the unstable manifold were independent of the position of injection of the dye. Because of the Stokes-Einstein law, the diffusivity of Fluorescein in a UCON TM oil/water mixture 10 times more viscous than pure water is 10 times smaller than the diffusivity of Fluorescein in water, i.e. of the order of κ = 5 × 10 -11 m 2 /s. This value was checked by measuring the traverse thickness κ/γ (Batchelor scale) of the filament in the stretching flow of the hyperbolic point of strength γ ∼ Γ/D 2 from the temporal decrease of its maximum concentration e -γt . The corresponding Péclet number P e = ω 0 R 2 0 /κ = 25 -100 × 10 6 is very large. However, we do not focus in this study on the mixing properties of the flow (for which diffusion matters) but only on its stirring (advecting) properties. Our present discussion is thus independent of the Péclet number.

III. BASE FLOW A. Mean flow

PIV measurements allowed to extract the instantaneous horizontal velocity fields which were then averaged in time. The mean velocity field is shown in Fig. 2(a) and clearly reveals the presence of the hyperbolic point at the middle between the rotating cylinders. The velocity is very strong and nearly axisymmetric around each rotating cylinder, which can be modeled by two point vortices with a circulation 18 Γ = 2πR 2 0 ω 0 . However, a pair of two stationary point vortices is not a solution of the vorticity equation because a co-rotating vortex pair is rotating at the angular velocity Ω = Γ/(πD 2 ). The flow is thus modeled by a co-rotating vortex pair in the frame of reference rotating at Ω, which imposes that the velocity is in solid body rotation at -Ω far from the cylinders. The stream function can be written in non-dimensional form

Ψ 0 = 1 4π log |r -r C | + log |r -r C | -2|r| 2 (2)
where the center O of the reference frame is taken at the middle between the cylinders and where r C = (1, 1)/ √ 2 and r C = (-1, -1)/ √ 2 correspond to the centers of the cylinders. The theoretical streamline starting at the hyperbolic point O is plotted in Fig. 2(a) and shows a very good agreement with the experimental velocity field. By contrast with an earlier study [START_REF] Gence | Efficient stirring in planar, time-periodic laminar flows[END_REF] , the presence of the background rotation prevents an analytical derivation of the streamlines, which are thus calculated numerically.

The mean vorticity field ζ is plotted in Fig. 2

(b)

. There is some negative vorticity close to the rotating cylinders of the order of unity. This is consistent with the mean theoretical vorticity which is uniform and equal to -2/π. However, the vorticity decays far from the cylinders. This is probably due to the viscous friction at the bottom and to the presence of the oscillating cylinder which clearly modifies the mean velocity field (see Fig. 2a). However, along the streamline starting from the hyperbolic point O, the vorticity is close to the theoretical value within 20%.

In order to quantitatively compare the theoretical and the experimental velocity field, we have plotted the mean velocity components u 0 = ∂Ψ 0 /∂y and v 0 = -∂Ψ 0 /∂x along the streamline in Fig. 3. They are plotted as a function of time, i.e. for a fluid particle starting close to O. There is a fairly good agreement, although v 0 is slightly underestimated close to the oscillating cylinder. This is due to the deflection of the flow by the presence of the oscillating cylinder which accelerates the fluid. Indeed, the wake of the oscillating cylinder in the mean flow u 0 creates a small correction which can be written (from the potential flow around a cylinder [START_REF] Lamb | Hydrodynamics[END_REF] )

u corr = |u 0 (r p )| r 2 1 |r -r p | 2 cos(2 θ corr ) sin(2 θ corr ) . (3)
Here θ corr is the angle between the vector rr p and the mean velocity u 0 (r p ) at the center r p = (x p , y p ) = (1.15, 0.07) of the oscillating cylinder. Adding this mean correction to the mean flow creates a velocity along the streamline which is plotted as thin lines in Fig. 3, in better agreement with the experimental data.

B. Periodic perturbation

The flow created by the oscillation of the cylinder can be measured experimentally by phase averaging the instantaneous velocity fields and then subtracting the mean flow. It is plotted in Fig. 4(a) at a phase where the cylinder is moving toward positive x.

This flow is again modeled as the potential flow around a cylinder (as for the correction of the mean flow). In non-dimensional form, the cylinder has a radius r 1 and is oscillating in the x direction at the frequency ω with an amplitude . The oscillating flow can thus be written in cartesian coordinates (here θ p is the angle between the vector rr p and the x-axis)

u 1 = ω cos(ωt) r 2 1 |r -r p | 2 cos(2 θ p ) sin(2 θ p ) . ( 4
)
This velocity field is plotted in Fig. 4(b) and is in excellent qualitative agreement with the experimental velocity field. There is only a minor discrepancy above the cylinder. This is probably due to the shade created by the cylinder in the laser sheet, which alters the PIV measurements.

A quantitative comparison between these two fields can be done by taking velocity profiles along the solid line (passing through the center of the oscillating cylinder). It is plotted in Fig. 5(a) and shows that the theory overestimates the v 1 velocity by about 20%. However, this may come from the noise in the measurements which is large because u 1 is a first order velocity much smaller than u 0 . The temporal variation of this velocity is plotted in Fig. 5(b) which confirms that the velocity is oscillating sinusoidally in time. There is again a small discrepancy between the experiment and the theory which slightly overestimates v 1 .

IV. MELNIKOV FUNCTION

In order to quantify the transport properties of this flow, a blob of dye is injected close to the hyperbolic point O. The dye stretches along the unstable manifold, is advected around the rotating cylinder and comes back to the hyperbolic point O. Fig. 6 shows the shape of the dye filament when it reaches the hyperbolic point for various amplitudes and oscillating frequencies ω. It exhibits undulations whose amplitude is larger for larger oscillations of the cylinder. Moreover, the wavelength is smaller when the oscillating frequency is larger.

As sketched in Fig. 7, these undulations are due to the perturbing flow u 1 of the oscillating cylinder. Intuitively, the fluid particles are advected between point D and E to the right or to the left depending on the phase of the perturbation. The fluid particle is thus displaced a distance δ at point E. This distance to the unperturbed streamline increases when the fluid particle reaches the hyperbolic point O. This is clearly visible in Fig. 8(a) where the undulations grow in amplitude close to the hyperbolic point. The maxima and minima of these undulations have been measured on several images. They are plotted in Fig. 8(b) and seem to be located on a hyperbola although based on non-orthogonal axes (x , y ). Indeed, and with perturbation (dashed lines). The thick (resp. thin) dashed line corresponds to the case where the time for the particle to go from D to E is equal to half an oscillating period (resp. a full period). The distance δ between the unstable and stable manifold increases close to O due to the divergence of the streamlines.

the flow around O can be Taylor expanded as

u 0 v 0 = γ -Ω Ω -γ x y (5)
where the symmetric part γ = 4/π of the velocity gradient is due to the point vortices and the anti-symmetric part Ω = 1/π reflects the weak background vorticity. The presence of Ω makes the eigenvectors non-orthogonal (see Fig. 8b) with opposite eigen values ±λ = ± γ 2 -Ω 2 . The flow near O is a 'tilted' stagnation point. The value of the strain λ has been measured experimentally by PIV and was found to be very close to the theoretical value (within 1%). The coordinates (x , y ) of a fluid particle thus evolve exponentially in time as

x ∼ e λt and y ∼ e -λt with λ = γ 2 -

Ω 2 = √ 15/(4π). ( 6
)
As a consequence, the product x y is constant which explains why the maxima and minima are located on a tilted hyperbola. The amplitude of the hyperbola x y = χ has been The Melnikov function M is defined as the distance between the stable and the unstable manifolds multiplied by the velocity of the unperturbed flow. In the schematic view of Fig. 7 where the perturbation is localized between points D and E, it corresponds to the product δu 0 . This product is exactly equal to the product χλ we measured previously χ = x y since δ = x and u 0 = λy . This is why the product χλ of the maxima and minima of the undulations should be predicted by the maximum M max of the Melnikov function.

The main result concerning the Melnikov function is that it can be calculated analytically along the unperturbed trajectory r 0 (t) solution of the mean flow u 0 . Indeed, if the flow is incompressible (i.e. Hamiltonian in dynamical systems), it is given by

M (τ ) = t=+∞ t=-∞ u 0 [r 0 (t)] × u 1 [r 0 (t), t + τ ]dt (7)
as a function of the phase τ . This formula is the precise formulation of the mechanism explained earlier in Fig. 7 for a localized perturbation where the distance δ is simply the integral of the normal velocity between points D and E. The Melnikov function is of course proportional to because u 1 is proportional to . Moreover, it is oscillating sinusoidally as a function of the phase τ . The Melnikov function has been calculated numerically by integrating the formula (7) along the trajectory r 0 (t). In our case, r 0 (t) was also found numerically because it was not possible to find an analytical solution due to the background vorticity term. The maximum M max for τ varying over one period is then plotted (thick solid line) as a function of ω in Fig. 9(b). The Melnikov function increases and presents a peak at ω ≈ 2. FIG. 9: Melnikov function as a function of (a) the amplitude and (b) the frequency ω of the oscillating cylinder. Symbols correspond to experiments at ω 0 =0.5 rad/s (•), ω 0 =1 rad/s (2), ω 0 =2 rad/s ( ). Lines correspond to the theory without (solid line) and with (dashed line) the deflection u corr of the mean flow by the presence of the oscillating cylinder. The dash-dotted line corresponds to the theory given by Eq.( 21) for a flow with no background vorticity [START_REF] Gence | Efficient stirring in planar, time-periodic laminar flows[END_REF] .

This 'resonance' can be understood in simple terms (see Fig. 7) since δ(E) is maximum if the time for a particle to go from D to E is equal to half an oscillating period (case of the thick dashed line). In the case where the time to go from D to E is equal to one period (thin dashed line), the distance δ(E) is always equal to 0. This is why there is an oscillating frequency ω where the unstable manifold is most sensitive to the perturbation. Indeed, assuming that the time to travel from D to E is roughly equal to 2r 1 /u 0 ≈ 1, the maximum should be obtained around ω ≈ π.

This theoretical prediction is compared to the experimental value χλ/ measured from the maxima and minima of the tracer dye pattern undulations (Fig. 9). There is a good qualitative agreement since both curves present a maximum. There is a good quantitative agreement on the amplitude of the maximum, which is close to 0.2 in both experiments and theory. However, the maximum is found theoretically for a frequency ω ≈ 2 smaller than the experimental observation ω ≈ 4 (both values being close to π, see above). This discrepancy is probably due to the inadequate model of the mean flow. Indeed, the simple addition of the correction u corr to the mean flow due to the presence of the oscillating cylinder leads to the dashed line which is in better agreement with the experiment. Moreover, it was shown that the background vorticity was damped by the bottom. The extreme case (with zero background vorticity) corresponds to a flow containing only two point vortices [START_REF] Gence | Efficient stirring in planar, time-periodic laminar flows[END_REF] . Redoing the calculation for such a flow leads to a theoretical prediction given as a simple integral (see appendix). This prediction is plotted as a dash-dotted line (for y p = 0) in Fig. 9(b). For such a mean flow, the maximum is obtained at ω ≈ 6. It is thus possible to tune the background vorticity in order to obtain any agreement between the theory and the experiment. However, such a fit is of no interest for this study, which only aimed at checking the validity of the Melnikov function in a real flow.

Finally, it is interesting to see how the Melnikov function depends on the distance from the cylinder to the hyperbolic point. This was done theoretically by changing the position x P of the perturbing cylinder from 1.15 to 10, as shown on Fig. 10(a). It is clear that the amplitude depends strongly on the distance of the perturbing cylinder, decreasing by a factor 40 when the distance x P increases from 1.15 to 5. This is natural since the perturbing FIG. 10: Theoretical Melnikov function as a function of the perturbing frequency ω for various positions of the perturbing cylinder. The solid lines correspond to (x P , y P ) = (1.15, .07) as in the experiment. Dashed lines correspond to (x P , y P ) = (3, .07) and dash-dotted lines correspond to (x P , y P ) = (10, .07). The theory is calculated in the presence (a) and in the absence of background vorticity. In (b), thick lines correspond to the full theory (21) and thin lines correspond to the approximation of a cylinder located far from the hyperbolic point (8).

velocity field (4) scales as |r -r P | -2 such that the Melnikov function should scale as x -2 P for large x P . Moreover, when the perturbing cylinder is far enough, there are multiple resonant peaks. This can be qualitatively understood by the fact that the fluid particle can spend an odd number of half periods in the interaction zone for the displacement to be maximum. However, it is surprising to see that these multiple peaks disappear in the absence of background vorticity, as shown on Fig. 10(b). This is probably due to the fact that the streamline is at right angle in the case without background vorticity, whereas it has an angle slightly larger than 90 degrees in the presence of background vorticity. When the oscillating cylinder is far from the hyperbolic point, this integral of the Melnikov function can be even calculated analytically, leading to a simple expression for the maximum of the Melnikov function:

M max = π 2 r 2 1 ω 2 8x 2 p 2 cosh(π 2 ω/8) . (8)
This approximate solution is plotted as thin lines in Fig. 10(b)and is close to the full solution when x p is larger than 3. This simple formula clearly shows that the Melnikov function scales as x -2 P at large x P .

V. CONCLUSIONS

We have studied experimentally the transport properties of a 2D flow with a large mean velocity perturbed periodically in time. The flow was realized using a stratified and viscous fluid in order to ensure perfect 2D motion. We focused on the case of a mean flow containing a homoclinic point perturbed periodically by an oscillating flow. Such a flow is well known to create an undulation of the unstable manifold leading to a large transport of scalar from inside to outside the homoclinic streamline starting from the hyperbolic point. The undulations of the unstable manifold have been measured quantitatively and compared to the prediction from the Melnikov theory. The amplitude of the undulations are maximum for a given frequency, which can be estimated by assuming that the mean flow advects a fluid particle over the perturbed area in half a period. There is a good quantitative agreement between the theory and the experiment, given that there is no fitting parameter in the model. However, the resonant frequency is slightly underestimated by the theory probably due to small corrections to the mean flow that have not been taken into account.

This study interestingly underlines the effect of a small perturbation on the transport properties of a mean flow. Moreover, it validates the Melnikov theory which has been widely used in the literature but which has never been tested experimentally. The first reason is probably that it is difficult to create a 2D flow. This technical problem has been solved here by a subtle combination of salt and UCON TM oil in order to create a viscous stratified fluid. The second reason is also that it is difficult to create a flow with a homoclinic point (or two heteroclinic points [START_REF] Rom-Kedar | An analytical study of transport, mixing and chaos in an unsteady vortical flow[END_REF] ). This flow topology has been realized here by two co-rotating cylinders, which lead to a flow predicted by a simple theory with no adjustable parameter. This is a major advantage since it allows to test the Melnikov theory accurately.

The initial goal of this study was to quantify the transport of dye from inside to outside the streamline starting from the homoclinic point. Indeed, the Melnikov theory can be used to predict the surface of the lobes of the unstable manifold and thus to evaluate the amount of dye which exits the streamline. However, experiments have shown that the position of injection of the dye was critical for the late evolution of the dye. If the dye was located too far from the central streamline of the contracting direction, it would become homogenized by diffusion in a band that would never reach the hyperbolic point. If the dye was located too close from the streamline, it would exit the streamline very rapidly in the stretching direction, before being homogenized on the inner part of the streamline, thus preventing the measurement of the amount of dye exiting the streamline. However, these results indicate that the transport of dye from inside to outside this streamline is extremely rapid close to the streamline. The global transport at late stages is thus limited by the slow advectiondiffusion far from the streamline (i.e. close to the vortex centers), which is strongly damped by the presence of KAM torii. It thus seems that the study of advection-diffusion in a weakly perturbed vortex is of primary importance for the understanding of 2D mixing, an extension of this study that we leave for future research.

which can be simplified into

x 2 + y 2 2 = xy (11)
The mean velocity on this trajectory can be simplified using (10) to replace the fractions by polynomials whose degree can be further reduced by using (11). This leads to simple differential equations for the homoclinic trajectory:

Here, we have used (11) to calculate (x 2 -y 2 ) 2 = (x 2 + y 2 ) 2 -4(xy) 2 as a function of p. Introducing the new variable q = 1/(2p) leads to a simple differential equation whose solution is q = cosh(±8t/π) from which p can be evaluated as: p = x 2 + y 2 = 1 2 cosh(±8t/π) (14) Using (11), it is easy to evaluate (x + y) 2 and (x -y) 2 which can be simplified using trigonometric functions such that x + y = cosh(±4t/π) 2 cosh(±8t/π)

xy = sinh(±4t/π) 2 cosh(±8t/π) (15) from which x and y are derived as x = exp(-4t/π) 2 cosh(8t/π) y = exp(4t/π) 2 cosh(8t/π) .

Here, the signs have been chosen to follow the trajectory around C in the right direction. The velocity of the perturbation is given by (4) which can be rewritten as

The Melnikov function defined by (7) since u 0 given by ( 12) can thus be evaluated as a simple integral with polynomials of degree 5 in x and y at the numerator and of degree 4 at the denominator. Using the relation (11), the degree of these polynomials can be reduced to 3. Introducing the temporal dependence of x and y from ( 16) leads to a rational fraction in e 4t/π which imposes the change of variable s = e 4t/π and thus ds = 4s π dt.

Using the fact that cos(ω(t + τ )) = Re(e iωt ) cos(ωτ ) -Im(e iωt ) sin(ωτ ) = Re(s iωπ/4 ) cos(ωτ ) -Im(s iωπ/4 ) sin(ωτ ) (19) where Re(•) and Im(•) denote real and imaginary parts, the Melnikov function is thus written s iωπ/4 ds.

M (τ ) =
(

) 21
The maximum of the Melnikov function is obtained for tan(ωτ ) = Im(I)/Re(I) and is equal to M max = |I|. The integral can be calculated analytically when the oscillating cylinder is far from the hyperbolic point, i.e. by assuming that x p is much larger than x, y and y p , leading to

M max = π 2 r 2 1 ω 2 8x 2 p 2 cosh(π 2 ω/8) . (22)

R 0 FIG. 1 :

 01 FIG. 1: Experimental set-up showing the streamlines around two cylinders of radii R 0 , co-rotating anti-clockwise. The flow features a tilted saddle point at the mid-distance between the cylinders centers, separated by D. A plane laser sheet illuminates an isopycnal, from left to right. The dye is fluorescein, density matched at the plane of illumination. The perturbing oscillating cylinder with radius R 1 is shown in Fig. 2.

FIG. 2 :

 2 FIG. 2: Mean velocity (a) and (b) vorticity field for ω = 2.47, = 0.35 and Re = 125. The rotating cylinders are centered in C and C and the oscillating cylinder is centered in P .

FIG. 3 :

 3 FIG.3: Profile of velocity component u 0 = ∂Ψ 0 /∂y (solid line, •) and velocity component v 0 = -∂Ψ 0 /∂x (dashed line, 2) along the homoclinic streamline. Symbols (•,2) correspond to experimental data obtained by PIV measurements whereas solid and dashed lines correspond the theoretical prediction of Eq. (2) without (thick lines) and with (thin lines) the correction given by Eq. (3) induced by the oscillating cylinder. Here, ω = 2.47, = 0.35 and Re = 125.

FIG. 4 :FIG. 5 :

 45 FIG. 4: Perturbation velocity field u 1 obtained (a) experimentally by phase-average and (b) theoretically from Eq. (4). ω = 2.47, = 0.35 and Re = 125.

FIG. 6 :

 6 FIG. 6: Visualisation of the dye injected close to the hyperbolic point after one rotation around the rotating cylinder visible in the top right corner of the image. Top row: ω 1 = 1.36 rad/s and ω 0 = 2.00 rad/s are held constant while the perturbation amplitude A is varied. (a) A = 0.006, (b) A = 0.011, (c) A = 0.024. Bottom row: Rotating frequency ω 0 = 1.00 rad/s and perturbation amplitude A = 0.024 are held constant while the perturbation frequency is varied. (d) ω 1 = 0.63 rad/s (e) ω 1 = 1.15 rad/s (f) ω 1 = 1.99 rad/s.

FIG. 7 :

 7 FIG.7: Schematic of the trajectory of a fluid particle without perturbation (solid line) and with perturbation (dashed lines). The thick (resp. thin) dashed line corresponds to the case where the time for the particle to go from D to E is equal to half an oscillating period (resp. a full period). The distance δ between the unstable and stable manifold increases close to O due to the divergence of the streamlines.

FIG. 8 :

 8 FIG. 8: Dye visualization of the unstable manifold and (insert) position of the maximum and minimum of the dye undulation at different times. The solid line corresponds to the fit with a hyperbola in the new variables (x y = χ). ω 0 = 0.5 rad/s, ω 1 = 0.84 rad/s and A = 0.024.

2 + y 2 ) ( 12 )

 2212 Introducing the new variable p = x 2 + y 2 allows to get a 1D differential equation

u 1 (

 1 x, y, t + τ ) = ωr 2 1 cos(ω(t + τ )) |r -r p | 4 (x -x p ) 2 -(y -y p ) 2 2(x -x p )(y -y p ) .

  (4sx p -s 2 + (s 4 -3)x 2 p ) + 2y p (s 5 -s + (1 -3s 4 )x p ) -s 2 y 2 p (s 4 -3) (s 2 -2sx p + x 2 p -2s 3 y p + y 2 p + s 4 (x 2 p + y 2 p )) 2

		Re(I) cos(ωτ ) -Im(I) sin(ωτ )	(20)
	with
	I ωr 2 1	=
	∞	s 2
	0

ACKNOWLEDGEMENTS

The authors would like to than the french "Agence Nationale de la Recherche" for the funding of the ANR-DFG TurbMix.

APPENDIX

The goal is to calculate the Melnikov function for the flow of two point vortices (without background vorticity) whose streamfunction is given by

The calculation is similar to the calculation done by Raynal and Gence (1995) [START_REF] Gence | Efficient stirring in planar, time-periodic laminar flows[END_REF] but for a different perturbation. We also perform the calculation with different axes (rotated by 45 degrees with respect to their axes). The details of the calculation are different but the method is very similar and we will only give the main steps here.

In the absence of perturbation, the homoclinic trajectory (starting at O) is defined by the fact that the streamfunction is constant and equal to log(1/16)/(2π). Introducing this value into (9) gives, on the homoclinic trajectory, the following relation


Thomas Steiner

Lorenzo Sutton

Sabine Spiller
email: sabine.spiller@easterngraphics.com

Marilena Lazzaro

Francesco Nucci

Vincenzo Croce

Alberto Massari

Antonio Camurri
email: antonio.camurri@unige.it

Anne Verroust-Blondet

Laurent Joyeux
email: laurent.joyeux@inria.fr

Jonas Etzold
email: jonas.etzold@hs-fulda.de

Paul Grimm
email: paul.grimm@hs-fulda.de

Athanasios Mademlis
email: mademlis@iti.gr

Sotiris Malassiotis
email: malasiot@iti.gr

Petros Daras
email: daras@iti.gr

Apostolos Axenopoulos

Dimitrios Tzovaras
email: tzovaras@iti.gr

One Size Does Not Fit All -Multimodal Search on Mobile and Desktop Devices with the I-SEARCH Search Engine

Keywords: H.3.4 [Information Systems]: Information Storage and Retrieval-World Wide Web Multimodality, Rich Unified Content Description, IR

In this paper, we report on work around the I-SEARCH EU (FP7 ICT STREP) project whose objective is the development of a multimodal search engine targeted at mobile and desktop devices. Each of these device classes has its specific hardware capabilities and set of supported features. In order to provide a common multimodal search experience across device classes, one size does not fit all. We highlight ways to achieve the same functionality agnostic of the device class being used for the search, and present concrete use cases.

INTRODUCTION

Even in 2012, search is a mainly text-driven operation. Albeit recent developments in the mobile and desktop worlds have introduced voice search as an additional input modality, a truly multimodal search experience with multimodal in-and output is still missing. In the scope of I-SEARCH, industrial and academic partners are working together to investigate ways to provide such a multimodal search experience across device classes. We provide an overview of the project in its entirety in [START_REF] Steiner | I-SEARCH -A Multimodal Search Engine based on Rich Unified Content Description[END_REF]. An important step towards multimodal search in the scope of I-SEARCH was the creation of a unified annotation format named Rich Unified Content Description (RUCoD), which was detailed in [START_REF] Daras | Introducing a Unified Framework for Content Object Description[END_REF].

In this paper, we focus on taken actions and future plans to deal with device constraints to support the in-and output modalities audio, video, rhythm, image, 3D object, sketch, emotion, geolocation, and text. The I-SEARCH project is in its second year now, and some basic functionality is in place. We maintain a demonstration server1 , and have also recorded a screencast 2 showing features of the search engine.

USER-FACING PROJECT GOALS

I-SEARCH is a complex project that touches on many research areas treated by the different project partners. One important goal is to hide this complexity from the end user through a consistent and context-aware user interface based on standard HTML5, JavaScript, and CSS, with ideally no additional plug-ins like Flash required. We aim at sharing one common code base for both device classes, mobile and desktop, with the user interface getting progressively enhanced [START_REF] Champeon | Progressive Enhancement and the Future of Web Design[END_REF] the more capable the user's Web browser and connection speed are. Search engines over the years have coined a common interaction pattern: the search box. We enhance this interaction pattern by context-aware modality input toggles that create modality query tokens in the I-SEARCH search box. Figure 1 shows three example modality query tokens for audio, emotion, and geolocation.

USE CASES

In order to give the reader an idea of intended I-SEARCH usage and to motivate multimodality, we introduce three use cases and involved modalities as defined by the project.

UC1: Music Expert (Desktop, Mobile). A music expert

with access to a big music archive does research on the in- fluence of traditional folk music on today's popular music. She inputs a rhythm to the I-SEARCH system in order to search the archive for similar rhythm patterns. She refines her query by adding geolocation to limit results to a certain region and by uploading an image from a disco club.

UC2: Interior Designer (Desktop). An interior designer wants to give her client a realistic impression of available office chairs. She uploads a 3D model of a chair that almost matches her client's expectations to the I-SEARCH system, together with an image of the desired upholstery. She uses a hand-drawn sketch of the chair's shape as a refinement.

UC3: World Traveler (Mobile).

A world traveler uses her cell phone with the I-SEARCH application to create media content with associated geolocation data like videos and images of the sights she walks by to retrieve related media content of other travelers, text descriptions, and 3D models she wants to use to map her trip on a virtual globe.

MODALITIES ACROSS DEVICES

In this Section, we focus on input modalities across mobile and desktop device classes and their support in I-SEARCH.

Audio, Image, Video. We describe audio, image, and video modalities together, as they share the same interaction patterns. On desktop devices, audios, images, or videos can be uploaded from the user's hard disk via a file upload dialog or via drag 'n' drop. On some mobile devices (e.g., iOS devices) file uploading is prohibited, which is why in the longterm, as support advances, we aim at using the getUser-Media API [START_REF] Burnett | getUserMedia: Getting access to local devices that can generate multimedia streams[END_REF]. The fallback solution is a Flash uploader.

Rhythm. On desktop devices, we support entering a rhythm by key presses or mouse tapping, whereas additionally on mobile devices a rhythm can also be captured via the device orientation API [START_REF] Block | DeviceOrientation Event Specification -Editor's Draft 12[END_REF] by tilting the device rhythmically.

3D Object. We support 3D objects on mobile and desktop via the COLLADA 3D asset exchange schema [START_REF]COLLADA -3D Asset Exchange Schema[END_REF]. 3D objects can be inserted via a file upload dialog or drag 'n' drop.

Sketch. Hand-drawn sketches can be created on mobile and desktop devices alike using a simple touch-based HTML5 canvas [START_REF] Hickson | HTML5 -The canvas element[END_REF] sketch editor.

Emotion. In order to accompany a query by basic emo- tional feedback, we have adapted an open-source emotion input solution [START_REF] Little | Smiley Slider. Avail[END_REF] for mobile and desktop that transfers the slider user interface pattern to emotions from sad to happy.

Geolocation. For retrieving and tracking a user's physical location, we use the HTML5 geolocation API [START_REF] Popescu | Geolocation API Specification -Editor's Draft 10[END_REF], which is available in Web browsers on mobile and desktop devices.

Text. On mobile and desktop, text can be entered using the keyboard or using the speech input API [START_REF] Sampath | Speech Input API Specification -Editor's Draft 18[END_REF].

FUTURE WORK AND CONCLUSION

We have introduced the I-SEARCH project and three of its use cases and have shown how different input modalities are supported on mobile and desktop. Now we need to integrate the project partners' services in the back-end, in order to support multimodal output besides multimodal input.

Figure 1 :

 1 Figure 1: I-SEARCH search box with three modality query tokens for audio, emotion, and geolocation. Below, the rhythm modality toggle is active.

Demonstration: http://isearch.ai.fh-erfurt.de/

Screencast: http://youtu.be/-chzjEDcMXU

ACKNOWLEDGMENTS

This work was partially supported by the European Commission under Grant No. 248296 FP7 I-SEARCH project.


François-Xavier Coudert

Rodolphe Vuilleumier

Anne Boutin
email: anne.boutin@lcp.u-psud.fr

Dipole moment, hydrogen bonding and IR spectrum of confined water

Keywords:

come

1 and thermodynamics of water confined in carbon micropores or nanotubes [START_REF] Ohba | [END_REF]3] and zeolites. [4][5][6][7][8] However, the quantum nature of bonding in water can only be captured by ab initio calculations. Elaborate treatments of the electronic density are usually limited to small clusters (or a few adsorbed molecules) and restricted to equilibrium structures. The Car-Parrinello Molecular Dynamics method (CPMD) [9] offers an alternative route to capture the electronic properties of molecules, as well as dynamics effects. Such DFT-based ab initio molecular dynamics calculations have been already applied to bulk water [10], interfacial water on Si surfaces [11], and zeolitic materials. [12,13] Most of the CPMD studies of confined water deal with the dynamics of one-dimensionnal water chains and helices in hydrophilic zeolites with narrow, non-connected, cylinder pores. [12,13] We have used here this method for the first time to investigate water confined in a hydrophobic zeolite with large interconnected pores. The LTA zeolite displays supercages of diameter ≃ 13 Å, connected to one another in a cubic symmetry by 8-ring windows of diameter ∼ 7 Å, and smaller sodalite cages of diameter ≃ 7 Å. This zeolite is, thus, a good candidate for studying the effect of confinement in open structure hydrophobic nanoporous materials. We have studied the thermodynamic and electronic properties, and the vibrational infrared spectrum of the confined water. It is worth noticing that while infrared measurements are a powerful tool to explore the structure of confined fluids, IR spectra are often complicated to interpret. Vibrational spectra of confined fluids have been computed some years ago using normal mode analysis on minimal-energy structures or using polarizable forcefields and electrooptical models in classical molecular dynamics simulations. [14,15] Most studies use the velocity auto-correlation function that provides vibrational frequencies but not IR intensities, resulting in a quite different vision of the overall spectrum. This is the first time, to our knowledge, that the dipole moments and IR spectrum of confined water are calculated from ab initio dynamics. This technique was developed recently, based on an estimator of the dipole moment in periodic boundary conditions [16,17], and was shown to successfully reproduce infrared spectra of aqueous systems. [18][19][20][21] We have first computed the water adsorption isotherm at 300 K following the Grand Canonical Monte Carlo methodology of Desbiens et al. [8,22] As it was experimentally observed on other siliceous zeolites [23], the all-silica LTA is found to be hydrophobic, with liquid intrusion occuring at ∼ 70 MPa. The maximum loading is found at ∼ 20 water molecules per unit cell. Starting from these classical GCMC configurations we have performed CPMD simulations using plane-wave basis set and norm-conserving pseudopotentials on siliceous LTA with various hydration rates.

The effect of confinement on the molecular dipole of water is shown in Figure 1 for two molecular loadings: 15 and 20 H 2 O molecules per unit cell of zeolite (one supercage plus one sodalite cage). For comparison, the water dipole of the gas phase water molecule and the distribution of dipole moments for 32 bulk water molecules computed using the same DFT and Car-Parrinello parameters are also plotted.

The present bulk data are consistent with the original results of Silvestrelli et al. [24] The dipole distribution for 20 confined water molecules has a maximum at 2.9 D, close to the bulk water maximum found at 3.1 D, and displays a smaller band around 2 D, close to the gas phase value of 1.8 D. This latter peak corresponds to the water molecule located in the small sodalite cage. This seems to show that the polarization induced by the zeolite framework is quite small compared to the self-polarization of water fluid. From this point of view, this result is in good agreement with studies of smaller water clusters in siliceous silicalite by means of classical simulations using a polarizable water model. [5] However, unlike what was observed in silicalite, where the dipole distribution displays several peaks, the distribution observed in siliceous LTA is unimodal (apart from the water molecule in the sodalite cage). The multimodal dipole moment distribution was observed in silicalite but not in hydrophilic Na-LSX zeolite [25], and this has been interpreted in term of a intrinsic property of hydrophobic zeolites. Our results seem to indicate that a multimodal behaviour is related to the existence of multiple, strongly non-equivalent, adsorption sites in narrow pores (channels and intersections of silicalite, or the sodalite cage in the present case). In a more open structure, such as LTA supercage and LSX zeolite, the dipole moment distribution appears smoother.

The dependence of the water dipole moments on the number of adsorbed water molecules can also be compared from one zeolite structure to another. We observe an increase of about 0.04 D per extra adsorbed molecule. This value is 20 times greater than the one previously observed in hydrophilic Na-LSX zeolite. [25] In this cationic aluminosilicate material, the electrostatic field induced by the zeolite is much stronger than in pure siliceous LTA zeolite, and an extra water molecule in Na-LSX has less effect on the overall field felt by other adsorbed water molecules. This is consistent with the fact that the apparent water dipole moment is larger than the bulk value in an aluminosilicate zeolite (because of the large electric field created by the framework) and smaller than the bulk value in an hydrophobic all-silica zeolite.

The water dipole moment is found to be smaller than in bulk water but larger than its gas phase value.

In the large pores of LTA, water molecules self-organize through hydrogen bonds which build up a relatively large dipole. We have identified these hydrogen bonds by means of a geometric criterion involving the Acceptor, Donor, and Hydrogen atoms. [26] The number of hydrogen bonds among the 20 water molecules confined in the zeolite, calculated using this geometric criterion, is reported in Table 1. Very few waterzeolite hydrogen bonds are observed, while the difference in water-water H bonds ratio between bulk and confined water (∼ 0.3) is small even though most of the water molecules are very close to the zeolite surface (less than 5 Å). In confined spherical hydrophobic pores, the 15-20 water droplet self-organizes and increases its cohesion energy. This is in keeping with the observation of cluster formation of 1 nm size in hydrophobic graphitic nanopores. [START_REF] Ohba | [END_REF] The lifetime of hydrogen bonds defined from a purely geometric criterion are extracted from Figure 2.

The water-water hydrogen bonds lifetime is found to be 1.5 ps, similar to the lifetime of such bonds in bulk water using the same methodology. Hydrogen bonds between confined water and the framework oxygen atoms, however, are found to have a lifetime of only 120 fs. Such OHO alignments are indeed observed but they don't correspond to true hydrogen bonds as proven by the absence of any water O-H strain. In this specific case, usual geometric criteria are not appropriate to characterize hydrogen bonds. The nonexistence (or weakness) of zeolite-water hydrogen bonds between water and SiO 2 framework is in keeping with experimental diffuse reflectance infrared Fourier transform spectroscopic (DRIFT) measurements in different zeolites which showed that zeolites with low Si:Al ratio exhibit only weak interaction between the water molecules and the zeolite oxygen atoms. [27] Finally, we have studied the confinement effect on the water-zeolite infrared spectrum. We report in Figure 3 the infrared spectrum of the hydrated zeolite, as well as the separate IR spectra of the confined water and the zeolite. The zeolite spectrum is very similar to that of the dry solid, which we also computed (not shown here). Both spectra are in reasonnable agreement with the experimental data [28]. We do not observe any significant effect of the confined water on the vibrationnal spectrum of the zeolite framework and the two sub-systems are not correlated. Indeed, the total spectrum for the system matches the sum of the two separate spectra for water and the zeolite at frequencies higher than 300 cm -1 .

Figure 4 shows the OH-stretch region of both the confined and bulk water IR spectra. For confined water, the ν OH band appears to be composed of a large band and a narrower high-frequency peak. The existence of a narrow high-frequency peak in the OH stretch region of interfacial water has been revealed by the sum-frequency generation (SFG) technique, which is a highly surface-specific vibrational spectroscopy of liquid interfaces. This peak was attributed to non hydrogen-bonded OH bonds. [29] The dangling OH peak is more prominent for water near hydrophobic surfaces than in the hydrophilic case and, thus, can be used as a signature of hydrophobicity. The analysis of the velocity autocorrelation function of OH distances for H atoms involved in water-water hydrogen bonds and H atoms directed toward the zeolite (i.e. not involved in hydrogen bonds) demonstrates that the high frequency modes correspond to OH bonds that are not involved in the hydrogen bond network. Our results in the case of a more realistic system confirm the attribution of the high frequency ν OH peak to dangling hydrogens.

We have reported here DFT-based ab initio Molecular Dynamics results of water confined in a large pore LTA hydrophobic zeolite. We have studied the molecular dipole of confined water molecules, hydrogen bonding properties, and we have computed the system infrared spectrum.

It was found that the infrared spectrum of the structural zeolite is decorrelated from the confined water zeolite indicating very small interaction between the host and the guest species. This was confirmed by the study of hydrogen bonds which showed the absence of genuine water-zeolite hydrogen bonds. The water OH-stretch band shows similar shape and frequency with respect to bulk water, except for a narrow peak at 2300 cm -1 attributed to OH bonds directed towards the zeolite. The lifetime of water-water hydrogen bonds in confined water was found to be similar to those in bulk water, indicating a similar H-bond strength within confined water. Finally, we observed a slight decrease of the water dipole moment with respect to its bulk value.

The resulting dipole moment is, however, still largely enhanced with respect to its gas phase value, due to hydrogen bonding. Further studies on other systems are now needed to understand the role of pure confinement with respect to possible specific interaction with the host structure and the role of confinement geometry. DFT-based ab initio MD also offers a possible route for studying the chemical reactivity of confined water.

Computational Procedure

The Molecular Dynamics simulations of anhydrous and hydrated zeolite were performed within the Car-Parrinello method [9] as implemented in the CPMD software package [START_REF] Cpmd | Copyright IBM Corp[END_REF], using the Kohn-Sham formulation of DFT. We employed the gradient-corrected BLYP functional. [START_REF] Becke | [END_REF]32] A planewave basis set with an energy cutoff of 70 Ry was used and only the valence electrons were explicitly considered, with semilocal norm-conserving Trouillier-Martins pseudopotentials.

The siliceous Linde Type A zeolite structure was taken from Ref [START_REF] Baerlocher | Atlas of zeolite framework types[END_REF]. The unit cell structure (Si 24 O 48 ) is cubic (Pm 3m symmetry and a = 11.9 Å) and contains one supercage and one sodalite cage. All hydrogen atoms were deuterated. A timestep of 7 a.u. (0.17 fs) and a fictitious electron mass of 1000 a.u. were used. (A 1.5 ps test run with an electronic mass of 700 a.u. and a timestep of 4 a.u. showed no significant difference.) A first equilibration run of 1.2 ps was performed on each system, using a Nosé-Hoover thermostat [START_REF] Nosé | [END_REF][35][36] with a frequency of 3800 cm -1 . Production runs of 3 ps in the microcanonical NVE ensemble were then performed. It is worth mentionning that the simulation time is rather short for a full phase-space sampling. This could lead to a large uncertainty of the hydrogen bonds lifetimes.

Trajectories of the total dipole moments were obtained using the Berry phase approach [16] and their autocorrelation function was used to compute the IR absorption coefficient, α(ω), in the linear response theory. [18] To compute the dipole moments of individual water molecules, the electronic wavefunctions are replaced by the maximally localized Wannier functions [17] and the Wannier centers are assigned to each water molecule. [19,21,37] A harmonic quantum-classical correction was then applied to the classical correlation function to account for the quantum aspects of the hydrogen motion, as was shown to be adequate in previous works [20,21,38]. The resulting infrared spectrum was then smoothed by a linear filter as described in Ref. [

Figure 2 :Figure 3 :

 23 Figure 2: Autocorrelation function of hydrogen bonds defined from a purely geometric criterion: waterzeolite hydrogen bonds (dashed line), water-water H bonds for confined water (dash-dotted line) and bulk water (solid line).

Figure 4 :

 4 Figure 4: The OH stretch band of the infrared spectrum of the hydrated zeolite containing 20 deuterated water molecules (upper panel) compared to 32 bulk water molecules (lower panel).

Table 1 :

 1 21].Figure1: Distribution of the dipole moment for 20 (dashed line) and 15 water molecules (dotted line) confined in siliceous LTA zeolite, as compared to bulk water (solid line) and gas phase water (µ ≃ 1.8 D). Number of water-water and water-zeolite hydrogen bonds in the zeolite supercage, as defined by the geometric criterion, and ratio over the total number of water molecules in the supercage. The number of hydrogen bonds in a 32 bulk water molecules system is also indicated for comparison.

	20 confined H 2 O	bulk water
	15 confined H 2 O
	isolated
	H 2 O
	2.5	3		3.5
	Water dipole (Debye)
				number ratio
	water-water H bonds for 20 confined H 2 O	30.8	1.54
	water-zeo H bonds for 20 confined H 2 O	4.1	0.21
	water-water H bonds for 32 H 2 O in bulk	59.7	1.86

** We acknowledge the Institut du