Hadi Hachem

Hengbo Cui

Takao Tsumuraya

Reizo Kato

Olivier Jeannin

Marc Fourmigué

Dominique Lorcy

Dominique Orcid

Lorcy

Single-component conductors based on closed-shell Ni and Pt bis(dithiolene) complexes: metallization under high pressure

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Single

Introduction

The quest for single component conductors, i.e. conducting molecular materials based on one single molecule (at variance with prototypical charge transfer salts and ion radical salts), is currently an active research topic, particularly because the absence of any counterion can favor three-dimensional intermolecular interactions with associated 3D Fermi surface. This quest was initially considered using neutral radical species such as spiro-bis(phenalenyl) boron radicals, 1 , 2 dithiadiazolyl, 3 , 4 or dithiazolyl radicals. 5 The strong tendency of such radicals to dimerize in the solid state was recently overcome in quinone-bridged bis(dithiazolyl) radicals with an insulator-to-metal transition observed under pressure above 3 GPa. 6 Another broad class of single component conductors is based on the bimolecular association of two tetrathiafulvalene (TTF) moieties, either through coordination of TTF-dithiolate ligands around a metal center, 7,8,9 or through hydrogen bonding interactions between TTF-catechol moieties [START_REF]thiazdt) 2 ] (mg) were dissolved in 15 mL of CH 3 CN. The current intensity was adjusted to 0.5 μA, and the current was maintained during nine days[END_REF] or zwitterionic TTF-extended dicarboxylate radical (TED) (Chart 1). 11 All these formally neutral compounds exhibit highly conducting properties attributable to internal charge transfer. A third class more recently investigated relies on neutral radical gold bis(dithiolene) complexes (Chart 2a). 12 Indeed, the d 8 closed-shell anionic complexes [Au(dt) 2 ] -1 oxidize reversibly to the neutral radical complexes with solid state association often avoiding the typical face-to-face dimerization of -type radical species. Many such derivates exhibit semi-conducting properties, 13 but complexes derived from N-alkyl-1,3-thiazoline-2-thione-4,5-dithiolate (abbreviated as R-thiazdt), [Au(R-thiazdt) 2 ] • , were shown to become metallic under pressure (for R = Et above 2.1 GPa) 14,15 or even at ambient pressure and temperature for R = Me. 16 Chart 2 .

(a) (b) .

[Au(R-thiazdt) 2 ] -1, However, the necessity to work with radical complexes to stabilize a metallic state in single component materials has been recently questioned. For example, the presence of a small HOMO-LUMO gap in closed-shell nickel bis(dithiolene) complexes such as the prototypical [Ni(dmit) 2 ] 0 (dmit = 1,3-dithiole-2-thione-4,5-dithiolate), 17 suggested that under pressure, these insulating materials 18 could become metallic if the expected increase of band dispersions under pressure could reach a point where the gap would close. This was successfully realized using Diamond Anvil Cell (DAC) on [Ni(dmit) 2 ] 0 itself. 19 It exhibits indeed a low conductivity under ambient pressure at RT,  RT = 6×10 -2 S cm -1 (E act = 0.14 eV) but was shown to become essentially metallic above 15.9 GPa. Tight-binding calculations coupled with the interatomic repulsion model and ab initio DFT calculations showed that, under high pressures, an overlap of the HOMO and LUMO bands arises, suggesting an internal charge transfer. The calculations also indicated the presence of 2D and 3D Fermi surfaces under those high pressures.

Considering the close structural proximity between the dmit and thiazdt ligands and their A preliminary investigation showed that a monoclinic phase of the ethyl-substituted complex, mono-[Ni(Et-thiazdt) 2 ] 0 exhibits an activated conductivity with  RT = 1.4 10 -2 S cm -1 and an activation energy of 0.2 eV, but only slightly reduced to 0.17 eV at 1.2 GPa. 20 We described here the preparation of both methyl-and ethyl-substituted complexes with both Nickel and Platinum, affording four novel phases, a triclinic phase noted tricl- [Ni(Et-thiazdt)

Results and discussion

Syntheses

The general strategy used to form the nickel and platinum dithiolene complexes starting from the cyanoethyl-protected 1-R proligands (R = Me, Et) CN. Before analyzing the solid-state properties of these complexes, their electro-and spectro-chemical properties will be described.

R = Me R = Et 1-Me 1-Et [Ni(R-thiazdt) 2 ] -1 [Pt(R-thiazdt) 2 ] -1

Solution properties

The redox properties of these four anionic complexes have been analyzed by cyclic voltammetry in CH 2 Cl 2 using NBu 4 PF 6 as supporting electrolyte while the UV-Vis-NIR absorption properties of the radical anion species, were measured in CH 2 Cl 2 at room temperature. Spectro-electrochemical experiments give access to the absorption properties of the neutral species generated at the electrode, however without possibility to evaluate the corresponding absorption coefficients, due to partial precipitation of the insoluble neutral species. A representative example is given in Figure 1 for [Bu 4 N][Pt(Et-thiazdt) 2 ] while all redox potentials, maximum absorption wavelengths and absorption coefficients (on anionic complexes only) are collected in Table 1. The properties of the nickel complexes compare with those described earlier. 20 The neutral Pt complex [Pt(Et-thiazdt) 2 ] has been reported by Arca et al. in low yields from the sulfuration of ethyl-2-thioxothiazolidine-4,5-dione with Lawesson's reagent in the presence of PtCl 2 . 22 Its structure was not reported but its redox properties, which compare indeed with those obtained here from the soluble monoanionic salt. However, as noticed earlier for the [Ni(Et-thiazdt) 2 ], 20 the [Pt(Et-thiazdt) 2 ] exhibits three redox processes (Figure 1a). This third process, not mentioned earlier, is associated to the oxidation of the neutral species into the cation radical one (Table 1). For the N-methyl complexes this third redox process is not observed presumably due to a lower solubility of these derivatives compared to the N-Et ones and also due to strong adsorption phenomena.

Table 1 Redox potentials (E in V vs SCE), absorption maxima  max (nm) and molar extinction coefficients  (M -1 cm -1 ) for the NIR absorptions of the [Ni(R-thiazdt) 2 ] and [Pt(R-thiazdt) 2 ] (R = Me, Et) complexes. The UV-vis-NIR spectroscopic investigations carried out on the four complexes allowed us to determine the absorption maxima ( max ) of the lowest energy NIR electronic transitions for the monoanionic species as well as the neutral complexes. As expected, a hypsochromic shift is observed for the absorption band at low energies when going from the monoanion to the neutral species. The nature of the alkyl group has no significant influence on the wavelength of the NIR absorption band. On the other hand, the nature of the metal induces discrepancies. The Ni complexes present slightly red shifted  max by 20-28 nm for the mononanions as well as for the neutral complexes. Moreover, the extinction coefficients for the Pt monoanions are 1.5 times higher than those of the Ni complexes.

E 1 -2/-1 E 2 -1/0 E 3  max ( (nm, M -1 cm -1 )

Solid state properties

Good quality single crystals for X-ray diffraction studies were obtained for the monoanionic crystallizes in the monoclinic system, space group C2/c, with the nickel atom on an inversion center (Fig. 2a) and the phosphorous of the Ph 4 P + cation on a two-fold axis. Pertinent bond distances and angles are collected in Table 2.

Table 2 Intramolecular bond distances within the anionic and neutral complexes [M(Rthiazdt interactions within the stacks (Fig. S2). Interestingly, the monanionic [Ni(Me-thiazdt) 2 ] -1 complex in both structures adopts a trans, ordered configuration while, when crystallized with the Et 4 N + counter ion, this unsymmetrical dithiolene ligand was found to be disordered on two positions. 21 The Ph 4 P + salt of the Pt complex, namely [Ph 4 P][Pt(Et-thiazdt) 2 ].toluene, crystallizes as toluene solvate in the monoclinic system, space group C2/c with the Pt atom on an inversion center and the phosphorous of the Ph 4 P + cation on a two-fold axis (Figure 2b). The molecules organize into alternating layers of cations and anions in the ac plane (Fig. S3). The monoanionic [Pt(Et-thiazdt) 2 ] -1 complex is obtained also as the trans isomer. A common trend within the four structures is the formation of uniform, non-dimerized stacks with the complexes interacting sideways (Figure 3). We have reported recently that dimerization within the stacks of such complexes was most often a consequence of overlap interactions between open-shell species, as found indeed in several neutral, but radical gold dithiolene complexes. Among the few reported neutral platinum dithiolene complexes, only [Pt(edt) 2 ] is actually dimerized, 23 while [Pt(dddt) 2 ], 24 [Pt(tfd) 2 ] 25 and [Pt(timdt) 2 ] 26 crystallize into uniform stacks. The overlap mode between two neighboring complexes within the stacks is shown in Figure 4. This is in sharp contrast with what was observed for the analogous gold complexes AuMe and Au Et, where the shortest distance between the exocyclic sulfur atoms was found for the AuMe 16 and not for AuEt. 14 From these contrasted observations, it appears that intermolecular interactions within the stacks are most probably quite weak, perhaps stronger in the N-methyl complexes which exhibit a more favorable overlap, while few short S•••S contacts can be also identified between stacks.

The conductivity of the four complexes and its temperature dependence reflect these observations. As shown in Table 3, the four complexes exhibit a semiconducting behavior in the whole temperature range, with a higher conductivity and smaller activation energy for the N-methyl complexes. 2.910 -3 0.18 0.43 (a) From Ref. 20. (b) Tight binding calculations.

Band structures calculations (tight-binding) were performed on these series of four neutral complexes to rationalize their transport properties, in relation with their actual solid-state structure (Figure 5). We note for the four structures very limited band dispersion, in accordance with the structural analysis developed above. This band dispersion is negligible in the N-ethyl complexes, a direct consequence of the weaker, shifted overlap within the stacks. Besides, the direct gap between the HOMO and LUMO bands ranges from 0.31-0.33 eV in the N-methyl complexes NiMe and PtMe while it exceeds 0.60 eV in the N-Ethyl complexes. Transport properties and electronic calculations can be compared here with those reported recently for neutral [Ni(dmit) 2 ], with  RT = 1.6×10 -2 S cm -1 and E act = 0.14 eV at ambient pressure. [Ni(dmit) 2 ] was shown to become essentially metallic above 8.3 GPa, a striking result which lets us infer a similar behavior in the complexes reported here, and particularly in the most conductive one, i.e. NiMe. The evolution of its conductivity under high pressure was accordingly determined in a diamond anvil cell (DAC), as reported for [Ni(dmit) 2 ]. 19 For comparison purposes, a similar investigation has been made on the tricl-NiEt phase. Although a diamond anvil cell (DAC) is useful for high-pressure measurements, the pressure generated by a DAC tends to be anisotropic and its effect is often different from that of hydrostatic pressure. The DAC technique developed by some of us can generate high-quality quasi-hydrostatic pressures and was applied to the present NiMe and tricl-NiEt systems, as shown in Figures 6 and7. When the pressure is increased from 1 bar to 22.5 GPa in NiMe (Fig. 6), the room temperature conductivity is increased by 5 orders of magnitude (up to σ RT = 166 S.cm -1 ) and the activation energy is reduced down to 0.1 meV at 19 GPa. However, even at the highest pressures, NiMe keeps its semi-conducting nature. Note also that the evolution of the activation energy (Figure 6 right) is not regular, indicating that a structural transition might have taken place already at 13 GPa. As a consequence, the ambient pressure structure cannot really be used as a starting model for anticipating the evolution of the band structure of NiMe under high pressure.

The temperature dependence of the conductivity of the platinum complexes was also investigated. The resistivity measurements on PtMe show a semiconducting behavior at ambient pressure, with a room temperature conductivity of 1.66×10 -2 S.cm -1 with an activation energy of 0.16 eV (Fig. S4) which is the same order of magnitude of the NiMe analog. The calculated activation energy is 0.16 eV which goes in line with the predicted value from the band structure calculation (Figure 5). The very small size of the samples prevented the realization of resistivity measurements under pressure.

As anticipated above from the crystal structures, the room temperature conductivity of PtEt is smaller and amounts to σ RT = 2.9 × 10 -3 S.cm -1 with an activation energy of 0.18 eV.

The pressure dependence of the conductivity was investigated here, showing that the semiconducting state was maintained even at 12 GPa, with  RT (p = 12 GPa) at 5.8 S.cm -1 and E act (p = 12 GPa) at 0.058 eV (Fig. S5). This behavior contrasts with that of the isostructural NiEt complex which turns metallic already above 4.4 GPa.

To understand the evolutions of the structural and electronic properties of NiMe under pressure, structural optimization with first-principles DFT calculation was performed by keeping crystal symmetry (constraint for space group) as the experimental structure at ambient pressure (Fig. 8). The optimized structure at 4 GPa predicts a semimetallic band structure (Fig. 8b), while experiments show an insulating behavior. The full clarification of structural properties of NiMe above 4 GPa with a possible phase transition inferred from the pressure dependence of the activation energy (Figure 8b) is left for future studies. At variance with NMe, a quasi-metallic behavior is already observed in tricl-NiEt (Fig. 7) in the low temperature range (<100 K) when the pressure reaches 4.4 GPa, while a further increase of the pressure to 6.9 GPa realized a quasi-metallic behavior over the whole temperature range, with a room temperature conductivity reaching 250 S.cm -1 . Note that this successful metallization process is observed here at a notably lower pressure (4.4 GPa) than in the reported [Ni(dmit) 2 ] 0 (8.3 GPa). 19 First-principles calculations were also performed on the tricl-NiEt complex. As shown in Figure 9a, the calculated ambient-pressure band structure shows insulating character with an indirect band gap of 0.3 eV. The cell parameters and internal coordinates of tricl-NiEt complex were then relaxed at several given pressures with a non-local electron correlation functional of vdW-DF2. 27 The electronic structure is changed upon applying pressure and the calculated band structure at 6 GPa (Fig. 9b) confirms indeed the appearance of a metallic state, with the Fermi level cutting the HOMO and LUMO bands at different k vectors in the reciprocal space, where 3D electron pockets around the -point and 2D cylindrical hole Fermi surface surrounding the U and R points are found (Fig. 10c). This result agrees with the experimental results shown in Figure 7 which indicates the conducting behavior at 6 GPa. Next, analysis of the changes in the structures under pressure is performed. The calculated evolution of the crystal structure of tricl-NiEt under pressure is shown in Figures 11 and12 (See Tables S1-S5 in ESI for crystallographic data at different pressures). With increasing pressure, the lattice constant a increases, which is associated with an inclination of [Ni(Et-thiazdt) 2 ] molecules along the a axis. This is also linked to the significant decrease of the lattice constant c. It should be noted that the ethyl group rotates around the N-C bond cooperating with the lattice compression along the c direction as shown in Figure 12. When the band structure becomes that of a metallic state, the intermolecular overlap of the Et-thiazdt ligand becomes more efficient with the - stacking distance shorter than 3.5 Å (Fig. 12 and Fig. S8). This results in the increased bandwidth of the conduction bands (especially LUMO bands along the -X direction). S4).

Conclusions

Four neutral, formally closed-shell, Ni and Pt complexes formulated as [Ni(R-thiazdt) 2 ] 0 and [Pt(R-thiazdt) 2 ] 0 (R-thiazdt: 2-alkyl-1,3-thiazoline-2-thione-4,5-dithiolate; R = Me, Et) were obtained by electrocrystallization from the corresponding monoanionic species. Their crystal and electronic structures confirm their semi-conducting behavior, and show the presence of a large HOMO-LUMO gap in the ethyl (R = Et) substituted complexes while the less sterically hindered methyl-substituted ones exhibit higher conductivities and smaller activation energies.

Application of high-quality quasi-hydrostatic pressures in the nickel series using a Diamond Anvil Cell (DAC) strongly enhances the conductivity of [Ni(Me-thiazdt) 2 ] 0 (NiMe) up to 166 S.cm -1 (E act = 0.1 meV) at 19 GPa. On the other hand, the N-ethyl derivative, [Ni(Et-thiazdt) 2 ] 0 (tricl-NiEt) turns metallic in the low temperature range (<100 K) when the pressure reaches 4.4

GPa, while a further increase of the pressure to 6.9 GPa turns it metallic over the whole temperature range. As for NiMe, the discrepancy between the first-principles calculations predicting metallization under pressure and resistivity measurements probably originates from a possible structural transition under pressure. In tricl-NiEt, on the other hand, a favorable situation for metallization is highlighted here, associated with the presence of an indirect gap in the semiconducting regime. At higher pressures, the gap closing is then observed at different k vectors, leading to the semi-metallic Fermi surface. Remarkably, the presence of the bulkier ethyl substituent does not hinder the metallization, which expands possible molecular design for single-component molecular conductors based on such small, non-radical, molecular complexes.

Experimental

General. Chemicals and materials from commercial sources were used without further purification. All the reactions were performed under an argon atmosphere.

First-Principles Density Functional Theory Calculations

To study electronic structures of [Ni(Me-thiazdt) 2 ] and tricl- [Ni(Et-thiazdt) 2 ], we perform first principles calculations based on the density-functional theory. 32,33 One-electron Kohn-Sham equations are solved self-consistently by using a pseudopotential technique 34 with planewave basis sets adopting the projected augmented plane wave (PAW) method. 35 The structural relaxations under constant pressures are performed by calculating the stress tensors with a local density functional of generalized gradient approximation (GGA-PBE) 36 and a non-local electron correlation functional 37 (van der Waals density functional of vdw-df2-b86r), 38 which is implemented in a scalar relativistic code of Quantum Espresso 6.3. 39,40 The plane waves prepared with the cutoff energy of 65 and 70 Ry were used for NiMe and tricl-NiEt, respectively. Cutoff energies for electronic charge and potentials are set to be 588 and 488 Ry for NiMe and tricl-NiEt, respectively. Used uniform k-point meshes are 8 x 4 x 4 and 6 x 6 x 4

for NiMe and tricl-NiEt, respectively with a gaussian smearing method during self-consistent loops.

Transport measurements. Single crystals of

  -component conductors based on closed-shell Ni and Pt bis(dithiolene) complexes: metallization under high pressure † Hadi Hachem, a HengBo Cui, b Takao Tsumuraya, c Reizo Kato, b * Olivier Jeannin, a Marc Fourmigué* a and Dominique Lorcy* a a Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) -UMR 6226, F-35000 Rennes, France b Condensed Molecular Materials Laboratory, RIKEN, Wako-shi, Saitama 351-0198, Japan c Priority Organization for Innovation and Excellence, Kumamoto University, Kumamoto 860-8555, Japan

Fig. 1

 1 Fig. 1 (a) Cyclic voltammetry (b) and UV-Vis-NIR monitoring of the electrochemical oxidation of [Bu 4 N][Pt(Et-thiazdt) 2 ]

  nickel complex [PPh 4 ][Ni(Me-thiazdt) 2 ] as needles. A minor phase co-crystallizing in the form of thin plates was found to be a CH 2 Cl 2 solvate. Note that the ethyl analog [Ph 4 P][Ni(Etthiazdt) 2 ] was already described 20 while both platinum salts [NBu 4 ][Pt(R-thiazdt) 2 ] (R = Me, Et) could not be obtained in the form of high quality crystals. As mentioned above, a few crystals of [Ph 4 P][Pt(Et-thiazdt) 2 ] obtained as a toluene solvate phase could only be characterized by X-ray diffraction studies. The non-solvated salt [Ph 4 P][Ni(Me-thiazdt) 2 ]

  ) 2 ] -1,0 M = Ni, Pt and R = Me,

  (a) As Ph 4 P + salt.(b) As Ph 4 P + salt, CH 2 Cl 2 solvate. (c) From Ref.20 In the crystal, the anion radical [Ni(Me-thiazdt) 2 ] 1-species organize into uniform stacks running along the b axis, further interacting sideways along a. These ab anionic layers are alternating along c with Ph 4 P + layers (Fig.S1). The shortest intermolecular S•••S contacts exceed 3.96 Å, a large distance which lets us infer very weak magnetic interactions between the S = ½ radical species. The cocrystallization of this salt with its CH 2 Cl 2 solvate prevented us to measure the actual magnetic susceptibility and its temperature evolution. The minor solvate phase crystallizes in the orthorhombic system, space group P2 1 ca, with anion, cation and CH 2 Cl 2 molecule in general position. The [Ni(Me-thiazdt) 2 ] -1 moiety exhibits weak deviation from planarity and is organized into stacks running along the b axis, with again very limited

Fig. 2

 2 Fig. 2 Molecular view of the anion radical species [Ni(Me-thiazdt) 2 ] -1 in [Ph 4 P][Ni(Me-thiazdt) 2 ] (top) and [Pt(Et-thiazdt) 2 ] -1 in [Ph 4 P][Pt(Et-thiazdt) 2 ] (bottom).

Fig. 3

 3 Fig. 3 Projection views of the unit cells of the neutral complexes.

Fig. 4

 4 Fig. 4 Projection views of the overlap between neighboring complexes within the stacks in the four complexes.

Fig. 5

 5 Fig.5 Calculated band structure for the four complexes, determined by tight-binding methods, where  = (0,0,0), X = (1/2,0,0), Y = (0,1/2,0), Z = (0,0,1/2), and M = (1/2,1/2,1/2). The HOMO and LUMO bands are highlighted respectively in red and blue.

Fig. 6

 6 Fig. 6 Temperature dependence of the resistivity of NiMe as a function of temperature, and at different pressures between 1 bar and 22.5 GPa (left). Pressure dependence of the activation energy of NiMe (right).

Fig. 7

 7 Fig. 7Pressure dependence of resistivity of tricl-NiEt between 1 bar and 6.9 GPa

Fig. 8

 8 Fig. 8 Band structure of NiMe calculated with GGA for the structures at (a) ambient pressure and (b) 4 GPa. The dotted lines at Energy = 0 eV in (a) and (b) represent the top of the valence bands and Fermi energy respectively.

Fig. 9

 9 Fig. 9 First-principles band structure of tricl-NiEt at (a) ambient pressure and (b) 6 GPa. See Figure S6 for the calculated band structures at 2, 4 and 8 GPa and Figure S7 for details of the first Brillouin zone of the optimized structure of 6 GPa. The dotted lines at Energy = 0 eV in (a) and (b) represent the top of the valence bands and Fermi energy respectively.

Fig. 10

 10 Fig. 10 Calculated Fermi surface of tricl-NiEt at 6 GPa. (a) First Brillouin zone; (b) 2D plane of the Fermi surface perpendicular to the b*-axis containing the Γ-point, and (c) Bird's view of the Fermi surface of 2 x 2 x 2 cell of the first Brillouin zone. Color bar indicates Fermi velocity. The figures are plotted using FermiSurfer 2.1.0.28

Fig. 11

 11 Fig. 11 Pressure dependence of DFT optimized lattice parameters in tricl-NiEt. The structural optimization is performed on the basis of exchange-correlation functional of vdW-DF2. Solid circles, triangles, and squares are lattice angles α, β, and γ, respectively.

Fig. 12

 12 Fig. 12 Crystal structures of tricl-NiEt at (a) ambient pressure and, (b) 6 GPa. The structural parameters at 6 GPa are obtained from the structural optimization with first-principles calculation based on the exchange-correlation functional of vdW-DF2 (See TableS4).

NiMe sample 1 ,

 1 tricl-NiEt and PtMe (with an average size of 0.15  0.02  0.015 mm3 ) and NiMe sample ( 20.09  0.02  0.015mm 3 ) were used for the high-pressure measurements. The sample was mounted in the DAC by using the same technique as that used for [Ni(ptdt) 2 ].41 The sample was encapsulated with a mixture of epoxy and alumina. The diamond with culet size of 0.7mm and tension annealed stainless steel SUS301 were used for NiMe sample 1 and tricl-NiEt, and the diamond with culet size of 0.56 mm and Inconel 625 for NiMe sample 2. Electrical contacts were obtained by attaching four gold wires ( 10 or 5 μm) with gold paint, and the four-probe DC method was used for all measurements. Daphne Oil 7373 was used as the pressure transmitting medium. The pressure was determined by the shift in the ruby fluorescence R1 lines at room temperature.

Table 2

 2

	(continued)
		d	e	f	g	h
	Nickel complexes
	[Ni(Me-thiazdt) 2 ] -1(a)	1.739(5)	1.727(6)	1.672(6)	1.370(7)	1.393(7)
	[Ni(Me-thiazdt) 2 ] -1(b)	1.759(9)	1.76(1)	1.672(9)	1.35(1)	1.40(1)
	[Ni(Me-thiazdt) 2 ] 0	1.727(4)	1.744(4)	1.649(4)	1.362(5)	1.373(5)
	[Ni(Et-thiazdt) 2 ] -1(c)	1.739(2)	1.735(3)	1.664(3)	1.362(4)	1.398(3)
	tricl-[Ni(Et-thiazdt) 2 ] 0	1.733(3)	1.750(3)	1.640(4)	1.366(4)	1.376(4)
	mono-[Ni(Et-thiazdt) 2 ] 0(c) 1.733(2)	1.755(2)	1.640(2)	1.372(3)	1.378(3)
	Platinum complexes
	[Pt(Me-thiazdt) 2 ] 0	1.734(16)	1.71(2)	1.668(18)	1.35(2)	1.39(2)
	[Pt(Et-thiazdt) 2 ] -1(a)	1.754(5)	1.726(8)	1.668(6)	1.353(9)	1.406(6)
	[Pt(Et-thiazdt) 2 ] 0	1.740(11)	1.742(11)	1.639(11)	1.366(13)	1.379(12)

Table 3

 3 Electronic properties (conductivity, activation energy, band gap) of the neutral complexes.

	Complex	σ RT at 1 bar (S/cm)	Exp. E act (eV)	Calcd. (b) direct band gap (eV)
	[Ni(Me-thiazdt) 2 ]	510 -2	0.11	0.27
	tricl-[Ni(Et-thiazdt) 2 ]	4.310 -4	0.21	0.53
	mono-[Ni(Et-thiazdt) 2 ]	1.410 -2 (a)	0.20 (a)	0.55
	[Pt(Me-thiazdt) 2 ]	1.610 -2	0.16	0.28
	[Pt(Et-thiazdt) 2 ]

  Melting points were measured on a Kofler hot-stage apparatus and are uncorrected. Mass spectra were recorded by the Centre Régional de Mesures Physiques de l'Ouest, Rennes. Methanol, acetonitrile and dichloromethane were dried using Inert pure solvent column device. CVs were carried out on a 10 -3 M solution of complex in in CH 2 Cl 2 with NBu 4 PF 6 0.1 M Potentials were measured versus Saturated Calomel Electrode (SCE). The spectroelectrochemical setup was performed in CH 2 Cl 2 with Bu 4 NPF 6 0.2 M using a Pt grid as the working electrode, a Pt wire as the counter electrode and SCE reference electrode. A Shimatzu 3600 spectrophotometer was employed to record the UV-vis-NIR spectra. The proligands 1-Me,21 1-Et,14 and the Ni complex14 [Ph 4 P][Ni(Et-thiazdt) 2 ] were prepared as previously reported. Elemental analyses were performed at Institut de Chimie des Substances Naturelles (CNRS, Gif/Yvette, France) Et-thiazdt) 2 ] (NiEt). A monoclinic phase has been obtained earlier when using Et 4 NBr as electrolyte, together with a few crystals of a triclinic phase that had escaped our attention at that time. The latter triclinic phase has been obtained here almost pure when using Et 4 NPF 6 or Me 4 NPF 6 as electrolyte, with the best crystals in the presence of Et 4 NPF 6 .

	[C 24 H 42 N 3 PtS 8 ]: C, 34.97; H, 5.14; N, 5.10; S, 31.12. Found: C, 34.94; H, 4.89; N, 5.06; S,
	31.12.
	[NBu 4 ][Pt(Et-thiazdt) 2 ]. To dry MeOH (20 mL) under inert conditions, sodium metal (34 mg,
	1.5 mmol) was added. The protected ligand 1-Et (150 mg, 0.47 mmol) was then transferred to
	the mixture. After complete dissolution the solution was stirred for 30 min at room temperature.
	Then a solution of K 2 PtCl 4 (101 mg, 0.24 mmol) and NBu 4 Br (170 mg, 0.52 mmol) in pure
	water (10 mL) was added followed by 18 hours of stirring. The formed precipitate was filtered
	and recrystallized from chlorobenzene/acetone 80/20 at 0°C to afford the monoanionic complex
	[NBu 4 ][Pt(Et-thiazdt) 2 ] as dark red brown crystals. Yield: 37% (75 mg) ; Mp = 154°C; MS
	(TOF MS ES-) calcd. for [C 10 H 10 N 2 PtS 8 ] -1 : 609.82 Found: 609.82; Elem. Anal. Calcd. for
	C 26 H 46 N 3 PtS 8 : C, 36.64; H, 5.44; N, 4.93; S, 30.10. Found: C, 36.12; H, 5.04; N, 4.68; S, 29.95.
	[PPh 4 ][Ni(Me-thiazdt) 2 ]. Under inert atmosphere, a solution of Na (35 mg, 1.5 mmol) in MeOH
	(20 mL) was added to the proligand 1-Me (150 mg, 0.5 mmol). After complete dissolution, the
	solution was stirred at room temperature for 30 mn. Then a solution of NiCl 2 ,6H 2 O (60 mg,
	0.25 mmol) in MeOH (5 mL) was added, followed 6 hours later by the addition of PPh 4 Br (210
	mg, 0.5 mmol). After stirring for 15 h, the formed reddish precipitate was filtered and
	recrystallized in the air from CH 2 Cl 2 /MeOH 20/80 to afford the monoanion complex
	[PPh 4 ][Ni(Me-thiazdt) 2 ] as dark red crystals. Yield: 48% (94 mg); Mp = 190°C. HRMS (ESI)
	Calcd for [C 10 H 10 N 2 S 4 58 Ni 80 Se 4 ] -: 663.57466 Found: 663.5737. Elem. Anal. Calcd. for
	C 32 H 26 N 2 NiPS 8 : C, 48.98; H, 3.34; N, 3.57. Found: C, 48.22; H, 3.20; N, 3.57.
	[NBu 4 ][Pt(Me-thiazdt) 2 ]. To dry MeOH (20 mL) under inert conditions, sodium metal (70 mg,
	3.0 mmol) was added. The protected ligand 1-Me (300 mg, 0.99 mmol) was then transferred to
	the mixture. After complete dissolution the solution was stirred for 30 min at room temperature.
	Then a solution of K 2 PtCl 4 (210 mg, 0.5 mmol) and NBu 4 Br (330 mg, 1.02 mmol) in pure water
	(10 mL) was added followed by 18 hours of stirring. The formed precipitate was filtered and [Pt(Me-thiazdt) 2 ] (PtMe). Bu 4 NBF 4 (200 mg) and the platinum complex [Bu 4 N][Pt(Me-
	recrystallized from chlorobenzene/acetone (80/20) at 0°C to afford the monoanion thiazdt) 2 ] (10 mg) were dissolved in 10 mL of CH 2 Cl 2 /CH 3 CN (3/7). The current intensity was
	[NBu 4 ][Pt(Me-thiazdt) 2 ] as dark red brown crystals. Yield: 70% (290 mg); Mp = 202°C; MS
	(TOF MS ES-) Calcd for [C 8 H 6 N 2 PtS 8 ] -1 : 581.79 Found: 581.79; Elem. Anal. calcd. for

Electrocrystallizations. They were systematically performed in two-compartment cells with

Pt electrodes under inert atmosphere with degassed solvents. Albeit neutral complexes are obtained, the choice of the electrolyte added in the cell to lower its resistance is particularly important to favor a given phase and/or high-quality crystals. [Ni(Me-thiazdt) 2 ] (NiMe) Ph 4 PCl (200 mg) dissolved in 10 mL of CH 2 Cl 2 /MeOH (7:2) was introduced in both compartments as supporting electrolyte. The nickel complex [Ph 4 P][Ni(Methiazdt) 2 ] (10 mg) was introduced in the anodic compartment. The current intensity was adjusted to 0.6 μA, and the reaction was left during seven days. Crystals of the neutral Ni complex [Ni(Me-thiazdt) 2 ] were collected on the anode as long needles.

[Ni(adjusted to 0.5 μA, and the current was maintained during five days. Crystals of the neutral Pt complex [Pt(Me-thiazdt) 2 ] were collected on the anode.

Table 4

 4 Crystallographic data for anionic complexes

	Compound	[PPh 4 ]	[PPh 4 ]	[PPh 4 ]
		[Ni(Me-thiazdt) 2 ]	[Ni(Me-thiazdt) 2 ],	[Pt(Et-thiazdt) 2 ],
			CH 2 Cl 2	toluene
	Formulae	C 32 H 26 N 2 NiPS 8	C 32 H 26 N 2 NiPS 8 , CH 2 Cl 2	C 34 H 30 N 2 PtPS 8 , C 7 H 8
	FW (g.mol -1 )	784.71	869.63	1041.27
	System	monoclinic	orthorhombic	monoclinic
	Space group	C2/c	P2 1 ca	C2/c
	a (Å)	18.180(3)	22.3714(18)	26.190(3)
	b (Å)	6.9147(11)	6.8300(6)	7.3028(7)
	c (Å)	27.469(4)	24.2552(18)	24.991(2)
	α (deg)	90	90	90
	β (deg)	92.999(8)	90	115.389(3)
	γ (deg)	90	90	90
	V (Å 3 )	3448.4(9)	3706.1(5)	4318.1(7)
	T (K)	296(2)	150(2)	296(2)
	Z	4	4	4
	D calc (g.cm -1 )	1.511	1.559	1.602
	µ (mm -1 )	1.120	1.190	10.291
	Total refls	14792	28970	34302
	Abs corr	multiscan	multiscan	multiscan
	Uniq refls (R int )	3917 (0.0699)	7983 (0.0798)	4632(0.0496)
	Uniq refls (I > 2σ(I)) 1964	6101	4230
	R 1, wR 2	0.0499, 0.1215	0.0621, 0.1326	0.0454, 0.1044
	R 1, wR 2 (all data)	0.1347, 0.1611	0.0948, 0.1485	0.0501, 0.1074
	GOF	0.919	0.969	1.225

Table 5

 5 Crystallographic data for neutral complexes

	Compound	NiMe	tricl-NiEt	PtMe	PtEt
	Formulae	C 8 H 6 N 2 NiS 8	C 10 H 10 N 2 NiS 8	C 8 H 6 N 2 PtS 8	C 10 H 10 N 2 PtS 8
	FW (g.mol -1 )	445.32	473.39	581.72	609.77
	System	triclinic	triclinic	monoclinic	triclinic
	Space group	𝑃1	𝑃1	P2 1 /c	𝑃1
	a (Å)	4.2398(11)	5.987(2)	6.2481(11)	5.9582(5)
	b (Å)	6.4701(14)	7.255(3)	4.6675(5)	7.2585(7)
	c (Å)	13.666(3)	10.734(4)	25.802(5)	10.8670(8)
	α (deg)	93.863(6)	98.084(11)	90	98.508(7)
	β (deg)	96.356(7)	96.421(11)	94.826(18)	97.392(7)
	γ (deg)	90.152(6)	109.878(11)	90	109.362(8)
	V (Å 3 )	371.71(15)	427.7(3)	749.8(2)	430.49(7)
	T (K)	296(2)	296(2)	293(2)	293(2)
	Z	1	1	2	1
	D calc (g.cm -1 )	1.989	1.838	2.577	2.352
	µ (mm -1 )	2.411	2.101	10.454	9.110
	Total refls	8252	8870	5906	4422
	Abs corr	multiscan	multiscan	multiscan	multiscan
	Uniq refls (R int )	1717 (0.0722)	1955 (0.0347)	1807(0.1020)	2008 (0.0656)
	Uniq refls (I > 2σ(I)) 1107	1628	1063	1713
	R 1, wR 2	0.0438, 0.0808 0.0306, 0.0639 0.0984, 0.1514 0.0417, 0.1042
	R 1, wR 2 (all data)	0.091, 0.0941	0.0445, 0.0732 0.1837, 0.1750 0.0489, 0.1087
	GOF	0.981	1.112	1.112	0.704

Published on 20 July 2020. Downloaded by Bibliotheque de L'Universite de Rennes I on 7/20/2020 12:22:26 PM.

Acknowledgements

This work was supported in part by Université de Rennes 1 (PhD grant to H. H.) and by the JSPS KAKENHI (Grant Numbers JP16K17756, JP19K21860, and JP16H06346). The stay of H. H. to RIKEN was supported in part by RIKEN International Program Associate and by Rennes Métropole. Their support is gratefully acknowledged. T.T. is partially supported by MEXT Japan, Leading Initiative for Excellent Young Researchers (LEADER). The computations were mainly carried out using the computer facilities of ITO at the Research Institute for Information Technology, Kyushu University, MASAMUNE at IMR, Tohoku University, and HOKUSAI-GreatWave at RIKEN, Japan.

Conflicts of interest

There are no conflicts to declare.


PhD Gabriel Hurel

Ing Jerome Laborde

Pr Louis Jézéquel

Simulation of the dynamic behavior of a bi-cable ropeway with modal bases

Keywords: ropeway, dynamic, modal basis, substructuring, quasi-static

This article presents the building of a dynamic model of a bi-cable ropeway. Thanks to the assumption of quasi-static advance of the vehicles, the calculation is performed step by step. At each step, a transient linearized dynamic solution is calculated around the quasi-static equilibrium using modal bases. The ropeway system is substructured considering the different elements: track rope, hauling rope and vehicles represented by pendulums. The results of time integration give the accelerations felt by the passengers according to the load case.

Introduction 1.Problematic

In order to improve mobility in cities, new types of public transport are investigated. In particular, ropeway is highlighted because it presents several benefits. First, the cost of building is relatively low compared to subway or tramway. It only needs to build stations and some pylons. The space used by the infrastructure on the floor is very low: unlike bus and tramway, the ropeway is not in the way of streets. Moreover, the speed of displacement is quite high and the throughput is similar to that of a tramway. Finally, this is one of the most secured type of transport. The rate of injuries and deaths per passengers is the lowest of all types of transportation. On the other side, ropeways have drawbacks. The regulation can be an obstacle to the proximity between the cabins and habitation buildings. In fact, the ropeway can create some discomfort for the neighborhood. The noise and the obstruction of the view can degrade the comfort of residents. It might also have some problems for the comfort of the passengers. The comfort criteria are thermic, acoustic and vibratory. Within the I2TC project, the objective of this article is to provide a tool able to solve dynamic and vibratory issues of an urban ropeway. In fact, the dynamic requirements for public transports are higher than touristic installations. For this, a dynamic modelling of a ropeway line is performed. Thus we aim to understand the dynamic behavior of the line and be able to predict the acceleration felt by passengers. The sensitive parameters can be found and an optimization can be performed.

The 3S cable-car

One of the technologies considered for urban transportation using ropes is the 3S cable car. As its name indicates, the number of cables is three. Two of them are track ropes which sustain the vehicles. They are fixed and the cabins are rolling on them like a train on a railroad. The third cable is the hauling rope. Its role is to pull the vehicles along the line. This cable is moving at the same speed as the vehicles, since they are clamped on it. The track ropes are embedded in the first and the last station. Their tension is tuned few times in the year in order to compensate the thermal expansion. In service the tension is varying mainly due to the load of vehicles. The tension of the hauling rope is kept constant at the first station by a hydraulic cylinder. The tension at the last station is imposed by the engine to haul the vehicles. The vehicles are composed of three main parts: the cabin, where the passengers are, is hanged to a carriage by a hanger. The hanger is fixed to the carriage by a damped revolute joint. The carriage is fixed to the hauling rope by a clamp and it is rolling on both track ropes.

Bibliography

The theory of vibration of a cable was mainly developed by Irvine [START_REF] Irvine | The linear theory of free vibrations of a suspended cable[END_REF] in the seventies. He developed analytical models able to calculate the shapes and the frequencies of the first eigenmodes of a cable with a small sag. Sack [START_REF] Sack | Transverse oscillations in travelling strings[END_REF], Simpson [START_REF] Simpson | On the oscillatory motions of translating elastic cables[END_REF] and Triantafyllou [START_REF] Triantafyllou | The dynamics of translating cables[END_REF] studied the vibrations of a cable in translation. Sergev and Iwan [START_REF] Sergev | The Natural Frequencies and Mode Shapes of Cables With Attached Masses[END_REF] were ones of the first to study a cable with masses. They represent a taut cable by a succession of segment. Rosenthal [START_REF]Vibrations of slack cables with discrete masses[END_REF] used an iterative method to find the modes of a cable with sag and masses. Cheng and Perkins [START_REF] Cheng | Free vibration of a sagged cable supporting a discrete mass[END_REF] calculated the eigenmodes when the position of the mass is varying from one end of the cable to the other. Al-Qassab [START_REF] Al-Qassab | Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass[END_REF] computed these eigenmodes with a Galerkin method. The first model of a ropeway is certainly that of Portier [START_REF] Portier | Dynamic phenomena in ropeways after a haul rope rupture[END_REF]. The vehicles are represented by pendulums and the cable by springs. The results are compared with experiments. Brownjohn [START_REF] James | Dynamics of an aerial cableway system[END_REF] built a model with a small sag cable to modelize the ropeway of Singapore. Sofi [START_REF] Sofi | Dynamic analysis of suspended cables carrying moving oscillators[END_REF] represented the cabins with damped oscillators.

Model building 2.1 Presentation

The proposed model shown in figure 1 corresponds to a span between two pylons. Since the model is planar, only the half of the system is considered: one track rope, a half of the hauling rope and half of the vehicles. Both pylons are assumed to be infinitely rigid. The cables are assumed to be elastic, with a mass. Because of low angles of bending, the bending rigidity is neglected.

Each vehicle is modelled by a pendulum as shown in figure 1. At the top, the carriage is represented by a point mass. It is in sliding contact with the track rope and clamped on the hauling rope. The hanger is attached to the carriage by a damped cylindrical joint. It has a rotational inertia and a longitudinal stiffness. Another point mass represents the cabin. In this model, dynamic effects that could occur between cables and the atmosphere are not considered.

Assumptions

Considering the studied system, two strong assumptions are made. First, the speed of the vehicles C is low enough to consider the motion of the vehicles have no dynamic effect on the system. In other words, the cabins are slow enough to consider their advance as quasistatic. The system can be represented by a succession of static equilibriums. To validate this assumption, the results of a simple model of a mass moving on a taut cable is compared Figure 1: Model of the 3S cable car (red line: track rope, green line: hauling rope, circle: carriage, square: cabin, blue line: hanger) with the quasi-static solution. Figure 2 shows the state of the cable when the mass is at the middle of the cable for three values of speed: a low speed similar to the speed of the cable car vehicles speed, a high speed similar to the speed of high speed trains and a transitional speed. The solid line represents the quasi-static solution. In every cases, the inertial forces tend to separate the cable from its static shape but in the high speed case these forces are higher so the error on the displacement cannot be neglected. At low speed (10 m/s), figure 3 shows that the average error E on the displacement is below 1%.

E = 1 T T 0 1 L L 0 u R -u u R dxdt ( 1
)
Where T is the period required by the mass to travel on the cable, L is the length of the cable, u R is the reference displacement of the cable and u is the calculated displacement.

A correction of the quasi static solution can be made by adding the inertial forces of the mass and the cable calculated with the succession of equilibrium states. The results with this correction shown in red line on figure 3 are better, in particular at speeds between 10 and 60 m s -1 . Around these static equilibriums, we assume the dynamic displacement is small enough to linearize the behavior equations. This important assumption allows us to project the problem on the eigenmodes of the structure. Average error E (%)

Quasi-static solution Quasi-static + inertial forces

Computation strategy

Thanks to the first assumption, the computation is performed step by step. The advance of the vehicles is discretized. Each step corresponds to a position of the whole of vehicles along the cables. At each step a non-linear static equilibrium will be computed. Under the assumption of small dynamic displacement, linear eigenmodes of each cable part are calculated, taking into account the position of the vehicles and parameters of the static equilibrium: shape and tension of the cables. The eigenmodes of the entire track rope constitute a modal basis on which the behavior equations are projected. A part of the hauling rope is the portion between two vehicles or between a vehicle and a pylon. The extremity of each part of the hauling rope are not always stationary but may be linked to the vehicles. Static response modes have to be added to the natural modes. The behavior of the pendulums embodying the vehicles are considered as non-linear to keep a good coupling with cables. After assembling all parts: reduced track rope, reduced hauling rope parts and vehicles, a time integration is performed at each step. The initial conditions of a step are provided by the final state of the previous step. The global behavior of the system is given by the sum of static and dynamic results.

3 Static equilibrium

Static equation of a cable

The force on the elementary portion ds at the position (x, y) are the weight and the tension on each side:

µds g + T (x) + T (x + dx) = 0 ( 2
)
Where µ is the linear mass, g the gravitational acceleration and T (x) the tension of the cable at the global coordinate x. The vector equation 2 is projected on x and y axes:

dT x (x) dx = 0 (3) dT y (x) dx = µg ds dx (4)
The linear mass µ is not constant because of the elastic strain:

µ = µ 0 1 + T ES (5)
Where E and S are the Young modulus and the area of the section of the cable respectively. In the ropeways case, the tension T is negligible compared to the product ES. The order of magnitude of the ratio is about 5 × 10 -3 . So we consider µ as a constant. The equations 3 and 4 give us the differential equation:

d 2 y(x) dx 2 = 1 τ 1 + dy(x) dx 2 (6)
The constant τ is homogeneous to a length and equal to T x µg . The solution of the equation 6 corresponds to a catenary curve:

y(x) = τ cosh x τ + K 1 + K 2 (7)
The constants K 1 and K 2 are calculated with the boundary conditions for each part of the cable. The expression of the tension of the cable is given by:

T (x) = T x cosh x τ + K 1 (8)

Equilibrium of a vehicle

The forces exerted on a vehicle with a mass M at the abscissa x M are the gravitation, the tension of the hauling rope T H on the left side and on the right side and the reaction of the track rope N :

M g + T L H (x) + T R H (x) + N = 0 (9)
The contact between the vehicle and the track rope is frictionless, hence the force N is orthogonal to the track rope. However the angle of the cable on the ϕ L is not the same as the angle on the right side ϕ R . The angle ϕ M of the force N is chosen as the average of the angles of the track rope:

ϕ M = ϕ L + ϕ R 2 ( 10
)
The equilibrium of the point of the track rope in contact with the vehicle is given by:

T L (x) + T T (x) = N (11)
The projection on the direction orthogonal to N shows that the tension of the track rope T T is equal on the left and on the right of the vehicle.

Equilibrium of the span

In the same way as the linear mass, we consider the length of the track rope L c is not varying because of its elasticity, hence it is constant:

L c = B A ds = X B x A 1 + dy c (x) dx 2 dx = n+1 i=1 Xi xi-1 τ ci d 2 y c (x) dx 2 dx = n+1 i=1 Xi xi-1 cosh x τ ci + K 1ci (12)
The number n is the number of vehicles on the span. Consequently there are n + 1 parts on each cables in the span. The equations of the equilibrium of the vehicles 9 and 11 and the equation 12 are implemented in a nonlinear solver to determine the constants K 1i and K 2i of each cable part. Figure 4 shows the shape of the cables of a span with three vehicles in a certain position. Because τ ci > τ hi , the sag of the hauling rope is more important than the sag of the track rope. The tension of both cables are shown in figure 5 for the same position of the vehicles. The tension of the track rope is continuous whereas the tension of the hauling rope has discontinuities at each vehicle.

Results

Dynamic response

The objective is to predict the dynamic response of the system while the vehicles are moving forward. Hence, we need to perform transient simulations. First, this kind of simulation is computationally expensive. The less number of degrees of freedom there is, the faster the computations are. Secondly we are interested by the low frequency dynamic phenomena of the system. Hence we choose to make a modal reduction of the cables. This method allows to take a small amount of generalized degrees of freedom while the low frequency phenomena are well described. However, at each step, the system is changing. The modal bases have to be recalculated. The computation of modes has to be fast. The structure of a cable car is characterized by elongated parts with very small interfaces represented by points in the model. The substructuring method appears as a good solution to our problem. The

Track rope

The dynamic equations of an inclined cable with a mass density are given by Irvine [START_REF] Irvine | The linear theory of free vibrations of a suspended cable[END_REF]: At the curvilinear abscissa s, the static position of the point of the cable is described by the coordinates U (s) and V (s) in the frame of reference ( e u , e v ). The coordinates u(s, t) and v(s, t) are the dynamic displacements of the point at the curvilinear abscissa s at the time t. The tension T can be split up in a static and a dynamic contribution:

µ ∂ 2 u(t, s) ∂t 2 -g sin α = ∂ ∂s T (s,
T (s, t) = T S (s) + T D (s, t) (15)
The equations 13 and 14 describe the dynamic and static behavior. The static terms can be subtracted:

µ ∂ 2 u ∂t 2 = ∂ ∂s T S (
Because the track rope is only in frictionless contact with the vehicles, the modes of the whole span of the cable are calculated. However, in order to better represent its behavior, masses corresponding to the vehicles are added for the computation of eigenmodes. These masses are removed before the reduction and replaced by pendulums for the assembly step.

The modes are computed with a finite difference algorithm. Figure 6 shows the variations of the frequencies of the first eigenmodes with respect to the positions of the vehicles. The frequency of the first mode of the cable without any vehicle is f 0 .

Hauling rope

The hauling rope is moving with the vehicle with a velocity C. Convection terms appear in its dynamic equations [START_REF] Sack | Transverse oscillations in travelling strings[END_REF][START_REF] Simpson | On the oscillatory motions of translating elastic cables[END_REF]:

µ ∂ 2 u ∂t 2 + 2C ∂ 2 u ∂t∂s + C 2 ∂ 2 u ∂s 2 + dC dt ∂u ∂s = µg sin α + ∂ ∂s T ∂u ∂s + dU ds (21) µ ∂ 2 v ∂t 2 + 2C ∂ 2 v ∂t∂s + C 2 ∂ 2 v ∂s 2 + dC dt ∂v ∂s = -µg cos α + ∂ ∂s T ∂v ∂s + dV ds (22)
By considering a constant speed of the cable, subtracting the static terms and replacing the dynamic tension with the Green-Lagrange strain, we obtain: The mixed partial term creates an antisymmetric damping, resulting in complex modes. The shape of the first mode of a portion of a hauling rope of 100 m is represented on figure 7 for two values of C.

µ ∂ 2 u ∂t 2 + 2µC ∂ 2 u ∂t∂s = dTS ds + 2ES dV ds d 2 V ds 2 -

Vehicle

K = 1 2 m c ( u2 c + v2 c ) + 1 2 J c φ2 c + 1 2 J p β2 (25) U = 1 2 k p δ 2 + g [m c (u c sin α + v c cos α) + m p (u c sin α + v c cos α -(l p + δ cos(β + α))] (26)
Where m c , u c , v c , J c and ϕ c are the masses, the displacement in both directions, the moment of inertia and the rotation angle of the carriage respectively. The variables δ, l p , J p , β p are the elongation, the length, the moment of inertia and the angle of the hanger respectively and m p is the mass of the cabin. By applying the Lagrange equations, the dynamic matrix equation is obtained:

M v Ẍ + C v Ẋ + K v V = F g + F NL (β, β, δ) (27)
The vector X is the vector of the five degrees of freedom of the pendulum:

X = u c v c ϕ c β δ T (28)
The matrix of mass M v and the vector of gravitation force F g are not constant but depend on the β angle. The non-linear terms are gathered in the nonlinear force vector:

F NL =       -m p (l p β2 sin β -β δ cos β) -m p (l p β2 cos β + 2 β δ sin β) 0 -2m p l p β δ m p l p β2       (29)

Time integration

At each step p, the track rope, the portions of the hauling rope and the pendulums are assembled to make the matrices of mass M p , damping C p and stiffness K p . The generalized degrees of freedom Q p associated are a combination of the modes of the carrying and hauling ropes and the physical degrees of freedom of each pendulum X. Then, a transient calculation is performed on a duration of the step ∆t:

M p Qp + C p Q + K p Q p = F Qg + F QNL (Q) + F I (30)
The external forces F Qg , F QNL (Q) and F I are respectively the gravitational forces, the nonlinear terms of the pendulums and the inertial forces due to the quasi-static assumption calculated with the succession of static equilibriums. The initial conditions of the transient calculation at the step p are given by the previous step projected from the previous modal basis Φ p-1 to the current basis Φ p :

Q p (0) = Φ -1 p Φ p-1 Q p-1 (∆t) (31)
5 Results

Start with an angle

In this case, a train of three vehicles cross the span from left to right. Each vehicle arrives on the track rope with different angles: 10°, 20°and 30°. Figure 9.a shows the variations of the angles of the cabins. The acceleration felt by the passengers increases with the growth of the start angle.

Emergency braking

The objective now is to simulate an emergency braking of the ropeway. With the quasi-static assumption, it is not possible to make a deceleration on the hauling rope because at each step, the vehicles are not moving in the model. To represent the deceleration, a braking force is applied on both extremity of the hauling rope. Figure 10 shows the accelerations felt by the passengers after the emergency braking.

Figure 2 :

 2 Figure 2: Comparison of the shape of the cable for three different speeds of the mass and the quasi static solution

Figure 3 :

 3 Figure 3: Average error with the quasi static assumption for different speeds of the mass

Figure 4 :

 4 Figure 4: Shape of a span with three vehicles.

Figure 5 :

 5 Figure 5: Tension of the ropes

Figure 6 :

 6 Figure 6: Frequencies of the first ten modes of the track rope with the vehicles as punctual masses with respect to the progression of the track rope

Figure 7 :

 7 Figure 7: Shapes of the first mode of a portion of a hauling rope for a speed of 0 and 50 m s -1 at different instants corresponding to factions of the period T .

Figure 8 :

 8 Figure 8: Model of a vehicle

Figure 9 :

 9 Figure 9: (a) Angles of the hangers of the vehicles (b) Longitudinal acceleration of the cabins (c) Vertical acceleration of the cabins

Figure 10 :

 10 Figure 10: (a) Braking force (b) Angles of the hangers of the vehicle (c) Longitudinal acceleration of the cabin (d) Vertical acceleration of the cabin

Figure 11 :

 11 Figure 11: Contributors and funders

  The expression of dynamic tension 15 is replaced in the equations 13 and 14. The equations are linearized neglecting the terms in u and v with an order greater or equal to two:

	µ	∂ 2 u ∂t 2 =	dT S ds	+ 2ES	dU ds	d 2 U ds 2	∂u ∂s	+ T S + ES	dU ds	2	∂ 2 u ∂s 2	(19)
			+ ES	dU ds	d 2 V ds 2 +	dV ds	d 2 U ds 2	∂v ∂s	+ ES	dU ds	dV ds	∂ 2 v ∂s 2
	µ	∂ 2 v ∂t 2 =	dT S ds	+ 2ES	dV ds	d 2 V ds 2	∂v ∂s	+ T S + ES	dV ds	2	∂ 2 v ∂s 2
			+ ES	dU ds	d 2 V ds 2 +	dV ds	d 2 U ds 2	∂u ∂s	+ ES	dU ds	dV ds	∂ 2 u ∂s 2
							s)	∂u(t, s) ∂s	+ T D (s, t)	∂u(t, s) ∂s	+	dU (s) ds	(16)
		µ	∂ 2 v ∂t 2 =	∂ ∂s	T S (s)	∂u(t, s) ∂s	+ T D (s, t)	∂v(t, s) ∂s	+	dV (s) ds	(17)
	Previously, we assumed the global length of the cable is constant because the tension was
	neglected compared to the stiffness. However, in order to express the dynamic tension, we
	consider the local strain of the cable ε(s, t) with the Green-Lagrange deformation:
	T D (s, t) = ESε(s, t)
	= ES		∂u(s, t) ∂s	dU (s) ds	+	∂v(s, t) ∂s	dV (s) ds	+	1 2	∂u(s, t) ∂s	2	+	∂v(s, t) ∂s	2	(18)


Mercedes Ruiz
email: mercedes.ruiz@aeroespacial.sener.es

V Gómez

P Fajardo
email: pfajardo@ing.uc3m.es

J Navarro
email: janavarr@ing.uc3m.es

R Albertoni
email: riccardo.albertoni@airbus.com

G Dickeli

A Vinci
email: vinci@cnrs-orleans.fr

S Mazouffre
email: stephane.mazouffre@cnrs-orleans.fre

N Hildebrand
email: nils.hildebrand@ast-space.com

HIPATIA: A project for the development of the Helicon Plasma Thruster and its associated technologies to intermediate-high TRLs

Keywords: Helicon Plasma Thruster, HIPATIA, H2020. Acronyms/Abbreviations

HIPATIA (HelIcon PlasmA Thruster for In-Space Applications) is a project recently awarded with an European Commission H2020 grant for the development of the Helicon Plasma Thruster and the technologies associated to it. The goal of the HIPATIA Project is to verify the function and performances of an Electric Propulsion System based on the HPT technology, for its application in non-geostationary satellites constellations and other small spacecraft.

Introduction

Among the different technologies that can improve Space platforms and missions performances, the use of Electric Propulsion (EP) for orbit transfers and attitude control has attracted considerable attention in the last years.

The utilisation of EP introduces important savings in terms of propellant consumption when compared to chemical thrusters. In the last 2-3 decades, EP has been mostly used for secondary propulsion tasks (e.g., station-keeping manoeuvres of GEO platforms). However, in the past few years, the use of EP thrusters for other applications (such as LEO-MEO constellations' satellites and GEO platforms delivery to final orbit) has been proposed and it is currently under implementation by several operators. This new kind of applications enhanced, or even enabled, by the use of improved EP concepts, are key to expand the position of the European Space sector.

To date, electrostatic thrusters such as the Hall Effect Thruster (HET) and the Gridded Ion Engine (GIE) have been the preferred solution when introducing EP in different satellites platforms and missions. They offer high design maturity and reliability, achieved after many years of development, but still present challenges regarding implementation impact and costs.

The Helicon Plasma Thruster (HPT), a technology under development by SENER and UC3M, is a radiofrequency powered plasma propulsion technology that can offer a good level of performance while eliminating many of the design and manufacturability issues -electrodes, high voltage electronics, and complex fabrication -which have afflicted EP systems to date. Given the relatively simple and robust design of the HPT technology (no grids neither cathodes), HIPATIA has the potential for providing a costeffective solution for large constellation of small satellites (<500 kg, <750W of power for EP).

The HIPATIA Project

Background

SENER and UC3M started to collaborate on the development of the first HPT prototype in 2015. The HPT-05 was firstly ignited in October 2015 at ESA premises, and it was subject in different test campaigns at the UC3M Electric Propulsion Laboratory since spring 2016. It was a 1kW experimental platform providing flexible architecture and operation capabilities, in order to maximise the knowledge obtained from the characterisation tests [START_REF] Merino | Development of a 1 kW-class helicon antenna thruster[END_REF].

The knowledge collected from this first prototype, as well as a review of the market needs at that moment, resulted in the decision to go for a lower power version of the HPT. The HPT-05M was an intermediate model developed to validate different design modifications that are required for the system transition from 1kW to 400W.

In 2018 the evolution to a higher TRL model, the HPT-03 started. The most important change with respect to HPT-05M was the substitution of the coilbased magnetic generator by a permanent magnet set-up. The HPT-05M and HPT-03 were extensively tested in 2018-2019, its performances results been reported in [START_REF] Navarro-Cavallé | Development and Characterization of the Helicon Plasma Thruster Prototype HPT05M[END_REF]. At that point, it seemed the HPT could be an interesting technology for the small platforms market. So far, the development had focused in the thruster and the electronics, but a complete propulsion subsystem development was necessary to ensure the impact of the technology in the in-Space propulsion scenario. Therefore, the idea behind HIPATIA is to develop the whole propulsion subsystem to a TRL level that ensures in can be flight-ready in the defined timeframe. For this to be done, several gaps, needs and related activities were identified when preparing the proposal: definition of a use case, development of a deep market survey to derive requirements, improve the propulsive performances, further investigate the plasma physics behind the helicon concept, perform coupling tests… These needs were translated into the following goal and objectives for the HIPATIA Project.

Goal and objectives

The goal of the HIPATIA Project is to verify the function and performances of an Electric Propulsion System based on the HPT technology, for its application in non-geostationary satellites constellations and other small spacecraft.

To achieve this goal, the HIPATIA Project Team will work focused on the following objectives:  Advance in the HPT technology development to fit market needs. Assessing the performances of the technology, identifying requirements and analysing the HPT impact in the Space platform.  Improve the performance of the HPT. Through key research and testing activities during the course of the Project, developing a better understanding of the plasma physics in helicon sources and thrusters.  Raise the TRL of the HPT and its associated technologies (fluidics and electronics) to TRL6. Detailing the design of the different units that will support the thruster operation, defining interfaces and performing thorough analyses (mechanical, thermal, EMC…) supported and validated by testing activities.  Plan the development for higher TRLs and industrialisation. Exploitation of the Project results includes the final assessment of HIPATIA achievements, the roadmapping of additional developments towards full qualification for flight as well as business planning.  Create and consolidate a collaboration scheme among the Consortium Partners, integrating key players in the value chain.

The Consortium

The HIPATIA Consortium, led by SENER Aeroespacial, counts with the participation of Universidad Carlos III de Madrid (UC3M), AIRBUS Defence and Space, the Centre National de la Recherche Scientifique (CNRS) and Advanced Space Technologies (AST) GmbH..

The Consortium is complementary (as shown in Table 1) from the perspective of serving the value chain of the Project. The Team covers the design, analysis, manufacturing and testing capabilities required to fulfil the Project objectives. Table 1. Competences and complementarity within the HIPATIA Consortium.

SEN UC3M ADS CNRS AST Coordination X Systems Engineering X X X TU X X RFGPU X PFCU X Final User X Testing X X X Plasma physics X X

The Helicon Plasma Thrusters 3.1 The Helicon Plasma Thruster Concept overview

The Helicon Plasma Thruster is a disruptive electromagnetic thruster for in-Space propulsion, which is under research [START_REF] Navarro-Cavallé | Experimental characterization of a 1 kW helicon plasma thruster[END_REF] and development [4,[START_REF] Phasefour | Data gathered from[END_REF][START_REF] Pavarin | 31th International Electric Propulsion Conference[END_REF] in several countries around the World.

The physical elements of a HPT are (Fig. 2): a cylindrical dielectric chamber; a gas injection system, usually at the back of the chamber; an external antenna (including a small matching circuitry) wrapped around the chamber and emitting RF waves, typically in the range 1-26MHz; and a magnetic field generator (permanent magnets for HIPATIA) that creates a longitudinal magnetic field, typically in the range 10 2 to 10 3 Gauss. Outside the chamber, the divergent magnetic topology creates a magnetic nozzle that channels the supersonic plasma flow, transforming the plasma internal energy into axially directed one, in a process very similar to the expansion of hot gas in a conventional solid nozzle.

The HPT functional mechanism can be split into the following basic processes. First, the propellant, typically an inert gas, is ionized by exciting it with an electromagnetic RF field. Broadly, this corresponds to an inductively coupled plasma discharge, giving a quasi-neutral plasma where the populations of electrons and ions interact with each other, maintaining a mean neutral electrical charge, which is contained in a dielectric discharge chamber. Simultaneously, an external stationary magnetic field is applied to the plasma discharge with three roles. At the plasma production chamber, the magnetic field enhances the RF-wave propagation and plasma heating, optimally reaching the desired Helicon mode. This mode is characterised by an inherent high plasma density and moderate electron temperature. The second role of the magnetic field is to shield the plasma from the chamber walls with the purpose of reducing thermal loads and erosion, thus, enlarging the lifetime of the thruster. Furthermore, at the external region of the discharge chamber, the close magnetic field typically shapes a divergent nozzle, or magnetic nozzle in the specialised literature. This magnetic nozzle is responsible for converting the thermal energy of the plasma within the discharge chamber, mostly carried by the electrons population, into axially directed ion kinetic energy. Electrons, which are fully magnetised (at the 200-2000G range) will expand outwardly following the magnetic field lines. Because ions are heavier than electrons and are just weakly magnetised (at this field ranges), an ambipolar electric field arises within the plasma to keep its quasi-neutral character. This potential drop along the nozzle expansion, which is highly related to the electron temperature at the plasma production source, accelerates the ions downstream, producing thrust.

HPT-03 reported performances

As explained in the background section, SENER and UC3M have been working together on the development of the HPT concept for five years, having integrated and tested several breadboards to demonstrate the concept and to research its fundamental physics, the HPT-XX family. In parallel to the thruster, SENER has designed its PPU unit, the so-called Radio Frequency Generator and Processing Unit (RFGPU), manufacturing and testing a breadboard model (BBM) that can work with powers up to 1kW. In late 2018, a successful coupling test campaign with both the HPT-03 BBM, in the 300-600W range and the RFGPU BBM, marked the consecution of TRL4 for the integrated TU+RFGPU System. The main results achieved in this campaign are depicted in Table 2.

Table 2. HPT-05M performances for Xenon propellant at 450W power at RFGPU output. In early 2020, it was expected to have the HPT-03 EM ready for test. However, due to the outbreak of COVID-19, the integration of this Engineering Model was delayed. The characterisation tests for the HPT-03 EM have started already in the summer 2020 but they have not concluded yet. Performances will be reported in coming publications.

The HIPATIA System Concept

The impacts associated to having a disruptive thruster in high TRLs would not be achieved unless the complete EP System has proven its integration and operation consistency. HIPATIA will advance the development status of the HPT up to TRL6-7, but it will also face the integration challenges of a complete EP System.

Propulsion system design around Electric Propulsion thrusters for in-Space propulsion differs quite substantially from that of Chemical Propulsion subsystems. The first ones are much more complex since still implementing propellant management assemblies, they are also required to manage large amounts of power, magnetic fields, etc... The constituting blocks of the HPT propulsion subsystem are shown in Figure 3, being the Thruster Unit (TU) the principal element of the subsystem. In order for this to operate appropriately, it shall be provided with the required conditioned RF power and propellant, being all of these inputs properly managed by adequate sensing and control means.

In the case of the Helicon Plasma Thruster, in addition to the TU, the EP system also counts on:  An RFGPU to power and control the whole System.

It converts DC power from the spacecraft bus into the required RF power to the thruster antenna. In addition to this, the RFGPU includes an Within this System, the main interfaces of the TU are the propellant inlet that interfaces the PFCU, the RF connector interfacing the RFGPU via the bidirectional coupler. Apart from these, the different elements constituting the thruster are mounted on a structure that is the main interface towards the spacecraft, both at structural and thermal levels. The main interfaces of the RFGPU within the HIPATIA System are the RF connector that allows routing the radiofrequency power to the TU through a dedicated harness, the interface with the PFCU that allows telemetry/telecommand for control.

The HIPATIA development context 4.1 Market needs

One of the first tasks HIPATIA Consortium has undertaken is the review of the market status and its middle term perspectives. This analysis stands on two different and complementary analyses: the overall satellite market projections and the identification of specific platforms and users needing a simple and prospectively low cost EP system as HIPATIA.

Initial identification of the most suitable market fit for the HPT, considering its current development status, operation range and its performances, has led to target HIPATIA to the small satellites market. The small satellite market size has increased notably in the last years due to the development and deployment of large satellite constellations [START_REF]Large LEO satellite constellations: Will it be different this time?[END_REF]. These constellations are being operated in the LEO-MEO region and are usually constituted by hundreds of satellites. The size of the platforms usually ranges in the 150-300kg interval. For upcoming constellations, the expected trend is towards platforms ranging higher in mass, probably up to 1000kg. The use of the HIPATIA system in such platforms induces some functional, operational and performance requirements on the HPT. A complete set of specifications have been compiled for the HIPATIA system attending to the small satellites market needs, and they have been flown down to unitary level.

Other markets might be open in the long term to the introduction of HPT for other applications considering the disruptions the technology may achieve. For instance, air-breathing satellites in very low orbits could make use of the HPT when an appropriate intake is developed for air breathing, since the HPT provides a cathodeless solution that can operate in the conditions of those orbits. Scalability of the HPT might open its application to the GEO platforms and the Space-tugs market on the large platforms side, due to its prospective high thrust-to-power-ratio. At the opposite point of the scale, smaller versions of the HPT could be used in CubeSats.

Development plan

HIPATIA will advance the development status of the HPT up to TRL6-7, but it will also face the integration challenges of a complete EP System, constituted by the Thruster Unit, the Radiofrequency and Power Unit that feeds it with power and the Propellant Flow Control Unit that controls the propellant pressure and mass flow. The start and target TRLs for the HIPATIA system and its units is provided in Table 3. For the Units, EQMs will be manufactured, assembled and unitary tested, for their later integration in a coupled System configuration. The integrated System will be tested in relevant environment to verify overall functionalities and performances. In addition to this, a second TU EQM will be subject to environmental testing to advance towards TRL6-7.

• Phase 4: Project results assessment. Once the research, design, development and test related tasks have been completed, HIPATIA results will be assessed in order to serve as a basis for the Business Plan, development roadmap and exploitation plan completion.

Conclusions

HIPATIA is an ambitious Project developed by a strong Consortium for advancing in the development and verification of a propulsion subsystem based on the Helicon Plasma Thruster technology up to TRL6 by end 2022.

The goal of verifying the function and performance of an integrated HPT based EP System is achieved in two steps, first at EBB-EM level, then at EQM level. The tests at EBB-EM level run parallel and fertilise the analysis and design activities of the EQM Units and System, following a de-risking approach.

The inter-related activities of design -development and verification -testing are also supported by a continuous research activity including modelling and simulation as well as laboratory tests.

When fulfilling the Project's objectives, and including additional development at its conclusion, the HIPATIA Team will be ready to introduce a qualified and prospectively cost-efficient propulsion subsystem in the small satellite market by end 2023.

Fig. 1 .

 1 Fig. 1. HPT-05M running at UC3M facility.

Fig. 2 .

 2 Fig. 2. Conceptual design of the HPT and its main constituents.

[

Fig. 3 .

 3 Fig. 3. Block diagram for the HIPATIA System, including the main interfaces with the spacecraft.

Table 3 .

 3 Start and target TRLs for the HIPATIA system and units.

		System	TU	RFGPU PFCU
	Starting TRL TRL3	TRL5	TRL4	TRL5
	Target TRL	TRL6	TRL6 TRL5-6	TRL6
	To achieve this development progress, the HIPATIA
	Project has been organised following three main action
	lines:

Acknowledgements

This Project has received funding from the European Union's H2020 research and innovation programme under grant agreement No. 870542.

The Consortium, led by SENER AeroespacialBreadboard Model (BBM) Elegant Breadboard (EBB) Engineering Model (EM) Electric Propulsion (EP) Engineering Qualification Model (EQM) Geosynchronous Orbit (GEO) Gridded Ion Engine (GIE) Hall Effect Thruster (HET) Helicon Plasma Thruster (HPT) Low Earth Orbit (LEO) Medium Earth Orbit (MEO) Propellant Flow Control Unit (PFCU) Power Processing Unit (PPU) Radiofrequency and Power Unit (RFGPU) Technology Readiness Level (TRL)


J Sarton

Y Remion

L Lucas

Distributed out-of-core approach for in-situ volume rendering of massive dataset

Keywords: Interactive visualization, large volume data, out-of-core, multi GPUs, biomedical imaging

This paper proposes a method that allows a fluid remote interactive visualization of a terabytes volume on a conventional workstation co-located with the acquisition devices, leveraging remote high performance computing resources. We provide a study of the behavior of an out-of-core volume renderer, using a virtual addressing system with interactive data streaming, in a distributed environment. The method implements a sort-last volume renderer with a multi-resolution ray-guided approach to visualize very large volumes of data thanks to an hybrid multi-GPUs, multi-CPUs single node rendering server.

Introduction

Several scientific fields rely on the visualization of data represented in the form of 3D regular voxel grids. The characteristics of this representation are particularly well suited to the architecture of modern GPUs. These have become essential to benefit from an interactive visualization of this type of data, with a good rendering accuracy. However, the increase in the size of volume data in science, and particularly in biomedical imaging, is very rapid. The latter is faster than the increase in the physical capacity of the on-board memory on GPUs. One solution to address this problem is to design an out-of-core approach that allows on-demand data streaming of small chunks (bricks) of a large volume to the GPU during interactive visualization. Although these methods are now effective, data transfers to the GPU are still a bottleneck and can be restrictive to allow a fully pleasant interactive visualization. High-performance computing environments can help to reduce this bottleneck. In addition to offering an increase in computing power, useful for interactivity and visualization quality, they increase storage capacities on several GPUs and allow to distribute the load of transfers. The presented method propose a distributed out-of-core management that offer interactive data streaming on heterogeneous node, to allow scientists to visualize large volume data directly after their acquisition from their usual workstation.

Contributions:

The use of an out-of-core approach with a virtual addressing system based on a page table for multi-resolution volume is particularly well suited for the visualization of very massive volume data [START_REF] Hadwiger | Interactive Volume Exploration of Petascale Microscopy Data Streams Using a Visualization-Driven Virtual Memory Approach[END_REF]. However, to our knowledge, any work has been carried out on the possibilities of using this structure in high-performance computing environments for all stages of the pipeline allowing in-situ visualization. In this paper, we present a distribution method to use such out-of-core data structure in distributed environments, on single multi-CPUs, multi-GPUs compute nodes. We address the distribution of virtual addressing space in very large volumes, in line with a distributed sort-last rendering approach for volume ray-casting. Our system is composed of a:

-GPU-based multi-resolution volume ray-casting with a ray-guided approach to render large volume data ; complete out-of-core pipeline from disk to GPU with a multi-level, multiresolution page table hierarchy, completely managed on GPU ; multi-GPUs sort-last volume renderer and a distributed strategy of the outof-core solution on a multi-CPUs, multi-GPUs single node server; remote solution to display, on a thin client, a high frame rate coming from a high-performance rendering server.

Related work

Volume ray-casting, introduced and improved by Levoy [START_REF] Levoy | Display of surfaces from volume data[END_REF][START_REF] Levoy | Efficient Ray Tracing of Volume Data[END_REF], is nowadays the most intuitive and efficient approach to apprehend direct volume rendering and solve the volume rendering equation [START_REF] Max | Optical models for direct volume rendering[END_REF]. Its implementation on GPUs was first proposed in 2003 [START_REF] Roettger | Smart Hardware-Accelerated Volume Rendering[END_REF][START_REF] Kruger | Acceleration Techniques for GPU-based Volume Rendering[END_REF] and then improved in 2005 [START_REF] Stegmaier | A simple and flexible volume rendering framework for graphics-hardware-based raycasting[END_REF][START_REF] Scharsach | Advanced GPU Raycasting[END_REF], taking advantage of hardware advances and introducing optimization techniques. Afterward, some work has focused on out-of-core approaches for rendering of large volumes that exceed the amount of memory available on the GPU and even on the CPU. Gobbetti et al. [START_REF] Gobbetti | A single-pass GPU ray casting framework for interactive out-of-core rendering of massive volumetric datasets[END_REF] were among the first to propose an outof-core approach for volume ray-casting on GPU, based on a multi-resolution octree. Crassin et al. [START_REF] Crassin | Gigavoxels: Ray-guided streaming for efficient and detailed voxel rendering[END_REF] also use an octree and provide a very efficient ray-guided pipeline for rendering large voxelized scenes. While many works in this context have focused on a tree structure to address an entire multi-resolution volume with out-of-core storage, Hadwiger et al. [START_REF] Hadwiger | Interactive Volume Exploration of Petascale Microscopy Data Streams Using a Visualization-Driven Virtual Memory Approach[END_REF] introduced a hierarchical page table for efficient virtual addressing. They show that their structure is more suitable than an octree for very large volumes of data. Fogal et al. [START_REF] Fogal | An analysis of scalable GPU-based ray-guided volume rendering[END_REF] provide a detailed analysis of ray-guided out-of-core approaches on GPU. For more details, we can also refer to a complete state of the art [START_REF] Beyer | State-of-the-Art in GPU-Based Large-Scale Volume Visualization[END_REF]. Parallel volume rendering has also been studied to distribute the computational workload over different units and thus operate on multi-GPUs architectures for efficient rendering [START_REF] Zhang | Survey of Parallel and Distributed Volume Rendering: Revisited[END_REF]. Molnar et al. [START_REF] Molnar | A sorting classification of parallel rendering[END_REF] proposed a classification of parallel rendering methods. Although some work in multi-GPUs volume rendering is focused on a sort-first approach [START_REF] Moloney | Sort-First Parallel Volume Rendering[END_REF], most methods are oriented towards a sort-last approach [START_REF] Müller | Optimized Volume Raycasting for Graphics-Hardware-based Cluster Systems[END_REF][START_REF] Marchesin | Multi-GPU Sort-last Volume Visualization[END_REF]. In addition to providing a computational scaling, the latter also provides a memory management scaling. This aspect is the main bottleneck in an on-demand streaming context for interactive rendering of very large volumes of data. Finally, there are very few methods that combine multi-GPUs rendering with an out-of-core approach. Fogal et al. [START_REF] Fogal | Large Data Visualization on Distributed Memory multi-GPU Clusters[END_REF] propose an out-of-core volume renderer with an MPIbased compositing to render large datasets on multi-node clusters up to 256 GPUs. Beyer et al. [START_REF] Beyer | Distributed terascale volume visualization using distributed shared virtual memory[END_REF] present a distributed version on 4 GPUs of an octreebased virtual addressing system to visualize a very large volume.

Compared with these works, we propose to introduce a distribution method of an out-of-core approach based on an efficient GPU virtual addressing and caching system [START_REF] Sarton | Interactive Visualization and On-Demand Processing of Large Volume Data: A Fully GPU-Based Out-Of-Core Approach[END_REF] on multi-GPUs, multi-CPUs single node server. Combined with a ray-guided volume renderer with sort-last compositing for interactive visualization on datasets exceeding terabytes.

3 Our method 3.1 Out-of-core approach Figure 1 summarizes the proposed pipeline. It includes an out-of-core data management in order to handle very large volumes that can exceed the amount of GPU and CPU memory. It is based on a virtual addressing system using a multi-level multi-resolution page table hierarchy and a brick cache on GPU. The underlying structure, implemented in GPU texture memory, is fully maintained on the GPU to optimize the communication load with the CPU [START_REF] Sarton | Interactive Visualization and On-Demand Processing of Large Volume Data: A Fully GPU-Based Out-Of-Core Approach[END_REF]. This system is able to interactively address a whole multi-resolution volume decomposed into small voxel bricks entirely stored on disk with compression. The bricks required for interactive visualization are streamed to the GPU cache when requested by the application. On the GPU, the navigation in the multi-resolution volume is performed in a normalized virtual volume. The full parallel GPU implementation of our virtual addressing structure management includes a brick request manager. This one takes care of sending to the CPU a list containing the IDs of the bricks required by the interactive application during its whole execution. The streaming of these bricks to the GPU cache is performed asynchronously with the GPU visualization step in order to maintain a constant interactivity for the user. A dedicated CPU thread manages the lists of the required bricks to provide them to the GPU after reading and decompressing. Unlike [START_REF] Hadwiger | Interactive Volume Exploration of Petascale Microscopy Data Streams Using a Visualization-Driven Virtual Memory Approach[END_REF] and [START_REF] Sarton | Interactive Visualization and On-Demand Processing of Large Volume Data: A Fully GPU-Based Out-Of-Core Approach[END_REF], we are interested here in the distribution of this out-of-core management solution on a heterogeneous node that includes several GPUs and CPUs with an approach including remote rendering allowing a complete in-situ visualization pipeline.

Sort-last distributed ray-casting

The bottleneck of a distributed renderer combined with an out-of-core system lies in the heavy loads of the voxel bricks, streamed to the different rendering units, and in the updates of their associated GPU caches. In this context, a sortlast approach is more appropriate than a sort-first approach to minimize these issues. By pre-determining a sub-domain of the volume on each GPU, this allows limited CPU/GPU and GPU/GPU data transfers and avoids cache flushes.

In association with our sort-last approach, we propose to use a multi-resolution ray-guided volume renderer that efficiently and naturally integrates our out-ofcore loading method. This approach ensures to load only the useful bricks on the different GPUs, according to the sampling along the rays in the volume. Our renderer is also suitable for the multi-resolution volume representation by choosing an adapted level of detail for each sample based on its distance to the camera. This allows us to adapt the sampling step, and thus reduce the number of texture memory lookup for areas containing less detail.

In our system, the compositing step, involved by the sort-last rendering, is implemented on GPU with a basic approach applying the OVER operator [START_REF] Porter | Compositing Digital Images[END_REF] in front-to-back. At each rendering pass, the local pixel buffer of each GPU is communicated to the pre-defined master GPU, in charge of the compositing. We propose to initiate these transfers from the master GPU, with peer-to-peer communications using CUDA Unified Virtual Addressing system if possible, i.e. if the GPUs are in the same addressing space as the master GPU. Otherwise, our strategy switches to explicit transfers via the CPUs.

Multi-GPUs virtual addressing

The volume partitioning is done on a normalized virtual volume, used on each GPU to navigate through all the multi-resolution volume and to virtually access to any voxels (Fig. 1(a)). This distribution only consists of restricting the addressing range in the normalized virtual volume. This method makes it possible to implicitly distribute the entire multi-resolution representation of the volume. The virtual addressing structure, used to ensure access to all voxels of a very large volume, is distributed as follows. Each GPU has its own instance of this structure with its own brick cache, completely independent of other GPUs. However, a single virtualization configuration is used for all the GPUs. Thus, the size of the bricks, blocks in the page table and the number of virtualization levels in the structure do not differ from one unit to the other. We also implement a single common CPU brick cache. We use a multi-threaded strategy with OpenMP on the different CPU(s) of the server to communicate with all the GPUs. For each of them, the corresponding CUDA context is linked to one and only one OpenMP thread. The affinity of each thread is essential and is achieved with respect to the CPUs locations according to the server topology. Thus, a thread in charge of communicating with a GPU is necessarily placed on a physical core of the CPU that has a direct physical link with that GPU. At the initialization step, each GPU is responsible for creating all the necessary resources, especially allocating its brick cache and its page table. Then, each OpenMP thread first communicates to its associated GPU the addressing subspace of the volume on which it must perform its part of the rendering. Each thread can then independently manage the requests and the streaming of the bricks to its associated GPU during the whole duration of the execution of the interactive application.

Remote rendering

In order to exploit resources offered by high-performance computing environments from lightweight devices, we propose to integrate a remote visualization system in our method. Thus, after each rendering and compositing pass, the resulted pixel buffer is directly compressed into an H.264 stream on a designated master GPU of the rendering server node. Then, the compressed buffer is copied to the CPU before being sent over the network. A thin client that receives the content of this H.264 stream, decompress it and simply display the result in an interactive display environment. This configuration allows us to provide a single pipeline that can be seen as an in-situ solution in the sense that the visualization can be done on a standard PC in place of the data acquisition. However, this requires sending all the acquired data to the remote rendering server where they are then handled for a pre-processing step. This step only includes the creation of the bricked multi-resolution representation of the 3D volume. The creation of page table entries is done on the fly as needed during the visualization. The initialization of our virtual addressing structure on the different GPUs only consists of allocating the necessary texture memory space for the different cache levels.

Results

The results presented here, were obtained on a NVidia Quadro VCA rendering server. It consists of a single computing node containing eight Quadro P6000 GPUs with 24 GB of VRAM, two CPUs Intel Xeon E5-2698 2.2 GHz and 256 GB of RAM. The display is performed on a full HD viewport 1920×1080. To illustrate the results, we used two datasets :

-Hippocampus: a 2160 × 2560 × 1072 volume with grayscale 16-bits voxels (11.8 GB) of a primate hypocampus from a light sheet microscope. -Tera Mouse Brain: a 64000 × 50000 × 114 volume with RGBA 32-bits voxels (1.45 TB) of a histological slices stack of a mouse brain.

The evaluation is based on these two datasets with 64 3 voxels bricks. In addition, the bricks of the Tera Mouse brain volume are stored on disk, cached on CPU and transferred to the GPU with 256 3 voxels, which includes 4 3 bricks of 64 3 voxels.

Display frequency

Figure 2 shows the average FPS, based on the number of GPUs used, for two different zoom level. These results were obtained by measuring the number of First, we can note that the behavior of our system is the same for both datasets and, the number of FPS are almost the same. This allows us to show that the performance of our approach does not depend on the input size of the volume to be visualized. The difference between the FPS for the two datasets is actually due to the different transfer function used. With a single GPU, we already achieve interactive visualization time. We also see the gain brought by the multi-GPUs system for the global rendering time. However, there is a significant drop in performance beyond four GPUs. It is due to the topology of the server node where four GPUs are connected to one CPU while the other four are connected to another CPU. According to this topology, four GPUs are not in the same address space as the master one. In this scenario, it is not possible to take advantage of direct GPU to GPU communications with CUDA peer-to-peer and UVA, for these GPUs. The communications with the master GPU are therefore made by explicit transfers, passing through the CPU and crossing a QPI port between the two processors. In order to validate this analysis, figure 4, provides details of the different steps required for rendering. We can see the impact of these transfers on the overall rendering time. This behavior could be fixed by using compute nodes that provide direct communication between all GPUs, with the NVLink technology of NVidia for instance.

Data loading

Figure 5 shows the results obtained by evaluating the data loading time in our multi-GPUs out-of-core management context. This evaluation is done on the loading of all the needed bricks of a complete HD view, in a worst-case scenario, from empty GPU and CPU caches. All the data are therefore only present on the server disk and stored with compression. The trend of these curves shows that the data loading time is greatly reduced by the number of GPUs used for rendering, from few seconds for a single GPU to one second or less with eight GPUs. Indeed, our sort-last rendering solution allows distributing the bricks loading on the different GPUs. Moreover, these values are once again mostly the same for both datasets although their dimensions are very different.

Conclusion and Future Work

In this paper, we have presented a method that proposes a solution to allow in-situ visualization of high dimension volume data. We use an out-of-core approach, based on an efficient virtual addressing system and a GPU caching mechanism, to handle very large volumes of data, in a context of remote parallel volume rendering. The distribution of our out-of-core model is combined with a sort-last ray-guided volume renderer in a multi-GPUs single node environment. This method reduces the main bottleneck of on-demand data streaming, from mass storage to GPU, used by out-of-core approaches to handle data exceeding GPU and CPU memory. The overall data block loading response is accelerated by distributing the charge across all GPUs. In addition, the balancing of the rendering workload allows a smooth interactive visualization. These results are observed on data exceeding terabyte on a server with 8 GPUs. The use of a multi-resolution page table, introduced by Hadwiger for out-of-core addressing of large volumes of data on GPUs, is particularly well suited for very large volumes of data. Moreover, we can conclude with this paper that this structure is also efficient and particularly well suited for the use in a distributed environment on a multi-GPU multi-CPU single node and that its behavior allows to visualize volumes exceeding the terabyte remotely on standard PC. The proposed out-of-core structure opens up a broad application framework allowing complete support of the all pipeline from data acquisition through processing to interactive visualization. We could then consider performing all these steps with our virtual addressing structure to propose an efficace in-situ solution allowing to remotely visualize the data during their acquisition and not only after their acquisition.

Fig. 1 :

 1 Fig. 1: Pipeline overview. Example of our remote out-of-core rendering pipeline on a 4-GPUs and 2-CPUs server. This pipeline includes the following steps: (a) Virtual multi-resolution volume distribution (b) Out-of-core virtual addressing structure and brick cache (c) Ray-guided volume renderer (d) Local rendering pixel buffer (e) GPUs communications for sort-last compositing (f) H.264 GPU compression.

Fig. 2 :

 2 Fig. 2: Out-of-core multi-GPUs volume ray-casting FPS. Average FPS according to two different zoom level for both data sets. (a) For a medium zoom at an intermediate level of detail (see figure3(a, c)). (b) For a high zoom level with a highly detailed full-screen volume (see figure3(b, d)). The averages are calculated on measurements taken over the entire duration of a scenario of several camera rotations around the volume.

Fig. 3 :

 3 Fig. 3: Rendering illustrations. Rendering of the Hippocampus dataset (a, b) and the Tera Mouse brain dataset (c, d) at two different level of detail.

Fig. 4 :

 4 Fig. 4: Analysis of the different step of the rendering. These measurements represent the time required for the different rendering steps according to the number of GPUs for the Tera Mouse brain dataset. (a) For a high zoom with full-screen volume display at a high level of detail (see figure 3(d)). (b) For a medium zoom with an intermediate level of detail (see figure 3(c))

Fig. 5 :

 5 Fig. 5: Loading time of a complete HD viewport in a worst-case scenario. These measurements represent the loading times of all the bricks required to generate the complete HD viewport presented in figure 3(b) and 3(d), based on the number of GPUs used, for the two datasets. They are obtained in a worst-case scenario, with empty GPU and CPU caches.

Acknowledgments

This work is supported by the French national funds (PIA2'program "Intensive Computing and Numerical Simulation" call) under contract No. P112331-3422142 (3DNeuroSecure project). We would like to thank all the partners of the consortium led by Neoxia, the three French clusters (Cap Digital, Systematic and Medicen), Thierry Delzescaux and the Mircen team (CEA, France) for the two datasets as well as the Centre Image of the University of Reims for the VCA server used.


Malcolm Walsby

Figure 1 :

 1 Figure 1: Portrait I, L7r

Figure 3 :

 3 Figure 3: The mirror of death, title page woodcut

Figure 4 :

 4 Figure 4: 'Figure la roue solaire', B1v