Dr Iurii Dovgaliuk
email: iurii.dovgaliuk@mail.chimie.ens.fr

Irena Senkovska
email: irena.senkovska@tu-dresden.de

Xiao Li

Vadim Dyadkin
email: vadim.diadkin@esrf.fr

Yaroslav Filinchuk
email: yaroslav.filinchuk@uclouvain.be

Dmitry Chernyshov
email: dmitry.chernyshov@esrf.fr

Drs Iurii Dovgaliuk

Prof. Yaroslav Mr Xiao Li

Filinchuk

Kinetic Barriers and Microscopic Mechanisms of Noble Gas Adsorption by Nanoporous γ-Mg(BH 4 ) 2 Obtained by Means of Sub-Second X-Ray Diffraction

Keywords: nanoporous frameworks, kinetics, selectivity, crystal structure, synchrotron Xray diffraction References

teaching and research institutions in France or abroad, or from public or private research centers.

Crystalline porous materials such as metal-organic-frameworks, covalent organic frameworks, and zeolites are one of the most blossoming fields in chemistry and material science [1][2][3] due to their regular porosity and great potential for selective adsorption, separation and storage of guest molecules of interest. [4] In the last decades more and more attention has been paid to flexibility of the crystalline porous materials, seriously affecting guest adsorption/desorption and a mechanical response of the material to perturbation of external conditions. It is also a key feature in several fascinating adsorption-driven phenomena, such as "breathing", [6,7] "gate opening/closing", [8,9] (photo)switching [10,11] and negative gas adsorption (NGA). [11] Notably, structural flexibility of the host is often provoked by adsorption and thus the kinetics of the guest uptake and of the framework transformation are coupled. So, the monitoring of dynamics in such materials play a key role for the materials science and for further materials development. To enable such investigations, a wide range of advanced in situ characterization methods were explored in recent years, including diffraction, scattering, vibrational and NMR spectroscopies. [12,13] Thanks to the crystallinity, the in situ X-ray, electron, and neutron diffraction methods became indispensable techniques for understanding the mechanisms of gas adsorption or separation in porous crystalline materials, and present a new possibility to crystallographically evaluate the population of individual adsorption sites, to study the cooperativity and to visualize the isotherms of individual pores in materials with hieratical porosity. [12,14,15] A common scheme for the structural characterization of a dynamic process, such as adsorption and desorption, assumes crystal structure determination at few different static states representing different stages of adsorption process, [16] frequently augmented by macroscopic evaluation of thermodynamics and kinetics as well as by theoretical calculations. [17] However, the time resolved tracking of guest molecules inside the porous framework upon adsorption has not been reported before. This work addresses a possibility to implement a sub-second X-ray powder diffraction for determination of kinetic barriers and visualization of the possible microscopic gas adsorption mechanisms simultaneously, from a single experiment. This approach has a potential to resolve site-specific kinetics of guest uptake, that is not accessible to microscopic methods.

As an object for the time-dependent study, we selected a microporous γ-Mg(BH4)2, a representative of metal borohydrides which attract much attention as multifunctional materials. [18] This framework has tubular-like pores with ca. 7 Å in size, that is between one and two kinetic diameters of Kr and Xe atoms (3.6-7.2 Å for Kr and 3.95-7.9 Å for Xe), showing a significant non-isothermal kinetics upon Kr adsorption [19,20] , therefore interesting for potential separation of these gases. [21][22][23] In particular, the selective capture of Xe and Kr from the radioactive products generated from nuclear fission is highly needed. [START_REF] Kerry | Industrial Gas Handbook Gas Separation[END_REF][25][26] The light elements host structure of γ-Mg(BH4)2 enhances a significant X-ray contrast for the guest atoms such as Ar, Kr or Xe because of sufficient difference between low scattering (form) factors of Mg (Z = 12), B (Z = 4) and H (Z = 1) and comparable or higher scattering (form) factors of noble gas molecules (e.g. for Kr at 2θ = 0°, it equals to the atomic number Z = 36). For this reason the noble gas atoms can be easily localized in the structure close to the center of the pore, while the light B and H atoms contribute little to the total scattering. The additional fluorescence signal of Kr atoms can be observed as an increase of all background points, which originates from the Kr K-edge X-ray absorption (14.3256 keV or 0.8655 Å), [27] achievable in our experimental conditions with higher energy (15900 keV or 0.77936 Å), see Fig. 1. Such combination of the host and guest responsiveness makes this compound ideal candidate for in situ investigations by Xrays. The Kr adsorption experiments were performed at 170, 180, 190 and 200 K, in which the sample was exposed to 0.5 bar Kr and four diffraction patterns were collected per second for 2500 seconds. The in situ data show significant changes in the peak intensities in the XRD patterns of γ-Mg(BH4)2 with the Kr adsorption time (see Fig. 1 for 170 K). The variation of the background is related to the increase of Kr fluorescence due its progressive adsorption by the framework, [18] which we used as an independent measure of Kr adsorption kinetics.

Sequential Rietveld refinement to the multitude of diffraction patterns confirms the two-phase model, used in our previous variable-temperature experiment, [20] see Figs. S1 andS2, and Table S1. Kr atoms in the phase (2), having smaller unit cell parameter, are closer to the center of the pore cavities, as compared to the dominant phase (1). However, a small amount of the secondary phase (2) present in the mixture, a strong peaks' overlap for the two phases, and the limitation of the X-ray powder diffraction to locate hydrogen atoms do not allow to capture structural differences associated with the smaller unit cell volume for the phase (2). We think that the two phases differ by the orientation of the [BH4] -groups, a detail that is hardly seen in an X-ray experiment. The two phases have therefore been treated as isostructural with only slight difference in unit cell dimensions and location of Kr atoms.

In the phase (1) Mg(BH4)2•xKr, the guest atoms are located in the 1D channels running along the body diagonal of the cubic unit cell, at the crystallographic position 32e (x, x, x). Secondary Mg(BH4)2•yKr phase (2) can be represented as a special case of phase (1), where the Kr atoms adopt the crystallographic position 16b with (1/8, 1/8, 1/8) coordinates right in the middle of the pore, see Fig. 2. The total Kr uptake for kinetic analysis was extracted using the Kr occupancies in each phase and their refined weight fractions. In the first approximation, Kr adsorption on γ-Mg(BH4)2 can be considered as an addition reaction, where Mg(BH4)2•qeKr adduct is forming (qe is the total amount of Kr adsorbed at equilibrium for a given temperature and pressure). In an attempt to describe the transformation from empty γ-Mg(BH4)2 to Mg(BH4)2•qeKr, the time-dependent occupancy of Kr (qt) was derived from the Johnson-Mehl-Avrami-Kolmogorov (JMAK) relation, [28,29] widely used to describe kinetics of different chemical reactions: [30] 𝑞

𝑡 = 𝑞 𝑚𝑖𝑛 + (𝑞 𝑒 -𝑞 𝑚𝑖𝑛 )[1 -exp ( -(𝑘𝑡) 𝑛 )] (1)
The equation ( 1) is a fractional order kinetic model, where qmin is amount of preoccupied Kr positions before data collection, qe is an equilibrium value that sets the maximum for a given thermodynamic conditions, k is Avrami kinetic constant, n is an order of reaction (expected to be 0.5 ≤ n ≤ 1 for a diffusion controlled case), [30] t is the time elapsed from the beginning of the process. This relation is widely used to describe adsorption kinetics of various gases/vapors on activated carbons and is known as Linear driving force (LDF) model, if n = 1. [31] The LDF model is consistent with a single rate constant (k), relaxation time, and barrier for diffusion into a periodic porous structure. [32] However, the least square fit of the data collected between 170 and 200 K with equation ( 1) has shown the need of one additional term to model pore depopulation likely due to radiation damage, at least for the data collected at 200 K. Therefore, the equation ( 1) was modified as follows:

𝑞 𝑡 = 𝑞 𝑚𝑖𝑛 + (𝑞 𝑒 -𝑞 𝑚𝑖𝑛 )[𝐴(1 -exp(-(𝑘 1 𝑡) 𝑛 )) -(1 -𝐴)exp(𝑘 2 𝑡)] (2)
Here A stands for the non-degraded part of the sample, and the decay constant k2 maps the rate of sample degradation.

The corresponding Sharp-Hancock plots form the equation ( 1) and the obtained Arrhenius plot of the rate constant from equations ( 1) and ( 2) versus T -1 result in unexpected behavior. They show partially anti-Arrhenius slope suggesting higher adsorption rates at lower temperatures (190 -170 K), while the rate at 200 K is an outlier of the general trend (Figs. S3 andS4). The anti-Arrhenius behavior is quite rare and usually can be observed during significant structural transitions in the kinetic process of guest uptake, [33][34][35] while the outlier point indicate a possible need of a different model for the kinetic process. [20] and kinetic data obtained using equation (4). The fitted values of qe fall in the middle of the kinetic hysteresis loops, and thus gives even better estimate of the equilibrium Kr content that the quasi-equilibrium variable-temperature experiments.

One of the possible kinetic models, enabling to coherently describe the data is the one assuming two barriers: [32] 𝑞 𝑡 = 𝑞 𝑚𝑖𝑛 + (𝑞 𝑒 -𝑞 𝑚𝑖𝑛 )[𝐴(1 -exp(-𝑘 1 𝑡)) + (1 -𝐴)(1 -exp(-𝑘 2 𝑡))]

3)

Similarly to the equation ( 2), the double exponent equation ( 3) can be modified for the sample degradation at higher temperatures, via inclusion of additional parameters: A1 (part of the adsorbed Kr limited by a rate constant k1), A2 (part of the adsorbed Kr limited by a rate constant k2) and k3 maps the rate of the sample degradation:

𝑞 𝑡 = 𝑞 𝑚𝑖𝑛 + (𝑞 𝑒 -𝑞 𝑚𝑖𝑛 )[𝐴 1 (1 -exp(-𝑘 1 𝑡)) + 𝐴 2 (1 -exp(-𝑘 2 𝑡)) -(1 -𝐴 1 - 𝐴 2 )(exp(𝑘 3 𝑡))] (4)
Indeed, the resulting equation ( 4) successfully describes the experimental data for all investigated temperatures and the fitted qe confirms the Kr content obtained from isobaric experiments, see Fig. 3. On the other hand, equation (3) works equally well for the data below 200 K due to the smaller effect of the radiation damage. The equation ( 4) applied to the Kr fluorescence background shows rates that are very similar to those fitted from Kr occupancies, see Fig. 4 and Fig. S5. Kr fluorescence is an independent probe to the adsorption kinetics, free of the Rietveld refinement of thousands of powder diffraction patterns and of the related assumptions. However, it is giving access only to the kinetics of the adsorption without the underlying microscopic (structural) picture, and is limited to guests showing strong fluorescent signal, such as Kr. These independent measures suggest that Kr uptake is taking place in the crystalline part of the sample only.

Kr adsorption isotherms were also measured volumetrically at 170, 180, 190 and 200 K up to 1 bar (Fig. S6). The adsorption rate analysis was performed at 0.5 bar equilibrium Kr pressure using LDF approximation. The obtained mass transfer coefficients follow the same trend as from the in situ X-ray data (Table S1), proving the reliability of the proposed approach.

The Kr adsorption isotherms were fitted using Langmuir model (Figs. S7 andS8) and the derived equilibrium constants were used to extract the thermodynamic parameters from the van't Hoff plot (Fig. S9). The resulting values of ΔH of 18.4(7) kJ/mol of adsorbed Kr and ΔS of 140(4) J/(mol·K) are close to the initial estimates of ΔH = 21-24 kJ/mol and ΔS = 103-113 J/(mol·K) made from non-isothermal diffraction data. [18] 3) and (4) (bottom). Left: Kr occupancies obtained using Rietveld method (each point is an independent refinement of the Kr occupancies in phases ( 1) and ( 2)); Right: measured Kr fluorescence background and corresponding fit obtained using equations ( 3) and ( 4).

In contrast to the equations ( 1) and ( 2), Arrhenius plots derived from the rate constants fitted by equations ( 3) and ( 4) demonstrate the ordinary behavior, see Fig. 5a. Linear fits to the Arrhenius plots yield kinetic barriers that are nearly equal for kinetic models (3) and ( 4). According to the equation ( 4 Based on structural consideration, we propose two simultaneous Kr diffusion mechanisms in γ-Mg(BH4)2 that agree with this observation. The lower barrier represents Kr diffusion along the quasi 1D channels of the nanoporous γ-Mg(BH4)2, similarly to previously determined gas diffusion along 1D channels in microporous structures (e.g. Xe diffusion in TCF-1 with 7.1 kJ/mol activation energy), [36] while the higher diffusion barrier is more common for the guest-promoting rotary motions in tight channels of some crystal structures. [37][38][39] In particular, the origin of the higher kinetic barrier of Kr adsorption in γ-Mg(BH4)2 can be related to the rotational motions of the [BH4] - groups in the structure. Notably, previously reported activation energy for [BH4] -reorientations around 2-fold (C2) axis in β-Mg(BH4)2 polymorph has a very similar value of 13.3 kJ/mol. [40] [BH4] -rotations near the 2-fold axis may therefore be considered as a predominant structural mechanism associated with the higher barrier of Kr diffusion. The barriers for [BH4] -orientational jumps in γ-Mg(BH4)2 are significantly higher and include at least two motions. [41,42] Taking into account these considerations together with the crystal structure of y-Mg(BH4)2, we propose two concerted mechanisms for Kr adsorption: the first is caused by Kr diffusion along 1D channels running in c direction and it dominates at high temperatures (>175 K), while at low temperatures (< 175 K) the second mechanism, namely the diffusion through the windows between channels, governs the kinetics, see Fig. 5d. The first kinetic mechanism involves a larger (≈ 5.8 Å) aperture of the channels, which does not affect the diffusion of Kr (kinetic diameter of 3.6 Å) to such extent as a smaller interchannel aperture with ≈ 5.0 Å in size. According to contact surface analysis made with Mercury using 0.7 Å grid spacing, [43] the smaller aperture is suitable for a diffusion of the guest molecules with a kinetic diameter smaller than 3.4 Å. Thus, rotational motions of [BH4] -around 2-fold (C2) axis of Mg-BH4-Mg bonds with an activation barrier of 13 kJ/mol can support the diffusion of Kr molecules (kinetic diameter 3.6 Å) via a pedal-wheel mechanism, see Fig. 5d.

The characterization of the size and shape of γ-Mg(BH4)2 by scanning electron microscopy (SEM) reveals the presence of two shapes of Mg(BH4)2 particles (see Fig. S11). One type of these particles belongs to the porous γ-Mg(BH4)2 and another one apparently is the amorphous polymorph of Mg(BH4)2, suggested by the Refs. [41,44] and our volumetric data. This makes impossible to get the correlations between particle size of γ-Mg(BH4)2 and Kr uptake time and requires additional studies for the conditions of its shape/size and yield control. In order to link microscopic diffusion mechanisms with the crystal structure of y-Mg(BH4)2 and the size of the guest molecules, we additionally performed the kinetic analysis for the smaller Ar (kinetic diameter σ = 3.4 Å) and the larger Xe (σ = 3.95 Å) atoms, see Fig. 6. Contrary to the Kr, they both follow a single barrier resistance with expectedly lower activation energy for Ar (5.4(3) kJ/mol) and the higher one for Xe atoms (9.5(6) kJ/mol), see Figs. 6, S12 and Tab. S5. This suggest that Ar atoms diffuse easily along 1D channels as well as between them within the investigated temperature range. On the other hand, larger Kr atoms (3.8 Å) have higher activation barrier along 1D channels (8(1) kJ•mol -1 ) as well as through the interchannel aperture, where its size is matching the penetration limit. The diffusion along the interchannel aperture is likely hindered by the dynamic rotation of the [BH4] -groups between Mg atoms, resulting in higher activation barrier (13(2) kJ•mol -1 ). The largest Xe atoms (σ = 3.95 Å) apparently do not diffuse through the interchannel apertures at all due to large size. In such case, the obtained intrachannel activation barriers increase in accordance with their larger kinetic diameters in a series Ar > Kr > Xe, being common upon adsorption by other porous materials, see Fig. S13.

The understanding of adsorption mechanisms and their corresponding energetic characteristics is of high importance for predictions of the adsorption selectivity. Particularly, the evaluation of structure-and guest-defined activation barriers in dynamic materials may explain such phenomena as selectivity of adsorption-induced phase transitions. [47] The latter enable to use the same porous framework for separation of various guests, depending on temperature regime. In our case the potential separation of Kr over Xe by γ-Mg(BH4)2 will be limited by the rotational motions of [BH4] -groups below 175-188 K and by the guest diffusivity along 1-D channels above this temperature range. The similar kinetic characterization of the Xe adsorption in γ-Mg(BH4)2 should demonstrate the preferable high temperature (> 188 K) range for Xe over Kr kinetic selectivity, providing that its hindered interchannel diffusivity is confirmed experimentally. In line with the previously presented capability to resolve individual site-specific guest uptake characteristics, like thermodynamics [13] and/or adsorption isotherms, [14] this work also shows a promising potential of sub-second X-ray powder diffraction to monitor kinetics of guest adsorption for multi-adsorption site frameworks, as this information is completely inaccessible by classical bulk (volumetric, gravimetric, calorimetric) methods. Despite the fact, that sequential Rietveld analysis of thousands of diffraction patterns remains challenging, in the near future it can be combined with other computational methods, like Principal Component Analysis (PCA), [48] which will open much room for its implementation in numerous kinetic studies.

Figure 1 .

 1 Figure 1. Time-dependent powder diffraction from γ-Mg(BH4)2 loaded with Kr gas (p(Kr) = 0.5 bar, T = 170 K, λ = 0.77936 Å). The significant change of the intensities of Bragg peaks and of the fluorescent background correlate with the amount of the adsorbed gas.

Figure 2 .

 2 Figure 2. Fragments of the crystal structures representing the phases (1) and (2) of Mg(BH4)2 loaded with Kr. The minor phase (2) has smaller cell parameter and is modelled by occupation of the middle of the pore (coordinates 1/8, 1/8, 1/8) by Kr atoms. The pores are organized into channels running perpendicular to the plane of the figure.

Figure 3 .

 3 Figure 3. Comparison of calculated Kr content from the isobaric variable-temperature experiments[20] and kinetic data obtained using equation(4). The fitted values of qe fall in the middle of the kinetic hysteresis loops, and thus gives even better estimate of the equilibrium Kr content that the quasi-equilibrium variable-temperature experiments.

Figure 4 .

 4 Figure 4. The experimental, calculated, and difference kinetic curves for Kr adsorption at 200 K (top) as well as comparison of the experimental kinetics and fits obtained using equations (3) and (4) (bottom). Left: Kr occupancies obtained using Rietveld method (each point is an independent refinement of the Kr occupancies in phases (1) and (2)); Right: measured Kr fluorescence background and corresponding fit obtained using equations (3) and (4).

  ) applied to Kr occupancies, the radiation damage at 200 K affects about 0.05 part of the sample with the rate k3 approximately 20 and 230 times lower than k1 and k2, respectively, see Tabs. S2-S4. The parametrization of equation (4) below 200 K gives similar result for 190 K and much lower values for 180 K and 170 K indicating a suppression of the radiation damage at low temperatures. We therefore neglected the radiation damage contribution and used double exponent equation (3) for the data collected below 200 K. The Arrhenius plots obtained from Kr occupancies and fluorescence background yield the first kinetic barrier of 8(1) and the second one of 13(2) kJ/mol. Analysis of the temperature evolution of the pre-exponential factors suggests a dominant contribution of the smaller kinetic barrier above 175 -188 K, see Fig. 5b and Fig S10. Such a behavior indicates two parallel adsorption mechanisms with different contributions, which change within investigated temperature intervals.

Figure 5 .

 5 Figure 5. a) The representation of quasi 1D channels with the corresponding pore cavities of empty γ-Mg(BH4)2 and their filling by Kr molecules. The forming Mg(BH4)2•(x, y)Kr are presented along the (-1 1 1) crystallographic direction. b) The Arrhenius plots of kinetic rates calculated from the equations (3) and (4) and partial contributions (c) of each exponential component both for the calculated Kr occupancies using Rietveld refinement of powder patterns and the fluorescence background. The corresponding temperature-dependent mechanisms (b and d) of the limiting Kr kinetic rates are shown as a smooth transformation from red to blue: via diffusion along the 1D channels with large pore apertures above 175 -188 K (red) and diffusion between these 1D channels, promoted by the rotation of [BH4] -groups located in the small apertures below 175-188 K (blue).

Figure 6 .

 6 Figure 6. The Arrhenius plots of Ar, Kr and Xe adsorption kinetics and the schemes of corresponding microscopic diffusion mechanisms. Ar and Xe follow a single exponent adsorption behaviour, while Kr has a double exponent parallel kinetics, denoted as the first and the second kinetic barriers. The smooth transition from the domination of interchannel to the intrachannel activation barrier upon Kr adsorption by γ-Mg(BH4)2 is presented by gradient change of colour from blue to red (temperature). Colour code: Arpurple, Bolive, Hgrey, Krorange, Mgred.

Acknowledgements

This work was supported by the Académie Universitaire Louvain (AUL, Belgium) under Grant ADi/DB/1058.2011 and FNRS (CC 1.5169.12, PDR T.0169.13, EQP U.N038.13).


Jérôme Gallard

Adrien Lèbre
email: adrien.lebre@emn.fr

Oana Goga

Christine Morin

Décembre

VMdeploy: Improving Best-Effort Job Management in Grid'5000

Keywords: Virtualization, Grid, Best Eort jobs, Scheduling, Resource Management

Virtualization technologies have recently gained a lot of interest in Grid computing as they allow exible resource management. Grid'5000 (G5K) is a French national Grid platform used for computer science research to experiment all layers of Grid software. Computer scientists reserve G5K nodes prior to their experiments. In G5K some low priority jobs are executed in best eort mode on the node idle time slots when the latter are not part of any reservation.

However, best-eort jobs may be killed at any time by the Grid job scheduler when the nodes they use are subject to higher priority reservation. This behaviour potentially leads to a huge waste of compute time or at least requires users to deal with checkpoints of their best-eort jobs.

In this paper, we describe the design and implementation of the VMdeploy framework, which exploits virtual machines for executing best eort jobs in order to solve the best-eort issue in the G5K platform. VMdeploy manages snapshots of the best eort jobs transparently to their users and thus ensures the progress of these jobs avoiding most of the waste of resources. Results of a preliminary experimental evaluation are presented. While designed in the context of G5K, VMdeploy can be used in combination of any job scheduler in clusters and grids.

VMdeploy: Comment améliorer la gestion des travaux de type "best-eort" dans Grid'5000.

Résumé : Les technologies de virtualisation ont récemment eu un gain d'intérêt dans le domaine de la Grille et cela est dû principalement au fait qu'elles permettent une plus grande exibilité dans la gestion des ressources. Grid'5000 (G5K) est une Grille nationale Française utilisée pour des expérimentations scientiques à grande échelle. Pour pouvoir réaliser leurs expérimentations, les utilisateurs de G5K doivent réserver leurs n÷uds. Dans G5K, des travaux de faible priorité ("best-eort" faire au mieux) sont exécutés sur des n÷uds disponibles, c'est-à-dire, ne faisant parti d'aucune réservation. Ces travaux de type "best-eort" peuvent être retirés des n÷uds à tout moment par l'ordonnanceur de la Grille quand des travaux de priorité supérieure sont soumis. Ce comportement conduit potentiellement à des pertes de temps de calcul, ou, contraint les utilisateurs à mettre en place des méthodes de sauvegarde/restauration de point de reprise de leurs travaux "best-eort".

Dans ce document, nous décrivons l'architecture ainsi que l'implémentation de VMdeploy, notre prototype. VMdeploy exploite les fonctionnalités des machines virtuelles (VM) pour exécuter des travaux de type "best-eort" an d'optimiser leur gestion. VMdeploy gère la création ainsi que le déplacement et la suspension/redémarrage des VM de manière transparente pour les utilisateurs an de réduire au mieux la perte de temps de calcul. Les premières expérimentations que nous présentons se montrent concluantes. Enn, bien qu'il ait été conçu dans le contexte de G5K, VMdeploy peut être utilisé avec n'importe quel ordonnanceur de grappe ou grille.

Mots-clés : Virtualisation, Grille, Travaux de type "best-eort", Ordonnancement, Gestion des ressources. [START_REF] Adabala | From virtualized resources to virtual computing grids: the in-vigo system[END_REF]

Introduction

Clusters and grids are used for a wide range of applications providing high-performance computing, large storage capacity, and high throughput communication. The most common way of exploiting this kind of distributed architectures consists in using dedicated services in particular batch schedulers in order to get resources at (i) a particular time ("reservation"), (ii) as soon as possible ("interactive") or (iii) when the resources are idle ("best-eort").

Several works have been extended to provide more exibility to users (deployment of dedicated environments [START_REF] Vallée | Tutorial: System-level Virtualization and Management using OSCAR[END_REF][START_REF] Bolze | Grid'5000: a large scale and highly recongurable experimental Grid testbed[END_REF], lease concept [START_REF] Sotomayor | Combining batch execution and leasing using virtual machines[END_REF], . . . ). However, cluster and grid usage is still based on a reservation scheme where a "static" set of resources is assigned to a "job" (or a "user") during a bounded amount of time. This model of using clusters or grids leads to a coarse-grain exploitation of the architecture since resources are simply reassigned to another job/user at the end of the slot without considering the real completion of applications. In the best case, the time-slot is larger and resources are simply under used. In the worst case, running applications are withdrawn from their resources leading potentially to the loss of all the performed calculations and requiring to execute once again the same request. In other words, the set of resources assigned to a job/user cannot evolve in time according to (i) application needs and (ii) cluster or grid resource changes.

In this paper, we focus on this lack of dynamicity in cluster or grid use. The dierent modes for exploiting clusters or grids (i.e. reservation, interactive or best-eort) imply several issues to consider. As a consequence, we voluntary chose to rstly address the case where applications are fatally taken out from resources.

Usually exploited for fault-tolerance issues, checkpointing solutions, like checkpointing-based resource preemption, have been proposed to partially improve dynamicity in clusters. However, these methods are strongly middleware or OS dependant [START_REF] Paul | Berkeley lab checkpoint/restart (blcr) for linux clusters[END_REF][START_REF] Thain | Distributed computing in practice: the condor experience: Research articles[END_REF]: they require either to link applications with dedicated checkpointing libraries or to exploit a checkpointing capable OS. Thus, moreover requiring specialized software stacks, these methods are not appropriate for a heterogeneous environment such as a grid (checkpointing dependencies, both hardware and software, limiting the locations where the application can be restarted).

Thanks to the latest improvements, virtualization tools could solve such issues and thus tackle the challenge addressed in this paper: improving transparent dynamicity in grid usage.

Virtual machines (VMs) become more and more popular [START_REF] Primet | HIPCAL: State of the Art of OS and Network virtualization solutions for Grids[END_REF] in the context of Grid and more recently Cloud Computing, providing exible, isolated and powerful execution environments. By specically using VM capabilities such as snapshot, migrate, suspend and resume, it becomes possible to signicantly reduce the loss of computation time and to provide a more dynamic usage of distributed architectures such as clusters and grids.

In this paper, we analyze what are the main challenges in designing and implementing a generic framework exploiting snapshotting and migration VM capabilities in coordination with any batch scheduler in a grid context. This framework aims at providing a more "dynamic" use of distributed architectures and so, at signicantly reducing loss of computation time and thus power consumption. Keeping in mind each constraint that we have to take into account, we present a rst prototype addressing the best-eort issue in the Grid'5000 architecture [START_REF] Bolze | Grid'5000: a large scale and highly recongurable experimental Grid testbed[END_REF]. Thanks to this prototype, called VMdeploy, best-eort jobs can be transparently submitted in VMs, so that the computation can be dynamically migrated or suspended and then resumed each time the resources are taken away from the users. Such an approach results in better performance concerning the total execution time of best-eort requests and a large benet according to power consumption. Our framework is able to automatically take in consideration best-eort requests, to deploy them into VMs and monitor them until their completion.

RR n°6764

Advanced features such as dynamical load-balancing is out-of-scope of this paper. The aim of this work is to address the dierent challenges that the community has to tackle in order to provide an appropriate framework solving the dynamicity criteria in cluster and grid usage.

The remainder of the paper is organized as follows: Section 2 motivates our work by addressing the impact of a coarse-grain management of the Grid'5000 best-eort jobs and the benets of the latest VM capabilities in such a context. Section 3 is devoted to the challenges of each mandatory step to schedule and monitor a VM job at cluster and grid level. Section 4 describes the implemented prototype and discusses experiments. Related work is addressed in Section 5.

Finally, Section 6 concludes and gives several perspectives.

Motivations

The main objective of this work consists in providing a way to improve dynamicity in the manner of using clusters and grids to ner exploit them. After emphasizing how coarse-grain management of best-eort jobs can lead to an important loss of computation (and power consumption) this section focuses on the benets of using VM technologies to reduce these issues.

Best-eort and Current Batch Schedulers

The best-eort concept has been suggested in the batch scheduler context in order to back-ll clusters or grids during free slots, which do not t well time-bounded requests. This particular mode does not provide any guarantee and jobs can be cancelled before the end of their allowed time. This leads to utilization problems since the jobs are simply withdrawn from their resources without considering the potential loss of the performed calculations. As shown in the next section, this behavior becomes more and more signicant as the number of best eort jobs increases in a large cluster or in a grid such as G5K.

Current Status in Grid'5000

G5K aims at building a highly recongurable, controllable and monitorable experimental Grid platform gathering 9 sites geographically distributed in France featuring a total of 5,000 processors. This is a heterogeneous architecture exploited by multiple users and several kinds of applications (business, scientic). The batch scheduler used in G5K is OAR [START_REF] Capit | A batch scheduler with high level components[END_REF]. It provides an extension, entitled oargrid, to manage grid resources as it does at cluster level. Last but not the least, G5K allows the deployment of customized environments on the grid nodes thanks to the Kadeploy software [START_REF] Bolze | Grid'5000: a large scale and highly recongurable experimental Grid testbed[END_REF]. Kadeploy enables to deploy any user environment directly on the bare hardware. Unfortunately, it does not provide any feature to suspend or restart the physical images.

To show the importance of taking into consideration the best-eort issue, we gathered and made some statistics on the OAR traces available from the Grid Workloads Archive [START_REF] Iosup | The Grid Workloads Archive[END_REF] To avoid data loss, users of best-eort jobs have to setup complex systems to either periodically save results or to dynamically resubmit (once again) the lost jobs. The available solutions based on checkpointing methods are often not appropriated to the grid and/or to the applications. and snapshotting capabilities, we can exploit them to correct this particular weakness by running such jobs inside VMs.

Benets of Virtualization Technologies

Virtualization is an active research subject since the 70's. The recently increased world-wide interest of researchers, developers and enterprise businesses in virtualization sparked a few years ago with the development of lightweight hypervisor technologies [START_REF] Barham | Xen and the Art of Virtualization[END_REF][START_REF] Bellard | QEMU, a Fast and Portable Dynamic Translator[END_REF]. Over the past years the technology has matured up to the point that processor manufacturers, like Intel and AMD, have incorporated hardware virtualization support in their products.

VM technologies provide exible and powerful execution environments, oering isolation and security mechanisms, customization and encapsulation of entire application environments. Moreover, they allow the bare hardware to be strongly decoupled from the system software, which is a predominant feature in the context of distributed architectures such as grids. Grids are composed of several resources, which can be heterogeneous, geographically distributed and, which can potentially belong to distinct administrative areas. In addition, grids are exploited concurrently by multiple users, who want to execute their applications in a secure and ecient way. In this particular context, VMs can be exploited to encapsulate jobs and then make grid resource management easier. The challenge of managing applications on grids is moved to the problem of managing VMs on grids. Thanks to VM capabilities, developing a framework to improve dynamicity in grid usage could be reached: VMs can be either suspended and resumed or migrated from one physical architecture to another at any time.

The next section addresses the dierent challenges to tackle in order to design and implement such a VM management framework at grid level.

RR n°6764 3 Designing a VM Management Framework

The goal of our framework consists in exploiting snapshotting and migration VM capabilities on top of traditional batch scheduler or reservation services in order to provide a more "dynamic" usage of distributed architectures.

Designing and implementing such a framework requires to consider each step of a common job submission in a grid context : (i) VM image creation (initial setup), (ii) VM image repository (central/distributed, clusterwide/gridwide) (iii) job submission, VM deployment and job starting, (iiii) VM/job life cycle (live migration, suspend/resume, periodical snapshots, . . . ) and nally (iiiii) job completion and VM shutdown. Based on this scenario, we outline three major points that we clearly identied as challenges: (i) VM storage management, (ii) network conguration and mobility and (iii) real-time VM management.

VM Storage Management

Image Creation

Our framework should be able to select the right VM image according to the user's needs. Two cases have to be considered : (i) the submitted job can be executed on top of a standard environment (e.g. Gnu/Linux) or (ii) it requires a particular environment. If the rst case can be easily solved by using a standard VM, the second one implies the creation of a particular image. From our point of view, the creation itself must be done externally by using an advanced mechanism such as a webservice application. However and due to the large number of environment creation utilities, it is important to be able to convert a particular environment into a VM image format understandable by our framework.

Initial Deployment

The deployment of a VM can be divided in two distinct phases : (i) deployment of an appropriate hypervisor on target nodes and (ii) deployment of the VM. Like the image creation, ecient deployment of the hypervisor system itself (the host OS) is beyond the scope of the paper. The proposal should provide a generic layer in order to request hypervisor deployments when required. However, the current trends in the use of VM in grids let us think that each node will provide an hypervisor (leading to simply skip this step).

The ecient VM deployment issue can be compared to previous hardware deployment challenge: providing and setting up an OS from one node to several others. Three solutions can be considered: Diskless approach, it has been for a while one of the famous approaches to set up particular operating systems on several nodes. It consists in using a distributed le system (from the well-known NFS server to the most recent distributed le systems such as Lustre) as a repository for all images. In our particular case, each node can launch a particular VM image by mounting the distributed le system. This approach implies consistency issues between several nodes executing the same VM (and thus saving their changes on the same le hierarchy physically stored on the distributed le system). Exploiting a separate hierarchy for each node executing the same VM leads quickly to space storage problems. A better solution consists in exploiting Copy-On-Write techniques [START_REF] Havard | Tools and techniques for managing virtual machine images[END_REF] where each VM saves its own modications in a particular le. This di le can be written either locally or on the distributed le system. Unfortunately, diskless approaches strongly depends on distributed le system scalability and limitations. For example, only few distributed le systems can be eciently exploited at grid level.

INRIA

Local VM image, this approach consists in deploying once and for all the VM images on each node (exploiting the large local storage space available). When a job requires a particular VM, the hypervisor can simply access the local image instead of a remote one. However propagating the changes of each VM to each node could become really complex. Moreover it can be expensive (even with copy-on-write approaches). In addition, this approach can lead to security issues since we should ensure that no user can access hard drives in order to corrupt VM images.

Ecient VM image copy from a dedicated repository to the target node(s), The idea consists in exploiting advanced tools in order to dynamically deploy the VM image from a central repository to the target node(s). A central repository is used to store the VM environments.

VMs are dynamically distributed to the target nodes when required thanks to an advanced copy mechanisms.

Due to the simplicity of the latter solution with regard to the former ones, initial deployment in our proposal is based on an ecient copy approach. It exploits the TakTuk utility [START_REF] Taktuk | Taktuk welcome page[END_REF] that provides a dynamic deployment using a binomial tree.

Management of VM Snapshots

Snapshotting VM periodically leads to another storage challenge. For each running VM, we have to consider two contents : (i) the current image that is the reference image initially deployed plus the modications applied since the beginning of the execution (the di le formerly introduced) and (ii) the current volatile state that is the le representing the memory. These two contents should be periodically saved for each VM running in the cluster or the grid. Retrieving the current image of suspended VMs is a particular case of snapshot management where the memory state has been already serialized in a specicle. As a consequence, this section does not directly address this issue.

Considering that reference VM images are available on a central repository, using a Copyon-Write strategy in order to store VM image modications on each node would really improve eciency. Thanks to that, the snapshot process can be reduced to periodically save the di le and the memory state. Nevertheless and even if the amount of data per VM is less signicant than a complete copy, saving these states in an ecient manner is still a challenge and requires to analyze several possibilities: Using a distributed le system, as we previously described. This approach depends on distributed le system scalability and grid limitations.

Saving snapshot locally seems to be an interesting approach at rst sight. Snapshot data is stored locally and when another job with a higher priority preempts the node, the VM can be simply killed or suspended. It can be restarted (i) when the new job completes or (ii) when new resources are freed in the grid. In that particular case the VM state has to be copied in the free node and restarted. Unfortunately such an approach can signicantly impact the performance of the local node since the new job competes with the copy operation that intensively uses hard drive and network card resources. Moreover in the event of a node crash, data is not reachable. So, saving snasphot locally would require an independent and reachable hard drive similar to current management network cards available in recent servers.

Copy from the target node(s) to a dedicated repository leads unfortunately to important bottlenecks since a unique job can imply hundreds of VMs.

RR n°6764

Saving snapshots in an ecient way is a real challenge and is still under investigation. Currently, our proposal copies each snapshot to a dedicated repository. Each copy overwrites the latest one.

Network Conguration and Mobility

From the network point of view, the challenges depend on the VM network management provided by each hypervisor. The issues could be divided in two points: (i) conguring MAC and IP addresses gridwide and (ii) take into account VM migration from one site to another one.

VM network card conguration

During the VM creation process (when the reference image has been built), each environment has been congured with specic network parameters for both MAC and IP addresses. As a consequence, we have to ensure that the current network conguration of a VM is not going to disturb physical infrastructure or other VM network conguration before starting it. The challenge consists in dynamically assigning a new MAC and/or a new IP when needed. In order to be able to dynamically reassign a MAC and/or a new IP, we have to set up particular mechanisms: considering a central DHCP server: in this particular case, VMs send a DHCP request and receive their complete network conguration as physical nodes do in a cluster. In addition to deal with the scalability issue, designing and implementing a Grid DHPC server seems to be technically not possible. Firstly, each site of a grid belongs potentially to a distinct network class and usually exploits its own DHCP server. Secondly, the VM MAC assignment is based on the address of each hypervisor and it is not possible to guarantee that two VMs on two distinct nodes do not receive the same MAC addresses. deploying a hybrid DHCP server per job: this approach consists in exploiting one more node for each reservation (ie, if the user requests for 100 VMs deployed on 100 physical nodes, then, the system makes a reservation for 101 nodes). This node is in charge of assigning a particular ID to all virtual machines belonging to the job. Each VM statically sets its network conguration (IP, hostname, . . . ) according to the IDs received from the master. Indeed, in addition to solve the network conguration issue, we exploit it as the dedicated repository to save the snapshots. The master node acts as a new frontend from where we can directly access all the virtual machines and run jobs inside them (see Figure 3).

Taking into account VM migration at grid level

Each VM migration at grid level (ie, between two distinct sites) implies an ARP protocol issue that we have to take into account. All active connections of the migrated VM should be migrated with the VM, ie, if V M 1 is sending a packet to V M 2 on the same cluster, the migration of V M 2 to another cluster should be transparent for V M 1. The idea of mobility in grids is a well-known issue: mobile IP, this the rst approach to solve the mobility issue. It consists of exploiting a xed agent. Roughly, when a node moves from a network to another, it informs the agent of the destination network that it is joining the group. The agent establishes a tunnel with the previous agent of the source network. When packets arrive on the originate network, they are redirected by the old agent to the new network. The IPV6 protocol integrates natively the mobility of nodes whereas specic add-ons are required for IPV4. In both cases, the mobile services should be enabled by the user of the VM and cannot be automatically congured by a generic framework (dependence between OS, security issues, . . . ) VLAN at grid level, the VLAN concept is commonly used at cluster level. It enables the creation of virtual networks in the same network. The advantage is that the computers in a Vlan are isolated from the others just like a LAN. The benets will be complete level 2 isolation enabling for instance to exploit ARP ooding techniques in case of live migration from one site to another. From our best knowledge, any tool is currently available. The Grid'5000 consortium is actively working on the extension from cluster to grid level of the G5K KaVlan tool.

Network issues due to live migration from one site to another site is not addressed in the current prototype.

RR n°6764

VM Management During Execution

In this section, we analyze the technical issues to tackle in order to transparently monitor, snapshot, and suspend/resume VMs.

VM Monitoring

In order to determine when VMs have to be migrated, suspended or resumed, our framework should be able to access information grid resources. Keeping in mind that designing and developing a complete framework is a tedious and a complex task, we chose to exploit monitoring utilities already deployed in grid infrastructures (such as Ganglia or Nagios system) to collect this information. This choice implies to develop a wrapper for each monitoring system.

Distributed Suspend/Restart

Checkpointing, suspending and restarting parallel programs are well-known complex problems.

A typical scenario consists of a job spread over multiple VMs communicating with each other.

In that particular case, we have to ensure that suspend and resume operations of the pool of VMs are transparent from the communication point of view. In other words, all VMs involved in a job should be suspended in a parallel manner, allowing them to be resumed as if they had never been interrupted.

Thanks to their external position with regards to VMs, hypervisors can store the entire state (including the network state) of any guest domain running on top of it. Within the assumption that network communications between distributed processes use a reliable protocol and that the suspend/restart of all VMs can be done before fatal timeouts, it is possible to save all the VMs with a coherent network state.

VM scheduling

An advanced management implying a lot of live migrations, suspend/resume operations to optimize particular criteria (such as performance, energy consumption, . . . ) is beyond the scope of the paper. We emphasize that one of our objectives is to address the dynamicity issue in cluster and grid usage in its globality. Each mechanism could be separately addressed in future works.

Implementation and Experiments

Based on the former analysis, we designed and implemented a rst prototype. This framework, entitled VMdeploy 1 , solves the best-eort issue in G5K. We voluntary chose to implement a nonintrusive prototype: VMdeploy interacts with the OAR scheduler to forward best-eort requests and exploits Kadeploy when the deployment on an hypervisor is required.

Due to the fact that we simply interact with OAR to retrieve computation slots for the best-eort jobs, we do not know when OAR revokes them (and thus kills submitted best-eort jobs). So, there is no way to cleanly suspend the job before revoking it. As a consequence, our framework makes periodical snapshots of the dierent VM deployed (see Figure 4) and each snapshot is physically stored on the master node as previously described in Section 3.2.1.

Initial Deployment

This experiment corresponds to the execution of a best-eort job through VMdeploy. First, a default image providing an hypervisor is physically deployed on nodes thanks to Kadeploy.

Second, the default VM is deployed on each node taking part of the experimentation.Third, the VM conguration process starts (VM boot and network conguration). Finally best-eort job is launched. These rst results show that the deployment time of the Kadeploy hypervisor environment is quite consumming (around 10 minutes). However, we emphasize that this step is going to disappear since the use of hypervisor becomes more and more common (the Grid'5000 default environment will shortly include XEN). on providing the user with a highly congurable environment, which meets the needs of their application requests. Such approaches have been developed by the GLOBUS alliance with its

RR n°6764

Workspace Service [START_REF] Keahey | Virtual Workspaces in the Grid[END_REF], and by many other organizations.

Haizea [START_REF] Sotomayor | Combining batch execution and leasing using virtual machines[END_REF] is a system able to manage the overhead of the management of VMs before the start of the reservation. However in this system fault tolerance is not provided and physical nodes need to be homogeneous. In addition, the implementation of Haizea with a real batch scheduler has not been done yet.

Other works are focused on the energy consumption in grids. As performance increases more and more, the power consumption increases too. Several researches are concentrating on nding a way to save power by shutting down the unused system nodes. The problem is when to decide to shut down some nodes. Several strategies have been proposed (IVS [START_REF] Chen | Reducing Power with Performance Constraints for Parallel Sparse Applications[END_REF], CVS [START_REF] Elnozahy | Energy-ecient server clusters[END_REF] and VOVO [19] [7]). In [START_REF] Hermenier | Power Management in Grid Computing with Xen[END_REF] the Xen virtual machine and the VOVO power saving strategy are combined to save power. The idea is to concentrate the virtual machines on a minimal subset of nodes allowing the other unused nodes to be shut down.

Other projects focus on the deployment and management of virtual clusters by working on network virtualization and load balancing between physical clusters. For example, the HIP-CAL [START_REF] Primet | HIPCAL: State of the Art of OS and Network virtualization solutions for Grids[END_REF] or VIOLIN [START_REF] Jiang | Violin: Virtual internetworking on overlay infrastructure[END_REF] projects work on network virtualization. VIOLIN combined with

VioCluster [START_REF] Ruth | Viocluster: Virtualization for dynamic computational domains[END_REF] allows load balancing between physical clusters using virtualization.

In-VIGO [START_REF] Adabala | From virtualized resources to virtual computing grids: the in-vigo system[END_REF] and VMPlants [START_REF] Krsul | VM-Plants: Providing and Managing Virtual Machine Execution Environments for Grid Computing[END_REF] allow to create VMs and congure them automatically.

Other works are based on multiple scheduling levels focusing on the communication between the cluster scheduler and the scheduler of the virtual cluster (Condor [START_REF] Thain | Distributed computing in practice: the condor experience: Research articles[END_REF], Maestro-VC [START_REF] Kiyanclar | Maestro-vc: a paravirtualized execution environment for secure on-demand cluster computing[END_REF]).

More generally, all these works focus on a particular issue and do not address the dynamicity challenge in a transparent and a generic way from the user's point of view.

Conclusion and Future Work

In this paper we have presented the design of VMdeploy, a framework for ecient and transparent management best-eort jobs in Grid platforms. We have implemented a rst prototype of this RR n°6764 framework experimented in the context of the G5K experimental Grid platform. VMdeploy relies on the use of VM for executing best-eort jobs. As killed operations requested by the unmodied OAR Grid scheduler cannot be detected, VMdeploy relies on a job manager periodically saving snapshots of best eort jobs. VMdeploy relies on existing monitoring tools to detect killed jobs.

Using our framework, users are thus relieved from the management of checkpoints of their applications and less resources are wasted. In preliminary experiments performed with G5K, we have measured the cost of the VM deployment and snapshot operation implemented in our prototype.

We voluntary chose to address the particular case where applications are fatally taken out from resources. Indeed, the dierent modes of exploiting clusters or grids (i.e. reservation, interactive or best-eort) imply several issues to consider. For instance, a particular user could book several nodes for a dedicated slot ("reservation") without really requiring all requested resources during the whole amount of time and a "naive" approach based on an event notication when the application completes will be not sucient to provide a ne management of the distributed architecture. In this particular case, the assignment policy between the resources delivered by the batch scheduler request and job/user real needs requires to exploit complementary mechanisms (for instance, monitoring probes). Such advanced mechanisms will be addressed in a next work.

In contrast to other similar environments, VMdeploy is able to manage parallel jobs running in dierent virtual nodes of virtual clusters deployed in a Grid environment. VMdeploy paves the way to scientic clouds.

  . The traces were gathered from September 2005 (beginning of G5K initiative) to August 2008. Figure 2.1.1 presents the results. As we assumed, best-eort jobs are quite used on G5K (25% of the jobs) and 22% of them are simply withdrawn by the OAR scheduler leading to more than 100,000 wasted days.

FinallyFigure 1 :

 1 Figure 1: Best-eort usage in Grid'5000

Figure 2 :

 2 Figure 2: Network conguration

Figure 3 :

 3 Figure 3: Access to the VMs

Figure 4

 4 Figure 4 presents the architecture of VMdeploy. It is composed of two major elements: the besteort wrapper (FW) and the job manager. The rst one provides a dedicated API to submit best-eort jobs and to specify execution constraints (Kadeploy environment to convert or VM 1 https://www.grid5000.fr/mediawiki/index.php/VMdeploy

Figure 4 .

 4 1.1 gives the dierent time for each step.

Figure 6 :

 6 Figure 6: Snapshot analysis Time is given in min:sec and network trac in MB

http://www.inria.fr ISSN 0249-6399

The INRIA team carries out this research work in the framework of the XtreemOS project partially funded by the European Commission under contract #FP6-033576.

Concerning the VM deployment, the time to copy the VM is signicantly growing from 8 images (more than 10 minutes). These results do not match our expectations. The rst analysis showed an important network trac from the master node.

Snapshot Management

In this section, we analyzed the overhead of a complete snapshot operation from time and network trac points of view. Results are given in Figure 6. As for the initial deployment, the more VM images we have the more expensive the snapshot operation. This can be explained by the bottleneck implied by the dierent copies from physical nodes to the master one.

Preliminary results in both experiments show the importance of the storage management in such a framework aiming at dynamically managing VMs at grid level.

Related Work

Historically, batch schedulers are used to manage jobs on clusters. The combination of several jobs with several priorities (for instance, best-eort, interactive, or reservation) on the same resources is a well-known issue [START_REF] Margo | Impact of Reservations on Production Job Scheduling[END_REF]. The backlling model [START_REF] Shmueli | Backlling with Lookahead to Optimize the Performance of Parallel Job Scheduling[END_REF] belongs to the most interesting solutions of this issue. To improve performance of backlling, solutions like checkpointing were set up. These solutions are implemented in (i) user space, i.e., at application level (a relinkage with special libraries are generally required) or (ii) in kernel space (with generally the use of a specic OS) [START_REF] Paul | Berkeley lab checkpoint/restart (blcr) for linux clusters[END_REF][START_REF] Thain | Distributed computing in practice: the condor experience: Research articles[END_REF].

In this context the use of VMs could give us a lot of interesting functionalities. This is the reason why SGE [START_REF] Fallenbeck | Xen and the art of cluster scheduling[END_REF] or Moab were upgraded to take advantage of the VM functionalities.

However these two projects are cluster-based and do not take into account grid constraints.

INRIA


The lid of the spinet organ built for L. F. Behaim in Nuremberg, 1619: music at the heart of an encomiastic life story governed by the signs of the months, the seasons, and the planets.

Florence Gétreau

In the intersection between visual arts and music, certain images, created from the end of the Middle Ages to the close of the 17 th century, bear witness, in both high and popular culture, to beliefs and customs linked to the parts of the day, the months, and the seasons under the effect of the stars. From refined books of hours with unicum status to printed almanacs containing multiple images that were more widely distributed, a range of media conveyed ancestral beliefs -particularly influenced by ancient and biblical texts that were revived during the Renaissance -in the power of the planets over the cycles of earthly life and human activities. Labours, and even more so leisure activities, naturally summon music, in the evening or at night, unbridled in February (carnivals and hullabaloos), gallant or even erotic in April and May under the influence of Gemini and Taurus, conducive to inebriation in autumn, and recreational in the idle moments at the end of the year. Among these abundant visual sources, often conceived by artists in thematic series (the times of day and night, the months, the seasons, the signs of the zodiac, and the Planet-Gods), we will look at a singular case, likely unique in its kind: the decoration of a spinet lid, whose programmatic complexity embodies with particular symbolic richness a patrician patron who placed music at the heart of his existence.

Time cycles and astrological themes in musical iconography

Tilman Seebass, in his article on music iconography as a discipline within musicology, 1 after defining its field of knowledge and discussing its historiography and methods, turns to the examination of its principal themes. He mentions symbols, allegories, and emblems, but not the cycles of life or the planets. However, he provides two references useful for our subject: Marie-Thérèse d'Alverny's study on the medieval period 2 and Kathi Meyer-Baer's examination of the Pythagorean writings, those of Plato and the Neoplatonists, the Gnostics, and the Fathers of the Church, with visual representations on mosaics and in illuminated manuscripts, which predate our subject. 3 For the period that interests us, from the 15 th to the 17 th centuries, Albert Pomme de Mirimonde is a prolific author whose works on these subjects endure. 4 In particular, he discusses the allegories placed under the protection of Venus and Mercury. Furthermore, in his work L'iconographie musicale sous les Rois Bourbons, Mirimonde devotes the first chapter of the volume dedicated to the 17 th century to allegories of music, with a special section on the 'Allegories of the Seasons, Months and Parts of the Day'. He states that: 'Calendars, designed to show auspicious dates and nefarious days, were religious long before they became civil and served to measure the passage of time. As the centuries succeed one another, Time is more and more considered as the primary cause. It regulates the course of the stars and determines the fertile union of the elements. Consequently, the seasons that give rise to this action, the months, subject to the zodiac, each sign of which has a god as its protector, and the parts of the day become in their turn divinities that preside over the evolution and mutations of the universe. [...]. The painted or engraved suites devoted to these subjects enjoyed a persistent favor during the Renaissance, and then in the 17 th and 18 th centuries'. 5 Mirimonde then illustrates how certain months are characterised by musical allusions: January and February with entertainments marking the change of year and Carnival; April, under the sign of Taurus, as one of the 'houses of Venus'. December, under the sign of Capricorn, a 'house of Saturn', the protector of some of the liberal arts. The Seasons are expressed through subjects that respond to the same type of inspirations, with Autumn for example inviting the triumph of Bacchus. For the Parts of the Day, the images bring Diana and the Moon together, and the scenes of gallantry and even nocturnal debauchery in music often offer contrasting images with a strongly moral message.

In his book Astrologie et musique, 6 Mirimonde also brings together 150 images, with commentary, on three subjects that associate music with Mercury, Venus, and the patron gods of Gemini. Mercury's attribute is the flute or the lyre, which he invented from a tortoise shell.

In the Hellenic legends he is said to be the educator of humanity. From the Renaissance onwards, he became the protector of all the liberal arts, including musicians, painters, sculptors, architects, and goldsmiths. Because of his multiple aptitudes, 'the "children" of his planet were industrious and shone in the intellectual and artistic disciplines, especially as musical instrument makers and performers. The lyre had a sacred role, but it had ceased to be used in the Middle Ages. In the Christian world, it was replaced by the organ, which became an attribute of the "children" of Mercury'. 7

The spinet lid commissioned by L. F. Behaim and its related studies It is thus possible to understand the traditional and symbolic context of the lid we are studying (Fig. 1). It both protected and decorated the polygonal spinet built by Paul Wissmaier, 8 completed in 1619, at the request of the Nuremberg patrician Lucas Friedrich Behaim von Schwartzbach (1587-1648), 9 to form a claviorganum prepared jointly by the organ builder Steffan Cuntz. This double instrument has disappeared, except for its cover, which was acquired in May 1960 by the Germanisches Nationalmuseum (GNM) from a descendant of the Behaim family. An archive from this family is kept at the same institution, which has made it possible to document the acquisition extensively. In a well-attested article on the prominent role that L. F. Behaim played, not only in his private life but also in the musical life of the city of Nuremberg in the first half of the 17 th century (he was considered the 'Musik-Herr' of the city), Heinz Zirnbauer is the first scholar to describe in detail this painted panel with the aid of archival documents, 10 to decipher its iconographic programme, and to attempt to confirm an attribution to the painter Friedrich von Valkenburg 11 (1565-1623). This hypothesis can be traced back to the catalogue of the sale of the collection of Hans Albrecht von Derschau, who was the owner at the time, in Nuremberg in 1825. It was not until Andreas Tacke's monumental catalogue raisonné of 17 th -century paintings in the Germanisches Nationalmuseum, published in 1995, that a new critical study -this time by an art historian -presented fresh arguments to the discussion. 12 As the bibliography of this lid, compiled by Tacke, demonstrates, for more than three decades this spinet lid has been commented on by organologists 13 and music iconographers. 14 The commission of this exceptional hybrid instrument by this highly educated patrician is documented through payments from January to December 1619. These payments are directed to builder Stefan Cuntz, 15 as he is creating a 'six-stop organ case' with recumbent pipes intended to be placed under the pre-existing spinet built by 'Paul Wissmeher' -which appears in the account books of L. F. Behaim since 1617 for the maintenance of his instruments -to the cabinetmaker who prepared the instrument's backrest seat, and to the paintermentioned several times but not named, which omission suggests that he was a very regular visitor to the house.

The pictorial programme of the spinet lid

The spinet lid consists of a banded upper section (originally hinged to the main panel and intended to act as a front flap to protect the instrument's keyboard) with seven cartouches featuring trompe l'oeil borders that imitate fittings. The subject is the seven Planet-Gods (Saturn, Jupiter, Mars, Apollo, Venus, Mercury, and Diana) in the form of statues in the Antique style, each surmounted by the corresponding signs of the zodiac, surrounded by contemporary scenes (Fig. 1b).

The principal part of the cover depicts a music scene in the open air in the Behaims' garden at the Thumenberg manor house, with the city of Nuremberg in the distance (Fig. 1c). On either side of the concert, the four seasons are depicted with their associated work and leisure activities: Spring and Summer (Fig. 1d), and Autumn and Winter (Fig. 1e), along with other family homes.

Heinz Zirnbauer (1960) and Andreas Tacke (1995) have identified almost all of the figures: in the centre, playing the double instrument of spinet and organ, whose two manuals are clearly visible, the master of music of the house, Johann Staden the Elder (1581-1634), whose career is well-known in the city of Nuremberg, seems to greet us by turning around. The resemblance between his figure in the painting and his portrait engraved by Johann Pfann (1648-1663) two decades later can be verified (Fig. 2). Note also that under the musician's left elbow, on the organ case, and on the back of his chair, the date 1619 is painted twice. Around him, from left to right, Paulus Behaim (1557-1621), the father of the patron, holds his grandson Georg Friedrich (1616-1681) in his lap. Next to them the head of the family and patron, Lucas Friedrich Behaim, plays a bass viol. His likeness can be compared with his portrait by Michael Herr (1591-1661), 16 painted in 1637, and with another engraved by Georg Walch (fl. 1632-1654), probably after 1648 (Fig. 3). On this plate, printed thirty years later than the spinet lid, his being overweight is visible and his resemblance to his father is quite striking.

In the centre, aligned with the keyboard instrument, Lucas Behaim's wife Anna Maria Pfinzing von Henfenfeld (1591-1654) brings fruit trays with her sister, while her granddaughter Anna Sabina (1615-1681) closes the circle of violin and viola players surrounding the spinet in the foreground, in symmetry with her younger brother. In front of a large wine cooler, one of the bottles of which bears her mother's coat of arms, she is raising a glass of wine in a toast. Behind her, farther to the right, gazing at the viewer with the same intensity as the musicians and the family, are the lid painter holding his paint pot and palette, the harpsichord maker with his tuning key, and the organ builder holding a pipe (Fig. 1h).

Four family homes around Nuremberg -in Schoppershof, Gleisshammer, Platnersberg, and the Pfinzig family pond house -are depicted in the background, the first two of which still exist today. On either side of the music scene, the activities of each season, from Spring and Summer on the left to Autumn and Winter on the right, are depicted in tableaux that are both naively realistic and conventional, with masters and servants mingling. Andreas Tacke has suggested that some of the details of the grape pickers, card players, and drinkers are borrowed from Jost Amman's engraved series of months, especially the month of October. 17

The seven compartments of the small lid-flap, representing the figures of the Planet-Gods, are associated with the signs of the zodiac, and are taken directly from a series engraved by Jan 16 Tacke, Die Gemälde des 17. Jahrhunderts (as fn 12), p. 116ff., n° 53. 17 Tacke, Die Gemälde des 17. Jahrhunderts (as fn 12), p. 381.

Pietersz Saenredam (ca. 1565-1607) after Hendrick Goltzius (1558-1617), representing The Seven Planets. 18 But the artist has supplemented and adapted the works of each season around these symbolic figures, with both recent historical scenes and significant scenes from the life of the Behaim family. Saturn, accompanied by the signs for Capricorn and Aquarius, presides over the harvest (Fig. 4); Jupiter, under the signs for Pisces and Sagittarius (Fig. 5), offers the occasion to display scholars, a musician playing the harp, and, also, hidden behind the statue, the painter, who represents himself a second time, from behind, in front of his easel (Fig. 6); Mars, with the signs for Aries and Scorpio, presides over battles; and Apollo, with the Sun and Leo (Fig. 7), makes it possible to evoke the ennoblement of L. F. Behaim by Emperor Matthias (1556-1619), the knighthood having taken place in 1612 in Frankfurt (even though the landscape in the background shows a view of Nuremberg). Both his castle and the emperor's entry into the imperial city in 1612 are notable, with two details reported in the chronicles: the erection of a triumphal gate designed by the painter Frederik van Valckenborch and fireworks. The fireworks explosion is depicted with the brutality of a single detonation. In the same compartment, Paulus II Behaim, the father, is shown receiving the Bohemian fiefs from the emperor, together with Georg Volckamer. Venus, with Libra and Taurus (Fig. 8), offers the occasion for a small love concert showing a gambist wearing the same light-coloured jacket as the painter, a young singer, and a lute player in the same severe costume as the concert musicians in the lid's centre.

Mercury, with Gemini and Virgo (Fig. 9), evokes commercial activities -a trademark on one of the barrels is perhaps that of the Behaim family. And finally, with Diana, accompanied by the Moon and Cancer (Fig. 10), the maritime landscape, vessels, and turbaned oriental figures certainly allude to the long journey undertaken by L. F. Behaim through Italy to Constantinople and Jerusalem between 1608 and 1610. 19 Love and music, power, travel, trade, the career of honours, and war are associated with these ancient figures, and with the evocation of the seasons and astrological signs, by so many contemporary subjects evoking the career and social life of Lucas Behaim in the political context of the time. A sort of visual, moral, and encomiastic life story, it forms a counterpoint to the values conveyed by this astrological programme, which demonstrates that the destiny of men is influenced by that of the planets. As for the theme linked to wine, it is summoned three 18 Ilja Beldman: Goltzius' Zintuigen, Seizoenen, Elementen, Planeten en Vier tijden van de dag: van allegorie naar genre-voorstelling, in: Netherlands Yearbook for History of Art 42/43 (1991-92), p. 307-336; special issue devoted to Hendrick Goltzius. See chapter IV.1 »De zeven planeten, gegraveerd door Jan Saenredam (1596)«, p. 325ff. 19 See note 1.

The absence of the artist's name in the account books of the Behaim archives, mentioned above in connection with the making of the spinet and its lid, may be surprising. In our opinion, this can be explained by the fact that the artist was one of the family's loyal followers. As Heinz Zirnbauer mentions, a master painter contributed to the artistic education of L. F. Behaim's children: Paul Juvenel the Elder (1579-1643). 21 As such, we have sought to understand whether this artist could be a potential candidate for the attribution of this lid. The son of the painter Nicolas Juvenel (Dunkirk 1540-Nuremberg 1597), who worked in Hainaut, he studied painting with Adam Elsheimer in Frankfurt. A painter of religious subjects and church views, he painted the altar shutters of St. Matthew's Church in Herolsberg, and became a member of the Nuremberg guild in 1609, the year in which the first of his four children, all of whom were to become painters, was born; he took part in the restoration of Nuremberg's town hall in 1613 and was also commissioned to paint thirty-three compartments of its vault as well as the portraits of the emperors Ferdinand II, Matthias, and Rudolf I and II.

We have a portrait of Paul Juvenel in 1620, when he was forty-one years old, as shown in an engraving by Georg Strauch (1613-1675) printed in 1655 (Fig. 12). 22 He presents himself to us holding his palette, brushes, and support stick. He has a very different physiognomy from that of Frederik van Valkenborch. He wears a beard, and his pourpoint appears to be made of copper-coloured silk lamé (or silk with a gadroon or pod pattern) that is closely related to the one worn by the painter shown twice in the lid painting. (Fig. 11a).

But it is a study of Paul Juvenel's works that provides the most serious arguments for the hypothesis that he could have fashioned the lid of this spinet. If we follow their chronology, in

The Baptism of Christ (Fig. 13), dated 1609, which is his masterpiece for admission to the Nuremberg guild, we can see interesting similarities with details of the lid. The almost naked body of Christ with a three-quarter back can be compared with the figures of Mars and Mercury (Fig. 13a). The face of John the Baptist compares with several male faces on the cover (Fig. 13b): in the season Spring, the man in red grafting a tree and the two men shearing a sheep. The muscularity of the figure seated in the middle foreground, seen from behind, compares with the figure of Mercury (Fig. 13c). Finally, the figures of the women bathing -and the naked childhave an anatomy close to the bodies of Venus and Diana, in particular the breasts, hands, and faces (Fig. 13d). In The Preaching of St. John the Baptist, a drawing from the 1620s in the National Museum in Warsaw,23 the tree depicted is very similar to the one in front of the inn on the right-hand side of the cover. On the latter, the kneeling woman bleeding the pig not far from the spinner, in the lower-right-hand corner of the Winter season, shows similarities with the kneeling woman holding a child on the right-hand side of the Baptism of Christ, dated 1621, which has passed into the art trade. 24 In the same painting, the face of Christ is very close to that of the old man, also on his knees, bleeding the same boar. The figure of St. John the Baptist from behind, extending his muscular arm, is reminiscent of the statue of the Planet-God Mars on the upper band of the lid. In the same religious painting, the muscular, naked bodies seen from behind, although more elongated and wiry, have many similarities with this statue of the god Mars. If we return to the kneeling old man, he has the same physiognomy as Joseph in Juvenel's drawing of The Visitation in the British Museum, dated 1622 (Fig. 14). [START_REF] Juvenel | The Visitation[END_REF] The figure of Mary is reminiscent of the woman between the spinner seen from behind and the grain threshers against the inn, and of the faces of the women on the far right of the cartouche dedicated to Diana. It should also be noted that the man with the oriental turban and the red coat is very similar to the figure of Joseph, who is also similar to the bearded man with a black coat and hat on the right of the cartouche of Jupiter (Fig. 14a). This figure is clearly related to the figure of the priest holding the child Jesus in The Presentation in the Temple, a work dated 1630, which was sold in Munich. [START_REF] Juvenel | The Presentation in the Temple, oil on panel[END_REF] As for the oriental figures in the background of this scene with Jupiter, they can be found on the cover in the centre of the panel with Diana, but also on numerous occasions in paintings by Juvenel, for example in another version of the Presentation in the Temple, sold at Koller's in Zurich in 2011, where the same scene occupies the right-hand side of a church view also comprising four oriental figures placed in the centre of the nave. Finally, in The Tribute to Caesar, an oil on canvas signed and dated 1630, [START_REF] Juvenel | Le dernier tribut à César, oil on panel, signed[END_REF] Caesar's face in profile is extremely close to the red-jacketed and turbaned oriental man kneeling on the right of the panel with Diana.

All these connections open up the debate on the hypothesis that the Behaim lid can be attributed to this artist or to his studio, even though according to Zirnbauer he contributed to the artistic education of the family's children. A more exhaustive examination of the archives kept at the Germanisches Nationalmuseum would undoubtedly allow us to confirm this.

Conclusion

Thomas A. Belz, author of a doctoral thesis presented at the University of Bamberg in 1996 on the paintings decorating plucked-keyboard instruments, has commented on this spinet lid.

According to Belz, we have a kind of updated summary of the theme of the gardens of love, but with the addition of family portraits, portraits of friends who are painters, builders, and musicians, the evocation of the months, the seasons, and the protective planets. He suggests, referring to Girolamo Cardano's treatise Opus novum de Proportionibus (Basel, 1570), in an effort to understand why this cover also evokes the musical order of the planets, 28 that the artist links in a single composition, based on the musical theory of Gioseffo Zarlino, the harmony of the cosmos (musica mundana), that of family and friends (musica humana), and finally that of the instrumentalists in a vision mis en abyme -for the observer of the double instrument when it was played -and of the musician at the keyboard (musica instrumentalis).

It can be assumed that Behaim, a highly educated man and very experienced traveler, gave his painter a quite prescriptive programme, encouraging, as in the education of his own children, friendship among the arts through the subterfuge of the children of Mercury and children of Venus. The ideal garden at the centre of this complex painting, like many other Antwerp virginal lids from the last decades of the sixteenth century, links these moments of Behaim's private life to the tradition of late medieval books of hours, placing them firmly within both his humanist culture and family background. 28 Belz, Das Instrument der Dame (as fn. 21), p. 196ff. Zirnbauer, Lucas Friedrich Behaim (as fn. 10), p. 344.

7

  Mirimonde: Astrologie et musique (as fn 6), p. 14f. 8 In archive documents his name is Wissmar or Wissmeher. 9 See Lucas-Frédéric Behaim's eulogy by Martin Beer: Martin Beer: Davids Liebe zu dem Hause dess Herrn bey christlicher Leichbegängniss dess […] Herrn Lucas Friedrich Behaims […], Nuremberg 1649. See especially »Erzählung dess Lebenslauffe«, p. 17-26. The journey to the Holy Land is then described p. 27-36. For modern literature see Anton Ernstberger (ed.

): Ludwig Camerarius und Lukas Friedrich Behaim: ein politischer Brief wechsel über den Verfall des Reiches 1636-1648, Munich 1961, p. 4-7. 10 Heinz Zirnbauer: Lucas Friedrich Behaim, der Nürnberger Musikherr des Frühbarok. Neue Dokumente zur städtischen und privaten Musikpflege in Nürnberg zur Zeit des Dreisigjährigen Krieges, in: Mitteilungen des Vereins für Geschichte der Stadt Nürnberg 50 (1960), p. 330-351, here 342-345. 11 Also known as Frederik van Valchenborg.

  Die Gemälde des 17. Jahrhunderts im Germanisches Nationalmuseum, Mains 1995, p. 376-385, Nr. 227; Der Behaimsche Spinettdeckel von 1619: Zu einem hochrangigen Kulturgeschichtlichen Zeugnis der Nürnberger Barockzeit, in: Der »Schöne« Klang. Studien zum historischen Musikinstrumentenbau in Deutschland und Japan unter besonderer Berücksichtigung des alten Nürnberg, ed. Dieter Kirckeberg, Nuremberg 1996, p. 143-157. 13 John Henry van der Meer: Sweelinck und Nürnberg?, in: Tijdschrift van de Vereniging voor Nederlandse Muziekgeschiedenis 20/1-2 (1964-1965), p. 37-44; Musikinstrumente, Von der Antike bis zur Gegenwart, Munich 1983, p. 177, 184, 194; Jürgen-Peter Schindler: Der Nürnberger Orgelbau des 17. Jahrhunderts: Leben und Werk der Nürnberger Stadtorgelmacher Steffan Cuntz und Nicolaus Manderscheidt (= Institut für Aufführungspraxis der Musik des 18. Jahrhunderts. Sonderbeitrag 10), Michaelstein/Blankenburg 1991, p. 40. 14 Lucas van Dijck and Ton Koopman: Het Klavecimbel in de Nederlandse Kunst tot 1800 -The Harpsichord in Dutch Art before 1800, Zutphen 1987, Ill. 51, without a date and under the title "The Four Seasons". 15 On this maker, see Konrad Dänhardt: Die Restaurierung der Cuntz-Orgen -mit Beiträgen von Stephan Thürmer und Dirk Zacharias, in: Festschrift anlässlich der Restaurierung der Cuntz-Orgel on 1627, ed. Klemens Unger und Peter Germann-Bauer,Regensburg 2015, p. 16-51.

12 Andreas Tacke:

21

  Zirnbauer, Lucas Friedrich Behaim (as fn. 10), p. 350; Thomas Aurelius Belz: Das Instrument der Dame. Bemalte Kielklaviere aus drei Jahrhunderten, PhD Diss., Otto-Friedrich-Universität Bamberg 1998, p. 198. 22 Georg Strauch (1613-1675): Portrait of Paul Juvenel, etching, 1655, 10,8 x 8,8 cm, The British Museum, Reg. Nr. 1865.0311.115. (Paulus Iuvenel Norib: Aetat: Suae XLI. Anno 1620).

Kathi Meyer-Baer: Music of the Spheres and the Dance of Death, Princeton 1970/1984.

Albert Pomme de Mirimonde: La Musique dans les allégories de l'amour, II. Éros, in: Gazette des Beaux-Arts(1967), p. 319-346; Les Allégories de la Musique I -La Musique parmi les Arts Libéraux, in: Gazette des Beaux-Arts (1968), p. 295-324; Les Allégories de la Musique II -Le retour de Mercure et les allégories des Beaux-Arts, in: Gazette des Beaux-Arts (1969), p. 342-362; Les allégories astrologiques dans l'histoire de Marie de Médicis peinte par Rubens, in: Gazette des Beaux-Arts (1977), p. 155-164.

 5 Albert Pomme de Mirimonde: L'iconographie musicale sous les Rois Bourbons. La musique dans les arts plastiques (XVII e -XVIII e siècles), vol. 1, Paris, 1975, p. 37-41

.6 Albert Pomme de Mirimonde: Astrologie et musique, Geneva 1977.

Paul Juvenel: The Preaching of St. John the Baptist, drawing, ca 1620, 34,7 x 26,8 cm, National Museum Warsaw, Inv. 4146560.

Paul Juvenel: The Baptism of Christ, oil on panel, 1621, 49 x 84 cm, London, Sotheby's, Auction catalogue from 27 Oct. 1993, lot 4.

times, as if to celebrate the completion of the double instrument: it is embodied in the evocation of the grape harvest in Autumn, by its presence in a house placed between Autumn and Winter where, under an awning, a group of card-playing drinkers is seated, and by two children bearing a toast. In fact, on the band dedicated to Jupiter, next to the painter who has represented himself again, but from behind and this time in front of his easel, we notice on his right a young boy (probably his son) who is raising a glass of wine to the viewer, just as little Anna Sabina did in the foreground. (Fig. 1i).

Who is the painter-inventor of this spinet lid?

The persistent enigma of the attribution of this lid remains to be addressed. Considered since 1825, in all publications prior to Andreas Tacke's catalogue, to be the work of Frederik van Valckenborch, the lid has fallen into anonymity because this art historian has meticulously deconstructed the attribution: there is inconsistency with the dates of van Valckenborch, his career, and his style; and there has been misidentification of the very legible monogram on the gable of the inn where the card players and drinkers are seated (Fig. 1j): it should read L[inverted]FB, i.e. the initials of Lucas Friedrich Behaim, which are also those of his motto (Laborum Finis Beatitudo), also present on his already-mentioned portrait, painted by Michael Herr (preserved at the Germanisches Nationalmuseum). Heinz Zirnbauer, in his 1960 argument, compared the portrait of the painter on the lid next to the two instrument-makers with a print by Georg Fennitzer (fl. 1671-1700), depicting 'Friderich von Falckenburg, Mahler in Nürnberg' [Frederik van Valkenborch] holding a rolled-up print in his hand (Fig. 11). Falcke agreed in 1995 that the facial features are comparable to some extent, but noted the absence of a beard. The facts remain that this portrait was executed postmortem, that Fennitzer did not know the artist because he was born fifteen years after his death, that no self-portrait of 'Friderich von Falchenburg' is known, and that Fennitzer is known for mediocre portraits that are of poor resemblance and unreliable. This engraving cannot therefore be considered in support of an attribution of the spinet lid. But even more crippling is the fact that stylistically