Elodie Bouzekri
email: elodie.bouzekri@irit.fr

Alexandre Canny
email: alexandre.canny@irit.fr

Célia Martinie
email: martinie@irit.fr

Philippe Palanque
email: palanque@irit.fr

Specific Task Modeling for Cyber Physical Systems

Keywords: Interactive Systems, Cyber Physical Systems, Model-based Design, Task Modeling

User interfaces for the command and control of systems usually integrate several types of interaction elements: physical space, hardware and software. Within such kind of environment, operators have to complete their tasks manipulating hardware and software elements that are distributed in the physical space. However, current tasks description notations do not take into account physical and hardware aspects beyond manipulation of input devices such as mouse and keyboard. This paper proposes a set of extensions to task modeling techniques in order to represent user goals and activities when interacting with distributed hardware and software user interfaces. These extensions are demonstrated with the HAMSTERS-XL notation and tool. These models can be analyzed and simulated to support identification of cumbersome tasks, motoric and perceptive efforts and sub-optimal UI distributions. We present how such information can be used for improving the user interface of the hardware and software distributed user interfaces. We exemplify the approach on a simple but realistic example: The Philips Hue light bulb system.

INTRODUCTION

User interfaces for the command and control of interactive systems, such as power plant workstations or aircraft cockpits, are made up of hybrid and distributed interaction elements including hardware and software components. Within this kind of environments, operations take place in the physical workplace and operators have to complete their tasks manipulating distributed hardware and software elements. During these activities, the performance of the users is impacted by the positions (within the physical working environment) of the hardware and software elements composing the command and control interactive system. We argue that representing hardware and software elements explicitly and systematically in task models contribute to the design, the assessment and the development of usable, reliable and safe distributed interactive systems. We propose a set of extensions to task modeling techniques in order to represent user goals and activities when interacting with distributed hardware and software user interfaces. We present the benefits of using such extensions as, for example the automation of analysis of the task models, and the predictive assessment of the duration and complexity of a task.

MODELING USERS TASKS WITH CPS

CPS are intended to be used by humans [START_REF]Cyber-Physical Systems Virtual Organization Home page[END_REF], via direct interaction [START_REF] Navarre | ICOs: A Model-based User Interface Description Technique Dedicated to Interactive Systems Addressing Usability, Reliability and Scalability[END_REF] and/or using a monitoring and control user interface [START_REF] Seiger | Modelling complex and flexible processes for smart cyber-physical environments[END_REF]. This section presents user tasks when using a CPS and a way to describe these tasks by modeling them with HAMSTERS notation and tool.

Taking into account user activities for the command and control of a CPS as well as the way they may interact with the CPS (directly or indirectly) requires precise and complete description of their activities. Furthermore, in order to be able to analyze potential user errors that may happen at runtime, the following set of requirements has to be match:

• Identify and describe, in a complete and unambiguous way, the user tasks with the CPS, whether they interact in a direct way or with the Command and Control of the CPS. • Identify and describe the Data (information, objects, knowledge) manipulated by a user for accomplishing her/his tasks.

Task modeling permits to describe user tasks with interactive systems. HAMSTERS-XL is an extension of HAMSTERS [START_REF] Martinie | Structuring and Composition Mechanisms to Address Scalability Issues in Task Models[END_REF] notation that proposes to go beyond the description of simple WIMP interaction. HAMSTERS-XL enables to add customized tasks. This extension permits to adapt the notation to tasks specific to a device, a context or a domain.

In term of input and output devices, interacting with WIMP interactive systems usually requires no more than perceiving what is rendered on screen and to be aware of the presence of a keyboard and a pointing device. For this reason, the standard HAMSTERS notation proposes a generic "Perceptive Task" that mainly corresponds to the visual perception of information on a screen. However, while describing perception when using a CPS, precise description of the sight sense is required. Thus, we propose to extend Paste the appropriate copyright/license statement here. ACM now supports three different publication options:

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perceptive task and to provide support to refine it to the sight task (see Table 1).

Table 1. Perceptive task integrated in HAMSTERS-XL

Perceptive task Example of use Icon Name

Sight Gathering data from outside of the aircraft (location in the airport, clouds, etc.), locating controls, assessing aircraft status from the screens and lamp in the cockpit, etc.

In the same way, while describing motoric actions when using a CPS, precise description of the several actions is required. We propose to extend motoric tasks and to provide support to refine it to the tasks described in Table 2 and Table 3.

ILLUSTRATIVE EXAMPLE OF THE HUE CPS

The Philips Hue smart lamp [START_REF] Philips | Hue lamp[END_REF], which is considered one of the typical IoT devices, and the most popular smart light system (see Figure 1). While the command and control is located on the remote control and/or on the mobile App, the physical device (the light bulb) is producing both light and heat that are both perceivable by the users. When using the remote control (which is only an input device and has no display on it), the user has to target the connection bridge (not the light bulb) and the only way to know the status of the device is to look at its hardware (physical) part. This section presents the tasks that have been identified to be performed by the user with the physical UI and with the command and control UI. In this example, we focus on the user tasks to switch off the light bulb. These tasks may be performed in several contexts and with different devices. The following sections presents these user tasks required to reach the goal: "Switch off light in a room". To reach this goal, several alternatives of tasks are described (under the choice "[]" operator). Figure 2 presents these alternatives.

Figure 3, Figure 4 and Figure 5 present the descriptions of the tasks that the user has to carry on to switch off light in a room. Figure 3 and Figure 4 respectively described this goal with HAMSTERS notation and HAMSTERS-XL notation. Figure 5 presents "Switch off light in a room with the Philips Hue smartphone app" goal with HAMSTERS-XL notation. Although the main aim of the Philips Hue light bulb is to enable end user programming of the home lighting, it is still possible to control it as a legacy home lighting system. A manual switch installed on the wall aims at providing the user a way to close or open the electrical circuit composed of the switch, the wires and the light bulb. In the task model depicted in Figure 3, these tasks are described in the branch "Switch off light with light switch". The user has to perform the following sequence of tasks (tasks described under the sequence ">>" operator):

• "Perceive the light switch" (perceive task) that requires to access to "Light switch device" (input/output device), • "Recognize light switch" (cognitive task),

• "Walk to light the switch" (user task),

• "Push off the light switch" (motoric task) that requires to access to "Light switch device" (input/output device), • "Switch off light bulb" (interactive input task) that requires to access to "Light switch device" (input/output device),

• "Light off" (interactive output task) that requires to store OFF state in "Light bulb lamp" (output device), • "Perceive light is off" (perceptive task) that requires to access to "Light bulb lamp" (output device), and then • "Deduce light is off" (cognitive task). In the task model depicted in Figure 4, "Perceive the light switch", "Switch off the light bulb" and "Perceive light is off" tasks of Figure 3 are refined to describe better user activity to reach "Switch off light of the room" goal:

• "Perceive the light switch" is refined with "Locate light switch" (iterative user task) disable by "Recognize light switch" (cognitive task). "Locate light switch" is refined in a sequence (tasks described under the sequence ">>" operator) of three tasks: o "Turn head right" (optional head right task) o "Turn head left" (optional head left), and o "Search light switch" (sight task) that requires to access to "Light switch device" (input/output device). • "Push off the light switch" is refined into a sequence of two tasks: o "Stretch arm to the light switch" (Arm right stretch task) o "Press light switch" (Hand right finger press task) that requires to access to "Light switch device" (input/output device)

• "Perceive light is off" (perceptive task) is detailed in "See light" (sight task) that requires to access to "Light bulb lamp" (output device).

Modeling User Tasks with Command and Control UI with HAMSTERS-XL

To switch off the light bulb, the user has the possibility to use one of two available command and control interfaces: a dimmer switch device or the Philips hue smartphone application. The Figure 5 describes the user tasks to switch off the light bulb with the Philips hue smartphone app. The user has to perform the following sequence of tasks:

• The user has to "Remember smartphone location" (cognitive task) or ("[]" operator) to "Locate the smartphone" (user task) until ("[>" operator) "Recognize the smartphone" (cognitive task) • Next, to "Stretch arm to the smartphone" (Stretch arm task), • To "Grasp the smartphone" (Grasp task),

• To "Interact with the smartphone to open light switch window" (interactive abstract task) using "Philips Hue app" (software application) and • To "Switch off light bulb" (interactive input task) using "Philips Hue app" (software application). • Then, then "Smartphone" (input/output device) "Send event to the bulb" (system task) to switch off the light thanks to the "Hue Bridge" (output device). • The "Light bulb lamp" (output device) switches off:

"Switch off light" (interactive output task). • The user can "See light is off" (sight task) only if the "User location" (information) is equal to the "Room" ("Test" arc between the sight task and the information); • Then the user has to "Deduce light is off" (cognitive task) to reach the goal "Switch off the light in a room".

MODELS ANALYSIS

This section analyses the tasks models of the previous section and presents the benefits of a specific task modeling notation like HAMSTERS-XL compared to a standard task modeling notation like HAMSTERS [START_REF] Martinie | Structuring and Composition Mechanisms to Address Scalability Issues in Task Models[END_REF].

Most of the task modeling notations, such as HTA [START_REF] John Annett | Task analysis and training design[END_REF] and CTT [START_REF] Paterno | Concur Tast Trees (CTT), W3C Working Group Submission[END_REF], enables to describe user tasks and goals, as well as manipulated objects. Task models built with such notations can embed additional textual information to refine the information about the types of tasks and the types of data required to accomplish the tasks. Although this is sufficient to understand and identify main user tasks and goals, a specific task modeling notation like HAMSTERS-XL improves the description power for the motoric and perceptive tasks of these standard task modelling notations. For example, move a cursor thanks to a mouse task and press a button task are described with the standard task modeling notation with the same task: a motoric task. The specific task modeling notation permits to categorize these motoric and perceptive tasks. In consequence, the analysis of the task model is no longer text parsing and can be more easily automatize. Indeed, it is possible to measure the number of occurrence and performance time of a type of motoric or perceptive task (grasp task for example) or of a particular couple of motoric or perceptive task with a particular object (grasp the smartphone task for example) necessary to reach a goal directly from the task model. For example, contrary to a standard task modeling notation, it is possible to measure the performance time of "stretch arm to the smartphone" task independently of the "Grasp the smartphone" task of the Figure 5. The relative execution time of the stretch task is after the user recognizes the smartphone or remembers the smartphone location to when s/he begins to fold his arm to bring the smartphone closer to her/him. It is also possible to associate a minimum and a maximum execution time to "Stretch arm to the smartphone" task to estimate an absolute execution time. In addition, the specific task modeling notation permits to detect automatically impossible tasks like two concurrent left hands tasks: grasp and release left hand tasks for example. Moreover, it is also possible to detect impossible tasks due to human limitation [START_REF] John Annett | Task analysis and training design[END_REF]. For example, to perform two non-automatic tasks concurrently.

Furthermore, the specific task modeling notation permits other task model analysis when coupled with a 3D space model of the user context. Indeed, it is possible to determine occlusion with objects position. For example, visual occlusion due to the user position can be determined. In addition, the specific task modeling notation permits to measure the quantity of movement and the effort cost of a motoric or perceptive task associated with a particular object thanks to the source point position and the destination point position. In addition, specific task modeling notation is useful for training. Training program for complex systems must cover all the tasks that the user has to carry out [START_REF] Martinie | Model-based training: an approach supporting operability of critical interactive systems[END_REF]. Determining complete and unambiguous user tasks to reach a goal, occlusion, workload and effort cost is necessary to establish training program of complex systems.

PERSPECTIVES

Due to the chosen domain and context, the example explores a limited set of perception and motoric tasks (sight, stretch arm, press with a finger, grab, and turn head left and right). For example, speech, touch, smell, be turned away from the light bulb or from the switch are not represented in this paper. Future work must address other domains, contexts and devices to analyze deeper specific task modeling notation for CPS.

Figure 1 .

 1 Figure 1. Overview of the Philips Hue system and its command and control systems.

Figure 2 .

 2 Figure 2. Description of user alternatives of tasks to "Switch off light in a room" with HAMSTERS notation. Modeling User Tasks with the Physical UI with HAMSTERS.

Figure 3 .

 3 Figure 3. Description of the user tasks to "Switch light off in a room" with HAMSTERS notation. Modeling User Tasks with the Physical UI with HAMSTERS-XL.

Figure 4 .

 4 Figure 4. Description of the user tasks to "Switch light off in a room" with HAMSTERS-XL notation.

Figure 5 .

 5 Figure 5. Description of the user tasks to "Switch light off with the Philips Hue smartphone app" with HAMSTERS-XL notation

Table 2 . Motoric limb tasks integrated in HAMSTERS-XL Motoric task Usage Icon (left/right) Limb Action

 2

	Finger	Press	Press button
	Hand	Grasp	Grasp joystick
			Reach
	Arm	Fold	interaction
			devices
			Reach
	Arm	Stretch	interaction
			devices

Table 3 . Motoric head tasks introduced in HAMSTERS-XL

 3

	Head
	Turn Left	Turn Right


Quentin Berrahal

Cyril Chacon

Hakim Amara

Amandine Bellec

Sylvain Latil

Vincent Repain

Sylvie Rousset

Jérôme Lagoute

Yann Girard
email: yann.girard@u-paris.fr

High density synthesis of topological point defects in graphene on 6H-SiC(000 1 ¯)

Keywords: Graphene, Grain Boundaries, Defect engineering, Growth, Silicon carbide, Scanning tunelling microscopy/ spectroscopy, Density functional theory

est destinée au dépôt

Introduction

Control of defect formation (either point-like or extended) in graphene is a challenge as they have long been seen as major drag on the pursuit of good quality graphene. However, they gained interest in the last few years as tuning knobs for the unique properties of graphene [START_REF] Wu | Spectroscopic investigation of defects in two-dimensional materials[END_REF]. One can, for example, change the position of the Dirac point through atomic substitution (doping) for n or p conductivity [START_REF] Joucken | Localized state and charge transfer in nitrogen-doped graphene[END_REF][START_REF] Zhao | Visualizing Individual Nitrogen Dopants in Monolayer Graphene[END_REF][START_REF] Zhao | Local Atomic and Electronic Structure of Boron Chemical Doping in Monolayer Graphene[END_REF][START_REF] Joucken | Electronic properties of chemically doped graphene[END_REF], or create resonant state through single atomic vacancies for monitoring the grafting or functionalization of molecules [START_REF] Ducastelle | Electronic structure of vacancy resonant states in graphene: A critical review of the single-vacancy case[END_REF]. Origin of defects in graphene is threefold: they either are native, induced by an external parameter during the synthesis or created afterwards. In polycrystalline graphene, Grain Boundaries (GB) are of the first kind. These 1D defects, mainly composed of pentagons, hexagons, heptagons and vacancies, mark out the separation between two domains of graphene which have different orientation with respect to each other [START_REF] Tison | Grain Boundaries in Graphene on SiC[END_REF][START_REF] Yang | Structure of graphene and its disorders: A review[END_REF]. Having almost all the possible orientations they can eventually form loops encompassing domains of small sizes. They are called Grain Boundary Loops (GBL) and the smallest GBL encompassing 24 atoms, called a one grain boundary loop or a "Flower Defect"(FD), can be seen as a ±π/6 rotation of seven rings inside a graphene grain [START_REF] Cockayne | Grain boundary loops in graphene[END_REF].

Recently, those FD have attracted great interest towards nanotechnological electronic applications. First, they induce very large modifications of transport properties compared to other point-like defects [START_REF] Linhart | Accurate modeling of defects in graphene transport calculations[END_REF]; second, they create a high spin polarization in zigzag graphene nanoribbon [START_REF] Kang | Spin Transport in Zigzag Graphene Nanoribbon with a Flower Defect[END_REF]; third, they are able to filter electrons from holes, which have applications for electron energy filtering [START_REF] Cresti | Growth, charge and thermal transport of flowered graphene[END_REF]; fourth, they are good candidates for allelectronic valley based-devices [START_REF] Chen | Structure and electronic properties of closed-ring defects in epitaxial graphene[END_REF]. From theoretical point of view, it is also interesting to note that similar flat geometric defects in honeycomb arrangement have been observed on hexagonal bilayer silica [START_REF] Björkman | Defects in bilayer silica and graphene: Common trends in diverse hexagonal two-dimensional systems[END_REF] and rubrene on Au(111) [START_REF] Pivetta | Two-Dimensional Tiling by Rubrene Molecules Self-Assembled in Supramolecular Pentagons, Hexagons, and Heptagons on a Au(111) Surface[END_REF]. Nevertheless, their formation on substrates is interesting for applications at wafer scale, but are very rare and rather uncontrolled. So, it is a challenging task to obtain an experimental process which induces selectively a large density of this defect. Some rare FD appear on various substrates, as a native defect in epitaxial graphene grown on silicon carbide (Si rich SiC(0001) and C rich SiC(0001) surfaces) [START_REF] An | Graphitization of 6H-SiC(000\bar1) Surface by Scanning Tunneling Microscopy[END_REF][START_REF] Rutter | Scattering and Interference in Epitaxial Graphene[END_REF][START_REF] Guisinger | Atomic-scale investigation of graphene formation on 6H-SiC[END_REF][START_REF] Simon | Symmetry of standing waves generated by a point defect in epitaxial graphene[END_REF], as an externally-induced defect during the Chemical Vapor Deposition (CVD) growth of graphene on copper or nickel [START_REF] Zhao | Local Atomic and Electronic Structure of Boron Chemical Doping in Monolayer Graphene[END_REF][START_REF] Park | Growth and properties of chemically modified graphene[END_REF][START_REF] Rasool | Atomic-Scale Characterization of Graphene Grown on Copper (100) Single Crystals[END_REF], as a result of a post-synthesis annealing in graphene on rhodium [START_REF] Yan | Electronic structures of graphene layers on a metal foil: The effect of atomic-scale defects[END_REF]. High density of FD, around 10 11 cm -2 , has already been obtained after a few tens of minutes annealing of SiC(0001) surface around 1 250-1 350 • C [START_REF] Cui | Structural Evolution of Flower Defects and Effects on the Electronic Structures of Epitaxial Graphene[END_REF], or assisted by bismuth (Bi) during the graphene synthesis on SiC(0001) [START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF]. Nevertheless, FD are always associated with an equivalent den-sity of other atomic and nanoscale defects as vacancies, mounds and nanotubes or substitutional atoms [START_REF] Guisinger | Atomic-scale investigation of graphene formation on 6H-SiC[END_REF][START_REF] Cui | Structural Evolution of Flower Defects and Effects on the Electronic Structures of Epitaxial Graphene[END_REF][START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF]. So, none of the existing works provide a procedure to achieve selectively a high density of FD.

We also have to mention that numerous experiments performed on suspended graphene have studied their formation, migration and annihilation under the beam of Transmission Electron Microscopy (TEM) [START_REF] Meyer | Direct Imaging of Lattice Atoms and Topological Defects in Graphene Membranes[END_REF][START_REF] Kurasch | Atom-by-Atom Observation of Grain Boundary Migration in Graphene[END_REF]. Associated to theoretical developments [START_REF] Cockayne | Grain boundary loops in graphene[END_REF][START_REF] Kotakoski | Mechanical properties of polycrystalline graphene based on a realistic atomistic model[END_REF][START_REF] Cockayne | Graphing and grafting graphene: Classifying finite topological defects[END_REF] and simulations [START_REF] Zhuang | Evolution of domains and grain boundaries in graphene: A kinetic Monte Carlo simulation[END_REF], it is now clear that this defect belongs to the family of topological defects conserving both the sp 2 hybridization character of the C-C bounds and also the number of C atoms par graphene unit area [START_REF] Terrones | The role of defects and doping in 2D graphene sheets and 1D nanoribbons[END_REF]. The basic units are elementary disclinations (rings of 5 or 7 atoms) which form 5|7 pair known as dislocation in order to minimize the elastic energy. The well known Stone-Wales (SW) defect is composed of two dislocations compare to the FD which has six of them. It must be noticed that among all the GB based on those dislocations, FD has the lowest formation energy per dislocation (1.2 eV) [START_REF] Cockayne | Grain boundary loops in graphene[END_REF] because of its nearly full strain relaxation. This explains its stability and its relative frequency of observation. Unfortunately, there is no known atomistic mechanism which could conduct to specific FD formation and simulations are required [START_REF] Zhuang | Evolution of domains and grain boundaries in graphene: A kinetic Monte Carlo simulation[END_REF][START_REF] Karoui | Nickel-Assisted Healing of Defective Graphene[END_REF].

In the following, we report Scanning Tunelling Microscopy and Spectroscopy (STM, STS) studies of a gold (Au) assisted two steps growth process that allows to produce selectively a high density of FD in the top Graphene Layer (GL) grown on 6H-SiC(0001). (Step 1) prepares the surface in order to have connected irregular small graphene islands presenting a high density of borders and stressed areas. We call it proto-graphene. (Step 2) conducts to : (i) extend laterally the previous graphene islands; (ii) form new GL below the first one and (iii) release elastic energy induces by irregular GB. This is completed by : (iv) the fundamental effect of Au which favors the formation of localized defects. (Step 1) and (step 2) drive together all the parameters which are crucial to obtain a high density of FD. This result is complemented by first-principles calculations which show that Au decreases significantly the FD formation energy. Moreover, we show by fine STS measurements and in depth analysis of FD electronic structure, that those GBL exhibit more localized states than previously reported. STS results are also mentioned concerning resonant states which arise around the Fermi energy E F , inside the phonon pseudo-gap [START_REF] Zhang | Giant phonon-induced conductance in scanning tunnelling spectroscopy of gate-tunable graphene[END_REF].

Methods

Sample preparation

Prior to graphene synthesis (step 1 & 2), the SiC(0001) single-crystals (10 × 5 × 0.5 mm -3 , C-face epi-ready, Si-Face optically polished) bought from Novasic SA were degassed under ultra-high vacuum (UHV) conditions by direct current heating for 6 hours at 700 • C before a 15 minute annealing at 850 • C in front of a Si evaporator to get rid of surface oxygen. During (step 1 & 2)'s annealing performed at high temperature, the pressure stays lower than 10 -8 mbar. After annealing, we stopped abruptly the heating power and the temperature decreased within a one minute characteristic time below 300 • C.

Temperatures are measured by a pyrometer in the 1.45-1.80 µm spectral bandwidth with a 0.9 emissivity. The sample is maintained laterally by two tantalum stripes on the sample holder and only 1/3 of the sample area is covered by graphene after synthesis. Gold was deposited using an electron beam evaporator EFM 3 (Focus GmbH) at a rate of 1.4 10 14 Au /cm 2 /min, calibrated by Rutherford back scattering.

STM/STS measurements

Except STM pictures reported Fig. 1(a,d) acquired at room temperature (RT), our STM/STS measurements were performed at 4.6 K using a Scienta Omicron Low Temperature STM running on liquid helium. STS spectra were recorded through lockin detection at frequencies around 700-800 Hz and with a peakto-peak modulation of 24 mV for the large energy scale spectra and 6 mV for the small energy scale spectra to reduce the broadening of the peaks. Prior to measurements on graphene, tungsten tips were systematically calibrated on Au(111) until the Shockley surface state is clearly measured in the STS spectra.

First-principles calculations

To investigate the formation energy of the flower defect in presence of Au atoms, we performed first-principles calculations based on density functional theory. We used the Quantum Espresso [START_REF] Giannozzi | QUANTUM ESPRESSO: A modular and opensource software project for quantum simulations of materials[END_REF] code within the projector-augmented wave (PAW) method [START_REF] Blöchl | Projector augmented-wave method[END_REF]. The generalized gradient approximation [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] was employed for all calculations. Integrations over the Brillouin zone are based on a 3×3×1 Monkhorst-Pack threedimensional grid for 162 atom cells. The size of the supercell in the c direction was set to 15 Å to avoid the interaction between neighboring defects. Calculations were performed at zero pressure, i.e., the relaxation of the atoms and the shape of the simulation cell are considered using the conjugate gradient minimization scheme. The initial lattice parameter is equal to 2.45 Å and is allowed to change during the simulations. The atomic positions were relaxed until the magnitude of the forces on all the atoms was smaller than 1.10 -5 Ha/Bohr. Description of the van der Waals dispersive forces has been accounted for via the D2 dispersion correction of Grimme [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. No SiC substrate was included in the DFT calculations insofar as our investigation has sought to highlight the intrinsic role played by Au in flower defect formation. In this context, DFT calculations were performed with various amounts of simulated deposited Au atoms ranging from 1 to 12 isolated atoms and also a 25-atom Au cluster. Moreover, the adsorption energy, E ads , is defined as :

E ads = E Au/substrate -E substrate -E Au , (1)
where E Au/substrate is the total energy of carbon substrate (graphene or FD) with the Au adatom attached, E substrate is the total energy of the pristine graphene or the FD layer, and E Au the total energy of an isolated Au atom. The more negative E ads is, the more strongly the atom of Au adheres to the carbon substrate.

Results and Discussion

3.1. Gold assisted flower defects synthesis : a two step process studied by scanning tunnelling microscopy In order obtain a large amount of FD, we improved usual process where rotationally faulted Few Layer Graphene (FLG) is produced by silicon (Si) sublimation from the substrate annealed between 1 100 -1 300 • C [START_REF] Mishra | Graphene growth on silicon carbide: A review[END_REF][START_REF] Hass | Why Multilayer Graphene on 4H-SiC(000-1) Behaves Like a Single Sheet of Graphene[END_REF]. Before our graphene synthesis, the SiC(0001) sample was cleaned in UHV as described in the Methods 2.1 section. Then, after this cleaning preparation, we proceeded in two steps. First step (step 1 in the following), around 14 10 14 Au /cm 2 , i.e. one monolayer (ML) of gold, is deposited onto the clean SiC substrate at RT (forming three-dimensional islands, not shown) and the sample is then annealed five minutes at an intermediate temperature of 1 050 • C (see Fig. 1(a)), the lowest temperature needed to synthesize graphene [START_REF] Forbeaux | High-temperature graphitization of the 6H-SiC (0001) face[END_REF]. At this point, the graphenization is not complete and one can see trenches between domains which can be seen in the line profile of Fig. 1(b). Those trenches disappear during the step 2 graphene synthesis and are the source of GB [START_REF] Tiberj | Multiscale investigation of graphene layers on 6H-SiC(000-1)[END_REF][START_REF] Biró | Grain boundaries in graphene grown by chemical vapor deposition[END_REF].

Second step (step 2 in the following), around one ML of Au is deposited at RT once more. This second Au ML follows also a Volmer-Weber (VW) growth mode on graphene at RT [START_REF] Liu | Slow Gold Adatom Diffusion on Graphene: Effect of Silicon Dioxide and Hexagonal Boron Nitride Substrates[END_REF]42]. Then, the sample is annealed at three increasing temperatures : 1 100 • C, 1 150 • C and 1 200 • C, 5 minutes each. Fig. 1(c) shows the surface after (step 2) and exhibits three graphene domains separated by rotational GB. Note that the bulk Au melting temperature is 1 064 • C (even lower for nanoparticles of 1-2 nm) and we can suppose that Au atoms are completely removed from the surface after (step 2) because of evaporation, or diffusion into the bulk [START_REF] Li | From the Au nano-clusters to the nanoparticles on 4H-SiC[END_REF]. We get FD (circled in red) with a density n around 7 • 10 11 cm -2 . As a FD is composed of 24 atoms, we can also say that ∼ 0.5 % of the atoms are part of FD. The defect-defect first neighbor mean distance is equal to 5.4 ± 2.3 nm (the minimum distance is the size of an isolated FD, i.e. around 2 nm). This result is consistent with a Poisson distribution where the nearest neighbor mean distance is 1/(2 √ n) = 6 nm. This shows that FD positions are random. In Fig. 1(c) one can see that larger GBL such as double FD (circled in green) are very scarce with a density around 10 11 cm -2 . Single FD are by far prevailing. This result is consistent with the fact that bigger GBL are less energetically favored than FD [START_REF] Cockayne | Grain boundary loops in graphene[END_REF]. Similar double FD have already been observed and some of them (with a non-conserved number of atoms) have been called conjoined-twin defect [START_REF] Cui | Structural Evolution of Flower Defects and Effects on the Electronic Structures of Epitaxial Graphene[END_REF]. The three graphene domains exhibit Moiré Patterns (MP) with different periodicity (mainly related to the twist angle between the two first graphene layers) and the amounts of FD are nearly equal on each one. On one side, this indicates a homogeneous distribution of FD all over the surface independently of the relative orientation of the underlying GL. On the other side, this shows that FD are not surrounded by the same atomic environment, and consequently, could have different mechanical and electronic properties. Effectively: i) FD belonging to a same grain are more or less in interaction laterally with each other's (and the surrounding GB) and these interactions could induce inhomogeneous stresses, which have a great importance concerning local mechanical properties [START_REF] Zhang | Mechanical properties of bilayer graphene with twist and grain boundaries[END_REF]; ii) FD seem to be randomly distributed, thus their electronic properties should also depend on their positions relatively to the underlying layer. A point which is discussed below in relation with local electronic spectroscopy.

Despite the fact that after this synthesis, either by STM or Auger electron spectroscopy we did not find any trace of Au, we cannot exclude the formation of gold carbides or silicides during the high temperature graphene synthesis. Effectively, AuC complexes have already been observed by TEM [START_REF] Westenfelder | Bottom-up formation of robust gold carbide[END_REF] and previous calculations [START_REF] Stolbov | Gold-doped graphene: A highly stable and active electrocatalysts for the oxygen reduction reaction[END_REF] have shown that Au-C binding energy could be around 0.5 eV higher than the cohesive energy of bulk Au (3.81 eV). Moreover, we can suppose that during annealing around 1 100 • C, as deposited Au form small liquid droplets before evaporation and constitute temporary sources for Au atoms/clusters diffusion on the surface, which could also form AuSi complexes.

Discussion about the importance of each step

Starting from the cleaning procedure, all the parameters in this double step process seem to be crucial. For example, we carried out (steps 1 & 2) without Au deposition and ended up with no FD. This means that Au (especially when deposited during (step 2)) plays a key role in the formation of the FD as catalyst. But proto-graphene is also essential.

Synthesis without proto-graphene

If (step 1) is not carried out, i.e. only one Au ML is deposited on the clean SiC substrate and the sample is then heated gradually until 1 200 • C, it exhibits no FD as shown on Fig. 1(d). Effectively, Au melting temperature being lower than 1 100 • C, we can assume that most of the Au evaporates from the surface before it can create defects. Thus, this case is similar to the usual FLG synthesis without Au and our results presented in Fig. 1(d) are comparable to previously obtained results [START_REF] Tison | Grain Boundaries in Graphene on SiC[END_REF][START_REF] Varchon | Rotational disorder in few-layer graphene films on 6 H -Si C ( 000 -1 ) : A scanning tunneling microscopy study[END_REF]. If we compare Fig. s 1(c) and (d), we remark that without (step 1) the final typical domain size is around five times smaller and the sample exhibits a high density of GB. This is also explained by the proto-graphene which, once created, could reduce the area available for new graphene nucleation sites during the (step 2) synthesis performed at higher temperature [START_REF] Norimatsu | Growth of graphene from SiC{0001} surfaces and its mechanisms[END_REF][START_REF] Biedermann | Insights into few-layer epitaxial graphene growth on 4H-SiC(000-1) substrates from STM studies[END_REF] and so, could increase the final grain size by limiting the proliferation of graphene flake boundaries.

Proto-graphene as a template for gold anchoring

The first very important point to notice is that after (step 1) graphene is not flat. As shown in Fig. 1(a,b), (step 1) is not sufficient to create extended graphene domains and the surface is rather similar to graphene obtained on various SiC reconstructions [START_REF] Hiebel | Graphenesubstrate interaction on 6 H -SiC ( 000-1 ) : A scanning tunneling microscopy study[END_REF]. The large atomic roughness in Fig. 1(b) indicates the presence of small islands or clusters of undefined species (Au, C, Si or their combination). We think that those areas are one way toward FD synthesis, as they induce locally important strain in the graphene, that increases the elastic energy. During (step 2), this energy will be released locally and consequently may promote a reorganization favorable to the FD. Note also that after (step 1), graphene island borders are connected to the SiC substrate which induces also a residual stress inside islands [START_REF] Tiberj | Multiscale investigation of graphene layers on 6H-SiC(000-1)[END_REF]. So, we argue that there are two main places where (step 2)'s Au would catalyze defects more easily : the small strained area in the graphene flakes and the graphene borders.

Gold as catalyst for the flower defects formation

Au on graphene at RT follows a VW growth mode but the Au island density depends strongly on the graphene defect density such as vacancies, graphene borders and GB [42,[START_REF] Pulido | Theoretical investigation of gold clusters supported on graphene sheets[END_REF]. All those defects are nucleation areas for island growth [START_REF] Irawan | Size-dependent morphology of gold clusters grown on nanostructured graphite[END_REF]. This means that proto-graphene, which exhibits a very high defect density, acts as a perfect template in order to obtain a high density of Au islands during (step 2). We think that it is this association which is the driving force for FD formation. We argue that Au islands of nanometer size trapped in the proto-graphene defects modify locally the formation/relaxation of graphene and the healing processes during (step 2). One consequence is the generation of small domains isolated from the rest by GBL such as FD or conjoined-twin defects. Containment of small areas within the rest of the environment has already been observed by TEM [START_REF] Cresti | Growth, charge and thermal transport of flowered graphene[END_REF] and a bulge nucleation mechanism has been proposed which has great similarities with our hypothesis. This could be confirmed by molecular dynamic simulations of GB migration [START_REF] Kurasch | Atom-by-Atom Observation of Grain Boundary Migration in Graphene[END_REF][START_REF] Zhuang | Evolution of domains and grain boundaries in graphene: A kinetic Monte Carlo simulation[END_REF][START_REF] Annevelink | Grain boundary structure and migration in graphene via the displacement shift complete lattice[END_REF] in presence of Au islands.

Comparisons with bismuth and platinum

(Step 2) is carried out at high temperature (around 1 150 • C) and the stability of Au islands during this step is the key point to increase the FD density. If islands evaporate before the carbon disclinations interact with each other under or at the island edges in order to form GBL, there will be no increase of FD density and no gain relatively to a situation without Au. On the contrary, if Au islands do not evaporate (as observed in the first two annealing at 1 100 • C and 1 150 • C, not shown), there could be defects under these islands, but they will obviously be invisible to STM. Since the Au melting temperature is lower than the second graphene synthesis temperature, it is the Au island size, and therefore their lifetime before total evaporation (which is related to the sublimation rate at this temperature) that controls two things. On the one hand, getting FD, and, on the other hand, removing all the residual Au islands or atoms which could modified the intrinsic flowered-graphene properties. An indirect proof of the importance of the metal melting temperature and the quantity of deposited atoms in (step 2) is to compare our results with those obtained with two other elements which have very different bulk melting temperatures (BMT) : platinum (Pt) and bismuth (Bi) with respective BMT of 1 380 • C and 271 • C, i.e. respectively above and below the (step 2) synthesis temperature. We used Pt instead of Au in (step 1 & 2) and, excepted a lot of residual big Pt islands, we didn't obtain any observable FD. Nevertheless, we cannot exclude the possibility that FD are located below those islands. Concerning Bi, we recall below that previous experiments [START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF] realized on the Si-rich face have also generated a great flower-like density, around 10 12 cm -2 , but associated with a nearly equal amount of undefined point defects. For Bi on SiC(0001) [START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF], (step 1) was not performed and (step 2) was repeated several times with two major differences compared to our experiments : a larger Bi thickness and a higher temperature, 1 350 • C. The consequence was a low amount of potential sites for the nucleation of Bi islands which could have catalyzed FD formation. Associated with its very low BMT (and so a very high sublimation rate at those temperatures), this explains why (step 2) has to be repeated several times before reaching a significant density of FD. Moreover, it must be pointed out that the graphene growth on the Si-rich surface is intrinsically not a good candidate to obtain selectively a high density of FD. The growth modes of graphene on the Si-rich and C-rich faces are very different. On the former, it is a rolling-carpet mechanism starting at the SiC step edges, while on the latter, it is a nucleation growth mode from the SiC terraces. It follows that on the Si-rich face, the first successive graphene planes (included the buffer layer) are in epitaxial relationship with the substrate and have very few grain boundaries, whereas on the C-rich face, the graphene planes are rotated relatively to each other, thus forming both MP and having a high density of grain boundaries constituted mainly by disclinations and vacancies. Since flower defects are obtained from the organized clustering of disclinations, it is clear that the more disclinations there are, the greater the density of flower defects will be. However, this is directly related to the density of point defects present during graphene synthesis. It is therefore expected to be more "difficult" to obtain a high density of flower defects on the Si side compared to the C side. This is indeed what is observed with bismuth assisted FD formation on the Si-rich face [START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF] or the necessity to synthetize the graphene at high temperature [START_REF] Cui | Structural Evolution of Flower Defects and Effects on the Electronic Structures of Epitaxial Graphene[END_REF] in order to obtain a high density of defects, among which a certain amount of FD.

First-principles calculation of FD formation energy

Once we have understood that after (step 1) a great amount of potential FD sites (among other extended defects) have been created along graphene flake borders and stressed regions, we theoretically investigate the role of Au during FD formation. So we calculate the FD formation energy, E f , by first-principles calculations (see Methods 2.3). We define E f as

E f = E(FD + n.Au) -E(GR + n.Au) (2)
where the first right-hand side term is the total energy of the FD in contact with n Au atoms, and the second one is the total energy of the corresponding pristine graphene structure also with n Au. To emphasize the catalytic role played by gold to form FD, E f is calculated for n Au atoms (n =1 to 12) located in direct contact with the defects. More precisely, our calculations show that the most stable position for one Au atom is in bridge between the pentagonal and heptagonal rings. Therefore, different configurations will be investigated further when the n Au atoms are close or far from each other on these specific sites. First of all, it can be seen that the formation energy without Au atom is equal to 7.20 eV which is in agreement with previous results [START_REF] Cockayne | Grain boundary loops in graphene[END_REF][START_REF] Kurasch | Atom-by-Atom Observation of Grain Boundary Migration in Graphene[END_REF]. Interestingly, our calculations show clearly that E f decreases significantly in presence of Au atoms to reach 3.05 eV for n = 12. As seen in Fig. 2, the decrease is not continuous. Indeed, it depends on the way Au atoms interact locally with the topological defects present in the graphene.

To go further, a flake of 25 Au atoms fully covering the FD is considered. They are forming a closed-packed structure which can be assimilated to the contact zone characterizing the interaction of a (111) facet of a nanoparticle with the FD. By doing so, the decrease in E f is even more pronounced and achieves a value of about 2.5 eV. Consequently, those results clearly show that Au promotes formation of FD. This catalytic role of Au is achieved through its strong interaction with the topological defects present in graphene. To highlight this mechanism, the adsorption energy (E ads ) of an Au atom on a SW defect is calculated and compared with pristine graphene (see Methods 2.3). The adsorption of Au atoms on graphene has been studied on several graphene sites, including the highly symmetric sites (top, bridge and hollow). According to our calculations, the most stable positon for the Au adatom is on top of a C atom for an adhesion energy of about -0.51 eV in line with data from the literature [START_REF] Chan | First-principles study of metal adatom adsorption on graphene[END_REF][START_REF] Nakada | Migration of adatom adsorption on graphene using DFT calculation[END_REF][START_REF] Manadé | Transition metal adatoms on graphene: A systematic density functional study[END_REF]. In the presence of the SW defect, E ads is equal to -2.51 eV revealing that the interaction of Au atoms with topological defects is very strong which suggests that Au atoms can play a crucial role for the formation of FD.

It is interesting to note that similar calculations have shown that the energy barrier for the elimination of SW defects (around 5 eV) [START_REF] Li | Defect energies of graphite: Densityfunctional calculations[END_REF] can be drastically decreased by adsorbed transition metal atoms [START_REF] Charlier | Catalytically Assisted Tip Growth Mechanism for Single-Wall Carbon Nanotubes[END_REF][START_REF] Wang | Metal-promoted restoration of defective graphene[END_REF]. In the present work, we were also able to highlight this effect. We performed the same kind of study done for FD with a SW defect. In a similar way, we observe a strong reduction of the formation energy in the presence of Au atoms. Indeed, the formation energy of a SW defect is 5.3 eV according to our calculations. In this particular case, the Au atom occupies the bridge position and tends to strongly decrease the defect formation energy by about 25% to reach 3.92 eV. Starting from 3 atoms, the E f value tends to stabilize around 3 eV. Note that once 5|7 pairs or SW defects are formed, by an unknown out of equilibrium atomic process during the graphene formation, they are stable in the temperature range that we use. So, our experimental and theoretical results show that Au, acting as a catalyst, decreases FD formation energy.

Finally, we can say that two main mechanisms act to form a high density of FD. On one hand, Au (and eventually Bi, Pt and other species) catalyzes FD and flower-like defects because it decreases the SW and loops formation energy. And, on the other hand, (step 1) increases the number of local stressed areas induced by trenches and graphene defects in the protographene, which thus prepares a lot of potential sites for Au anchoring during (step-2) and so favoring the formation of point- The topography of a FD is reported in more details in Fig. 3(a) and its appearance is similar to that previously reported [START_REF] Cockayne | Grain boundary loops in graphene[END_REF][START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF] (an atomic model is superimposed to the experimental image). The defect appears as a grey center located on the seven central hexagons, surrounded by a white crown located on the joined 5|7 pairs, prolonged by six lobes emerging from the heptagons. Far from the defect (bottom left part), one can see the honeycomb lattice of graphene and closer to it one can see the (

√ 3 × √ 3)R30
• electronic pattern due to electrons scattering by the defect [START_REF] Rutter | Scattering and Interference in Epitaxial Graphene[END_REF]. Note that all apparent heights (and so the grey scale from 0 to 1.1 Å) are not related to atomic corrugation but mostly to local variations of the electronic densities. Fig. 3(b) shows a STM image of five FD belonging to the same graphene domain exhibiting a unique moiré pattern (MP). Whatever the MP, we never noticed a clear crystallographic relationship between FD location and the apparent moiré periodicity. It means that, on one side, the underlying GL plays no role in the FD location, and, on the other side, that the seven rotated central hexagons are not exactly above the same underlying carbon stacking. Fig. 3(c) shows three differential conductance (dI/dV) spectra taken on three of the FD in Fig. 3

(b).

There are two broads peaks around -0.9 eV and 0.8 eV and a series of fine peaks at positive energies between 0.1-0.5 eV, just above the pseudo-gap [START_REF] Zhang | Giant phonon-induced conductance in scanning tunnelling spectroscopy of gate-tunable graphene[END_REF] centered at E F (see also Fig. 4(e)). These features in the eV range are consistent with previous reports [START_REF] Zhao | Local Atomic and Electronic Structure of Boron Chemical Doping in Monolayer Graphene[END_REF][START_REF] Cockayne | Grain boundary loops in graphene[END_REF][START_REF] Yan | Electronic structures of graphene layers on a metal foil: The effect of atomic-scale defects[END_REF][START_REF] Cui | Structural Evolution of Flower Defects and Effects on the Electronic Structures of Epitaxial Graphene[END_REF][START_REF] Hu | Bismuth mediated defect engineering of epitaxial graphene on SiC[END_REF] but our measurements display a better resolved fine structure. More precisely, FD electronic fingerprint is usually observed as a broad resonant peak in the graphene empty states located around 300 to 400 meV above the Dirac Point (DP). This localized resonance is characteristic of isolated SW defects [START_REF] Amara | Scanning tunneling microscopy fingerprints of point defects in graphene: A theoretical prediction[END_REF][START_REF] Lherbier | Two-Dimensional Graphene with Structural Defects: Elastic Mean Free Path, Minimum Conductivity, and Anderson Transition[END_REF] and similar to van Hove singularities which emerge in one-dimensional ordered GB [START_REF] Tison | Grain Boundaries in Graphene on SiC[END_REF][START_REF] Yazyev | Electronic transport in polycrystalline graphene[END_REF][START_REF] Luican-Mayer | Localized electronic states at grain boundaries on the surface of graphene and graphite[END_REF]. Note that FD which are within the same graphene grain, as in Fig. 3(b), exhibit very similar spectra (this has been systematically observed on several domains) : same peaks at the same energies with slightly different intensities. The number and energy position of these fine FD peaks centered around 0.25 eV in Fig. 3(c) strongly depend on the scanned graphene grain which suggests that these states are sensitive to the surrounding atomic arrangement (see also spectra reported in Fig. 3(d,e) obtained on two different grains, but with a lower resolution), but they are always in the empty states. Correlatively, the mapping of those states is very sensitive to the orientation of underlying GL. Those two observations are a strong indication that FD may interact not only with their lateral atomic environment, but also they couple with the underlying surface. This coupling could explain the multiple peaks structure observed between 0.1-0.5 eV and not predicted by first-principles calculations [START_REF] Cockayne | Grain boundary loops in graphene[END_REF] but presenting great similarities with previous STS measurements performed on flat regular GB on SiC(0001) [START_REF] Tison | Grain Boundaries in Graphene on SiC[END_REF]. Despite the large energy range we have experimentally explored ±1.5 eV, there is no localized state in the filled states.

Mapping of low energy states

Zooming the low energy range, i.e. few tens of meV, it is intriguing to see that spectra taken on the different lobes (heptagons) of a FD, see Fig. 4(a), have several clear peaks inside the gap and rather close to E F , see Fig. 4(e). We recall that most of the effective electron tunelling in graphene is inelastic electron tunelling mediated by phonons [START_REF] Červenka | Local enhancement of inelastic tunnelling in epitaxial graphene on SiC[END_REF] and that a typical STS spectrum on pristine graphene exhibits a gap-like feature (see also Fig. 3(c)) between -64 mV and +64 mV (which we confirmed using d 2 I/dV 2 measurements). Through an extended study of several defects at different positions on the sample and with different tips we always noticed that diametrically opposed lobes have very similar spectra. Differential conductance maps obtained from grid spectroscopy at different energies are reported in Fig. 4(b-d). That shows that opposing lobes "light up" at the same energy. We also notice that two or four lobes "light up" at the same time but never all six of them. This is surprising in the sense that it breaks the obvious six-fold symmetry that one could expect from the defect. Two possibilities are open. On one hand, the surrounding electronic modulation (induced by defects proximity, anisotropic strain, etc.) could be coupled to those electronic states and thus breaks the sixfold symmetry. On the other hand, FD belonging to the same grain are surrounded by the same MP induced by the twist angle of the graphene bilayer. It follows that the periodic transition from AB to AA local stackings of the graphene bilayer are locally disturbed by each FD. Thus, because of the FD ran- domness location, one should expect variable electronic states from FD to FD. For example, if a flower is in an AA stacking bilayer, its symmetry is not broken, and we should observe a 6-fold symmetry. In case of a Bernal-stacked bilayer we should observe a 3-fold symmetry, as already suggested [START_REF] Cockayne | Grain boundary loops in graphene[END_REF]. Note that a similar symmetry breaking processes induced by a defect in a graphene bilayer has previously been invoked in order to explain the shape of FD [START_REF] Simon | Symmetry of standing waves generated by a point defect in epitaxial graphene[END_REF]. Due to randomness of FD positions in a same grain (and also the same MP), they have not the same underlying stacking (except for the AA or AB stacking which are rather rare), which also breaks their symmetry. This second possibility is the more likely of the two because it is coherent with the spectroscopy done at high energy where all FD residing on the same MP exhibit the same spectrum whatever their proximity with other defects. We can not explain the physical origin of those in-gap states (these states have already been measured in a very different atomic configurations, i.e. along graphene nanoribbons on Au(111) [START_REF] Tao | Spatially resolving edge states of chiral graphene nanoribbons[END_REF] and along ridges on SiC(0001) [START_REF] Ridene | STM/STS investigation of edge structure in epitaxial graphene[END_REF])), but the FD special topology coupled to the interaction with the underlying graphene could induce new states due to electronic confinement. Recent calculations on circular quantum dots in twisted bilayer graphene are certainly a hint to understand those states [START_REF] Mirzakhani | Circular quantum dots in twisted bilayer graphene[END_REF].

Conclusion

In summary, scanning tunelling microscopy and spectroscopy studies of flower defect formation catalyzed by gold on fewlayer graphene on SiC(0001) have been presented. A very high density of flower defects is obtained thanks to a two-steps process. A proto-graphene layer creates a template for anchoring gold clusters which promotes the formation of those quasi-point like topological defects during the second step. First-principles calculations provide clear evidence for a drastic decrease of their formation energy with gold. These flowers exhibit localized electronic states all over the defect at high energy, and interestingly low energy states localized asymmetrically on the heptagons breaking the apparent flower defect 6-fold symmetry. The complex formation of those defects during the graphene synthesis on SiC could be studied by molecular dynamic simulations. The unknown in-gap states deserve future experiments and theoretical developments.

Figure 1 :

 1 Figure 1: (a) STM image of proto-graphene on SiC(0001) synthesized after (step 1), i.e. : one Au monolayer deposition at room temperature and a 5 minute synthesis at 1 050 • C (100×74 nm 2 ). (b) Topography along the red line showing the trenches between domains. (c) STM image of three domains of few layer graphene obtained after (step 1) followed by (step 2), i.e. : a second Au deposition and three successive 5 minute synthesis at 1 100 • C, 1 150 • C and 1 200 • C. On each of the domains, one have circled in red the flower defects. Bigger grain boundary loops are circled in green (100×100 nm 2 ).(d) STM image of several domains of few layer graphene obtained without (step 1), i.e. : one Au monolayer deposition at room temperature and a 15 minute direct synthesis at 1 200 • C (100×100 nm 2). For all the images V=1 V, I=50 pA.

Figure 2 :

 2 Figure 2: Flower defect formation energy as a function of the number of gold atoms. Insets : relaxed atomic positions of a flower defect without (left) and with 1, 8 and 25 Au atoms (left). Carbon atoms are in black and Au atoms are in yellow. Pentagonal and heptagonal rings are filled in red and blue, respectively.

Figure 3 :

 3 Figure 3: (a) Scanning tunelling microscopy image of a flower defect with the qualitative atomic model superimposed over it (4×4 nm 2 , V=1 V, I=100 pA).(b) Topographic image of 5 other flower defects (15×15 nm 2 , V=220 mV, I= 1 nA).(c) dI/dV spectra taken on three of the defects in (b). Offsets have been added for clarity. (d, e) dI/dV spectra taken on FD belonging to two other grains.

Figure 4 :

 4 Figure 4: (a) Topographic image of another flower defect (3.5×3.5 nm 2 , V=500 mV, I=400 pA) and differential conductance intensity maps taken from grid spectroscopy at (b) 63 mV (c) 4 mV and (d) -20 mV on the same defect. (e) dI/dV spectra taken on (a) with a set point at 500 mV and 400 pA. The black curve is taken on the graphene (white '+' in (a)) and shows the phonon gap. The red and blue curves are taken on two different lobes of the defect (red and blue '+'s in (a)) and show both the phonon gap and several peaks inside the gap.

Acknowledgments

The authors received no specific funding for this work.


Alexandre Didier

Jacques Millo

Serge Grop

Benoît Dubois

Emmanuel Bigler

Enrico Rubiola

Clément Lacroûte
email: clement.lacroute@femto-st.fr

Yann Kersalé

Ultra-low phase noise all-optical microwave generation setup based on commercial devices

. Close-to-the-carrier ultra-low phase noise microwave signals will now be available in laboratories outside the frequency metrology field, opening up new possibilities in various domains.

Introduction

Ultra-low phase noise microwave signals are being used in a growing number of fields. Industrial applications include telecommunication networks, deep-space navigation, high-speed sampling [START_REF] Valley | Photonic analog-to-digital converters[END_REF] and radar systems [START_REF] Scheer | Coherent radar system performance estimation[END_REF]. Fundamental physics tests and research experiments also benefit from ultra-stable microwave signals, as in atomic fountain clocks setups [START_REF] Guéna | Progress in atomic fountains at LNE-SYRTE[END_REF], Lorentz invariance tests [START_REF] Stanwix | Test of lorentz invariance in electrodynamics using rotating cryogenic sapphire microwave oscillators[END_REF] or Very Long Baseline Interferometry [START_REF] Grop | ELISA: A cryocooled 10 GHz oscillator with 10 -15 frequency stability[END_REF].

Such signals are usually generated in three different ways: from a quartz resonator, included in a frequency synthesis [START_REF] François | A low phase noise microwave frequency synthesis for a high-performance Cesium vapor cell atomic clock[END_REF][START_REF] Lautier | A compact micro-wave synthesizer for transportable cold-atom interferometers[END_REF] ; from a sapphire oscillator [START_REF] Green | A low phase noise microwave sapphire loop oscillator[END_REF], often cooled down to cryogenic temperatures [START_REF] Grop | 10 GHz cryocooled sapphire oscillator with extremely low phase noise[END_REF][START_REF] Hartnett | Ultralow-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators[END_REF] ; or from the optical domain, using an optoelectronic oscillator [START_REF] Salik | An ultralow phase noise coupled optoelectronic oscillator[END_REF] or a cavity-stabilized laser and an optical frequency comb [START_REF] Fortier | Generation of ultrastable microwaves via optical frequency division[END_REF][START_REF] Millo | Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock[END_REF]. In the latter case, a laser is locked to an ultra-stable Fabry-Perot (FP) cavity, thus providing an ultralow phase noise optical signal and a short-term relative frequency stability below 10 -15 . This signal is used to phase-lock the repetition rate of an optical frequency comb, which allows for dividing down the signal frequency from the optical to the microwave domain with minimal degradation [START_REF] Zhang | Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs[END_REF]. Progress in the past ten years has allowed to reach extremely low levels of relative frequency stability for FP cavity laser stabilization setups, both by improving the design [START_REF] Webster | Thermal-noise-limited optical cavity[END_REF][START_REF] Millo | Ultrastable lasers based on vibration insensitive cavities[END_REF][START_REF] Swallows | Operating a 87 Sr optical lattice clock with high precision and at high density[END_REF] and materials [START_REF] Seel | Cryogenic optical resonators: A new tool for laser frequency stabilization at the 1 Hz level[END_REF][START_REF] Kessler | A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity[END_REF] of the cavities. On the other hand, compact and portable FP cavities have been developped for field operation [START_REF] Leibrandt | Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments[END_REF][START_REF] Webster | Force-insensitive optical cavity[END_REF], and such setups are now commercially available. Fiber-based optical frequency combs have followed the same path and are becoming an essential tool in various experimental physics laboratories.

In this article, we present a setup for all-optical microwave generation based on both a commercial Fabry-Perot cavity and a commercial fibered optical frequency comb. We use this setup to generate an ultra-stable reference signal at 10 GHz, which will later be distributed through the laboratory for future phase-noise characterizations of other oscillators based on Sapphire, Quartz or optical resonators. It will also be complementary to an optical reference signal distributed to French time and frequency laboratories through the REFIMEVE+ network [22]. In the following sections, we outline the 10 GHz signal generation scheme and analyse the measured signal phase noise and frequency stability.

All-optical microwave generation setup

Our setup for all-optical microwave signal generation is described in Figure 1. A commercial continuous-wave (CW) laser at 1542 nm [START_REF]NKT Photonics Koheras Adjustik fiber laser[END_REF] is locked to a Fabry-Perot cavity using the Pound-Drever-Hall (PDH) technique. The ultra-stable The output of the stabilized femtosecond laser is detected by a fibered fast photodiode and filtered and amplified at 10 GHz. Characterization: the signal is electronically mixed with the output of a Cryogenic Sapphire Oscillator (CSO) at 9.995GHz. The resulting beatnote at 4.6MHz is monitored using a frequency counter referenced to a Hydrogen Maser. BDU: beat detection unit; LF: loop filter; PD: photodiode; BP: band pass filter.

cavity is a 5 cm long commercial spherical cavity [START_REF]The cavity is provided by Advanced Thin Films, and the vacuum housing by Stable Laser Systems[END_REF] based on a design by NIST [START_REF] Leibrandt | Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments[END_REF]. The spherical spacer is held at an optimized angle for minimizing vibration sensitivity [START_REF] Leibrandt | Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments[END_REF]. Fused-Silica mirror substrates are optically contacted to a spherical ULE spacer; ULE rings are placed on the SiO 2 substrates to adjust the cavity inversion temperature [START_REF] Kessler | Thermal noise in optical cavities revisited[END_REF]. The inversion temperature of our cavity was determined to be 10.5 • C, and we measured a finesse of about 400 000 for the fundamental TEM 00 mode.

We estimate that the thermal noise floor of our cavity will limit the stabilized laser phase noise to L(f ) = -106 dBc/Hz at 1 Hz with a 1/f 3 slope, corresponding to a relative frequency flicker σ y ≈ 8 × 10 -16 .

The cavity is pumped to ultra-high vacuum using a 2.5 l/s ion pump. The vacuum chamber and the free-space PDH optical setup are placed on a commercial active vibration isolation platform and inside a thermal insulation box, with a total volume of about 0.25 m 3 . We use homemade electronics for the loop filter, as those are on hand in our laboratory and are usually lower-priced, but similar systems are commercially available. An electro-optical modulator (EOM) modulates the laser phase at 22.5 MHz to provide the PDH error signal. The fast corrections are applied to an acousto-optical modulator (AOM) with a bandwidth higher than 100 kHz, while the slow corrections are applied to the laser's piezoelectric transducer(PZT), with a bandwidth of 50 Hz. This setup has proven to be very robust, and the laser can stay locked to the FP cavity for weeks without any external intervention.

We optically mix the stabilized laser output with an optical frequency comb produced by a commercial femtosecond laser [START_REF] Wg | Er fiber-based modelocked laser[END_REF] using the so-called "beat detection unit" provided by the manufacturer. This allows for locking the femtosecond laser repetition rate at 250 MHz. A fibered interferometer is readily aligned to detect the beatnote between the optical comb and the reference laser on a high sensitivity photodetector. The output voltage is then processed to generate a lock signal and fed back to an EOM and a PZT placed inside the femtosecond laser cavity to stabilize its repetition rate. The comb carrier envelope offset is stabilized to a radio frequency reference using the so-called f -2f technique [START_REF] Telle | Carrierenvelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation[END_REF]. This is all done using the electronics provided by the manufacturer. Our only addition is a small RF circuit that allows fo the substraction of the CEO to the optical beatnote signal, following Ref. [START_REF] Zhang | Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs[END_REF]. We obtained similar results with and without this substraction scheme.

We detect the 40th harmonic of the repetition rate, near 10 GHz, using a fast photodiode [28]. With an optical power of 3 mW, we obtain about -30 dBm microwave power at 10 GHz. This signal is band-pass filtered at 10 GHz and amplified using two low phase noise microwave amplifiers [START_REF]Hittite HMC606LC5 and Miteq[END_REF]. The residual phase noise added by such optical division schemes has been measured to be about -111 dBc/Hz at 1 Hz with an earlier version of the optical frequency comb [START_REF] Millo | Ultra-low-noise microwave extraction from fiber-based optical frequency comb[END_REF]. In principle, this value can even be lowered to -120 dBc/Hz at 1 Hz using additional noise-reduction techniques [START_REF] Zhang | Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs[END_REF].

The optical fiber link between the ultra-stable laser and the optical frequency comb is actively stabilized using a fiber-noise compensation scheme [START_REF] Lopez | Ultra-stable long distance optical frequency distribution using the internet fiber network[END_REF]. A fibered AOM is used to correct for optical path fluctuations, with a bandwidth of a few tens of kHz. This can be avoided by placing the FP cavity right next to the femtosecond laser, and using a short optical fiber.

The whole microwave generation setup has stayed locked for days without intervention, even through fairly high temperature fluctuations due to a temporary failure of our air conditionning system. The PDH and the Doppler-cancellation locks have proven to be the most robust, and the femtosecond laser seems to need a quieter acoustic environment. All-in-all, the system is robust enough to continuously provide a 10 GHz ultra-stable reference signal.

Measurements

The characterization setup of the optically generated microwave signal is illustrated in Figure 1. The output of a fast photodiode is filtered at 10 GHz, amplified, and then mixed with a 9.995 GHz signal generated by one of the Cryogenic Sapphire Oscillators (CSO) of the laboratory. The resulting 4.6 MHz beatnote is then sent to a frequency counter referenced to a Hydrogen Maser [32]. The CSO has been fully characterized and presents a relative frequency stability below 8 × 10 -16 for integration times between 1 and 1000 s [START_REF] Grop | Latest improvements in the performance of a cryogenic sapphire oscillator[END_REF]. The sapphire whispering gallery mode resonator is held at cryogenic temperature near its inversion point at 6 K, and is integrated in a Pound-Galani oscillator loop. The ultra-stable output is transfered to the "microwave photonics" room through a 20 m low-loss coaxial cable without any noise compensation.

We measure a relative phase noise L(1 Hz) = -102 dBc/Hz for the beatnote, competitive with state-of-the-art optically generated ultrastable microwave signals [START_REF] Fortier | Generation of ultrastable microwaves via optical frequency division[END_REF][START_REF] Grop | Latest improvements in the performance of a cryogenic sapphire oscillator[END_REF]. Figure 2 presents the phase noise spectrum. The noise floor is close to the photodetection shot noise limit at -137dBc/Hz (dashed line). The spurious peaks between 1 Hz and 100 Hz belong to the CSO phase noise. In particular, resonances at 1.4 Hz and its harmonics are related to the vibrations of the cryo-cooler [START_REF] Grop | 10 GHz cryocooled sapphire oscillator with extremely low phase noise[END_REF]. We plot the phase noise spectrum of the beatnote between two nearly identical CSOs for reference (dashed red line). It is worth noting that the two measurements do not differ by more than 3 dB between 0.1 Hz and 100 Hz, meaning that the optically generated microwave signal phase noise is very close to the CSO signal phase noise in this frequency range. Moreover, the 20 m coaxial cable might degrade the transfered CSO signal phase noise.

Between 0.2 Hz and 0.7 Hz, the spectrum fits the f -3 law (frequency flicker) with a value of -103 dBc/Hz at 1 Hz (black line). This would translate to a relative frequency stability floor of 1.2 × 10 -15 for the beatnote. The spectrum shows excess phase noise at frequencies below 0.2 Hz. We believe that this is due to temperature fluctuations in the room, which cause polarization rotations within the PDH optical setup. These rotations induce power fluctuations of the CW laser that couple to the FP cavity resonance frequency.

1 0 -2 1 0 -1 1 0 0 1 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 -1 4 0 -1 2 0 -1 0 0 -8 0 -6 0 -4 0 -2 0 L ( f ) ( d B c / H z ) f ( H z )
Fig. 2. Phase noise of the all-optical microwave signal compared to a CSO signal. Black curve: phase noise spectrum of the beatnote between the CSO and the cavity signals. Black line: f -3 fit of the spectrum between 0.2 and 0.7 Hz. Red dashed curve: phase noise spectrum of the beatnote between two identical CSOs. Dashed line: photodetection shot noise limit.

The phase noise of the CSO we use has been measured to be L CSO (1 Hz) = -106 dBc/Hz. By substracting this value to the beatnote phase noise, we obtain L opt (1 Hz) = -104 dBc/Hz for the optically generated 10 GHz signal. This is very close to the expected thermal noise floor of the ultra-stable cavity L cav (1 Hz) = -106 dBc/Hz. Figure 3 presents the relative frequency stability of the optically generated microwave signal versus the CSO. We obtain σ y (1s) = 1.9 × 10 -15 for the beatnote, higher than the flicker frequency floor (1.2×10 -15 ). This is mostly due to excess frequency noise at low frequencies. In particular, a parasitic modulation of the beatnote at 26 mHz (most likely due to room-temperature fluctuations) degrades the signal relative frequency stability between 1 and 20 seconds. We have numerically extracted the relative frequency power spectral density S y at this frequency from the drift-removed temporal dataset. We plot the relative frequency stability obtained with such a purely sinusoidal modulation added to the Flicker floor at 1.2 × 10 -15 for reference (gray line -see [START_REF] Kersalé | New temperature compensated sapphire-rutile resonator oscillator[END_REF] for details). The initial slope and frequency stability fairly agrees with our measurement.

The linear drift of the frequency leads to a 3.8 × 10 -16 τ stability for integration time longer than 200 s. Potential improvements of the short-term relative frequency stability include the better rejec- tion of the room-temperature fluctuations, as well as a refined measurement of the inversion temperature of the cavity.

1 1 0 1 0 0 1 0 0 0 1 0 -1 5 1 0 -1 4 1 0 -1 3 1 0 -1 2 ؓ y ( ؔ | ) ؔ ( s )

Conclusion

In summary, we have presented the first all-optical setup for microwave signal generation based on commercially available instruments. This setup shows a phase noise spectrum competitive with the best reported values both for all-optical setups [START_REF] Fortier | Generation of ultrastable microwaves via optical frequency division[END_REF] and cryogenic sapphire oscillators [START_REF] Grop | 10 GHz cryocooled sapphire oscillator with extremely low phase noise[END_REF]. To this day, such "microwave photonics" setups are still found mostly in metrology institutes, as they used to require the design of an ultra-stable FP cavity and/or optical frequency comb. The setup that we present in this article should allow the spreading of optical microwave generation outside of frequency metrology labs, thanks to the availability of the key-devices and the overall simplicity of the setup. This will pave the way to tantalizing new developments in fields such as high-resolution spectroscopy, atomic physics and very-long baseline interferometry.

Fig. 1 .

 1 Fig.1. All-optical microwave signal generation and characterization setup. Generation: A 1.5 µm laser is stabilized to a commercial ULE spherical cavity by Pound-Drever-Hall technique. The stabilized output of the laser is used to optically lock a commercial femtosecond laser. The output of the stabilized femtosecond laser is detected by a fibered fast photodiode and filtered and amplified at 10 GHz. Characterization: the signal is electronically mixed with the output of a Cryogenic Sapphire Oscillator (CSO) at 9.995GHz. The resulting beatnote at 4.6MHz is monitored using a frequency counter referenced to a Hydrogen Maser. BDU: beat detection unit; LF: loop filter; PD: photodiode; BP: band pass filter.

Fig. 3 .

 3 Fig. 3. Allan deviation of the all-optical microwave signal compared to a CSO signal. Red dashed curve: relative frequency stability with linear drift removed. Light gray curve: estimated contribution of the 26 mHz modulation to the Allan deviation.

Acknowledgements

The authors would like to thank Rodolphe Boudot and Vincent Giordano for their careful reading of the manuscript as well as Christophe Fluhr for fruitful discussions about the CSO and Maser performances.. This work is funded by the Fond Européen de développement Régional (FEDER). This work is also funded by the ANR Programme d'Investissement d'Avenir (PIA) under the Oscillator IMP project and First-TF network, and by grants from the Région Franche Comté intended to support the PIA.


Elodie Bouzekri
email: elodie.bouzekri@irit.fr

Alexandre Canny
email: alexandre.canny@irit.fr

Célia Martinie
email: martinie@irit.fr

Philippe Palanque
email: palanque@irit.fr

A Generic Software and Hardware Architecture for Hybrid Interactive Systems

INTRODUCTION

Hybrid Interactive Systems integrate both hardware and software elements so their engineering requires bridging the continuous analog real world and the discrete digital world. Cyber Physical Systems (CPS) are a specific kind of Hybrid Interactive Systems found in domains such as smart housing, transportation or healthcare.

For example, in smart-houses, users may use a remote control or a smartphone to operate systems such as light bulbs, window shutters or air-conditioning. However, the user can directly perceive cooling by getting closer to the air-conditioning device itself. From the HCI point of view, this means that the design and development of such hybrid systems require blending information from the two elements:

• The physical part of the CPS, (e.g. light bulbs or window shutters) that is (possibly) perceivable and actionable by the users and belong to the analog real world.

• The command and control part of the CPS (e.g. a remote control or a smartphone), that allows the user to use the CPS, might integrate a hardware and software part and may have (part of) their behavior described in the discrete digital world.

A classical interactive application (e.g. a desktop application such as Microsoft Word) belongs to the digital world and is most of the time designed without careful consideration of the hardware part of the interactive system that will host and allow users to manipulate it. Indeed, usually the assumption designers and developers make is that standard input and output devices will be used, and thus do not address them while designing the interactive software. This is particularly visible on interactive applications architectures such as Seeheim [START_REF]Proceedings of IFIP/EG Workshop on User Interface Management Systems[END_REF] of Arch [START_REF] Bass | The arch model: Seeheim revisited[END_REF] where input and output devices are not even mentioned. However, other work, such as the ones on multi-device applications make explicit (in a platform model) the execution platforms and theirs input/output devices [START_REF] Lo | Chameleon: a platform for developing multimodal application with comprehensive development cycle[END_REF]. This is also required when interaction must be reconfigured according to input devices failures as in [START_REF] Navarre | Usability Service Continuation through Reconfiguration of Input and Output Devices in Safety Critical Interactive Systems[END_REF]. Due to the recent evolution of interaction techniques and technologies (e.g. the large distribution of touch devices) more recent interactive systems architectures such as MIODMIT [START_REF] Cronel | Une approche pour l'ingénierie des systèmes interactifs critiques multimodaux et multiutilisateurs: Application à la prochaine génération de cockpit d'aéronefs[END_REF] make explicit the hardware parts (belonging to the input and output devices).

An architectural model similar to Seeheim but adapted to CPS would require making explicit all the components, their interrelations and what can be perceived and manipulated by the users. Indeed, in [START_REF] Broy | Challenges in Engineering Cyber-Physical Systems[END_REF], Broy et al. describe challenges in engineering CPS and state that regarding to their implementation, "new ways must be found to manufacture products that are software driven but have physical components".

The position paper presents a generic architecture for CPS that enables the separation into several components of both elements of CPSs. Such architecture supports the design and development of CPSs by decomposing a CPS into several, connected but loosely coupled components. To demonstrate its use and applicability, we describe two existing CPS with this architecture: the Philips Hue lighting systems [START_REF] Philips | Hue lamp[END_REF] and the Auxiliary Power Unit of a large civil aircraft.

A GENERIC ARCHITECTURE FOR CPS

Figure 1 presents a generic architecture, mixing both physical systems and software components, illustrating how a CPS can be broken down into generic components in order to support their engineering. In this Figure, we highlighted three parts: i) the "Monitored and Controlled CPS", ii) the "Transducing and Control" and iii) the "Command and Control System of the CPS". Each of them is divided into one or more hardware or software components.

The following paragraphs describe each one of these components from left to right.

The Monitored and Controlled CPS component

The CPS Physical Device

The CPS physical device is the concrete physical system to be operated using a command and control user interface. A detailed description of its inner behavior is not always known and not always mandatory to allow operations. The inner state of such device is usually accessible by means of sensors while it can be manipulated using actuators.

The Physical User Interface

The physical user interface of a CPS represents the physical phenomenon that can be perceived by the operator. It is for instance smoke, vibrations, explosion... The operators may perceive this information (e.g. by touching the device) and might be able to interact with the device directly (e.g. pushing or moving it).

The Software Interface

The software interface component of the "Monitored and Controlled CPS" part provides a view on how to handle the CPS physical device and how to assess its inner state. This component provides a set of observable parameters that are the result of the discretization of potentially continuous physical phenomenon. For instance, it could provide an integer value (produced by sensors) corresponding to an abstraction of a real engine speed. The Software Interface thus provides both a set of observation mechanisms and a set of commands that may be performed on the CPS physical device (for instance starting or stopping the device).

The Transducing and Control component

The transducing and control component is composed of a unique component: the behavioral model of the monitored and controlled CPS. This component is responsible for translating both low-level information from the Software Interface into higher-level data (e.g. the availability of an electric service only available if the engine speed is above a given threshold) and higher level commands from the operators into low-level commands acceptable by the device. In other words, this component is responsible for digitizing the behavior of the monitored and controlled CPS (which is, per definition, analog).

It is important to note that this component has been defined, within our architecture, as a "role" and not as a system. Indeed, we have come across different types of CPSs where the functions and data of that component has been located within the monitored and controlled CPS system itself, within its command and control system or within a third "intermediate" system.

The Command and Control System of the CPS

The command and control system of the CPS corresponds to the elements of the system designed in order to allow users to interact with the CPS. It is important to note that for one CPS there may be several command and control systems (e.g. a TV controlled with a dedicated remote control and a cellphone).

The Behavioral Model of the User Interface

The behavioral model of the user interface deals with both the rendering (towards the user) of parameters provided by the behavioral model of the CPS triggering of functions within the CPS following user's actions. This component may have some local interaction behavior that does not directly affect the device (for instance, some temporary states during operations before acting on the CPS). As this behavior may be complex, this component is usually broken down into smaller communicating sub-components.

The User Interface Device

The User Interface Device is a set of input and output devices dedicated to allow users to interact with the monitored and controlled CPS (for instance, in an aircraft it can be dedicated screens, keyboards, and physical buttons).

The proposed architecture enables the separation of a complex system into several components. These components are then easier to apprehend. Besides, these components are strongly consistent and loosely coupled. This allows the separation of concerns (for instance, the components related to the UIs are situated within the UI side) and the locality of modification (a modification within one of the components will not necessarily affect the other components).

ILLUSTRATIVE EXAMPLE WITH A CONSUMER GRADE PRODUCT

In this first illustrative example, we focus on a consumer grade-product, the Philips Hue smart light system illustrated in Figure 2. In this system, the user pairs a set of light bulbs to the Hue Bridge to be able to control their On/Off state as well as on their light color and brightness. The user operates these controls via a smartphone or a remote control. In this example, we consider that a light bulb is already paired with the Hue Bridge so the user can control it. Figure 3 presents the instantiation of the proposed architecture for the Philips Hue lighting system when a lightbulb is paired to the Hue Bridge.

The Monitored and Controlled CPS

Since this example focuses on controlling a light bulb in the smart light system, the monitored and controlled system here is the light bulb itself.

The CPS Physical Device

In the smart light system, the light bulb correspond to the CPS physical device ("Hue light bulb" in Figure 3).

The User Interface Device

In the smart light system, the physical user interface ("Hue PUI" in Figure 3) corresponds to both the light and heat produced by the light bulb that are directly perceivable by the user. Another possible interaction that may be described within this component is the fact that the user may decide to unplug the light bulb.

The Software Interface

This Software Interface (named "Hue SI" in Figure 3) describes the set of observation mechanisms allowing knowing if the light bulb is ON or OFF, its color, its intensity, …. It also describes the fact that the light bulb provides possibilities to manipulate its state: the possibility to turn it on, to turn it or, to change color or intensity.

The Transducing and Control

This component ("Hue BM" -for Behavioral Model-in Figure 3) represents the discrete behavior of the Hue light bulb. Concretely, the behavioral model both describes the different discrete states of the light bulb (such as "ON", "OFF", "Turning ON", "Turning OFF"….) and the different possibilities for state changes (e.g. how is it possible to switch from "ON" state to "OFF" state, going through "Turning ON" state). The Hue bridge integrates this behavioral model and is in charge of the role "transducing and control".

The Command and Control System of the CPS

As the Philips Hue CPS provides two command and control systems (a remote control and a smartphone), Figure 3 presents those two elements respectively named "Remote control" and "Smartphone". The following paragraphs describe the UIBM and UID for each of these command and control systems.

The Behavioral Model of the User Interface

Each command and control systems in the Philips Hue CPS, exhibits its own UIBM:

• The remote control UIBM ("Hue UIBM -Remote Control" -for Behavioral Model of the User Interfacein Figure 3) describes the behavior of the remote control. For instance, it describes the fact that a key of the remote control can have two states ("Pressed" or "Released"). • The smartphone UIBM ("Hue UIBM -Smartphone" -for Behavioral Model of the User Interface-in Figure 3) describes the behavior of the application that is running on the smartphone. For in-stance, this component describes the different modes of the application.

The User Interface Device

In the architecture for the Philips Hue CPS, the user interface devices are:

• For the remote control the concrete remote control device composed of the different keys of the remote control.

• For the smartphone the concrete device is the smartphone touchscreen.

This section has demonstrated that the various components of a CPS can be dealt with using the generic architecture.

The user interface makes it explicit that the user can perceive directly the state of the device (lamp on or off when he/she is collocated with the device) represented by the direct arrow between the CPS box and the user icon.

The user can also manipulate the device states using two different devices.

ILLUSTRATIVE EXAMPLE WITH THE APU OF AN AIRCRAFT

The Auxiliary Power Unit (APU) of an aircraft is a small engine designed to provide electricity and bleed air to the aircraft on ground or mid-air. An overview of the APU command and control system is presented in Figure 5. To operate the APU from the cockpit, pilots may use controls from the Overhead Control Panel (containing several buttons, see Figure 5) or the Control and Display System (made of the ECAM Control Panel (for input and a dedicated Display Unit for output). Pilots may also perceive the behavior of the APU through the noise and vibrations the turbine produces (especially on ground). Figure 4 presents the instantiation of the proposed architecture for the command and control system of the APU. In the same way as the Philips Hue, the generic architecture can be tuned to represent the components of this complex CPS.

CONCLUSION

Manufacturing products that are software driven but have physical components is one of the challenges in engineering Cyber-Physical System. To help overcome this challenge, we proposed an architecture in which we highlighted the components that seems relevant when designing both the controlled part and the command and control part of the CPS. We showed that a transducing component, located within or outside the monitored CPS, allows the discretization of the monitored system behavior through a Behavioral Model (BM). This BM is use to feed data to the command and control systems of the CPS. Each of these command and control systems use this BM to build its own behavioral model of the monitored system so user can easily take advantage of the available Input/Output. To illustrate the applicability of the proposed architecture, an instantiation on it on the Philips Hue lighting system and on the APU of an aircraft is provided.

Due to space constraints, we have not presented how the behavior of each component can be described and how to ensure that this behavior exhibits the expected behavior in terms of usability and user experience.

Figure 1 .

 1 Figure 1. The generic architecture for supporting the engineering of cyber physical systems.

Figure 2 .

 2 Figure 2. Overview of the Philips Hue system and its command and control systems.

Figure 3 .

 3 Figure 3. Application of the generic architecture to the command and control of the Philips Hue CPS (key is in Figure 1).

Figure 5 .

 5 Figure 5. Overview of the cockpit command and control systems of the Auxiliary Power Unit