based on research on a serious game used for training purposes, this chapter aims to analyze knowledge transfer related to emotional labor between gaming and work situations. After defining emotional labor, we will discuss issues related to the use of a serious game as mediation; whether or not it is accepted; and whether it contributes to the possibility of better regulating emotions. The results suggest that knowledge transfer, in and about work situations, is more related to the acceptance of mediation including its debriefing than to the playful attitude itself.

Introduction

Among the many definitions of serious games, we retain that of video game designers Chen and [START_REF] Michael | Serious Games: Games That Educate, Train, and Inform[END_REF]: "A serious game is a game that is designed for purposes other than pure entertainment." According to this definition, a serious game can apply to a large number of sectors : education, health, advertising, communication, politics, humanitarian, defense, religion, art, etc. -serious games can be digital or non-digital (Abt, 1987). To specify the digital form, the term "serious video game" may be used. 1 L. Martin, Occupational Psychologist-Researcher at the CRTD, J. Alvarez Joint Head of the DIU "Apprendre par le jeu" Université de Paris -INSPE Lille -DeVisu Laboratory, Université Polytechnique Hauts-de-France and A. Taly -Joint Head of the DIU "Apprendre par le jeu" Université de Paris -Researcher at the CNRS, Université de Paris Alvarez, Djaouti & Rampnoux (2016) define the serious game as a: "device, digital or non-digital, whose initial intention is to combine, with consistency, both utilitarian ("serious") aspects such as, in a non-exhaustive and non-exclusive way, teaching, learning, communication, or information, with playful motives (competition/challenge, rules of control, closure and procedure, scoring, the artificial character) stemming from the (video) game. Such an association is aimed at an activity or a market that goes beyond mere entertainment" (p.17).

"Utilitarian scenario" refers to the work of researcher Étienne Armand Amato, who in 2007 proposed the term " utilitarian game" to designate serious games. For Amato, "utilitarian " is understood as aiming at : [...] bringing about a transformation in their addressees in the sense of an improvement in skills (training), adaptation to the environment (treatment of phobias), understanding of a phenomenon (education) or greater adherence to the message conveyed (promotion, advertising, ideological video games, also known as political games) [START_REF] Amato | Vers une instrumentalisation communicationnelle des jeux vidéo : quelles formes de sé-duction idéologique ou publicitaire ?[END_REF]. Three main families of utilitarian functions to be associated with the game can be referenced: to broadcast messages, to train and to exchange data (Alvarez, Djaouti & Rampnoux, 2016).

Our research focused on a serious escape game (SEG). The principle of escape games (EG) is simple: players are in a room and have to get out in a limited time (usually an hour). Whether the room is real, in a live action escape game, or virtual, in board games or video EG, does not change this principle. Used by companies as entertainment in team-building seminars, EG has become a new type of serious escape game (SEG), and has begun to be used in training and recruitment schemes as well.

A French company has created a SEG dedicated to apprenticeship. This game is in a case divided into three boxes, each closed with a padlock and all the clues are recorded on a tablet. A company in the insurance industry wanted to adapt this SEG so that their employees could discuss in a playful way the emotional charge of customer relations, a key element of their activity. A major problem in customer relations is the emotional response to the various situations encountered at work. Understanding and regulating emotions can be a resource, a major asset in customer relations to manage incivilities, difficult situations and in order to make appropriate and professional decisions. The entire training aims to enable professionals to take a step back during difficult exchanges and to help them regulate their emotions. This implies that professionals need to know and master strategies to regulate their emotions. This is called "emotional labor".

There is a tension between the daily life of customer advisers in the field and the "frivolity" of gaming. Therefore, it remains to be determined whether games, and in particular the proposed SEG, is an appropriate mediation to address such issues with often overwhelmed professionals. Is the artefact used considered and experienced as a game? Does the training session produce a change in the behavior of the professionals at work? We proposed to address these questions through action research within the framework of the psychosociology of work (Lhuilier, 2013). The group interviews were analyzed using two methods:

-in-situ observations made during gaming activities.

-questionnaires submitted one month later.

The data studied analyze issues related to: whether or not a SEG is used as a mediator; whether or not such mediation is accepted; and whether or not it contributes to the possibility of better regulation of emotions. Through this process, it is possible to analyze learning transfer (Frenay & Bedard, 2011) in and on work situations.

Emotions, debriefing and learning

Emotional labor

To define emotional labor, we must distinguish between affects, emotions and feelings [START_REF] Martin | Activité de serious gaming en formation de management d'équipe : réflexions autour des émotions suscitées et retours d'expériences[END_REF]. [START_REF] Shouse | Feeling, Emotion[END_REF] explains the difference between "feelings, emotions and affects": affects are abstract and unconscious, feelings are personal and biographical, and emotions are social. An affect is an intense, unconscious experience. It is highly subjective, as affects cannot be fully expressed through language, they are unconscious (Massumi, 1987;[START_REF] Shouse | Feeling, Emotion[END_REF]. A feeling is a personal sensation related to prior experiences and life history, as each person has a distinct set of prior sensations from which to draw in order to interpret and categorize their feelings. An emotion would be the "showcase" of a feeling. An emotion can be an expression of one's internal state or can be adapted to meet social expectations.

Social rules impose the need to adapt one's emotions, what the American sociologist [START_REF] Hochschild | Travail émotionnel, règles de sentiments et structure sociale[END_REF][START_REF] Hochschild | Exploring the technology acceptance and flow state of a chamber escape game-Escape The Lab© for learning electromagnet concept[END_REF] calls "emotional labor". This work allows professionals to adapt and regulate their emotions in order to make them "appropriate" to the situation and context. In some professions, individuals need to adapt their emotions in order to adapt them to society's expectations. Emotional labor is the expression of emotions in the service of work. For example, a flight attendant must be smiling and welcoming and repress anger, indifference or worry in order to achieve "well-being" and recognition from passengers. Emotional labor involves changing the emotional state of employees through a variety of techniques and strategies. As a result, there may be a dissonance between what the person is feeling (affect/feeling) and the emotion they need to show, and this emotional labor can have a long-term cost on health. According to Hochschild, emotional labor is characterized by "transmutation", i.e. a transfer of emotions from the private to the public. Emotions, which are normally in the private domain, are managed and marketed by the company in the public space. [START_REF] Lhuilier | Compétences émotionnelles : de la proscription à la prescription des émotions au travail[END_REF] studied this evolution within organizations that range from the proscription to the prescription of emotions at work. Emotional labor is most damaging to health when the emotions prescribed at work do not accurately represent the experience and feelings experienced by the individual. Emotional dissonance among employees is strong when the customer is perceived as aggressive and harassing. In this case, it is more difficult to express positive emotions with an unpleasant and aggressive client [START_REF] Amato | Vers une instrumentalisation communicationnelle des jeux vidéo : quelles formes de sé-duction idéologique ou publicitaire ?[END_REF]. [START_REF] Zapf | Emotion work and psychological well-being -a review of the literature and some considerations[END_REF] demonstrated the importance of social support, including colleagues, in preventing dissonance.

Customer advisors are faced with emotional labor that can be difficult without having the theoretical background to understand it. The objective of the training is therefore to transfer this knowledge and to enable professionals to use it in their daily work. The learning is discussed during the debriefing to encourage knowledge transfer to work situations.

Learning in a game

With respect to learning through games, studies conducted by Sherry Turkle in 1986 showed the acquisition of skills through Pac-man [START_REF] Turkle | Les enfants de l'ordinateur[END_REF]. More recently, Rebetez and Bétrancourt (2007), albeit cautiously, listed a series of studies devoted to the psychological and cognitive contributions of video games: for example, improving performance related to mental processes by playing Tetris created by Pajitnov in 1984, or related to dynamic spatial reasoning by playing Marble Madness (Rebetez and Bétrancourt, 2007). Yann Leroux, for his part, identified a series of skills that video games could develop in terms of clinical psychology: controlling anxiety, establishing social contacts, integrating personality, etc. (Leroux, 2012, p.74-78).

This non-exhaustive list provides examples of how games could support different types of learning. In the workplace, it can also make sense to use games to provide training and companies invest in training to encourage the learning of expected "behavioral skills". In particular, games can facilitate cooperation within teams [START_REF] Schmidt | Analysis of Cooperative Work. A Conceptual Framework[END_REF]Taurisson and Chunikin, 2005), developing the ability to negotiate, discuss, collaborate, share emotions and ideas with others [START_REF] Sauvé | Une analyse des écrits sur les impacts du jeu sur l'apprentissage[END_REF]. Since SEGs are team games, it is tempting to use them to promote or evaluate teamwork. Two studies suggest that it is possible to develop group dynamics in the context of an EG [START_REF] Warmelink | Evaluating the Team-building Potential of a Mixed Reality Escape Room Game[END_REF][START_REF] Pan | Collaboration, Awareness, and Communication in Real-Life Escape Rooms[END_REF].

In our research, the question was to analyze whether games, debriefing and associated work groups promoted the transfer of learning in work situations.

The context and framework of the ESG

Difficulty in gamification

Customer relations imply performance, customer satisfaction and objectives responding to requirements in a complex and difficult relational environment. The training in our study aimed at:

-Making teams aware of the roles of emotions and their individual and collective regulation in customer relations.

-Providing operational means to develop the emotional competence of teams and manage work situations differently.

-Supporting managers in the implementation of the proposed system in terms of customer relationship issues.

The digital SEG thus conceived made it possible to combine theoretical concepts illustrated with practical cases to facilitate their appropriation, strong moments of collective reflection and exchange of experiences for:

-sharing the difficulties encountered on the theme and identifying appropriate actions;

-enriching the training with the experience and knowledge of the teams on the theme;

-allowing each participant to discover not only external resources (within the group), but also internal resources (individual potential).

These resources were explored during the various challenges offered in the game.

The challenges embedded in the SEG were illustrated with concrete examples from authentic work situations. For each of the learning objectives (cognitive biases, incivilities and people in difficult situations), the work situations encountered by the teams were detailed. When designing the game, each theoretical part was associated with practical cases from these work situations.

The training system

The training program involved 50 customer advisers, but only 45 were able to attend. The program consisted of a full day with the digital SEG and complementary half-days of 10/12 professionals to work and take the work situations modelled in the game further or any lived situation involving the adviser.

The day started with an introduction by the team leader explaining the game choice of the day and introducing the theme of emotions. The teams were randomly composed of three or four people, with the exception of the team of the three managers.

Once the game was introduced, each team could start playing. Only three participants had already made live action escape games. The game lasted from 1h15 to 1h30. Feedback from the game was achieved through the team's creation of drawings. Each participant was given a large sheet of A4 paper, then teams of 3 to 4 people had to make a collective illustration of what had happened during the SEG and indicate what they retained from the acquired knowledge to transfer it to work situations.

In the afternoon, the videos made by the participants during the game were viewed. Another group, other than the one who had made the video, reacted on the emotions the adviser could feel and how he could regulate them. Then the day ended with a quiz on the day's learning and a memento of the main knowledge from the training was distributed to each participant.

A research-action approach

We carried out an action-research that aimed at global and transformative change through the simultaneous process of action and research, the two being linked by critical reflection.

In this action research, we used a qualitative part with observations during and after the game as well as during debriefing and working groups, a process quite similar to the analysis of practices. We supplemented our observations with a questionnaire. The objectives of the questionnaire were both to collect data on the experience of the game, to analyze the involvement of professionals in the game itself, and the role of debriefing and working groups in learning.

Results

Observations during gaming

The 45 professionals were divided into 10 teams of 4 to 5 people during the SEG sessions. We could observe the surprise when they understood that "it was time to play". Some of them had played an EG a short time before and said they were very excited to play again. Most of the teams played in a good atmosphere and cooperated with each other. The competition between the teams came about relatively quickly. From our experience, the game seems to summon competition quickly. The teams evaluated each other by observing where the others were at. The music from some of the puzzles was a very good indicator and we heard: " What is that? We're not there yet," or when their music rang out, they said, "We're only there, they're ahead of us". This performance evaluation mainly concerned teams that were close to each other. The 10 teams and the layout of the room did not allow them to progress in the game and follow the progress of the other teams at the same time. Two teams caught our attention.

The first team because it was not having fun; two of the three members spent a lot of time thinking about and discussing all the puzzles, and it was very difficult for them to get involved in the game. The third member was bored and fed up because he couldn't have fun. We discussed with them the reason for this difficulty in getting into the game and both members expressed their disagreement with playing.

The second team played and collaborated throughout the game. Towards the end, people started to get nervous. They couldn't find the material to answer the riddles. At first we thought it was a logistical mistake and suddenly we realized that they had not opened the last box where all the puzzles were. When we talked to them, they explained that they were falling behind and that they wanted to go faster just by using the tablet. The fact was that this was not possible, the puzzles and the tablet worked together. The team's defense strategy was to say that the boxes had been badly prepared and the material was missing, which did not allow them to continue, so they lost time, they said. This behavior was similar to the behavior of the bad player who "destroyed" the game: "it is not a good game", they said when the results did not meet the team's expectations [START_REF] Mehl | Tricheurs et tricheries dans la France médiévale: L'exemple du jeu de dés[END_REF]. In this example, the team tried to cheat, i.e., they tried to go faster using only the tablet, although this was not possible.

These two examples are isolated, most of the teams played and expressed pleasure, in particular by making two videos to illustrate work situations related to the game. Playful behavior was then analyzed using the questionnaire sent to them after the game, the debriefing and the working group.

Post-game discussions

The debriefing session

After the "hot reactions" within each team, the second phase of the debriefing was carried out by creating a collective illustration within each team of what happened during the SEG and how people thought they would transfer the new knowledge to work situations.

The collective illustration was the result of the collective discussion according to three questions:

1. How did you find this experience? 2. What do you think of the way the team worked? 3. How can you learn from this experience and transfer it to your professional activity?

The idea of a collective creation was to get them to discuss and make visible what had happened during the SEG and what they had understood about emotional labor. The drawings were in light colors and showed the fun, enjoyment and discussion in the teams during the SEG. Experience was also depicted with brains, hearts and people talking together. The transition to work situations was illustrated with arrows ranging from learning to work situations. Only one team retrieved the drawing to share it in their workplace.

Working groups

Two months after the SEG and its debriefing, working groups were organized to deepen emotions at work. We had 4 groups of 10 employees and 1 group of managers.

We started the session by asking three questions: 1. What do you remember about the training? 2. Do you have a different approach to situations since the training? 3. What are your expectations today?

Regarding the first question, all appreciated the discussions and interactions with colleagues in the game: "several discussions on work situations"; "good collaboration with colleagues"; "importance of each colleague's skills". Most of them remembered the main topic of the EG and some of the teachings on emotion regulation: "importance of managing our emotions"; "emotion is a very personal feeling and above all very different from one individual to another"; "don't confuse your emotions with the situation"; "maintain distance from the situation". The EG was a good memory for all except one participant, a member of the team who was reluctant to play. Two participants were frustrated because they would have liked to go further in work situations and because of the competition. Going further was everyone's expectation for the work groups.

The question about transfer of learning was very interesting. For some (⅓), a transfer of learning occurred in everyday life: "more relaxed in person or on the phone, more fluid conversations"; "since the escape game, I try to pause before any reaction"; "I am more aware of my emotions, my reactions and what I can feel"; "I take a step back from other people's emotions, I let myself be less invaded by others' emotions"; "I know better how to react to a person in a totally stressful situation, distress. I have learned that the person is unable to receive information until the brain is calm and soothed. Only then will we be able to guide and help him. For others (⅔), the transfer did not take place: "the learning was blurred"; "too far to remember the content"; "I didn't really change"; "the game took over the content".

The expectations for the working groups were: "to manage my feelings by maintaining distance, but not too much"; "to gain a better knowledge of my colleagues' feelings"; "to manage my emotions according to the situations"; "to understand how to better manage customers who irritate me"; "to be more detached from my daily work"; "to better manage what irritates me; "to take a step back"; "to learn things, to put words to my feelings"; "to manage conflict situations". A few were looking for tools: "to find tools to manage conflicts or difficult situations on the phone". The difficulty was to make them understand that it was more important to understand an emotion than to banish it.

The second part of the working groups was devoted to explaining, for each of them, a work situation and the associated emotion in order to analyze it together. The ANACT model for analyzing a problematic situation was used [START_REF] Sanglerat | Les RPS et la méthode de la "situation-problème" l'organisation du travail à l'épreuve des risques psychosociaux[END_REF]. This model promotes interaction between participants in the identification of psychosocial risks and solutions. This involves: describing problem situations with the associated emotion, consequences, causes, risks and actions. Each person explained a work situation and the others asked questions.

After this analysis of the work situation, the professionals envisaged some changes: "maintaining discussions on work situations with colleagues"; "asking the question of causes: what makes the other person act/interact equally"; "analyzing emotions and taking a step back"; "choosing the right time to contact a client"; "asking a question at the end of the e-mail or conversation to encourage the answer"; "using key words: I am surprised ... I need ...".

From our observations, the majority of people were curious while maintaining a professional attitude despite the playful context of the training. A minority of 4/5 people, initially more reticent, resistant, assertive and very spontaneous, got involved and participated positively. Only one person remained on the sidelines and did not wish to participate and this person expressed it without giving a reason. All the professionals felt the need to speak, each with a personal anecdote to share. Some of them asked to continue the working groups.

Questionnaires

The questionnaires were completed by 25 of the 45 participants. The answers to the questionnaires were analyzed with the aim of analyzing: i) the perception of the training session as an authentic game, ii) the transfer of learning, in particular through the debriefing session and the post-game working groups, and iii) the potential impact of the training session on professional practices.

Professionals were asked about their perception of training through a series of questions. The questionnaire included closed-ended questions about the gaming experience in general and this experience in particular. Most of the questions were developed based on the results of initial research [START_REF] Muska & Lipman Martin | Les serious games en entreprise : récréation ou instrumentalisation managériale[END_REF]. The flow scale was used to subjectively assess learners' enjoyment and motivation in gaming [START_REF] Heutte | Optimal learning experience in digital environments : theoretical concepts, measure and modelisation[END_REF]. They were asked directly if they felt that SEG was a game. Almost all (24/25) responded that they thought it was a game.

The other questions were indirectly related to their perception of the session as a game: i) I felt that I had the ability to deal with the situation, ii) I did not see the time go by, iii) I felt constrained by the rules of the game, etc. These indicators were used to analyze whether each individual behaved as in a classic game situation (without the injunction to play): i.e. a person who did not see time passing, who did not feel constrained and who felt in control of the situation was considered to be playing, whereas a person who felt constrained and did not lose the notion of time was considered not to be playing. With this approach, two people were considered as not playing and four were considered neutral.

Another set of questions analyzed their perception of training. One of the questions asked whether, in their opinion, SEG was appropriate to address the issue of emotional workload in their work. Another questioned the debriefing to allow for the transfer of learning into work situations. Finally, a few questions questioned their behavioral change. One question asked if they used the memento handed during the training. Another question asked whether they had succeeded in transferring the knowledge acquired during the training into their work. Although the sample size was limited, it appears that the three observations (gaming, transfer and effect) were not independent (Friedman's test, sum of the ranks, p < 0.02). Looking at the paired associations, we found no significant association between play and effect (Kruskal-Wallis test by ranks, p>0.15). This is consistent with the idea that play behavior does not appear to be crucial in maintaining the effect of play itself. On the other hand, we observed a significant association between transfer and effect (Kruskal-Wallis test by ranks, p < 0.02). This confirms the importance of debriefing as suggested by others [START_REF] Garris | Games, motivation, and learning: A research and practice model[END_REF]. These results also demonstrate that the questionnaire is capable of capturing this association.

Discussion -Conclusion

This study shows that the effect of training on the participant's work situations was significant, although we limit ourselves to those for which there was no ambiguity (11/25), although this should probably be pursued with larger cohorts.

One of our questions was whether it is possible to use a game for an activity that has a very strong emotional imprint, as here with emotional labor. An interesting element is that although almost all participants defined the activity as a game, a significant fraction of them did not demonstrate play behavior. This was not surprising, given that the same game can have different meanings for different participants [START_REF] Juul | The game, the player, the world: Looking for a heart of gameness[END_REF]. Indeed, a study of adult education using a serious game revealed a significant effect of participants' previous experiences as players; this preliminary knowledge altered the playful experience and perception of the serious game as an evaluation [START_REF] Martin | Entraves à l'attitude ludique avec un jeu sérieux intégré dans une formation managériale: un exercice plus qu'un jeu?[END_REF][START_REF] Muska & Lipman Martin | Les serious games en entreprise : récréation ou instrumentalisation managériale[END_REF]. In addition, a small study of a SEG found a correlation between the gender of participants and the effect on their experience (the "flow") (Hou, 2012).

The questionnaires were designed to capture informations that are usually collected through observations or interviews. This should make it possible to collect data on larger cohorts in the future. However, the questionnaires showed less consistent responses with related responses suggesting that some questions could be improved. It may also be that some indicators are more appropriate than others. Another limitation of this study is related to the fact that the questionnaires were anonymous, which prevents direct comparison with the results of observations and interviews.

Emotions are the visible part of an affect. Emotional labor can consist of regulating this visible part, but what about the affect? If affect is the unconscious part of the emotion, therefore the part we do not control, how can we regulate it without analyzing and understanding it? Individuals are asked to regulate the visible part, the emotion, from a deeper part, the affect. In the distinction between feeling, emotion and affect, we can assume that debriefing allows us to discuss the feeling and to think about how to regulate it according to the prescribed emotions, which is emotional labor.

It is an illusion to believe that play is enough to promote learning. Debriefing is essential to establish links with work situations and thus promote knowledge transfer. The post-game working groups on the emotional load at work made it possible to deepen this link initiated during the debriefing. Our results are consistent with the notion that a game is a mediator and not the final solution, which made it possible to collectively discuss work situations during the debriefing.

In this example, the modification of feelings could be the "actual work" and the modification of emotions could be the "prescribed work". The effect would remain hidden or ignored. A tension may therefore arise between feeling, affect and emotion that can be harmful to health [START_REF] Lhuilier | Compétences émotionnelles : de la proscription à la prescription des émotions au travail[END_REF]. Interestingly, most participants told us that the support of managers and co-workers was essential to discuss these daily tensions and to express sadness, anger, tears and all the emotions prohibited at work, as well as in relationships with customers. This is what participants said the post-game working groups fostered. Since social support prevents dissonance [START_REF] Zapf | Emotion work and psychological well-being -a review of the literature and some considerations[END_REF], it can reduce tension because emotions are prescribed in front of consumers, not colleagues. In turn, reducing cognitive dissonance may improve health.


Eric Bourreau
email: eric.bourreau@lirmm.fr

Katyanne Farias

Thierry Garaix
email: garaix@emse.fr

Philippe Lacomme

Diego Martino
email: diego.perdigao_martino@etu.uca.fr

Ivan Pena Arena

First Constraint Programming based approach for the Truck Driver Scheduling Problem

Keywords: driver scheduling, constraint programming, EC regulation 561/2006

Introduction

In order to increase road safety, legal drivers' rules define a general framework of drivers' work conditions, including mandatory driver breaks and rest periods during workdays. This set of rules impose restrictions on driving time, working time, as well as the scheduling of several types of breaks along the shifts and weeks. The routes defined by solving classic vehicle routing problems are often long and do not respect these regulations. Thus arises the need to validate and adapt these routes so that they comply with the rules imposed. The Truck Driver Scheduling Problem (TDSP) aims to determine the sequence of driver activities according to the rules on drivers' hours and working time, so that the driver visits all customers in a given order, respecting the time windows of each client. Thus, let us consider a sequence of customer locations that must be visited by a truck, and the European Union (EU) regulations [1]. A work activity with a known duration must begin at each customer within a given time window. The driving time to go from one customer to another is known. In this work, we propose a first Constraint Programming (CP) model to solve the TDSP, meeting EU legal driver' rules for a planning horizon of one-week time. In more detail, we consider the following set of constraints: (i) a truck driver cannot drive more than 4.5 hours without a break of at least 45 minutes, referred to as a full break; (ii) a driver break of 45 minutes can be split into two periods of at least 15 minutes and 30 minutes each, in that order; (iii) after a total of 9 hours of driving, a driver must take a rest period (sleeping time) of 11 hours; (iv) the total driving time can be increased to 10 hours twice a week; (v) the rest period can be reduced to 9 hours three times a week; (vi) a working period of 6 hours must encompass a break of not less than 15 minutes; (vii) if uninterrupted working time is a minimum of 6 hours and a maximum of 9 hours, a break of 30 minutes must be done; (viii) finally, if uninterrupted working time is longer than 9 hours, a break of 45 minutes must be scheduled. Even the most recent works addressing the TSDP or the combined Vehicle Routing and Truck Driver Scheduling Problem (VRTSDP) simplifies several constraints and solves the problem for a week-long planning horizon. For example, [START_REF] Goel | Legal aspects in road transport optimization in Europe[END_REF], [START_REF] Goel | An exact method for vehicle routing and truck driver scheduling problems[END_REF] and [START_REF] Tilk | Bidirectional labeling for solving vehicle routing and truck driver scheduling problems[END_REF] do not include constraints (iv) and (v). Given that we consider a time horizon of 5 days, we do not include the rules for weekly limits on working time, driving, and rest period between weeks as well as most authors. As stressed in [START_REF] Goel | Legal aspects in road transport optimization in Europe[END_REF], night work is not profitable compared to day work, which justifies not considering night work. In this work, we propose an exact CP-based formulation that defines driving periods, working periods, breaks, waiting times, and rest periods according to EU regulations, respecting the visit order given by the route and the customers' time window.

Constraint Programming Model

The CP model is based on the evaluation of one sequence 𝜎 of customers that starts and ends at the depot, and compute for each customer 𝑖 ∈ 𝜎: the arrival time (𝐴 𝑖 ); the starting time of the service (𝑆𝑡 𝑖 ); the finishing time (𝐹𝑡 𝑖 ); the departure time (𝐷 𝑖 ); the duration of the break before the service (𝐵𝑓 𝑖 ) and after the service (𝐵𝑎 𝑖 ). For each customer 𝑖, we consider a service time 𝑝 𝑖 , a time window [𝑒 𝑖 , 𝑙 𝑖 ], and a transportation time 𝑇 𝑖,𝑗 to go from customer 𝑖 to 𝑗. Figure 1 presents an example feasible solution. The proposed formulation uses a modeling strategy based on set variables definition, which consists of defining subsets of customers with no more than 4.5 hours of driving, subsets no more than 6 hours of working time, and so on. The experiments have been carried out on a subset of 29 instances considering both makespan minimization and completion time. The instances, results and solutions, including an illustrative scheme of an optimal solution, are available on https://perso.isima.fr/~phlacomm/site3/CP_Roadef_2021.html.

Concluding remarks

This work presents the first approach to solve the TDSP using a CP-based approach. The proposed method seems to be well tuned for the problem, which is strongly constrained. A large majority of instances are solved to their optimality in less than 10 seconds. We are currently developing a timeefficient heuristic that will be used to generate an initial solution to be an input to the CP model and then accelerate its convergence to the optimal solution. We are also developing a second CP model based on automata scheme, which has been extensively studied recently. As presented by [START_REF] Goel | Legal aspects in road transport optimization in Europe[END_REF], in a significant number of cases, there is no feasible solution if night work is not considered. For this reason, we the importance of including the possibility of night work in future works.

Figure 1 .

 1 Figure 1. Description of a feasible solution


Aiman Ashmawy
email: aimanashmawy@yahoo.com.

Luc Gabolde
email: luc.gabolde@cnrs.fr.

Damien Laisney
email: dlaisney@gmail.com.

Dietrich Raue
email: dietrich.raue@uni-leipzig.de.

F Laisney

Fr Leclère

Payraudeau

PRELIMINARY RESULTS ON THE STUDY OF THE ORIENTATION OF THE TEMPLE OF RA-ATUM AT HELIOPOLIS AND THEIR HISTORICAL IMPLICATIONS

A GPS campaign of measures on the site of Helioplis, undertaken in order to document precisely the orientation of the remaining structures of the temple of Atum and to determine the azimuth of its axis, has provided us with improved data. These allowed us to formulate a hypothesis about the date of the temple's foundation ceremony and its direct connexion with the sun rise on the date recorded in the Berliner Leather Roll during the reign of Senuusret I

Prolegomene

The study of the Egyptian temples' orientation is a field of researches which has already produced fruitful results 5 . However, reliable an accurate data on the precise azimuth of the archaeological remains is required before taking into account the possibility that this orientation was connected with potential astronomical events. A program labelled OrTempSol in the framework of the Labex-Archimede at Montpellier, led by L. Gabolde, was thus launched in 2013 with the aim to determine precisely the orientation of some of the Egyptian temples devoted to solar deities, along the same line of work already accomplished at Karnak 6 and at Tell el-Amarna 7 . The program focuses specifically on the temple of Atum at Heliopolis and the temple of Amun-Ra at Tanis 8 . The present article provides and summarizes the preliminary results obtained at Heliopolis.

Aknowledgements

The mission was conducted with the financial support of the Labex-Archimede 9 . It benefitted of the scientific and logistical support of the joined mission of the Ministry of Antiquities of the Arab Republic of Egypt and the Leipzig University Museum at Matariya / Heliopolis, of which it was part of, under the direction of Aiman Ashmawy and of Dietrich Raue. A differencial GPS was very kindly lent by the IFAO.

The surveying operations carried out on-site (fig. 1)

The mission was conducted at Heliopolis from the 2 nd to the 4 th March 2014. Participants were L. Gabolde and D. Laisney with the extensive collaboration of the members of the Egyptian-German team.

Significant topographical points were taken on various parts of the site with the differential GPS, 170 :

-56 on the western part which may correspond to the entrance -13 on the remains of the two southern precinct walls -6 on the standing obelisk of Senusret I -1 on the naos base near the obelisk -2 at the limits of the "high sand" -8 on the gate of Ramses III at Tell el Hisn -35 on the northern ruins of Tell el Hisn, on the site of the column of Menrenptah and on the remaining portion of the precinct wall.

-Existing stations were also recorded and reported on the new topographical grid.

The historical records and surveys

Various plans generated during previous archaeological or historical researches were gathered and scanned in order include them in the new grid : Description de l'Egypte, Antiquités V, pl. 26, 1. Ravioli 1841 (Raue, Heliopolis, pl. 5) Hekeykian (British Library Additional Manuscripts 37458. 20 The new archaeological grid A new archaeological map was thus drawn by D. Laisney compiling the old and new data and providing the orientation of various structures (fig. 2)

Souk al-Khamis

Récolement des plans : -des fouilles de A.A. Saleh.

-des fouilles de la Mission Egypto-Allemande.

-du survey géophysique de T. Herbich. The results of the study of the orientations of the archaeological structures at the site.

The data related to the topographical orientation of the different archaeological structures at the site were then noted in detail on the new grid (fig. 3) The precise orientation of the surveyed structures is summarized in the following table 1. Among this series of measures, we have isolated those which are the most useful for our topic (i.e. the orientation of the temple of Atum, especially the buildings of Senustret I and the New Kingdom structures) and we balanced them taking into account their proper individual reliability. The historical issues The importance of the different remains for our own set of problems has now to be evaluated. First we must be aware that, though the religious occupation of the site may date back to the prehistoric times, all the documents of the Old Kingdom discovered on-site were found in a reused context 11 .

Site

Thus, the oldest remain preserved and visible in situ appears to be the obelisk which dates to the reign of Senusret I. This monument was part of a huge building or rebuilding program that was launched by this king at Heliopolis. This wide-ranging program is known to us thanks to the Berlin Leather Roll and through the Annals of Senusret I found at Bab el Tawfiq. This abundant documentation led us to specifically focus the potential astronomical researches on this epoch and on this reign.

From the Berlin Leather Roll 12 we know that the foundation of a new temple at Heliopolis was decided in year 3, III rd month of the inundation season (akhet), day, 8; the Annals of Bab el-Tawfiq are not dated but from the mentions of the pair of obelisks and because of the connexion between the obelisks and the jubilee (mentioned on the shaft of the still standing one), we can assume that the pair of monoliths was probably erected around year 30-31 of the king 13 .

Relative location of the standing obelisk in regard to the temple's axis

However, the question of the location of the standing obelisk "vis à vis" the temple has to be solved in order to correctly place the axis of the temple. Joseph Hekekyan in 1851-55 and David Jeffreys in 1999 14 had concluded from their observations that the obelisk was most probably the northern one of a pair on the west-east axis (that is the left-hand one when entering from the west). They had in fact equated a structure found 17 m south of the standing obelisk with the base of its counterpart. Therefore, they drew an axis south of the standing obelisk. However, this situation is in obvious contradiction with the contemporary customs concerning the orientation of the royal inscriptions on each side of an obelisk, in respect to the end of the temples: according to the inscriptions, the obelisk should be either the right one of a pair marking an access west-east, or the left one of an access south-north, with no other possibility (fig. 4). D. Jeffrey then supposed that the temple could have been entered from the east and/or that the obelisk could have been rotated on its base later on. However, a closer look at what Hekekyan had found 17 m South of the obelisk, reveals that it could not be a pedestal for an obelisk (fig. 5). It is in fact a much thinner base for a naos with an engraving on the upper surface which was carved to match a more or less temple-shaped wooden shrine with a pylon façade.

Fig. 5. The structure found south of the standing obelisk which is not the pedestal of its counterpart but the base of a temple-shaped naos (photo L. Gabolde).

Subsequently, there is no more reason not to equate the standing obelisk with the southern one, that is the right-hand one when entering the temple from the west, as required by the texts orientation; nor need one suppose the obelisk was rotated.

It is appropriate to mention here the fact that the obelisk was raised by around 2,50m in 1957 by the Krupp company on behalf of the Egyptian Antiquities Organization [START_REF] Habachi | The Obelisks of Egypt, Skyscrapers of the Past[END_REF] , because it was threatened by the high water table. However this purely vertical motion of the monolith was accomplished with hydraulic cylinders. This operation did not affect, albeit very marginally, its orientation. It thus remains a good clue as to the orientation of Senusret Is' buildings.

Besides the obelisk, New-Kingdom mud-brick walls have equally survived on the southern border of the site. Their orientation has been measured and altogether they always point to an azimuth of around 107° with very minor discrepancies; these data were inserted in table 2.

Finally, as already mentioned, excavations carried out in 2017 have brought to light the remains of a limestone wall located to the west-northwest of the obelisk, and oriented east-west. Its azimuth appeared to be close to 106,50°.

The main orientation of the temple of Atum of Senusret I can thus be provisionally established at around :

107° (± 2/3°)
The vertical angle of the eastern horizon line in that direction (i.e. towards the sun rise) can be determined : 1. by the altitude of the soil dating to Senusret I (z = 13.00 m a.s.l.) [START_REF] Jeffrey | An Account of Some Researches Near Cairo Undertaken with the View of Throwing Light upon the Geological History of the Alluvial Land of Egypt. I[END_REF] augmented by the altitude of the observer's eye (+ 1.50 m), resulting in z=14.50 m. 2. By the distance of the horizon (14 000 m) and its height (180 m).

The vertical angle (α) of observation is then calculated as follows : Tangent (α) = (180-14.50 )/14 000 = 0.011821429 Angle (α) = arc-tangent (0.011821429) = 0° 40' 38.23" For such an angle (α), the refraction is of 0° 29' 26.61", implying an actual observation angle of 0° 40' 38.23" -0° 29' 26.61" = 0° 11' 11.62".

In case of a solar observation, half of the solar diameter (0° 16') has also to be subtracted, resulting in a height under the horizon of 0° 11' 11.62" -0° 16' 00'' = -0° 4' 48.38".

The sun rise at Heliopolis in the reign of Senusret I.

Because the Lord of the temple, Ra-Atum, was a prominent solar deity, it is very likely that the azimuth of the sanctuary corresponds with a specific sun rise, as it was the case at Karnak 17 , at Tell al-Amarna 18 and Tanis 19 .

As the reign of Senusret I marked a major step in the building history of Heliopolis and, so far, provides the oldest architectural remains preserved in-situ we have chosen to focus our researches on this reign, and especially on the year 3 (8 th day of the III rd month of the akhet season) of this king -which, as recorded in the Berlin Leather Roll, corresponds to the first building activity of Senusret I on the site -, in order to evaluate the potential concordances between the azimuth of the temple and the sun rise.

The reign of Senusret I in absolute chronology

The first question to solve is the calibration of the reign of Senusret I in absolute chronology. The anchor date for such a research is the heliacal rising of Sirius recorded in the year 7 of Senusret III and reported in the Illahoun Archive on the IV th month of the peret season, 17 th day [START_REF] Krauss | Egyptian Sirius/Sothic Dates[END_REF] . The first apparent difficulty lies in the determination of the number of years filling the gap between the date of Illahun and the date recorded in the Berlin Leather Roll in year 3 of Senusret I, as the exact length of the intermediate reigns is not definitely fixed. We have estimated it here at 89 years [START_REF] Cl | Based of the following regnal years succession : year 45 of Senusret I= year 1 of Amenemhet II ; year 35 of Amenemhet II = year 1 of Senusret II ; year 8 of Senusret II = year 1 of Senusret III. Coregencies hypothesis have been here discarded, following the convincing conclusions of R. Delia, 'A New Look at Some Old Dates : A Reexamination of Twelfth Dynasty Doubled Dated Inscriptions[END_REF] . The second difficulty consists in finding the exact place of this reign in the second millennium BC. It depends, in fact, on which chronological theory (high, medium or low) is adopted for the fixing of the Illahun Sothic date. We shall examine here the results provided by the high chronology of U. Luft and those provided by the low chronology of R. Krauss. In the chronological frame of U. Luft [START_REF] Luft | Remarks of a Philologist on Egyptian Chronology[END_REF] the heliacal rising of Sirius in year 7 of Senusret III occurred on the 17 th July (in Julian calendar = 1 st July in Gregorian calendar) 1866 BC (=-1865). The year 3 of Senusret I would then correspond to 1955 BC (-1954).

In the chronological frame of R. Krauss 23 the heliacal rising of Sirius in year 7 of Senusret III occurred 35 years later, in 1831 BC. The year 3 of Senusret I would then correspond to 1920 BC (= -1919). Now we can check the date of the sun rise on the temple axis in both systems. In 1955 BC (= -1954), following the chronological frame of U. Luft, the sun rises in the axis of the Heliopolis temple (at an azimuth of 106° 59' 33.6") on the 25 th February (in Julian calendar, corresponding to the 8 th February in Gregorian calendar). A retro-calculation based on the date of Censorinus shows that this day corresponds to the 3 th day of the III rd month of the akhet season, i.e. 5 days before the date recorded in the Berlin Leather Roll.

In 1920 BC (= -1919), if we follow the chronological frame of R. Krauss, the sun rose in the axis of the Heliopolis temple (at an azimuth of 107° 10' 29.7") on the 24 th February (in Julian calendar, corresponding to the 7 th February in Gregorian calendar). A retro-calculation based on the date of Censorinus shows that this day corresponds to the 11 th day of the III rd month of the akhet season, i.e. 3 days after the date recorded in the Berlin Leather Roll.

It is quite remarkable that these two evaluations appear to be very close -the first 5 days before and the second 3 days after -to the date registered in the Berlin Leather Roll as this document had genuinely recorded the day chosen by Senusret I to convene with his courtiers in order to specifically decide on and implement the rebuilding of the Atum temple at Heliopolis.

It is thus very tantalizing to propose an intermediate chronological frame, between 1955 and 1920 BC, in which the determination of the temple's axis on the sun rise during the foundation ceremony would have followed immediately the decision of the king to rebuilt the temple. Empirically, the date which better fits these requisits appears to be Monday the 26 th February in Julian calendar (= 9 th February in Gregorian calendar) 1936 BC (= -1935). In the Egyptian calendar, retro-calculated from the Censorinus date onwards, this day corresponds with the 9 th day of the III rd month of the akhet season i.e. the days after the meeting of Senusret I with his courtiers. Astronomical computer calculations show that the sun rose on this very day at Heliopolis at an azimuth of 106° 50' 46,6'' (fig. 6), a result which fits very well with the topographical data we have recorded above.

Note that, interestingly enough, this day corresponds with a new-moon, the new crescent being visible at twilight24 , a circumstance considered as propitious for the foundation ceremonies as attested for the foundation date of the Akhmenu of Thutmose III at Karnak or that of the pylon of Ramses II at Luxor25 .

Conclusions

The new survey of the site and the recent excavations west of the obelisk have provided us with rather precise data regarding the original orientation of the temple of Atum, especially for the one rebuilt by Senustret I in the 3 rd year of his reign.

Though there remain some uncertainties (length of the intermediate reigns between Senusret I and III; exact position of the Illahun Sothic date in absolute chronology), we could find a remarkable convergence between the orientation of the Atum temple and the azimuth of the sun rise at the date recorded in the Berlin Leather Roll during the reign of Senusret I. This conjunction can hardly be considered as a mere coincidence. Moreover, this date was of particular significance for the king as it was the second anniversary of this father's assassination and of his own accession to the throne. And, in that respect, we can add that it was undoubtedly not a coincidence that, 16 years later, the temple of the same Senusret I at Karnak was clearly aligned, on purpose, on the sunrise at winter solstice.

The most enciting chronological hypothesis for Heliopolis is to fix the foundation ceremony on the 26 th February in Julian calendar (= 9 th February in Gregorian calendar) 1936 BC (= -1935) at dawn. This day corresponds with the 9 th day of the III rd month of the akhet season i.e. the day after the meeting between Senusret I and his courtiers. It was a new moon.

If this hypothesis were to be confirmed and widely accepted it could constitute a new milestone for the Egyptian chronology.

  -21) Lepsius, Denkmaeler, I, pl. 55. Petrie's excavations, Heliopolis, Pl. I & II. Abd el-Aziz Saleh, Tell el Hisn, pl. VI, fig. 6. Cadastral map of Cairo. Survey of Egypt 1/5 000 1977-78 Views from Googlemap. archéologiques, hypothèses astronomiques et conséquences historiques', in Hommages à Christiane Zivie-Coche in print. 9 Labex-Archimede Montpellier, program 'Investissement d'Avenir', ANR-11-LABX-0032-01 AAP 2, 2014, Axe 2 'Pouvoirs : Espaces de pouvoirs et constructions territoriales'; 'OrTempSol' project (Orientation des Temples à divinité Solaire en Égypte).

Fig. 1 .

 1 Fig. 1. Map showing the location of the structures surveyed by the mission OrTempSol.

  1

Fig. 2 .

 2 Fig. 2. The new archaeological grid realized by D. Laisney (OrTempSol Mission, Labex Archimède, Montpellier)

N

  ob éli sq ue : 10 7, 63 9 °enc ein te su d du No uv el Em pir e (fa ce su d) 10 7, 00 3 °enc ein te su d de la Ba sse Ep oq ue (fa ce no rd ) 10 6, 51 8 °bas e ob éli sq ue : 10 6, 98 9 °bas e en qu ar tz ite 11 2Equidistance des courbes de niveau : 1 m. Système de coordonnées : WGS84, projection UTM zone 36 enceintes restituées carroyage géophysique (T. Herbich, 2014) canaux actuels (IGN, 1978) canaux au 19e s. (J. Hekekyan, 1851) chemins au 19e s. (J. Hekekyan, 1851)

Fig. 3 .

 3 Fig. 3. Sites of the different archaeological structures which orientation could be determined and recorded during the 2014 mission.

Fig. 4 .

 4 Fig. 4. The two location possibilities of the sanctcuary vis à vis the obelisks in regard to the orientations of the inscriptions on the standing obelisk.

  11 R. Weill, 'Monuments royaux des premières dynasties. V. Un temple de Noutirkha-Zosir à Héliopolis', Sphinx 15, (1911-12), 9-19, sp. 9-10 ; K. Martin, Ein Garant-symbol des Lebens. Untersuchungen zu Ursprung und Geschichte der alta'gyptischen Obelisken bis zum Ende des Neuen Reiches, HÄB 3 (Hildesheim 1977) 42-43, fig. 3 ; L. Habachi, The Obelisks of Egypt (London, 1978), 42-43, fig. 7. 12 Berlin inv. P.3029 : A. de Buck, The Building Inscription of the Berlin Leather Roll, in : AnOr 17 (1938), 48-57 ; H. Goedicke, 'The Berlin Leather Roll (P Berlin 3029)', Festschrift zum 150jährigen Bestehen des Berliner Ägyptischen Museums, Mitteilungen aus der Ägyptischen Sammlung 8, Staatliche Museen zu Berlin (Berlin, 1974), 87-104 ; M. Lichtheim, Ancient Egyptian Literature I, The Old and Middle Kingdoms (Berkeley-Los Angeles-London, 1973), 115-118. 13 L. Postel, I. Régen, 'Annales héliopolitaines de Sésostris I er ', BIFAO 105 (2005), 237, 266, n. kk ; 273. 14 D. Jeffreys, 'Joseph Hekekyan at Heliopolis', in : A. Leahy/J. Tait (eds), Studies in honour of H.S. Smith. EES, Occasional Publication 13, (London, 1999) 160, 166-168, fig. 3, 4 ; followed by F. Contardi, Il naos di Sethi I da Eliopoli: un monumento per il culto del dio Sole (CGT 7002). Catalogo del Museo Egizio di Torino, serie primamonumenti e testi. (Milan, 2009), 17.

Fig. 6 .

 6 Fig. 6. Simulation on Voyager 4 ™ of the sun rise at Heliopolis on the 26 th February in Julian calendar (= 9 th February in Gregorian calendar) 1936 BC (= -1935)

CaptionsFig. 1 .

 1 Fig. 1. Map showing the location of the structures surveyed by the mission OrTempSol. Fig. 2. The new archaeological grid realized by D. Laisney (OrTempSol Mission, Labex Archimède, Montpellier) Fig. 3. Sites of the different archaeological structures which orientation could be determined and recorded during the 2014 mission. Fig. 4. The two location possibilities of the sanctuary vis à vis the obelisks in regard to the orientations of the inscriptions on the standing obelisk. Fig. 5. The structure found south of the standing obelisk which is not the pedestal of its counterpart but the base of a temple-shaped naos (photo L. Gabolde). Fig. 6. Simulation on Voyager 4 ™ of the sun rise at Heliopolis on the 26 th February in Julian calendar (= 9 th February in Gregorian calendar) 1936 BC (= -1935).

Site Azimut (in dec. Degrees) Kind of azimut determination Number on the map Sources

	South New Kingdom Precinct wall	106.704	Graphical measure	8	W. M. Fl. Petrie (1911-1912)
	South Late Period precinct wall (northern face)	106.518	Measured in situ in 2014	9	Excavations Ashmawy-Raue (2014); survey by D. Laisney
	South Late Period precinct wall (western part)	104.905	Graphical measure	9	W. M. Fl. Petrie (1911-1912)
	South precinct wall (western part)	103.207	Graphical measure	8 et 9	J. Hekekyan (1851)
	South precinct wall (western part)	110.007	Graphical measure	8 et 9	Description de l'Égypte (1798-1802)
	South Late Period precinct wall (eastern part)	108.685	Graphical measure (turned by 90°)	10	W. M. Fl. Petrie (1911-1912)
	South precinct wall (eastern part)	106.334	Graphical measure	10	Description de l'Égypte (1798-1802)
	Eastern precinct wall	106.706	Graphical measure (turned of 90°)	11	W. M. Fl. Petrie (1911-1912)
	Eastern precinct wall	105.765	Graphical measure (turned by 90°)	11	Description de l'Égypte (1798-1802)
	Northern precinct wall (south of Tell al-Hisn)	102.810	Graphical measure	15 et 16	J. Hekekyan (1851)
	Northern precinct wall (southern wall)	107.385	Graphical measure	15	W. M. Fl. Petrie (1911-1912)
	Northern precinct wall (northern
	wall)	105.988	Graphical measure	16	W. M. Fl. Petrie (1911-1912)
	Quartzite base ( Souk al-Khamis)	112.986	Measured in situ in 2014 (turned by 90°)	2	Excavations Ashmawy (2007-2008), survey by D. Laisney
	Northern precinct wall (western part)	112.748	Graphical measure	12a	Description de l'Égypte (1798-1802)
	Northern precinct wall (eastern part)	108.726	Graphical measure	12b	Description de l'Égypte (1798-1802)
	Northern precinct wall	118.000	Data published by W. M. Fl. Petrie	12a et 12b	W. M. Fl. Petrie (1911-1912)
	Western precinct wall (northern part)	133.609	Graphical measure (turned by 90°)	13	Description de l'Égypte (1798-1802)
	Western precinct wall (northern part)	131.977	Graphical measure	13	W. M. Fl. Petrie (1911-1912)
	Gate of Ramses III (Tell al-Hisn)	137.213	Measured in situ in 2014	3	Excavations A. A. Saleh (1976-1981)
	Gate of Ramses II (Tell al-Hisn)	129.833	Measured in situ in 2014 (turned of 90°)	4	Excavations A. A. Saleh (1976-1981)
	Temple (Tell al-Hisn)	125.364	Measured in situ in 2014	5	Excavations A. A. Saleh (1976-1981)
	Gate of Ramses II (Tell al-Hisn)	126.990	Measured in situ in 2014	6	Excavations A. A. Saleh (1976-1981)
	Axis of the obelisk (Senusret I) Western precinct wall, southern part	107.639 84.662	Measured in situ in 2014 Graphical measure (turned by 90°)	1 14	Survey by D. Laisney Description de l'Égypte (1798-1802)
	Base of the obelisk (modern) Western precinct wall, southern part Axis of the temple south of the obelisk (north of the obelisk) Corrected axis of the temple Western precinct wall, southern part	106.989 92.618 109.591 107.004 89.499	Measured in situ in 2014 Graphical measure Graphical measure Graphical measure Graphical measure	1 14 1 1 14	Survey by D. Laisney J. Hekekyan (1851) J. Hekekyan (1851) L. Horner (1855) W. M. Fl. Petrie (1911-1912)
	Limestone wall (west of the obelisk)	105.205	Measures deducted from the survey in situ in 2014	7	Geophysical survey by T. Herbich (2014)
	South New Kingdom Precinct wall (southern face)	107.003	Measured in situ in 2014	8	Excavations Ashmawy-Raue (2014); survey by D. Laisney

Table 1 .

 1 The geodesic orientations of the various structures identified on-site or adjusted on the grid from earlier publications (the decimalsThe mission of 2017 10 has led to the discovery of the remains of a new segment of limestone wall to the west-northwest of the obelisk, adding a new measure to the series :

	Segment of limestone wall found in situ in march 2017	≈ 106.50	Measured in situ by D. Raue 2017	7	Excavations SCA / Mus. Univ. Leipzig (2017)

are only for calculation and they have no significance for the exactness of the buildings' orientation taken into account the actual accuracy of the field measures and the poor state of the remains.)

Table 2

 2

		Azimut (in dec. degrees)	Kind of azimut determination	Number on the map	Sources
	Axis of the obelisk (Senusret I)	107.639	Measured in situ in 2014	1	Survey by D. Laisney
	Corrected axis of the temple (north of the obelisk)	107.004	Graphical measure	1	L. Horner (1855)
	Limestone wall (west of the obelisk)	105.205	Measures deducted from the survey in situ of 2014	7	Geophysical survey by T. Herbich (2014)
	Segment of limestone wall found in situ in march 2017	≈ 106.50	Measured in situ 2017	7	Excavations SCA / Mus. Univ. Leipzig (2017)
	South New Kingdom Precinct wall (southern face)	107.003	Measured in situ in 2014	8	Excavations Ashmawy-Raue (2014) ; survey by D. Laisney
	South New Kingdom Precinct wall	106.704	Graphical measure	8	W. M. Fl. Petrie (1911-1912)
	South Late Period precinct wall (northern face)	106.518	Measured in situ in 2014	9	Excavations Ashmawy-Raue (2014) ; survey by D. Laisney
	South Late Period precinct wall (western part)	104.905	Graphical measure	9	W. M. Fl. Petrie (1911-1912)
	South precinct wall (western part)	103.207	Graphical measure	8 et 9	J. Hekekyan (1851)
	South precinct wall (western part)	110.007	Graphical measure	8 et 9	Description de l'Égypte (1798-1802)
	South Late Period precinct wall (eastern part)	108.685	Graphical measure (turned by 90°)	10	W. M. Fl. Petrie (1911-1912)
	South precinct wall (eastern part)	106.334	Graphical measure	10	Description de l'Égypte (1798-1802)
	Eastern precinct wall	106.706	Graphical measure (turned by 90°)	11	W. M. Fl. Petrie (1911-1912)
	Eastern precinct wall	105.765	Graphical measure (turned by 90°)	11	Description de l'Égypte (1798-1802)
	Northern precinct wall (south of Tell al-Hisn)	102.810	Graphical measure	15 et 16	J. Hekekyan (1851)
	Northern precinct wall (southern wall)	107.385	Graphical measure	15	W. M. Fl. Petrie (1911-1912)
	Northern precinct wall (northern
	wall)	105.988	Graphical measure	16	W. M. Fl. Petrie (1911-1912)
	Northern precinct wall (eastern part)	108.726	Graphical measure	12b	Description de l'Égypte (1798-1802)
	Northern precinct wall	118. 000	Data published by W. M. Fl. Petrie	12a et 12b	W. M. Fl. Petrie (1911-1912)

. The geodesic orientations of the structures in direct relation with the orientation of the temple of Atum of Senusret I (the decimals are only for calculation and they have no significance for the exactness of the buildings' orientation)

Since 2016, the mission has worked in cooperation with Kai-Christian Bruhn and the University of Applied Sciences / Mainz.

The actual neomenia had occurred on the

th February (Julian calendar) at dawn. 25 Akhmenu : Urk. IV, 836,1-4 ; see J. von Beckerath, 'Ein Wunder des Amun bei der Tempelgrundung in Karnak', MDAIK 37 (1981) 41-51 ; Pylon of Ramses II at Luxor temple: KRI II, 346, 10-11 and KRITA II, 184.


J Cotxet

F Gutty

G Baili

L Morvan

D Dolfi

I Sagnes

G Beaudoin

K Pantzas

S Guérandel

D Holleville

G Lucas-Leclin

S Janicot

Progress on a Highly Compact Cesium CPT Clock Based on a Dual-Frequency VECSEL

Keywords: dual-frequency VECSEL, cesium, CPT I

We developed and tested a miniature optical bench to implement a cesium CPT clock based on a Vertical External Cavity Surface Emitting Laser (VECSEL) that provides two orthogonally polarized frequencies separated by a difference of 9.2 GHz. This work presents characterizations of the miniature optical power stabilization set-up as well as preliminary investigations of the VECSEL properties.

INTRODUCTION

One of the promising solutions for cesium (Cs) compact clocks is based on Coherent Population Trapping (CPT), where atomic interrogation is usually carried out by two phase-locked lasers with a frequency difference of 9.192 GHz for 133 Cs [START_REF] Tricot | Analyse et réduction des sources d'instabilité de fréquence dans une horloge CPT compacte[END_REF] or by an externally-modulated beam at half this frequency [START_REF] Hafiz | Toward a High-Stability Coherent Population Trapping Cs Vapor-Cell Atomic Clock Using Autobalanced Ramsey Spectroscopy[END_REF]. These laboratory clocks show frequency stability of few 10 -13 at 1 s of integration time, but their dimensions are not suitable for on-board applications yet. In order to reduce the size and complexity of these systems, we propose to implement a highly compact clock based on a dual-frequency dual-polarisation VECSEL (DF-VECSEL) associated to a miniature optical bench with similar clock frequency stability and drastically reduced size.

II. RESULTS

A miniature clock optical bench (i.e. less than 10 L for the physics package) has been designed and developed in collaboration with the French company Kylia. The clock optical and optoelectronic functions are implemented with discrete micro-optics assembled with a robust bonding technology (Fig. 1). The power stabilization stage adjusts the transmission of an acousto-optic modulator (AOM) comparing the signal to a voltage reference. This set-up has been extensively characterized with a monomode laser. The Relative Intensity Noise (RIN) of the laser is reduced by more than 20 dB at low frequencies and reaches a level below -155 dB/Hz between 100 Hz and 100 kHz, close to the voltage reference noise used for the lock loop (Fig. 2). The mid-term relative power fluctuations remain below 10 -5 over 3 h of integration time when the stabilization is on (Fig. 3).

Discrepancies between outloop and inloop optical beams stability are explained by thermal drift of optical coatings. The industrial DF-VECSEL prototype under study (Fig. 4) to inject the clock bench provides two linearly polarized orthogonal modes at 852 nm with adjustable frequency difference around 9.2 GHz. An optimized architecture of the pumping scheme has been developed to obtain in-phase correlated intensity noises between the two modes as well as low noise transfer from the pump laser to the VECSEL eigenstates [START_REF] Gredat | Optimization of laser dynamics for active stabilization of DF-VECSELs dedicated to cesium CPT clocks[END_REF]. First measurements show in-phase correlations between the two frequencies with a degree of correlation above 0.6 (Fig. 5).

III. DISCUSSIONS

The miniature power stabilization stage shows robust performances that are comparable to usual laboratory set-up. These results are compatible with clock stability aimed at short and mid-term [START_REF] Tricot | Power stabilization of a diode laser with an acousto-optic modulator[END_REF].

Mechanical stability of the cavity elements is now crucial to ensure in-phase correlated eigenstates of the DF-VECSEL. Under these conditions, optical power fluctuations reduction can be maximized.

IV. CONCLUSIONS

We developed the first stage of a miniature optical bench for a CPT Cs clock. The optical power stabilization demonstrated great reduction of the fluctuations.

We also started the implementation of a prototype of the DF-VECSEL, emitting in-phase correlated modes at 852 nm.

Optical power stabilization of the dual-frequency VECSEL is now in progress. Analysis of laser beams correlation and its impact on the power stabilization performances will be conducted. RIN reduction and mid-term power stability will be presented at the conference.

Fig. 1 :

 1 Fig. 1: Miniature optical bench for the optical power stabilization. AOM: Acousto-optic modulator; BS: Beamsplitter; PD: Photodetectors.

Fig. 2 :

 2 Fig. 2: Relative intensity noise of a monomode laser beam. Grey line: measurement floor.

Fig. 3 :

 3 Fig. 3: Relative power stability of the laser beam. Inloop beam: signal use for the stabilization; outloop beam: exploitable light for the clock.

Fig. 4 :

 4 Fig. 4: Design of the dual-frequency VECSEL. Red (resp. orange) beam represents the x-polarized (resp. y-polarized) mode. Purple beams are for pump laser. PBS: Polarizing beamsplitter; EO: Electro-optic crystals.

Fig. 5 :

 5 Fig. 5: Amplitude and phase of intensity noise correlation between the two polarizations emitted by the VECSEL.

ACKNOWLEDGMENT

This work was partly supported by the french RENATECH network. Acknowledgment for ANR and french MoD for their support within CHoCoLA Project.