Cécile Hérivaux
email: c.herivaux@brgm.fr

Jean-Daniel Rinaudo
email: jd.rinaudo@brgm.fr

Marielle Montginoul
email: marielle.montginoul@irstea.fr

Exploring the potential of groundwater markets in agriculture: results of a participatory evaluation in five French case studies

Keywords: Water market, Cap and trade, Participatory foresight, Groundwater, Agriculture, Irrigation, France

We used a participatory foresight method for assessing if, and how, groundwater markets could be incorporated into local groundwater management policies. We propose an institutional setup adapted to the French water policy context, with a cap and trade scenario introducing groundwater markets in the agricultural sector between now and the 2035 horizon. Considering the local hydrogeological characteristics, we applied this method to five French groundwater basins, and then analysed the public perception of our scenario by organizing 16 half-day workshops, involving a total of 44 institutional stakeholders and 80 farmers. Overall, almost half of the participants were opposed to the introduction of groundwater markets for various ethical, economic and technical reasons. Many of the preconditions for water trading are still far from being met, and major social and economic risks are anticipated. However, our results also suggest that there might be scope for developing groundwater markets compatible with

French water policy at a local scale; the preconditions for this are that specific local hydrogeological and agricultural situations are taken into account, and that a participatory process is developed, involving institutional stakeholders and farmers.

INTRODUCTION

Since the mid-1990s, mainstream environmental and resource economists have unfailingly promoted the development of water markets for reallocating water resources and regulating pollution control [START_REF] Rosegrant | Markets in tradable water rights: potential for efficiency gains in developing country water resource allocation[END_REF]Livingstone, 1995). This approach is based on establishing an aggregate cap on water-resource abstraction, on allocating individual abstraction rights to users, and on making these rights tradable. The argument, reflecting standard economic theory, is that markets are more cost-effective than command-and-control regulation for reaching an optimal allocation of limited renewable stocks, and that they are more flexible for adapting to an ever-changing economic and environmental context [START_REF] Young | Designing water abstraction regimes for an ever-changing and ever-varying future[END_REF]. The implementation of a system of tradable water rights was strongly supported by international financial institutions in the 1990s (World Bank, 1993;[START_REF] Thobani | Formal water markets: why, when, and how to introduce tradable water rights[END_REF], and has been adopted and implemented in various developed and developing countries [START_REF] Grafton | Integrated assessment of water markets: a cross-country comparison[END_REF]Easter and Huang, 2014). Historically, water markets were first established for managing surfacewater resources, in regulated river basins with significant infrastructure for storing and transferring water. More recently, their use has been extended to groundwater resources in several western states of the USA and Australia [START_REF] Thompson | Evidence supporting Cap and Trade as a groundwater policy option for reducing irrigation consumptive use[END_REF][START_REF] Lawson | Overcoming impediments to groundwater trading in Australia[END_REF][START_REF] Skurray | Institutional impediments to groundwater trading: the case of the Gnangara groundwater system of Western Australia[END_REF]Brozovic and Young, 2014;[START_REF] Wheeler | Lessons to be learned from groundwater -Trading in Australia and the United States[END_REF].

Water markets, when applied to groundwater management, do not always function as predicted, because several barriers may impede their development or operation [START_REF] Bauer | Bringing water markets down to earth: The political economy of water rights in Chile, 1976-1995[END_REF][START_REF] Bauer | Against the current: privatization, water markets, and the state in Chile[END_REF][START_REF] Skurray | Hydrological challenges to groundwater trading: Lessons from south-west Western Australia[END_REF][START_REF] Sandel | The moral economy of speculation: Gambling, finance, and the common good. The Tanner Lectures on Human Values[END_REF]Easter and Huang, 2014;[START_REF] Wheeler | Lessons to be learned from groundwater -Trading in Australia and the United States[END_REF]. In many groundwater basins where water markets were introduced, transactions remain limited and far below expected levels. This may be for different reasons, including an inadequate institutional framework, high transaction costs, overestimated caps (initial over-allocation), and problems of compliance and enforcement (Brozovic and Young, 2014). This has led to the need for a new approach to water markets by policy makers and managers.

It is thus clear that water markets are not a one-fits-all miracle tool that can be used by simply following a standard recipe from a Resource Economics handbook, and there is a growing recognition that these mechanisms cannot always be adapted to suit any hydrological and institutional context [START_REF] Green Nylen | Trading sustainably: critical considerations for local groundwater markets under the sustainable groundwater management act[END_REF][START_REF] Babbitt | Groundwater Trading as a Tool for Implementing California's Sustainable Groundwater Management Act[END_REF][START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF]. Furthermore, where they are deemed suitable, they must be carefully adapted to local socio-economic, institutional, environmental and cultural characteristics [START_REF] Babbitt | Groundwater Trading as a Tool for Implementing California's Sustainable Groundwater Management Act[END_REF]. As stressed by [START_REF] Tisdell | Attitudes toward water markets: an Australian case study[END_REF], water markets are unlikely to function optimally if social and cultural attitudes to trade are not duly considered. Stakeholders thus must be involved in the design of an institutional market set-up that best meets community needs.

Nonetheless, very little research has assessed or designed water markets with an active participation of stakeholders, in countries where such instruments are still in their infancy. Some studies have developed analytical frameworks for guiding allocation reforms (OECD, 2015), or, more specifically, for assessing if the administrative conditions for developing water-trading arrangements are met [START_REF] Wheeler | Developing a water market readiness assessment framework[END_REF]. While they represent a useful resource, such frameworks have not been used (to our knowledge) in the participatory design of water markets.

Other studies have used qualitative or quantitative surveys and workshops for analysing the stakeholders' willingness to adopt a new water-market instrument [START_REF] Zhang | Barriers to water markets in the Heihe River basin in northwest China[END_REF]Giannocaro et al., 2013;2016[START_REF] Lumbroso | Stakeholders' responses to the use of innovative water trading systems in East Anglia, England[END_REF][START_REF] Rahimova | Factors affecting water market acceptance: A case study of stakeholders in southern Alberta, Canada[END_REF], but then they did not involve stakeholders in the construction of a policy scenario.

Our research aimed at filling this gap by using a truly participatory research methodology, for assessing if and how water markets can be incorporated in a local groundwater management policy. A key assumption was that, given the political dimension of market instruments [START_REF] Heinmiller | The Politics of" Cap and Trade" Policies[END_REF], engaging all stakeholders involved in water use and management should help identifying three points: 1) The potential strengths and weaknesses of various forms of water-market mechanisms; 2) The preconditions for their effective implementation in each specific context; and 3) The potential barriers to acceptance and development. We also assumed that a combination of expert and lay knowledge will help when designing highly innovative institutional set-ups [START_REF] Rinaudo | The benefits of combining lay and expert knowledge for water management planning at the watershed level[END_REF][START_REF] Rinaudo | Envisioning innovative groundwater regulation policies through scenario workshops in France and Portugal[END_REF]. Stakeholder participation in the design of water-management instruments makes them more legitimate and thus more acceptable (OECD, 2015;Rinaudo et al., 2016b).

A second key assumption was that a long-term perspective is necessary when planning a groundwater market instrument with stakeholders [START_REF] Babbitt | Groundwater Trading as a Tool for Implementing California's Sustainable Groundwater Management Act[END_REF]; generally, several changes must be made to the water policy before trading can be considered. Therefore, we introduced the groundwater market as part of a broader cap and trade scenario through scenario workshops. Our study focused on France, where the idea of developing water markets has been discussed since the early 2000's, either in general terms or using modelling [START_REF] Strosser | Vers des marchés de l'eau en France ? Quelques éléments de réflexion[END_REF]Rinaudo et al., 2016a), but without involving stakeholders. We then tested the proposed methodology on five French groundwater basins.

The paper is organized as follows: Section 2 presents the methodological framework used for designing a tailor-made groundwater cap and trade policy scenario, and for assessing how it is perceived by local stakeholders. Section 3 provides background information on the French context and presents the cap and trade scenario and how it was adapted to each case study. Section 4 analyses and discusses the results of the scenario workshops. Section 5 concludes on the relevance of developing groundwater markets in the French context.

METHODOLOGICAL FRAMEWORK AND CASE STUDIES

The methodological approach comprised four main steps described below.

Step 1. Designing a cap and trade scenario

First, we designed a cap and trade scenario adapted to the French water policy context, which describes a potential pathway for allowing groundwater trading in the agricultural sector in France. In line with [START_REF] Wheeler | Developing a water market readiness assessment framework[END_REF] and OECD (2015), and based on a review of existing cap and trade policies in Chile [START_REF] Galaz | Stealing from the poor? Game theory and the politics of water markets in Chile[END_REF][START_REF] Bauer | Against the current: privatization, water markets, and the state in Chile[END_REF], Spain [START_REF] Rey | The Water markets in Spain: moving towards 21st Century mechanisms and approaches with 20th Century regulations[END_REF], the USA [START_REF] Howe | Policy issues and institutional impediments in the management of groundwater: lessons from case studies[END_REF][START_REF] Thompson | Evidence supporting Cap and Trade as a groundwater policy option for reducing irrigation consumptive use[END_REF] and Australia [START_REF] Boyd | Optimising sustainable use of groundwater: a challenge for science and water markets[END_REF]Brumley, 2004: Lawson et al., 2010;[START_REF] Hamilton | Addressing the challenges of groundwater trading in NSW[END_REF][START_REF] Ghd | A framework for managing and developing groundwater trading[END_REF], we identified three main components of the scenario (Fig. 1) and analysed the range of possible options for their definition. These components are summarized in Figure 1 and in the paragraphs below.

Fig. 1 Key components for designing a cap and trade policy scenario

General context

Several basic general conditions should be met before allowing farmers to trade water. First, the resource should be clearly delimited, its functioning should be understood, and abstraction properly monitored. This is essential for setting the cap, but also for controlling environmental consequences [START_REF] Skurray | Hydrological challenges to groundwater trading: Lessons from south-west Western Australia[END_REF].

The second condition is that water should be scarce, and considered as such by users and other stakeholders. Studies have shown that there may be a gap between experts' and users' perceptions regarding resource scarcity (Rinaudo et al., 2016b).

The third condition is that the proposed mechanism and the policymakers promoting it should be regarded as legitimate, i.e. having the users' trust and support. Compliance with the newly established allocation mechanism is clearly dependent upon these conditions.

Finally, trade only makes sense if there is a difference in marginal product value for the different users, generating opportunities for "win-win" voluntary exchanges of water-use rights. All these conditions must be met before policymakers can begin to envisage the possibility of implementing a cap and trade water policy.

Capping total water use for irrigation, defining water entitlements and initial allocations

Before implementing a cap and trade policy in the agricultural sector, total water use for irrigation (volume or total pumping rate) must be capped first. Two types of abstraction limits are needed (OECD, 2015): a long-term limit (the "cap") defines the maximum amount of water that can be abstracted from the groundwater resource; a shortterm limit (the "adjusted cap") defines the amount of water that can be abstracted within a specified period (e.g., a season or a year), depending on meteorological conditions and hydrological status. In parallel, "water entitlements" should clearly specify individual water-use rights and be aligned with the cap. "Water allocations" can be used for determining the amount of water that an entitlement holder is permitted to abstract within a specified period (OECD, 2015). Individual water allocations are aligned with the adjusted cap. The allocated initial volumes may be based on historical authorized water use, adjusted as a function of the reductions imposed by capping. An appropriate metering and penalty system should ensure satisfactory enforcement and compliance.

Defining water-trading rules

Once caps and individual volumes have been set, policymakers may allow water users to trade their water entitlements (permanent transfer) or water allocations within a given period (temporary transfer). Trade may be limited to the agricultural sector or authorized between sectors. Controlling environmental and social externalities is a major concern for policymakers and managers when water trading occurs, but trade-management rules can serve to limit the social and environmental effects. Trade regulation is highly dependent upon the hydrological, economic and social contexts, but it can be organized in diverse ways to ensure that it will be compatible with the existing institutional framework. For example, trade can be based on bilateral negotiations between buyers and sellers, which requires minimal supervision and may, or may not, involve brokers.

Step 2. Adapting the cap and trade scenario to local case studies

We selected five basins where groundwater use for irrigation is significant, all being representative of the diversity of hydrogeological and agricultural situations in France. Table 1 summarizes the key characteristics of the five case studies.

From April 2012 to March 2013, a dozen interviews with stakeholders (administrations, users, NGOs) were conducted for identifying the groundwater-management problems, issues and options in each basin. We also collected and analysed all existing studies and planning documents. This in-depth analysis of current water management in the five basins provided the basis not only for developing a theoretical cap and trade scenario, but also for selecting the institutional set-up that appeared to be the most appropriate for each basin. We evaluated how water policy is likely to evolve in each case study, if the reform is implemented over a decade or more. Our narrative descriptions were presented as press releases, giving details of the different reform steps to be implemented between 2020 and 2035. As a result of the field work, we could introduce very local references into the policy scenarios. Four alternative groundwater policy instruments were successively discussed during the workshops, the last being groundwater markets. We included several contrasted policy options (market, community, or State centred), to ensure that the research team was not perceived as being ideologically biased. This paper only deals with the groundwater-market-oriented policy option. Readers interested in the other three policy options will find more information in [START_REF] Figureau | Policy instruments for decentralized management of agricultural groundwater abstraction: A participatory evaluation[END_REF].

Step 3. Scenario workshops

Many ways exist of involving stakeholders in the design of a new instrument, including focus groups, consensus conferences and citizens' juries. For our research we chose scenario workshops, following the participative foresight method described by [START_REF] Figureau | Policy instruments for decentralized management of agricultural groundwater abstraction: A participatory evaluation[END_REF]. This allowed a critical analysis of the proposed cap and trade policy scenario together with stakeholders. The objective was to identify and draw on collective expertise (users, water managers, regulators), by comparing their perception of the proposed policy. In each case study, we created two or three stakeholder groups: one large group assembling representatives of the main institutional stakeholders (10 to 15 participants, including local and regional government representatives, farming representatives, water agencies, environmental associations and geological surveys), and one or two farmer groups (5 to 15 participants each). We deliberately separated farmers and other stakeholders, to encourage farmers to express their views more readily, which helped overcoming the deep mistrust that some may have for institutional stakeholders in France.

Overall, we organized 16 workshops lasting 4-5 hours each, from June 2012 to March 2013, and collected information from 124 participants (44 institutional stakeholders and 80 irrigating farmers).

The workshops started with a discussion of current groundwater-management rules, to ensure that existing institutional and policy frameworks were clearly understood. We then presented a baseline situation showing how rules and the general context could evolve by 2020. Following this, we introduced the first two components illustrated on Figure 1. After discussing the three instruments described in [START_REF] Figureau | Policy instruments for decentralized management of agricultural groundwater abstraction: A participatory evaluation[END_REF], we broached the subject of a groundwater market mechanism (third component on Figure 1).

Before the discussion, the participants were invited to fill in a questionnaire, to express their first impressions of the proposed instrument. They briefly described their position on groundwater trading (opposed, favourable under certain conditions, or totally favourable), and gave their own estimate of the percentage of groundwater volumes that would be traded if the scenario was introduced (negligible, 5-10%, 10-30%, over 30%).

They also stated whether they would accept buying or selling water, and, if so, occasionally or regularly. Finally, we invited the participants to express their opinions, opening the discussion to a lively debate.

Step 4. Analysis of workshop findings

During step 4, we analysed the completed questionnaires and the discussions that took place during the workshops.

All group debates were transcribed and thematically coded, about 30 hours in all; the methodology-described in detail in [START_REF] Figureau | Policy instruments for decentralized management of agricultural groundwater abstraction: A participatory evaluation[END_REF] and similar to the approach used by [START_REF] Hasselman | Market-based governance and water management: the limits to economic rationalism in public policy[END_REF]-involved constructing a database, with records of specific statements by individual participants during a workshop, Author-produced version of the article published in Water Economics and Policy (2019) The original publication is available at https://www.worldscientific.com/ https://doi.org/10.1142/S2382624X19500097 consisting of a few sentences of exact wording. When a statement was repeated during a workshop, only one record was entered in the database. We then grouped individual statements into six main categories, each comprising several sub-categories: (i) Preconditions related to general context (first component on Figure 1); (ii) Preconditions related to the capping process (second component of Figure 1); (iii) Principle stands; (iv) Advantages of groundwater trading, (v) Risks of market failure, and (vi) Options for improving the proposed instrument. Two of the authors repeated the analysis to check for potential interpretation bias. Finally, we used the database for calculating quotation frequencies in each sub-category of statements.

CAP AND TRADE SCENARIO

France has taken a firm step towards integrated water-resource management with its 1992 Water Law (Rinaudo, forthcoming), which introduced metering and licencing for water abstraction. The 2006 Water Law strengthened the legal framework for quantitative water-management issues [START_REF] Rinaudo | Quels instruments pour une gestion collective des prélèvements individuels pour l'irrigation ? Onema[END_REF][START_REF] Montginoul | Controlling groundwater exploitation through economic instruments: Current practices, challenges and innovative approaches[END_REF]. Hereafter, we describe the background to French groundwater policy, presenting the proposed cap and trade scenario and how it can be adapted to individual cases.

Policy background

The 2006 law imposed a cap on water use in basins with a structural groundwater deficit. In theory, the cap is designed to protect the good ecological status of groundwater-dependent ecosystems under normal climatic conditions, i.e. 4 years out of 5. The State attributes the capped volumes to the different economic sectors (cities, industries and agriculture). The volume allocated to agriculture is officially assigned to the newly formed Groundwater User Associations (GWUA), which are responsible for sharing the water among farmers. Under

State supervision, GWUAs must develop their own rules for determining individual entitlements. When we organized the workshops in 2012-2013, the GWUAs had only just been established.

Main components of the cap and trade scenario

The main components of the cap and trade scenario discussed with French institutional stakeholders and farmers during the workshops are set out below.

It was assumed that by 2020 most of the conditions required for establishing groundwater markets would have been met. Groundwater is a limiting factor for agricultural production in many basins, which are de facto closed to new entrants; the cap is in place, and users have clear water entitlements defined for a 10-year period.

The cap may be adjusted annually, depending on meteorological conditions and hydrological status. Individual water allocations are adjusted accordingly before the irrigation season. Although allocation rules may vary between GWUAs, most groundwater allocations are based on average historical use. In addition, the early signs of climate change announce an increasing water scarcity, especially during summer. Significant improvements in scientific understanding of local hydrogeology have removed much of the uncertainty (and controversy) about cap values, allowing more accurate assessment of the possible impact associated with changes in the spatial distribution of pumping. As the legal powers of GWUAs have been strengthened, they now can experiment with new allocation mechanisms, if equal treatment for all members is guaranteed. Several technological innovations have been widely

adopted, such as smart meters and the use of remote sensing. This has helped resolving the problems of compliance and enforcement.

In 2035, water allocations will become tradable between farmers who are GWUA members. Until 2037, farmers will only be able to trade their individual allocations on a temporary basis, for instance a season or a year.

Permanent trading of water entitlements will be possible after 2037.

GWUAs play a key role in trade regulation. They register all transactions, publish sale-and purchase offers on their website, as well as a summary of trading activities (volumes sold and prices) at the end of the irrigation season. They verify the absence of third-party impact before approving a transaction. Water trading is only allowed before the irrigation season starts, and only between farmers in the same groundwater management unit (GMU), as defined by the GWUA. Groundwater entitlements remain subject to administrative authorization;

at the end of their period of validity they can be adjusted, or even revoked, without compensation. The scenario thus introduces flexibility in groundwater allocation without modifying the foundations of French water policy.

Adaptation to local hydrogeological characteristics

We then adapted this scenario to fit the specific hydrogeological characteristics of each of the five selected groundwater basins. Our case studies broadly cover three types of aquifer. The first, illustrated by the Lyonnais aquifer, consists of three large alluvial systems characterized by high inertia. Given their very significant water reserves, they can easily buffer inter-annual fluctuations due to recharge (rainfall) or water abstraction by users.

Consequently, the total abstraction limit can be relaxed, and the cap can be based on an average abstraction limit over a 5-year moving-average period. This allows users to carry over part of their water entitlement from one season to the next; we assumed a 20% carry-over in the Lyonnais aquifer scenario.

Author-produced version of the article published in Water Economics and Policy (2019)

The original publication is available at https://www.worldscientific.com/ https://doi.org/10.1142/S2382624X19500097 10

The second type of aquifer is characterized by intermediate inertia. Based on observed groundwater levels at the beginning of the season, managers can make fairly reliable predictions about the volumes that can be pumped in the next six months, without putting dependent ecosystems at risk. Here, a yearly cap is set, and entitlements correspond to an annual pumping limit. If necessary, the cap may be reduced before the start of the season and individual water allocations readjusted accordingly. These assumptions were incorporated in the scenario discussed with stakeholders in the Tarn-et-Garonne plain and the Serre basin.

The third type of aquifer is characterized by low inertia. Here, it is difficult to predict the volume available during the cropping season as it depends on rainfall, and we assumed that a low value is set for the yearly cap.

Similarly, the individual allocations granted to farmers reflect this cautious approach. Such uncertainty diminishes a few months into the growing season, and the available resource can be predicted with greater precision.

Individual allocations can then be adjusted as a function of the available resource.

How the cap is defined has obvious implications for groundwater trading. In the high-inertia case, uncertainty is minimal because water can be purchased in advance and the volume traded can be fully guaranteed over a 5-year period. The second case is similar: the volume can only be guaranteed for the season, but it fluctuates from year to year. In both cases, we assumed that any trade in groundwater occurs before the start of the season.

In the third case, farmers leasing water entitlements before sowing their crop do not know how much water they will be allocated during the season. Therefore, we proposed that a first round of trading could be conducted before the growing season. A second round would be optional if additional volumes are allocated later in the season.

We assumed that trade is restricted to existing groundwater management units (GMUs), which vary in size from 6,000 to 40,000 ha, depending on the hydrogeological nature of the aquifer.

Author

RESULTS

Overview

Groundwater trading proved to be controversial. This was clear from the different case studies and participants' responses. On average, 45% of participants were against groundwater trading, while 43% supported the idea under certain conditions. Only 3% expressed their full support (Fig. 2a). The level of opposition varied from 25 to 69%, depending on the basins studied and the types of actors. Our tables and figures presenting the results obtained for each basin, rank the results from the highest mean opposition rate (Lyonnais aquifer: 61%) to the lowest (Tarn-et-Garonne plain: 38%). Farmers and institutional actors expressed similar positions, apart from the Valence plain and Serre basin where institutional actors are more favourable to the market than farmers.

While half of the participants consider that a cap and trade policy is a plausible future option for water policy, only 23% consider it desirable; Figure 2b reveals contrasting views between case studies and actors;

farmers' groups and institutional stakeholders in the same basin may have differing views regarding both probability (the Lyonnais example) and desirability (Valence plain).

Overall, the participants expressed serious concerns about the prerequisites for groundwater trading, given the general context (22% of statements) and the capping process (28% of statements) (Figs. 3a, 3b; Table 3). Even if the preconditions are met, the workshop participants (farmers and institutional stakeholders alike) expressed far more concern about the potential risks associated with groundwater markets (24% of statements) than interest in the advantages resulting from trade (4%). The original publication is available at https://www.worldscientific.com/ https://doi.org/10.1142/S2382624X19500097 1

Meeting the preconditions for trade is not for tomorrow

At first glance, an economist may argue that French water management and policy frameworks are sufficiently mature for introducing groundwater trading in the agricultural sector. Water use has been capped in basins with a structural deficit, all water abstraction is declared, and water use is systematically metered. However, a closer look at the five case studies reveals that several problems regarding the preconditions for trading have yet to be resolved, particularly concerning the first two components of the cap and trade policy scenario (General context, Cap, Fig. 1). The results also highlight significant differences between the basins, as shown in terms of the distribution of the opinions expressed (Table 3). These differences are linked to the contrasting situations in the basins, such as water scarcity and the history of existing quantitative management systems. It also shows that some basins may not be ready for the introduction of groundwater trading.

General context

The key elements related to the general context are mentioned in 22% of the statements; 11% of participants discussed the assumption that water scarcity will increase in the future. This was the case in several basins depending on the situation, such as in the Tarn-et-Garonne and Valence where surface water can be used as an alternative resource, in the Lyonnais and Serre where restrictions in groundwater use for irrigation are still rare, or in the Tarn-et-Garonne and Serre where hydrogeological modelling results remain controversial and have yet to be fully accepted. In some basins, the limited groundwater knowledge created problems (5% of statements). Some participants thought that acquiring the detailed geological and hydrological data described in the scenario would take decades. Setting up appropriate monitoring networks will effectively take years, as will subsequent data collection to allow statistical analyses.

Therefore, participants considered that water entitlements should not be made tradable before we have a better understanding of geological and hydrological issues. Until then, such trade might create insoluble political problems, particularly in the event of having to return to sustainable pumping levels. Moreover, groundwater resources are invisible and, in the case of high inertia (Lyonnais aquifer), they require long-term management.

This can be difficult for users to grasp. Some users still disagree with the assumption that water is scarce, and they refuse to reduce their allocation in response to environmental concerns. In the two basins with the greatest opposition to groundwater trading (Lyonnais aquifer and Valence plain), stakeholders can have very different perceptions of water scarcity, farmers discussing the issue twice as much as institutional stakeholders, which may reflect different levels of knowledge. These different perceptions suggest that there is a need for creating room for dialogue between the different actors in each basin, to facilitate the exchange of viewpoints.

The capping process

The capping process that came into force with the 2006 Water Law was a controversial issue in most of our case studies (28% of statements).

In basins where groundwater-management schemes were only recently introduced, main issue is linked to the cap on irrigation (7% of statements); there, users are just starting to grasp the basic principles of quantitative management. Some participants were against future cap reductions to meet environmental constraints.

The strongest opposition to capping was expressed in the Valence basin, where farmers have not yet experienced restrictions (20% of statements), but no specific opposition was reported in basins where capping has existed for several years, such as the Clain basin where water use has been capped since 1994.

Concerning the capping volume, most participants agreed that caps should be set for each groundwater management unit, but they also anticipate that this may pose practical and technical problems. Assessing the volume is likely to be controversial at a local level. Participants were positive about the proposal to adjust the cap annually based on observed groundwater and meteorological conditions. However, farmers argued that such adjustments should be announced before they decide on their cropping plan. This is long before the announcement date proposed in the scenario, which date will inevitably be the result of a trade-off between environmental and economic concerns.

There was no consensus about individual water entitlements and allocations (15% of statements).

Depending upon the type of cropping system, farmers highlighted different factors that hinder establishing a universal definition for individual water entitlements, such as their duration, or the timetable for adjusting annual water allocations. Many farmers were concerned by the proposed 10-year validity period for water entitlements.

Those who cultivate perennial crops (Tarn-et-Garonne and Valence plains) considered it was too short given the return period for their investments (15 years minimum for orchards), but farmers growing annual crops (Serre and Clain basins) argued that water entitlements should be redistributed each year to adjust for crop changes. They suggested that, depending on the cropping system, the proposed calendar for adjusting annual water allocations might be unsuitable, and should be carefully adapted to the constraints faced by different farmers if they were to accept it. In the Serre basin, for example, farmers grow vegetables under contract with agri-food companies that impose strict specifications, especially for the supply of irrigation water. It is inconceivable for these farmers to make a commitment to an industrial company unless they know how much water will be allocated to them.

The legitimacy of initial water allocations, commonly based on historical use, is problematic as well. Some participants challenged our assumption that entitlements could be based on historical water-use records.

They argued that individual allocations based on previous history would freeze the-apparently unfair and inefficient-allocation system now used. It would also be detrimental to farmers who invested in water-saving technology, instead of rewarding their efforts. However, there was no agreement on the criteria that should be used for calculating the initial allocation, to ensure that it would be fair and efficient.

Finally, the participants discussed the role allocated to the GWUAs in our scenario, agreeing that they should play a greater role when it comes to defining water-allocation rules. However, there was no consensus on the respective roles of users and the State in terms of monitoring and enforcement. In general, government agencies like to transfer certain responsibilities to farmers, such as monitoring water use, detecting illegal abstraction, or even sanctioning deviant behaviour, by excluding the defaulter from GWUA membership and thus cancelling his right to pump. But farmers are clearly reluctant to assume such responsibilities, in particular sanctioning, which they consider to be a State mission.

Anticipated negative effects and the demand for regulations

Anticipated risks may heighten opposition to groundwater trading; they represent 24% of the concerns raised during the workshops, and over 30% for the two basins with the highest opposition rates. Participants did not expect the proposed groundwater market to function as predicted in theory. Some (7% of statements) feared that water trading could disrupt the social and economic equilibrium of entire regions. The perceived risk is that the ownership of water rights, with a high marginal value, will be concentrated in the hands of a few large farmers.

Private firms outside the agricultural sector could also purchase agricultural water rights; this might disrupt agriculture at a regional level, causing the possible collapse of entire value chains and the economic decline of certain rural areas. Some participants were also concerned that water trading would increase competition between farmers, reduce cooperative initiatives, exacerbate social fragmentation, and erode rural solidarity. Some (6% of statements) were also concerned that the trading system might deviate from its primary objectives, the risk being that some farmers could gradually become water traders rather than agricultural producers. Beneficiaries of large water allocations might start speculating, through withholding water rights from productive use to create artificial scarcity on the market and raise prices. Some participants thus proposed that groundwater trading should be subject to strict regulations, for example with controls over time, geographic scale, tradable volumes and even prices. They strongly defended the idea that trade should only occur before the growing season and be prohibited once this is underway. Some participants pointed out that strict regulations would significantly restrict trade opportunities. Overall, these comments reveal an extreme suspicion about groundwater markets, which was further illustrated by frequent references to the stock option market.

Low levels of trading are expected

The case studies also raised questions about the potential benefits of groundwater trading. Some participants stressed that trading would remain very limited (4% of statements), especially in areas where GMUs are small and farming systems are little diversified. While two thirds of farmers declared that they would probably trade water if the proposed scenario was implemented, only 5% declared that they would do so regularly. Over 60% thought that the traded volumes would represent less than 10% of the total allocated volume (Fig. 4). These findings can be linked to the fact that only a minority of participants expressed an opinion about the potential advantages of groundwater trading (4% of statements). Some recognized that groundwater trading could improve flexibility, by allowing them to reduce irrigation without losing their water entitlement-in the case of illness or prior to retirement-or increase irrigation to boost crop yields at the end of the season if water is available. A minority declared that groundwater trading might provide an incentive for using more efficient irrigation techniques. This could increase total agricultural production at the basin scale, if farmers are encouraged to use dormant volumes.

DISCUSSION

The results presented above are consistent with the recent literature on water markets. They confirmed that, whether water trading will be a viable tool for ensuring sustainable groundwater management, will depend on a host of basin-specific factors [START_REF] Wheeler | Developing a water market readiness assessment framework[END_REF]Babbit et al., 2017;[START_REF] Green Nylen | Trading sustainably: critical considerations for local groundwater markets under the sustainable groundwater management act[END_REF].

Our study confirmed that shifting from a regulatory to a market-based water governance worried many water users and stakeholders, even when carefully adapting the cap and trade scenario to local conditions. The institutional arrangements we proposed to French stakeholders incorporate many safeguards against the risk of market failure. The factors explaining this rejection of cap and trade were globally the same as those reported in other papers analysing the limits of market-based forms of water governance [START_REF] Galaz | Stealing from the poor? Game theory and the politics of water markets in Chile[END_REF]Gianocarro et al., 2013;Hernandez-Mora and del Moral, 2015;[START_REF] Hasselman | Market-based governance and water management: the limits to economic rationalism in public policy[END_REF][START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF]. We review those factors below.

The views expressed by French stakeholders that preconditions for establishing cap and trade scenarios are not met, echoed findings in other countries. Several authors (e.g. [START_REF] Boyd | Optimising sustainable use of groundwater: a challenge for science and water markets[END_REF][START_REF] Skurray | Hydrological challenges to groundwater trading: Lessons from south-west Western Australia[END_REF] identified a good understanding of the groundwater resource and its functioning as one of the key scientific challenges for establishing groundwater trading.

Our analysis also showed that part of the opposition expressed by French stakeholders concerns the capping process. Both the cap setting and the initial allocation of water-use rights are major challenges that, if not properly addressed, can impede the establishment of a water market [START_REF] Mcallister | The overallocation problem in cap-and-trade: moving toward stringency[END_REF][START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF].

The capping process may be at different stages of development, and insufficiently mature for introducing water trading [START_REF] Easter | Formal and informal markets for water: institutions, performance, and constraints[END_REF]. Another major concern was the initial allocation of individual water-use rights where they do not pre-exist. Stakeholders were particularly concerned by-and had diverging views on-how water-use rights should be defined and initially allocated among users [START_REF] Syme | The determinants of perceptions of fairness in the allocation of water to multiple uses[END_REF][START_REF] Syme | Achieving sustainability in water reform: A Western Australia case study[END_REF][START_REF] Nancarrow | Developing fair processes for the reallocation of groundwater for long term sustainability in the Namoi Valley[END_REF]Rinaudo et al., 2016b). In over-allocated basins, users may advocate different rules for reducing allocations or entitlements, such as across-the-board reduction, or cancellation of dormant rights. This process raises a debate that focuses on the issue of distributive justice (Rinaudo et al., 2016b). Poor acceptance of this initial process will increase the risk of conflicts associated to trading. Moreover, the monitoring of groundwater abstraction remains a weak link in France (Montginoul et al., forthcoming) and elsewhere (Zhang, 2007, in China;Holley and Sinclair, 2018, for Australia). Compliance problems could increase with water trading as this increases financial incentives for disobeying the rules. [START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF] conclusion, which could apply to the French context, is that "if caps are exceeded due to illegal water extraction, if […] tradable water rights are not adhered to, and if stakeholders lack confidence that there is an equitable sharing of water, the entire edifice of the market can be undermined".

Once water use is capped and initial allocations are set, making the water-use rights tradable raises further significant opposition. In France and elsewhere, water users may contest the legitimacy of market-based forms of governance on ethical grounds. Because market mechanisms emphasize individual values and stimulate competition, they can erode community spirit and crowd out more ethical and moral behaviour [START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF]. Water markets are also contested by those who think that they encourage gaming-and possibly fraudulent-behaviour, but also may favour people making money by managing risk over those who use water for producing goods [START_REF] Hasselman | Market-based governance and water management: the limits to economic rationalism in public policy[END_REF][START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF]. This reflects a broader concern that our society is moving from a production economy to a speculation one [START_REF] Sandel | The moral economy of speculation: Gambling, finance, and the common good. The Tanner Lectures on Human Values[END_REF].

Another claim of French water-market doubters is that the market will benefit wealthier users and increase inequality. This is echoed in certain Australian studies based on qualitative or quantitative surveys; for instance, [START_REF] Wheeler | Reviewing the adoption and impact of water markets in the Murray-Darling Basin, Australia[END_REF] showed that early market adopters have higher education and income levels. The fear expressed by some French stakeholders, that water trading beyond the region may threaten business and employment, is also known from studies elsewhere; Connell (2015), for instance, reported that in the Australian Murray Darling basin, water sales outside local communities are perceived as a loss of control over the future. He noted that water trading has disrupted social cohesion between irrigators and their communities, creating stresses where previously there was a strong sense of shared destiny.

During our workshops, however, there were few discussions about spatial externalities despite the fact that the spatial reallocation of groundwater volumes is a major issue in the literature on groundwater trading as it can change the distribution and magnitude of pumping externalities [START_REF] Howe | Policy issues and institutional impediments in the management of groundwater: lessons from case studies[END_REF][START_REF] Brozovic | On the spatial nature of the groundwater pumping externality[END_REF][START_REF] Skurray | Hydrological challenges to groundwater trading: Lessons from south-west Western Australia[END_REF]Kuwayama and Brozovic, 2013).

Concerning the limited potential economic benefits generated by groundwater trading, the concerns expressed by French farmers again confirm findings reported in the literature. In Australia, where trade is restricted within a groundwater management unit, mostly to prevent environmental externalities, few transactions occur and the market remains quite thin [START_REF] Ghd | A framework for managing and developing groundwater trading[END_REF][START_REF] Skurray | Hydrological challenges to groundwater trading: Lessons from south-west Western Australia[END_REF][START_REF] Holley | Water Markets and Regulation: Implementation, Successes and Limitations[END_REF]; this is supported by the fact that transactions in the states of NSW and Victoria represent only 1% of groundwater allocation. At the national level, 75% of Australian groundwater trade occurs in three major alluvial aquifers, characterized by a high number of licences and large volumes, high water demand and low availability [START_REF] Ghd | A framework for managing and developing groundwater trading[END_REF]. specific hydrogeological features, the local groundwater management history, and local farming constraints are considered.

Hydrogeological characteristics necessarily influence the way a cap is defined, allowing for flexibility when it comes to adjusting annual abstraction volumes as a function of aquifer inertia. Existing quantitative management schemes, however, may not be ready to support groundwater trading, and it may be necessary to adapt individual entitlements and allocations to suit the needs of specific cropping systems.

In line with the subsidiarity principle of French water laws, national legislation would offer a framework for developing water trading, without imposing universal groundwater-trading rules and market regulations. It is likely that stakeholders in some pilot groundwater basins may start introducing trading systems, adopting a cautious approach with numerous trade restrictions. Over time, trading may be abandoned in some basins because of undesirable negative effects, or the small number of transactions. But,once the trading process has been demystified and trust develops among users, trading restrictions may be loosened in other basins [START_REF] Babbitt | Groundwater Trading as a Tool for Implementing California's Sustainable Groundwater Management Act[END_REF].

Other decentralized management approaches exist for providing flexibility and increasing efficiency in allocation. Some of these options, which rely on setting up water-user associations and decentralized selfmanagement by users, are a clear alternative to the dichotomy between State and Market. This option is discussed by [START_REF] Figureau | Policy instruments for decentralized management of agricultural groundwater abstraction: A participatory evaluation[END_REF] and [START_REF] Holley | A new water policy option for Australia? Collaborative water governance, compliance and enforcement and audited self-management[END_REF], among others.

From a methodological perspective, our study should help in designing and evaluating groundwater market instruments with local actors, and at groundwater-basin scale. It underlines the importance of involving both local farmers and institutional stakeholders in discussions on market mechanisms, ensuring that their different views are equally considered. Organizing workshops that allow the different stakeholders to express their opinions is a first step in a broader participatory process. The second step is to encourage discussion, to help the actors create a shared vision of groundwater management. As suggested by [START_REF] Babbitt | Groundwater Trading as a Tool for Implementing California's Sustainable Groundwater Management Act[END_REF], this may help reducing potential blockages due to misunderstandings.

More generally, the proposed participatory approach should encourage the GWUAs to consider the diverse views of users when they design future rules for managing groundwater allocation. Supporting such a participatory process requires an interdisciplinary approach to water markets, combining concepts and analytical frameworks from not only economics and groundwater science, but also from sociology, law, institutional theory and moral philosophy (Gomez-Baggethun and Muradian, 2015).

Fig

  Fig. 2 (a) Principle stands regarding the possibility of buying and selling volumes of water, per basin and per stakeholder type (% of participants), (b) probability and desirability of groundwater trading (the figure shows the % of participants considering water trading as a highly probable (X axis) or highly desirable (Y axis) per basin and per stakeholder type)

Fig. 4

 4 Fig. 4 Anticipated trading activity per case study: (a) percentage of farmers declaring they would participate occasionally or regularly and (b) estimation of the global percentage of allocated volume that would be traded if the groundwater market scheme was established.

Table 1 .

 1 Description of case studies in 2013 (more details in[START_REF] Figureau | Policy instruments for decentralized management of agricultural groundwater abstraction: A participatory evaluation[END_REF]

		Lyonnais	Tarn-et-	Serre basin	Clain basin	Valence
		aquifer	Garonne plain			plain
	Basin size (ha)	40,000	94,000	163,000	320,000	48,000
	Hydrogeology
	. Inertia	High	Intermediate	Intermediate	Low	Low
	. Aquifer type	Fluvio-glacial	Alluvial	Chalk aquifer	Karstic	Alluvial
		corridors	aquifer		aquifer	aquifer
	Agriculture
	. Number of irrigating farms	320	550	95	400	125
	. Irrigated area (ha; % UAA * )	7,000 (35%)	22,000 (25%)	4,000 (2.5%)	28,000 (11%)	9,800 (40%)
	. Main types of crops	Cereals, oil	Fruit, cereals	Vegetables,	Cereals	Corn, fruit,
		and protein		cereals		vegetables
		crops
	Agricultural groundwater abstraction
	. Mean annual volume (million m 3 / year)	9	29	6	25	5
	. Type of abstraction (individual/	Collective	Individual	Individual	Individual	Individual
	collective)
	Water scarcity
	. Crisis and restrictions in groundwater	Rare	Occasional	Rare	Frequent	Frequent
	use for irrigation
	. Surface water as an alternative resource	None	Dense surface	Very limited	Very limited	Dense
			irrigation			surface
			network			irrigation
						network
	* UAA: Utilized Agricultural Area.

Table 2 .

 2 -produced version of the article published in Water Economics and Policy (2019) The original publication is available at https://www.worldscientific.com/ https://doi.org/10.1142/S2382624X19500097 1 Main differences in the five case studies concerning the cap and trade scenario

	Lyonnais aquifer	Tarn-et-Garonne	Serre basin	Clain basin	Valence plain
		plain

Table 3 .

 3 Statements quoted by workshop participants per category and case study Number of workshops (out of 16) where the statement was quoted at least once.

			Number of statements per category		Number of
								workshops a
	Statement category	Total	Lyon-	Valence	Serre	Clain	Tarn
			nais				Garonne
	 GENERAL CONTEXT	209	26	27	39	26	91	16
	Water scarcity	106	12	16	17	12	49	16
	Knowledge groundwater functioning	43	3	3	13	6	18	11
	Knowledge of abstraction volumes	30	5	2	3	7	13	11
	Groundwater management units	22	4	5	6	0	7	8
	Heterogeneity of farming systems	8	2	1	0	1	4	5
	 CAP	264	41	45	62	57	59	16
	Individual water entitlement and	144	17	12	39	37	39	16
	allocation
	Establishing a cap for irrigation	65	9	30	9	4	13	15
	Monitoring and enforcement system	39	11	2	8	12	6	13
	Transparency and information	9	2	1	4	2	0	4
	Other	7	2	0	2	2	1	6
	 TRADE	475	73	78	88	135	101	16
	Principle stands	106	13	16	11	43	23	15
	Ethical positions	74	13	16	8	26	11	15
	Formalization of existing practices	29	0	0	1	17	11	7
	Other	3	0	0	2	0	1	2
	Advantages	42	5	2	15	12	8	13
	Flexibility	22	3	0	10	7	2	8
	Incentive for water savings	5	0	1	0	0	4	4
	Increase in agricultural production	5	0	1	0	4	0	2
	Other	2	0	0	0	1	1	2
	Self-regulated system	2	0	0	1	0	1	2
	Technical efficacy of irrigating water	2	0	0	2	0	0	1
	Efficiency of irrigation	2	2	0	0	0	0	1
	Environmental protection	2	0	0	2	0	0	1
	Risks of market failure	230	44	40	41	52	53	16
	Social and economic disorganization	65	11	12	8	25	9	14
	Misuse of the system	59	17	10	5	3	24	14
	Low level of trading activity	41	7	6	17	5	6	13
	Individual risk-taking for farmer	24	3	7	4	2	8	12
	System difficult to manage	19	2	3	5	6	3	10
	Third-party impacts	15	4	1	2	8	0	6
	Other	7	0	1	0	3	3	4
	Options	97	11	20	21	28	17	14
	Level of regulation	41	7	5	15	14	0	9
	Alternative options	17	2	5	4	4	2	9
	Types of groundwater trading	16	1	0	1	7	7	7
	Institutional arrangements	15	1	7	1	1	5	9
	Enable entry of new irrigators	4	0	2	0	2	0	4
	Other	4	0	1	0	0	3	2
	TOTAL	948	140	150	189	218	251	16
	a

Acknowledgements

This work was financially supported by ONEMA, as part of the Water Cap & Trade project (Era Net programme on Integrated Water Resources Management). The preparatory work for this chapter was made possible thanks to financial support from BRGM. We would like to thank the two anonymous reviewers for their helpful suggestions.

Author-produced version of the article published in Water Economics and Policy (2019) The original publication is available at https://www. of agricultural land [START_REF] Loubier | L'irrigation diminue-t-elle en France ? Premiers enseignements du recensement agricole de 2010[END_REF]. Farmers often use irrigation simply as an insurance for dry years. Trading is only expected to occur in large homogeneous groundwater units and areas with highly diversified farming systems, but France's implementation of the European Water Framework Directive has led to the identification of over 550 shallow groundwater bodies nation-wide. In areas where over-pumping is a problem, the cap should be defined at GMU scale, guaranteeing minimum water flow in connected surface-water systems. At this scale, the number and diversity of farming systems is expected to be low.

Overall, stakeholders' fears are understandable given the scope of a reform that would simultaneously reduce total water use by setting abstraction limits, define new water use rights, allocate them among users, and make them tradable. However, as illustrated by [START_REF] Wheeler | Reviewing the adoption and impact of water markets in the Murray-Darling Basin, Australia[END_REF], market adoption is a relatively long process.

It takes time for all users to fully understand the rules and potential benefits of water trading. It also takes time for institutions to adapt and reduce transaction costs. Recognizing the length of this process is essential. Thus, we fully support Babbitt's advice to Californian Groundwater Sustainability Agencies: "Because any agency is unlikely to design the rules perfectly at the outset, it might be prudent to start a trading program with lease onlyno permanent transfers. […] Testing trading rules with a handful of single year transfers can help Groundwater Sustainability Agencies to learn, better understand the incentives and effects of their rules, and trouble-shoot any issues that arise". This process is likely to be costly, given the depth of the institutional reforms that are needed.

CONCLUSIONS

This paper contributes to the future evolution of the French water policy, highlighting the key challenges of introducing groundwater trading in the agricultural sector. Our results concern five groundwater basins, showing that 50% of farmers and 40% of institutional stakeholders are opposed to groundwater trading for various ethical, economic and technical reasons. First, we do not yet meet the preconditions for introducing groundwater markets (water scarcity, sufficient knowledge on groundwater), and the capping process remains controversial in many French basins. Second, major negative effects are anticipated when developing a groundwater market. Regulatory measures to limit such negative impact may, in turn, hinder trading and call its very existence into question.

Despite these reservations, our results suggest that, with time, there may be scope for developing groundwater markets that are compatible with the French water policy context.


O Meski

F Belkadi

B Furet

F Laroche

Towards a knowledge structuring framework for decision making within industry 4.0 paradigm

Keywords: industry 4.0, knowledge reuse, modelling, decision-making. 

This article discusses the importance of data and knowledge structuring to allow their exploitation in emergent context of industry of the future. The complexity of integrating knowledge into decision support systems is particularly due to the heterogeneity of knowledge sources and the large volume of data to be analyzed. This problematic is challenging in the context of high-speed machining of aeronautical mechanical parts because of the high quality and safety constraints requested in this business area. To answer the above problem, this paper proposes a new semantic modeling framework covering both generic business knowledge and real time data. The application to the proposed semantic models for decision aid perspective within the SmartEmma project is also discussed.

INTRODUCTION

Based on recent developments in enterprise digitalization and information and communication technologies (ICT), the industrial sector is rapidly growing towards "intelligent manufacturing" and "connected factories". The manufacturing processes can be represented with a virtual copy (digital twin) and connected through cyber physical systems (CPS) and Internet of Things (IOT). These new technologies are at the heart of the Industry 4.0 paradigm.

Among the main sectors affected by this revolution, highspeed machining of mechanical parts in aeronautic industry present high challenges of quality and safety constraints. Indeed, the aeronautic parts are characterized by high added value regarding the whole airplane system. Their manufacturing process should be very accurate and produce the good part from the first time, while minimizing working time and costs. To satisfy these constraints, industries start using knowledge-based decision aid systems to support the monitoring and quality control along the production process. Erik [START_REF] Brynjolfsson | Strength in Numbers: How Does Data-driven Decision-Making Affect Firm Performance? Social Science Research Network[END_REF] argue that companies using this kind of systems can improve their performance and profitability by 5% compared to their competitor.

Decision aid solutions are generally based on the analysis of variety of information flows. In the aeronautic shop floor, the available data are collected from different sources. For example, the detection of the high-risk events is done using machine instrumentation to ensure the acquisition of a large amount of data representing the real behaviour. The processing of this data conducts to big data issues.

The SINTEF, one of Europe's largest independent research organisations estimated that 90% of the world's data were generated between 2010 and 2013. These data flows continue to increase in all fields. This research work focuses on the exploitation of data and knowledge to provide decision aid in the aeronautical mechanical machining industries. The literature survey argues that by 2026, the data generated annually in the aeronautics sector is expected to reach 98 billion gigabytes, or 98 million terabytes, according to an estimate made in 2016 by Oliver Wyman a leading global management consulting firm. Organizations must be able to analyse big data to extract knowledge and to use it at different decision levels: strategic, tactical and operational.

However, the decision process remains complicated due to several problems of industrial digital chain breakdowns. For instance, the lack of communication between businesses services, the interoperability between information systems, the diversity of technological solutions used, etc. In addition, the variety of information sources, and the large size of the databases to be recovered, implies an important step of preparation and structuring of the information flows.

As a support to this critical step, this paper proposes a semantic modelling framework that brings together all industrial information with the aim to handle data management and integration between all decision levels of the factory. This model is part of a decision aiding platform, to cover knowledge finding and interoperability issues.

The remaining of this article is organized as follows. The next section presents a state of the art on the paradigm of industry of the future and the related knowledge management applications. Section 3 explains the research methodology used to build the knowledge model. Section 4 describes the key parts of the proposed meta-model while the implementation perspectives of the models within the expert system are discussed in Section 5.

KNOWLEDGE-BASED DECISION MAKING

WITHIN THE INDUSTRIE 4.0 PARADIGM

The concept of "Industry 4.0" was invented in 2013 by the German government when they introduced their action plan and strategies for the development of the high-tech sector, which promote the digital revolution in industry.

The expression "Smart Industry" also describes the evolution of industrial technologies from microprocessors, and embedded industrial systems to cyber-physical systems. That has allowed connecting cleverly the different services of industry and the industrial chain, by internet [START_REF] Zuehlke | Smartfactory-towards a factory-ofthings[END_REF].

The virtual factory is based on the concept of digital twins. This technology represents a virtual model of an equipment, process, product, or service. It is used to detect problems, or to test and simulate scenarios on a physical model of a production unit. This digital twin also allows real-time analysis of operational data to improve the understanding of equipment functioning and to make timely decisions to optimize their efficiency [START_REF] Julien | L'usine du futur -Stratégies et déploiement: Industrie 4.0, de l'IoT aux JUMEAUX NUMERIQUES[END_REF].

Decisions take place in every department of a firm (i.e. product design, production policy, marketing focus, etc.). Each of those decision aims at improving the firm performance, either locally or globally. In the context of the Factory of the Future (FoF), a strong correlation exists between data and knowledge management and the performance of workers and industrial processes. Indeed, decision-makers usually need a good understanding of the operational process and resources' capacities.

To help deciders to overcome the psychological aspect of decision making [START_REF] Bazerman | Judgment in managerial decision making[END_REF], decision support tools have been developed. Previous researches enable to create a large corpus of qualitative or quantitative, determinist and stochastics or fuzzy, decision methods [START_REF] Triantaphyllou | Multi-criteria decision-making methods: a comparative study[END_REF]. They all rely on the integration of data and expert opinions; some of them also integrating simulation tools to estimate the alternatives' expected performances [START_REF] Daaboul | Value network modelling and simulation forstrategic analysis: a discrete event simulation approach[END_REF]. The actual scientific barrier is to enhance this decision making process by the integration of knowledge.

In particular, the smart factory aims to enhance the control and the optimization of factory processes based on advanced ICT tools for a better use of existing knowledge and data. This can be obtained from simulations as well as the analysis and inference of heterogeneous data [START_REF] Forestier | Modelling of spindle -self vibratory drilling head system for predictions of bearings lifespan[END_REF][START_REF] Guibert | Numerical simulator to predict the dynamical behavior of the Self Vibratory Drilling Head[END_REF]. To tackle these challenges, engineering systems have moved from being information-intensive towards knowledge-intensive systems [START_REF] Bernard | Knowledge Engineering Systems for Digital Enterprise Performance Improvement[END_REF]. Numerous systems and methodologies are developed with the aim to support knowledge modelling, storage and reuse [START_REF] Liao | Knowledge management technologies and applications literature review from 1995 to 2002[END_REF]. The first generation of knowledge-based systems was expert systems using a set of facts and rules [START_REF] Ulengin | Cognitive Map-KPDSS Integration in Transportation Planning[END_REF]. This kind of systems is composed of essentially two components: a knowledge base (KB) and an inference engine. Due to the increasing complexity of the knowledge-based systems and variety of application domains, knowledge modelling is a critical issue to guarantee the consistency of the knowledge base. Knowledge models must be based on a rich and structured representation [START_REF] Belkadi | A meta-modelling framework for knowledge consistency in collaborative design[END_REF] and should propose an adequate way for using this knowledge by several experts regarding their interest [START_REF] Demoly | Multiple viewpoint modelling framework enabling integrated product-process design[END_REF]. Ontologies are often proposed as knowledge repository for KB systems handling easier classification and finding of knowledge [START_REF] Sanya | A framework for developing engineering design ontologies within the aerospace industry[END_REF]. In the area of analysis and modelling processes, structures and information flows in factories, there are several methods available, customized to their individual application area.

Modelling is used in several fields such as cognitive sciences, engineering, management, and computer sciences. A model is generally used to represent and describe a complex system in a formal and simplified way from several points of view corresponding to different business objectives.

The term knowledge modelling is initially a concept of artificial intelligence. It is used to determine the list of knowledge to introduce into a computer system in order to make it "intelligent".

The modelling of data flows and industrial knowledge consists of structuring the most important company objects which are in direct contact with the product and process respectively. Several models have been developed in the literature to represent industrial knowledge. For instance, the following approaches can be cited:

-The Product, Process, Resources approach has been addressed in several works. [START_REF] Cutting-Decelle | Iso 15531 Mandate: A Product-Process-Resource Based Approach for Managing Modularity in Production Management[END_REF] (Borja Ramis et al, 2016) (Agyapong-kodua et al., 2014) highlight these three modelling objects and confirm that satisfactory data or knowledge models in this field must revolve around these three axes.

-The Function, Behaviour, Structure -Product Process Resource External Effects approach [START_REF] Labrousse | Proposition D'un Modèle Conceptuel Unifie Pour La gestion dynamique des connaissances d'entreprise[END_REF] extends the FBS (Function Behaviour Structure) model proposed in the work of [START_REF] Gero | Design Prototypes: A Knowledge Representation Schema for Design[END_REF]).

-The People, Process, Product approach that was first used by Motorola in its Six Sigma development. This is a very important one since it highlights the place of the human being in industry. The involvement of the human being remains indisputable.

Ultimately, from a modelling point of view, these approaches do not cover all the objects of the industrial digital chain, as well as the operational working context, at the same level. Therefore, with the ambition to provide an integrated framework, this research work addresses the problem of:

How to smartly model heterogeneous data and knowledge within decision aid perspective in context of industry 4.0?

METHODOLOGY OF MODEL CONSTRUCTION

The ambition of the proposed modelling framework is to be generic and robust enough to support variety of data and knowledge formats, required for the decision aiding system. This section explains the methodology used.

Data collection

The first step concerns the identification of all data sources and the classification of these varieties of data according to their nature and their contribution to the manufacturing and monitoring processes. The concept of data refers to all measured dimensions related to a given executed manufacturing process and its resulted products. Four categories of data sources are distinguished:

-The data bases connected to the machine and the related digital chain to collect real time and raw data.

-Product data sheets that informs about the result of an executed manufacturing process such dimensions, tolerances, and surface quality.

-Information systems data bases i.e.: MES (Manufacturing Execution System) and ERP (Enterprise Resource Planning) that contain additional data representing the context of the executed manufacturing process (manufacturing order, real time schedules, etc.).

-Other data bases that will store the resulted indicators after data processing.

Concretely, the "Monitoring & collected data" represents the databases collected from the industrial partners. This monitoring data are acquired through a tool for machining optimization and vibration analysis for composite and metal machining operations. It is composed of a hardware part that consists of a set of sensors and a software part that allows through them to collect "Real-time signals". The other types of data can be collected from a variety of sources.

The smart data are often extracted from the monitoring & collected data, using processing, interpretation, aggregation, etc. Data aggregation, using intelligent algorithms, allows to reduce the size of big data, and to structure them more significantly. This help to make processing and to facilitate data mining and knowledge extraction operations, in order to obtain the "Decision aid indicators".

Knowledge extraction

The concept of knowledge refers to all the generic information that allows the definition, the interpretation, and the processing of real time data as well as the evaluation of the resulted products.

The second step is then to identify the knowledge sources based on the analysis of the as-is situation and the decisionmaking objectives within the monitoring process. For instance, to understand the quality of the product, there is the need to compare the measured dimensions (collected data) with the specified dimensions (described in the Computer-aided design (CAD) model). Additional business rules can inform about the relation between a manufacturing operation and its impact on the part surface.

Manufacturers still generally curious to know: how other departments contribute in the production process? How they complement each other? How to share information to ensure the continuity of the digital chain? And finally, what opportunities for collaboration they may have?

In addition, manufacturers are also interested in the events that can affect product quality. The company's experts use their expertise to verify the quality of production, the qualification of the parts, and all the decisions to be taken when disqualifying a product. The competence of technicians represents an essential part of the knowledge base.

Other types of information are also important, such as temporal information that indicates business performance (useful time, net time, gross time, time required, etc). For this reason, in the area of industrial and production management, various indicators are often calculated, for example: the Economic Efficiency Rate (EER): indicator of the engagement of production means, or the Synthetic Efficiency Rate (SER): productivity indicator). This type of knowledge is included in the category of Key Performance Indicators (KPIs), which measure the efficiency of processes against a specific objective. KPIs are generally used for a common overall objective: management or continuous improvement.

The knowledge extraction method is based on the observation of operations, the analysis of technical documentation, and the classification of generic information available in information systems (CAD files, Programs, machine tools libraries, etc.). The definition of business rules is obtained from interview with experts and the analysis of reports.

Models building

In order to maintain the generic nature of the data model, the first two types of data and knowledge were confronted and enriched by other complementary data from the literature and standards. This will extend the scope of the data model to other industries in the future. In addition to the literature, standards and the monitoring database, the development of the data model is also based on the analysis of requirements resulting from the functions developed in the decisionmaking platform.

The specificity of this research work is the complementarity between the use of data and knowledge. The decision support system allows data processing through the use of a set of knowledge such as the capitalized business rules. Through these rules, the expert system generates new KPI that facilitate decision support and new knowledge "Inferred Knowledge" that can be integrated into the global database and easily reused.

Figure 1 shows the global categories of databases and knowledge represented respectively by the right and left axes. The reuse of data and knowledge allows the enrichment and updating of these databases.

Figure 1. Categories of data and knowledge

The following section of this paper focuses only on the knowledge dimension of the global modelling framework.

KNOWLEDGE META-MODELS

The objective of the knowledge models is to support the structuring of data used by the decision aiding platform. Consequently, the construction of these models will have to follow an incremental approach as well as the development of the platform. A first version of the model is defined and will be improved during the project. The generic knowledge model developed is essentially composed by the representative data model that represents a first level of knowledge, to which a second level of knowledge is associated such as KPIs, business rules, resource characteristics and specificities, etc.

Based on this first step of analysis and classification of data sources, the next step was to represent more formally, using modeling standards, the classifications of the identified data.

We therefore choose the UML (Unified Modeling Language).

It is a graphical language for object-oriented modeling. There are several advantages that justify the choice of UML language: the simplicity of the use, the modularity of the different kinds of models and especially the adaptability and the possibility of use in several domains. The object-oriented approach provides a unified representation of the different elements of a system, which corresponds to the need of modeling the different entities of the system.

The development methodology adopted is to begin from a generic meta-model and to add more and more granularity as we go along.

Based on product-oriented modelling approaches, the idea was to merge the 3 most important ones:

- The global knowledge model has been developed on the basis of a set of business rules which are originally the expertise of manufacturers. We also remind that the overall objective of developing this model is to capitalize and manage knowledge between the different departments. So, the development of this system allows the integration of knowledge among the company's stakeholders.

Thus, humans have a dual role in producing and exploiting knowledge. Consequently, the "tacit knowledge" class represents an important element of this package which allows the communication with others in order to reintegrate and improve the technicians' knowledge.

Otherwise, concerning the "Context" package, the idea is to develop a package that supports specific and necessary knowledge for the decision-making support system, in which we capitalize the entire context of the use. The Figure 4 represents the first version of the "Context" package model. The figure 5 shows a small overview about the use of these standards for the development of our knowledge model by defining generic classes, inspired from the detailed definitions presented in the norms.

The objective is to develop a model capable of gathering as much as possible of the useful knowledge for the development of our decision support system.

IMPLEMENTATION PERSPECTIVE

After the first phase of development of models for data and knowledge structuring, an implementation phase is required.

The implementation makes it possible to evaluate the efficiency of the models for the global organization of knowledge. It also provides an initial test phase to validate or to update the models during the development of the expert system.

In this project, the technology of multi-agent systems was chosen to ensure information piloting. This system is mainly composed by several agents and each one is specific to a precise role. We have traceability agents, configuration agents, reporting agents, decision support agents, etc.

The functioning of this system is based mainly on the global knowledge base. By using the knowledge models we will develop a complete ontology that combines all the data, knowledge, and business rules in a static way.

In order to develop the multi-agent system, several scenarios have been defined specifying the needs in terms of input and output data, also the departments concerned by these data and the mode and frequency of collection and restitution. A first scenario has been implemented. This initial scenario is integrated into the implementation of our first management axis in the project: "the reporting". The first multi-agent system prototype allows the traceability of several specific input data, to produce after a treatment, a set of output data. The system can also send treatment reports, by email, on demand.

The storage of this data is done in a traceability database in the form of a traceability point. It is also structured through a generic traceability database model. The storage on this database is dynamic.

The figure 6 illustrates our methods of knowledge management and capitalization of data.

Figure 6. Implementation strategy

The figure illustrates the decision aid framework system's ability to recuperate data from the global knowledge base structured using the Web Ontology Language (OWL) and store them in the traceability database developed with the Structured Query Language (SQL) in a dynamic way. This technique avoids duplication of the database. But above all, it allows us to validate and upgrade our structuring models so that they can support the consistency of our global base on one hand and the heterogeneity of knowledge on the other hand.

CONCLUSION AND OUTLOOK

The structuring of knowledge is the key to ensuring the generation and the reuse of new ones. This article details a methodology based on a meta-model for model construction. They are used to structure all the information and knowledge flows available mainly in the mechanical machining industries and especially the aeronautical ones.

The development of ontologies makes it possible to capitalize on the maximum of heterogeneous knowledge. The project is currently in the development phase of a knowledge repository, using ontologies and standards, the methods of questioning and interacting with this knowledge base remain our current research issues 7. ACKNOWLEDGEMENT These results were conducted within the project "SmartEmma" (Smart machine-tool and HSM process with Emma). This project has received funding from the French National Research Agency -ANR under agreement No ANR-16-CE10-0005 and labeled by EMC2. The authors would like to thank the industrial partners involved in this research.

  Product, Process, Resources Approach -Product, Process, Resources, Context Approach -People, Product, Process approach The merge of these three approaches produce the global package model: CR3P (Context, Resources, Product, Process, People). The Figure 2 represents the first version of the knowledge package model.

Figure 2 .

 2 Figure 2. Knowledge package model

Figure 3 .

 3 Figure 3. « People » package

Figure 4 .

 4 Figure 4. « Context » package

Figure 5 .

 5 Figure 5. Integration of Step-NC into KM


G Royer

J Jahan

N Mokus

Geometric shapes describing nuclear reaction mechanisms such as fusion, alpha emission and capture, binary and ternary fission, planar fragmentation and n-alpha nuclei

Different shape sequences useful to describe simply the fusion, alpha emission or capture, binary and ternary fission, planar and three dimensional fragmentation and n-alpha nuclei are gathered together. Their geometric characteristics allowing to determine the total energy and the dynamics of a nuclear system are provided, mainly the volume, the surface, the Coulomb function, the moments of inertia, the quadrupole moment and the rms radius.

Introduction

To describe macroscopically nuclear reaction mechanisms such as fusion [1], alpha emission and capture [2], binary and ternary fission [3], fragmentation [4] and n-alpha nuclei [5,6] one simulates the nuclear system by geometric shapes [7,[START_REF] Hasse | Geometrical Relationships of Macroscopic Nuclear Physics[END_REF] and determines the main geometric characteristics such as volume, surface, Coulomb function, moments of inertia, quadrupole moment and rms radius. In this work, the following shapes will be investigated: elliptic and hyperbolic lemniscatoids, prolate compact ternary shapes, tori and bubbles. Other multibody shapes such as linear chain, triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octagon and cube used to describe some light nuclei as alpha molecules have been used recently [5,6].

Elliptic lemniscatoids and pumpkin-like shapes

The fusion, alpha and cluster radioactivities and fission through compact shapes lead, in first approximation, from one sphere to two tangent spheres or vice-versa. Such a deformation valley can be simulated using two halves of different elliptic lemniscatoids. An elliptic lemniscatoid is the inverse of an oblate ellipsoid. One elliptic lemniscate is defined, in polar coordinates, by

R(θ) 2 = a 2 sin 2 θ + c 2 cos 2 θ, (1)
and the equation of the elliptic lemniscatoid is

a 2 x 2 + a 2 y 2 + c 2 z 2 = (x 2 + y 2 + z 2 ) 2 , ( 2
)
where the z axis is the axis of revolution. Assuming volume conservation, the ratio s = a/c of the neck radius to the half-elongation of the system defines completely the shape. When s decreases from 1 to 0 the lemniscatoid varies continuously from a sphere to two tangent equal spheres. When the perpendicular x axis is taken as axis of revolution the elliptic lemniscates generate pumpkin-like configurations (see Fig. 1). For the elliptic lemniscatoid the volume and surface are given by R 0 being the radius of the initial or final sphere and B s the dimensionless surface function. r, the distance between the mass centres of the right and left parts of the object, is given by

V ol = 4 3 πR 0 3 = π 12 c 3 4 + 6s 2 + 3s 4 √ 1 -s 2 sinh -1 2 s 2 1 -s 2 , ( 3
)
S = 4πR 0 2 B s = 2πc 2 1 + s 4 √ 1 -s 4 sinh -1 1 s 2 1 -s 4 , (4)
r = πc 4 1 + s 2 + s 4 3V . ( 5
)
The dimensionless perpendicular and parallel moments of inertia (relatively to the moment of inertia of the equivalent sphere 2 5 mR 0 2 ) are expressed as

I ⊥,rel = c 5 s 2 512(1-s 2 )R 0 5 112 s 2 + 8 + 30s 2 -135s 4 + 120s 4 -135s 6 √ 1-s 2 sinh -1 1-s 2 s 2 . ( 6
)
I ,rel = c 5 s 2 512(1-s 2 )R 0 5 32 s 2 + 48 + 100s 2 -210s 4 + 240s 4 -210s 6 √ 1-s 2 sinh -1 1-s 2 s 2 . ( 7
)
The dimensionless quadrupole moment is

Q = πc 5 s 2 96(1 -s 2 )R 0 5 16 s 2 -8 -14s 2 + 15s 4 - 24s 4 -15s 6 √ 1 -s 2 sinh -1 1 -s 2 s 2 . ( 8
)
Similar formulas are available for the pumpkin-like shapes [7].

To generalize the elliptic lemniscatoid shape sequence to asymmetric but axially symmetric shapes it is sufficient to join two halves of different elliptic lemniscatoids assuming the same transverse distance a (see Fig. 2 and [1,7]) and two different c 1 and c 2 half elongations and two different ratios s 1 = a/c 1 and s 2 = a/c 2 .

Fig. 2:

Two parameter shape sequence varying from two touching unequal spheres to one sphere or vice versa.

Hyperbolic lemniscatoids

The most commonly admitted fission path corresponds to elongated shapes with shallow necks. It can be simulated, in first approximation, by hyperbolic lemniscatoids. For the one-body configurations the hyperbolic lemniscatoids are defined by

x 2 = -z 2 + 0.5c 2 (s 2 -1) + 0.5c 8(1 -s 2 )z 2 + c 2 (1 + s 2 ) 2 . ( 9
)
For the two-body shapes the separated ovals are given by

x 2 = -z 2 -0.5c 2 (s 2 + 1) + 0.5c 8(1 + s 2 )z 2 + c 2 (1 -s 2 ) 2 . ( 10
)
Assuming the volume conservation, these shapes are one-parameter dependent. The ratio of the minor and major axes s = a/c can be used for the one-body shapes. When the ovals are separated, the opposite s of the ratio of the distance between the tips of the fragments and the system elongation can be retained (see Fig. 3). When s varies from 1 to -1 the shapes evolves from one sphere to two infinitely separated spheres. The volume of the system is, respectively for the one-body and two-body shapes: V ol =

πc 3 12 -2 + 6s 2 + 3 (1 + s 2 ) 2 2(1 -s 2 ) sinh -1 2 2(1 -s 2 ) 1 + s 2 , ( 11
) V ol = πc 3 12 -2(1 + s) 3 + 3 (1 -s 2 ) 2 2(1 + s 2 ) sinh -1 2(1 + s) 2(1 + s 2 ) (1 -s) 2 . ( 12
)
For the one-body shapes, the relative surface function reads

B s = c 2 4R 0 2 × 4(1 + s 2 ) + 2 2(1 + s 2 ) 1 -s 2 s 2 F sin -1 1 -s 2 , 1 √ 1 + s 2 (13) -2(1 + s 2 ) 2(1 + s 2 ) 1 -s 2 E sin -1 1 -s 2 , 1 √ 1 + s 2 .
E and F are incomplete elliptic integrals [7]. B s is calculated numerically for the two-body configuration. The distance r between the centres of the right and left parts is for the one and two-body shapes

r = c 4 8R 0 3 × (1 + 4s 2 + s 4 ) (14) r = c 4 8R 0 3 × (1 -s 2 ) 3 1 + s 2 . ( 15
)
For the one-body shapes the parallel and perpendicular moments of inertia and the quadrupole moment are given by

I = c 5 512(1 -s 2 )R 0 5 × 147 -27s 2 -15s 4 -225s 6 (16) - 15(1 + s 2 ) 2 (15 -34s 2 + 15s 4 ) 2 2(1 -s 2 ) sinh -1 2 2(1 -s 2 ) 1 + s 2 , I ⊥ = c 5 1024(1 -s 2 )R 0 5 × 269 + 251s 2 -145s 4 -255s 6 (17) - 15(1 + s 2 ) 2 (17 -30s 2 + 17s 4 ) 2 2(1 -s 2 ) sinh -1 2 2(1 -s 2 ) 1 + s 2 , Q = πc 5 192(1 -s 2 )R 0 5 × -5 + 61s 2 -23s 4 + 39s 6 (18)
+ 3(1 + s 2 ) 2 (13 -38s 2 + 13s 4 ) 2 2(1 -s 2 ) sinh -1 2 2(1 -s 2 ) 1 + s 2 .
For the two-body shapes these quantities are expressed as

I = c 5 512(1 + s 2 )R 0 5 × 147 + 225s + 27s 2 -15s 3 -15s 4 + 27s 5 + 225s 6 + 147s 7 (19) - 15(1 -s 2 ) 2 (15 + 34s 2 + 15s 4 ) 2 2(1 + s 2 ) sinh -1 2(1 + s) 2(1 + s 2 ) (1 -s) 2 , I ⊥ = c 5 1024(1 + s )R 0 5 × 269 + 255s -251s 2 -145s 3 -145s 4 -251s 5 + 255s 6 (20) +269s 7 - 15(1 -s 2 ) 2 (17 + 30s 2 + 17s 4 ) 2 2(1 + s 2 ) sinh -1 2(1 + s) 2(1 + s 2 ) (1 -s) 2 , Q = πc 5 192(1 -s 2 )R 0 5 × -5 -39s -61s 2 -23s 3 -23s 4 -61s 5 -39s 6 -5s 7 (21) + 3(1 -s 2 ) 2 (13 + 38s 2 + 13s 4 ) 2 2(1 + s 2 ) sinh -1 2(1 + s) 2(1 + s 2 ) (1 -s) 2 .

Comparison between the elliptic lemniscatoid and hyperbolic lemniscatoid shape valleys

In nuclear physics the question of reversibility of the fission and fusion mechanisms was a focus of discussions already in 1939 between Fermi and Bohr. The different possible shapes taken by a fissioning nucleus were firstly explore using a development of the radius in terms of Legendre polynomials, thinking that the fission process is only governed by the balance between the repulsive Coulomb forces and the attractive surface tension forces. This method leads naturally to smooth elongated one-body configurations resembling to hyperbolic lemniscatoids. This development cannot simulate strongly distorted shapes and the rupture into compact fragments or the alpha decay or capture and cluster radioactivity.

Furthermore, within liquid drop models, to reproduce the fusion data and the alpha and cluster radioactivities one must introduce an additional term, the so-called proximity energy, to take into account the strong nuclear interaction between nucleons of the surfaces in regard between almost spherical nuclei or in a deep crevice in one-body shapes. This proximity energy is evidently very small for elongated shapes with shallow necks and, then, it is often neglected but this term is important in fusion or fission through compact and creviced shapes. It exists a degeneracy in energy between these two deformation valleys.

The main available experimental data are the moments of inertia and quadrupole moments and it has been shown that they are similar in the two paths [START_REF] Mignen | [END_REF].

Prolate ternary shapes

One of the hypotheses to explain the nucleosynthesis in stars is the ternary fusion of three alpha particles to form the 12 C nucleus. In the decay channels the ternary fission has been observed even though its probability is much lower than the one of the binary fission. From the asymmetric binary shapes one may generate prolate ternary shapes (see Fig. 4) in cutting the smallest fragment along its maximal transverse distance by a symmetry plane. The shape is still only two-parameter dependent. For s 1 =s 2 =1 the shape corresponds to the initial or final sphere and for s 1 =s 2 =0 two spheres of radius R 1 are aligned with a central smaller sphere of radius R 2 .

Fig. 4: Evolution of the shape from a sphere to two equal spheres aligned with a smaller sphere between them.

Tori and bubbles

Beyond the pumpkin like shapes, ring torus may appear to finally desintegrate into n fragments emitted roughly in the same plane (see Fig. 5). The dimensionless parameter s t allows to follow this evolution

s t = (r t -r s )/2r s , ( 22
)
where r s and r t are the sausage and torus radii.

The different geometric characteristics are given by

V ol = 4πR 0 3 3 = 2π 2 r t r s 2 = π 2 c t 3 4 (1 + 2s t ), (23)
B s = 4π 2 r s r t 4πR 0 2 = πc t 2 4R 0 2 (1 + 2s t ), (26)
r s = R 0 2 3π(1 + 2s) 1/3 . ( 27
)
Bubbles of thick skin are often formed within violent reactions where the out of equilibrium effects play an essential role. Calculations within bubbles of constant density can give a first rough approach of the more complex reality [7]. Assuming volume conservation, the bubble characteristics can be calculated from the ratio p = r 1 /r 2 of the inner and outer radii.

n-alpha nuclei

Within an α-particle model the energy of the 12 C, 16 O, 20 Ne, 24 Mg and 32 S nuclei has been determined assuming different α-molecule configurations: linear chain, triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octagon, and cube [6].

Conclusion

Different shape sequences are proposed to describe simply the alpha emission or absorption, cluster radioactivity, fusion, fission, fragmentation and n-alpha nuclei. Their geometric definitions and properties are provided, mainly, the volume, the surface, the Coulomb function, the moments of inertia, the quadrupole moment and the rms radius. Within a liquid drop model approach, the total energy of a nuclear system, the dynamics of the processes and the angular distribution of the fragments may be determined.

Fig. 1 :

 1 Fig. 1: Evolution of the elliptic lemniscatoids generates by a revolution of the lemniscates around the horizontal axis and of the pumpkin-like shapes generates by a revolution around the vertical axis.

Fig. 3 :

 3 Fig. 3: Hyperbolic lemniscatoid shape sequence. At the scission point, the configuration is the Bernoulli lemniscate.

Fig. 5 :

 5 Fig. 5: Evolution of the torus configuration.