Jérémy Ranjatoelina
email: jt.ranjatoelina@iae.univ-lille1.fr

Tantely

What is an Inclusive Business Model ? An 'extended resource-based theory' definition built on the investigation of three inclusive enterprises in France

Keywords: inclusive business model, 'extended resource-based theory', "wasted" human resource, strategic intent, multiple case study

The research on inclusive business models is in general focused on developing countries' low-income people. However, some inclusive enterprises in developed countries, as France for instance, are established, and do not only fight against economic exclusion. This existence reveals the relevance and the necessity to (re)define, in a holistic perspective, what an inclusive business model is. In this paper, we forward the 'extended resource-based theory' and highlight an inclusive strategic intent in favor of a category of "excluded" or "wasted" human resources. We base our discussion on a multiple cases-investigation of three French diversified inclusive-enterprises, in order to suggest a (re)definition of the inclusive business model, and several implications for strategy and for society.

INTRODUCTION

Inclusive business models are generally viewed to be addressed, by multinational companies, at the 'base of the pyramid' (BOP) markets in the context of developing countries [START_REF] Prahalad | Serving the World's Poor, Profitably[END_REF][START_REF] Prahalad | The fortune at the bottom of the pyramid: Eradicating poverty with profits[END_REF][START_REF] Simanis | The Base of the Pyramid Protocol: Toward Next Generation BOP Strategies[END_REF][START_REF] London | Creating mutual value: Lessons from ventures serving base of the pyramid producers[END_REF][START_REF] Thompson | Business Models: Creating new markets and Societal Wealth[END_REF][START_REF] George | Innovation for Inclusive Growth: Towards a Theoretical Framework and a Research Agenda[END_REF][START_REF] Halme | Innovation for Inclusive Business: Intrapreneurial Bricolage in Multination Corporations[END_REF][START_REF] Reficco | Inclusive Networks for Building BOP Markets[END_REF][START_REF] Yunus | Social Business and big business: innovative, promising solution to overcome poverty?[END_REF]. Generally, the notion of "inclusive business" seems to emphasize "the core principle that organizations can and do, engage in social innovation activities to connect disenfranchised individuals and communities with opportunities that foster social and economic growth. In doing so, inclusive growth diminishes trade-offs between growth and inequality because the poor become enfranchised as customers, employees, owners, suppliers, and community members" (George et al., 2012: 661-662). More precisely, the "inclusive business model" is defined by the UNDP « Growing Inclusive Markets » initiative within the following words: "Inclusive business models include the poor on the demand side as clients and customers, and on the supply side as employees, producers and business owners at various points in the value chain. They build bridges between business and the poor for mutual benefit" (UNDP, 2008: 2). This consideration of the people living in poverty seems to drive social innovation within the private sector around the world. It also implies a large diversity of actors, which are federated by UNDP 'Business Call to Action' program (UNDP, 2008, 2010[START_REF]Breaking Through: Inclusive Business and the Business Call to Action today[END_REF].

Furthermore, the inclusive business model seems to have an empirical resonance with the core activities of every (social and classic) enterprise -including developed countries ones-which deliberately employs people who are in a situation of social exclusion in the majority of its human resources.

3 Lyon, 7-9 juin 2017

In France, the field of inclusive social enterprises -mainly analyzed in European research within the EMES 1 network 'work integration social enterprise' (WISE) prism [START_REF] Borzaga | The emergence of social enterprise[END_REF][START_REF] Nyssens | Social Enterprise. At the crossroads of market, public policies, and civil society[END_REF][START_REF] Defourny | Conceptions of Social Enterprise and Social Entrepreneurship in Europe and the United States: Convergences and Divergences[END_REF][START_REF] Gianfaldoni | Incentives, Procurement and Regulation of Work Integration Social Enterprises in France: old ideas for new firms?[END_REF]is particularly institutionalized. In this context, inclusive social enterprises are particularly regulated and categorized upon a specific categorization of exclusion situations. The different kinds of considered WISEs -by the EMES network related research i.e the structure d'insertion par l'activité économique (SIAE) cf. Borgaza & Defourny (2001); [START_REF] Gianfaldoni | Incentives, Procurement and Regulation of Work Integration Social Enterprises in France: old ideas for new firms?[END_REF]-do employ indeed, in a large majority, people who have been unemployed for a long period (two years and more). However, some inclusive-social-enterprise models seem to be unconsidered (or just simply forgotten) by the WISEs' French taxonomy: the entreprise adaptée (EA) 2 and the établissement et service d'aide par le travail (ESAT) 3 . In these two organization forms, workers in a situation of disability represent more than 80% of the global human resources. We advocate that an exploration of both and respectively EA and ESAT models, as the currently recognized WISEs (i.e. SIAE) and as the inclusive (classic) enterprises, should enrich the inclusive business model understanding, definition, and conceptualization.

We argue that the (recent) 'extended resource-based theory' [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF][START_REF] Fréry | Competing with ordinary resources[END_REF] sheds new theoretical insights on the highlighting of the social inclusion processes (or work integration, or employment) of "negatively-perceived" human resources, by an enterprise. [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF] suggest a new typology of resources -including strategic, ordinary and "negatively perceived" (in terms of performance), resources-, based on the subjective and intersubjective perception by respectively actors and markets. Thus, they took as an example for such a "negatively-perceived" -or "wasted" [START_REF] Morrow | American Negroes -a Wasted Resource[END_REF]-human resource (on the employment market) included by a performing (classic) enterprise: the Danish Specialisterne company -currently operating in 11 countries-which develops the work integration of people with Asperger syndrome. This illustration shows that "negatively perceived" "resources can be the basis of new business models when an entrepreneur creates new services (new uses) for them, leading to unsuspected performance" [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF](Warnier et al., : 1374)). [START_REF] Fréry | Competing with ordinary resources[END_REF] highlight the specificity of business models based on (massive) ordinary resources. In this 4 Lyon, 7-9 juin 2017 paper, we investigate within a similar approach the defining characteristics of business models which are built upon (and in favor of) "wasted" (human) resources. In this way, this communication seeks to answer to the following research question: What is an inclusive business model? We investigate empirically three inclusive enterprises: Vitamine T, APF Entreprises, and Ethik Investment. The paper consists of four parts. The first one presents a literature review of the 'extended resource-based theory' and our business model framework.

The second one explains our research design. The third part details the findings about the inclusive business models in France. Finally, in the fourth part, we (re)define and discuss the characteristics of an inclusive business model.

THE INCLUSIVE BUSINESS MODEL WITHIN THE 'EXTENDED RESOURCE-BASED THEORY'

THE 'EXTENDED RESOURCE-BASED THEORY' AND THE BUSINESS MODEL

Following [START_REF] Weppe | Quand les postulats d'une théorie induisent de mauvaises pratiques » La 'théorie des ressources' selon J. B. Barney[END_REF]2013), [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF] extend the resource-based theory by suggesting on the one hand, a new typology of resources including "strategic" ones, "ordinary" ones, and "negatively-perceived"-or "junk"-resources (Table 1).

Table 1: Three types of resources

Strategic resource

« A rare resource on the market, generally perceived as positive in terms of performance, i.e. with an expected level of productivity that is greater than its cost (acquisition or development). Such a resource is considered a potentiel source of rents »

Ordinary resource

« A common resource on the market, generally perceived as neutral in terms of performance, i.e. with an expected level of productivity equivalent to its cost (acquisition or development). Such a resource is considered, at best, as ensuring competitive parity » Junk resource « A resource overlooked or ignored by firms (i.e. not highly valuated on the market), generally perceived as negative in terms of performance, i.e. with an expected level of productivity lower than its cost (acquisition or development). Such a resource is considered as a source of costs or as destroying value by the firm that possesses it » Source: [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF]Warnier et al. ( : 1368-- Furthermore, this extension on resources consideration "raises new questions, echoing the recent work on resource management [START_REF] Sirmon | Managing firm resources in dynamic environments to create value: looking inside the black box[END_REF](Sirmon et al., , 2010) ) and business models from a resource point-of-view [START_REF] Demil | Business Model Evolution: In Search of Dynamic Consistency[END_REF])" [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF](Warnier et al., : 1375)). The recent development of research works on the 'extended resource-based theory' tends to confirm this echo. On the one hand, [START_REF] Fréry | Competing with ordinary resources[END_REF] compare business models focused on strategic resources, with business models focused on ordinary resources. They show how ordinary resource-based business models are changing the established rules in many industries through an Internet collaborative platform. On the other hand, [START_REF] Ranjatoelina | Inclure des Ressources Délaissées. Le groupe Vitamine T, un spécialiste de l'insertion[END_REF] highlight the resources' inherent orchestration-capability [START_REF] Sirmon | Resource orchestration to create competitive advantage breadth, depth, and life cycle effects[END_REF] in the deliberate inclusion of "wasted resources" [START_REF] Morrow | American Negroes -a Wasted Resource[END_REF]. [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF] define as a "junk" resource, "a resource overlooked or ignored by firms (i.e. not highly valuated on the market), generally perceived as negative in terms of performance, i.e. with an expected level of productivity lower to its cost (acquisition or development). Such a resource is considered as a source of costs or as destroying value by the firm that possesses it" (p.1371). [START_REF] Ranjatoelina | Inclure des Ressources Délaissées. Le groupe Vitamine T, un spécialiste de l'insertion[END_REF] explore the inclusion of these "negatively-perceived" human resources -oriented by the French public service for employment due to their "low-employability"-in a famous WISE. They demonstrate the implication of six key resources and competences, occurring at every strategic level of the organization, in the orchestration-capability developed by this inclusive social enterprise (Table 2). Thus, in an 'extended resource-based theory' perspective, as [START_REF] Fréry | Competing with ordinary resources[END_REF] define the platform business model as an ordinary resource-based one, we argue that the inclusive business model corresponds to "wasted" resource-based business model. Nevertheless, this deliberated focalization on "wasted resource" and the distinctive nuances between various existing kinds of inclusive enterprises (social or classic inter alia) tend to suggest the necessary development of a specific business model framework.

Entrepreneur level Organization level

Intersubjectivity

BUILDING THE 'SI-RCOV FRAMEWORK' OF BUSINESS MODEL

Inspired by [START_REF] Martinet | Formes de RSE et entreprises sociales[END_REF]2010) product centric approach to a focus on business model innovation, of which the product is but a subset" (Prahalad, 2012: 11)-our conceptual business model framework suggests to combine the [START_REF] Demil | Business Model Evolution: In Search of Dynamic Consistency[END_REF]2015) 'RCOV framework' with [START_REF] Itami | Killing Two Birds with One Stone: Profit for Now and Learning for the Future[END_REF] business model definition: "a business model is composed of two elements, a business system and a profit model […]. A firm's profit model is a model of its strategic intent to achieve various kinds of differentiation from its competitors (by product or price, etc.), while its business system is a system designed to realize that strategic intent" (Itami & Nishino, 2010: 364). We argue that the mobilization of the "strategic intent" concept [START_REF] Hamel | Strategic Intent. To revitalize corporate performance, we need a whole new model of strategy[END_REF] (and accessorily intentionally-related notions) appears here obvious, in order to characterize Although this research is abductive, we try to represent linearly our qualitative investigation design (Figure 2) to build a theoretical definition from a multiple cases study: "the process of building theory from case study research is a strikingly iterative one. While an investigator may focus on one part of the process at a time, the process itself involves constant iteration backward and forward between steps. For example, an investigator may move from cross-case comparison, back to redefinition of the research question, and out the field to gather evidence on an additional case" (Eisenhardt, 1989: 546). 10 Lyon, 7-9 juin 2017

THE MULTIPLE-CASES STUDY

The majority of research works on BOP seems generally to be oriented to developing countries.

Still, in France the inclusive business model currently knows a real empirical interest regarding CSR organizational networks like FACE (cf. IMS-Entreprendre pour la cité, 2013a, 2013b). FACE federates a more than 5.000-companies network, committed to act through a social- the case in which a person in a situation of exclusion or vulnerability creates its own enterprise.

FINDINGS: THREE DIVERSIFIED INCLUSIVE ENTERPRISES IN FRANCE

VITAMINE T

Founded in 1978, Vitamine T is one of the most famous inclusive social enterprises in France -one of the leaders of the work integration sector, and of the social and solitary economyachieving a turnover of 40 million euros and a consolidated net result of 1.6 million euros in 2013. Its unique shareholder is the non-profit association called Vitamine T. The entrepreneurial and strategic intent of its business models is to employ temporary people in a low-income and a long unemployment situation, within a 4 to 24 months' work-integration contract, to take them out of their individual social exclusion. Pôle Emploi -the French Employment Public service-relieves, to people who are looking for job for more than two years, an approval attesting this long unemployment situation and representing the pass for the incorporation of the person in the work integration social enterprise (SIAE). These target human resources represent 70% of Vitamine T's total employees -1.788 on 2.524 in 2013-. These people simultaneously participate to the value creation as they ensure their competences by learning one (or more) job within one (or more) of the 12 activities of Vitamine T's portfolio (Table 4).

12 Lyon, 7-9 juin 2017 Source: secondary data

To manage its social performance, the key indicators for Vitamine T and for the "temporary work integration sector" 10 , is the post-inclusion "dynamic pursuit rate" 11 of the included human resources. It implies the constraint for every temporary-inclusive enterprise to maintain the stability of the economic activity, despite the constant renewal of the majority of the human resources. This organization appears specific to temporary-inclusive business models. It suggests as well that the work-integration sector contributes, at the macro level, to relieve job market by actualizing the skills of wasted human resources. Thus, to maintain both economic and social performance, the business portfolio and its dynamics from its foundation -i.e. the organizational entrepreneurial capability-, appears to be a Vitamine T differentiating advantage. Indeed, since 1978, Vitamine T has launched (alone or in partnership) eighteen activities, has acquired four activities, and has known five cessations and three resales (Table 5).

10 « insertion par l'activité économique » 11 « taux de sorties dynamiques »

These dynamics and the six key resources and competences -identified by Ranjatoelina and Zaoual (2016)-, give to Vitamine T the ability to include its target human resources in activities which are in coherence with the job market needs. Indeed, to reach the social objectives -in terms of 'dynamic pursuit rate'-the permanent portfolio adaptation to activities and industries, which recruit today and tomorrow, appears within this form of work integration to be a key success factor. 14 Lyon, 7-9 juin 2017

APF ENTREPRISES

APF Entreprises is the first group of inclusive social enterprises in the French adapted sector.

It sustainably employs 3.200 people in situation of disability, on about 3.900 total employees. APF Entreprises manages and assists the business development of its 49 social enterprises, 24

ESAT and 25 EA, and its unique shareholder is the APF NGO. Since 2005 in France, every company having more than 20 employees has the legal obligation to employ disabled workers, up to 6% of its global workforce. Up to half of that quota, companies can buy goods and/or services from EA or ESAT, purchases to the adapted sector being considered under law as indirect employment of disabled workers. In an EA as in an ESAT, more than 80 % of the workforce is (individually) in a situation of disability. These two kinds of inclusive social enterprise share the same objective but differ on their respective targeted human resources and on their respective (internal and external) organization. Indeed, the situation of disability is institutionally recognized by the RQTH 12 , delivered by the CDAPH 13 of the MDPH 14 . The CDAPH also statutes on the level of disability of the person and orientates towards ESAT those who the commission believes that they would reach the requirements of the job market with difficultly. Because, while the EA is a "traditional" social enterprise -with traditional employment contracts-, the ESAT is a hybrid organization combining inclusive-socialenterprise activities, cares and eventually medical services, in which the targeted human resource is considered as worker but not as employee. In an ESAT, even if disabled workers received a remuneration in exchange of their work contribution to the value creation, they sign a "user contract" -governed by the Code for Social Action and Families and not the Labor Code, and for a period of one or two years renewable and generally renewed-and constitute in this way, the principal beneficiaries of the model. Although field actors consider EA and ESAT as a single sector -the adapted (and sheltered) sector-, the nuances between ESAT and EA suggest that each one corresponds to a specific business model. It is the reason why, after the strategic intent of APF Entreprises -which is common to APF's EA and ESAT-we present in this section, as one, the general results of the ESAT and EA business systems, insisting on their distinguishing nuances.

12 Reconnaissance de la qualité de travailleur en situation de handicap : "Recognition of disabled worker" 13 Commission des droits et de l'autonomie des personnes en situation de handicap : "Rights and autonomy commission of people with disability" 14 Maison départementale des personnes en situation de handicap : "Departmental house of disabled people" Lyon, 7-9 juin 2017 Property of a non-profit organization, in addition to being inclusive, the entrepreneurial and strategic intent of APF Entreprises is necessarily social (as Vitamine T's one). Indeed, APF is one of the main associations in France with 25.377 members, 13.572 employees, about 25.000 volunteers, and the main in the domain of social inclusion of people in a situation of disability.

The APF associative project for the period 2012-2017 is entitled: "Move the Lines! For an Inclusive Society"15 . In this way, the social mission of APF Entreprises -which in reality is a department of APF headquarter-is to include on a long term perspective, workers in a situation of disability through one of the 24 ESAT or 25 EA, and their respective activities.

APF Entreprises strategic intent was refounded with the arrival of the new management team in 2014. This year indeed, APF's board recruited a new General Manager, who nominated a new APF Entreprises Manager and his new team. The intent of this new management comforts EA and ESAT's belonging to the social economy and tends to incorporate a collaborative spirit, both vertical (inter-levels) and horizontal (intra-levels, and with competitors). These new collaborations, between subsidiaries (EA and ESAT), between APF Entreprises department and some subsidiaries, and also with competitors, sustain the group's development and lead to new synergies, ensuring both economic and social activities. One of the economic objectives included in the new strategic intent is also to reduce the dependency to subsidy revenues, to anticipate its probable reduction. Within more than three decades of existence, the year 2015 is the first with a positive net result, showing that this actualized strategic intent of APF is already bearing fruit for APF Entreprises.

The large majority -80% minimum-of both models human resources is composed by recognized disabled workers, i.e. they have a RQTH. In France, the unemployment rate of workers in a situation of disability is more than twice higher -22%-than the general unemployment of the total population -10,2%-, and the average period of unemployment is longer by 206 days for disabled people -799 days-than the entire population -593 days-16 . These numbers and facts highlight the "wasted" character of workers with disability as a human resource on the employment market. Generally, due to CDAPH's perception, the level of disability is higher among ESAT's beneficiaries than among EA's employees, making them 16 Lyon, 7-9 juin 2017 appear even more "wasted". To include their target human resources, the six key resources and competences can be found here with some nuances. On the one hand, APF Entreprises' governance is hybrid, the group develops and sustains partnerships and collaboration, and every EA or ESAT manages its own activity portfolio. On the other hand, APF Entreprises competence consists more in operations, sales and business than in entrepreneurship; the social and professional individualized coaching -which correspond to EA's practices-can be extended to cares and eventually medicals in ESAT; and, APF's APF Formation department acts like an internal training body, but not reduced to APF Entreprises. APF Formation seems more to emphasize the actualization of supervisors' competences rather than disabled workers' competences.

During the last three decades, APF Entreprises' organization has experienced a pendulum phenomenon from a centralized model to a territorial one and vice versa (verbatim). Since 2014, every EA and ESAT manages and develops its business portfolio activities according to market opportunities of their action perimeter. In terms of business, APF Entreprises segments its activities in eight poles of skills: communication products and services, administrative services, environment, logistic, electronic and electrical, mechanics and carpentry, other BtoB services, and APF Entreprises' products. Long-term market relations also lead to the development of innovative activities, business systems, and value proposals co-constructed on the specific local needs of customers become partners. For example, after analyzing -with KPMG-the next 5 to 10 years needs of its customers and prospects, APF's EA of Illkrich 17 is now the only Eastern-France company which develops electronic and electrical production on the same site. The specialization has allowed this EA to penetrate the market of radiofrequency and connected objects, thanks to a recent technological investment of 500,000 euro, and by creating four jobs.

Its products not exhaustively include: cables used by Alstom to equip French regional trains, receivers of digital terrestrial television, remote controls, programming suitcases for home automation systems, trackers for scooters, and GPS maps for fixing on trolley supermarkets.

Another example could be the APF's EA of Amiens 18 . Supported by Air France, the EA has invented a semi-automated process of reconditioning air-headphones, unique in the world. In 2016, Air France is the first customer for this business with a volume of 30,000 to 50,000 airheadphones from a total of 80,000 reconditioned headphones per day.

ETHIK INVESTMENT

Ethik Investment is an inclusive (classic) company. A part of 50% its total human resources is Founded in 2003 by two associates (now three in total), one of whom is in a situation of disability (blindness), Ethik Investment's entrepreneurial and strategic intent is defined by its General Manager as "doing business differently" and "change the point of view of society". Indeed, while one company out of five does not employ any disabled worker, and while the disabled workers' direct employment rate is 3,3% (when the law requires 6% since 2005), half of Ehtik Investment's human resources, and a third of its associates are in a situation of disability. Ethik Investment' subsidiaries simultaneously make for-profit business and include recognized disabled workers. This intent differentiates the group particularly from every Lyon, 7-9 juin 2017 market-competitors, from the adapted sector, appearing to be the basis of the group's social innovation.

Half of the global human resources is recognized as disabled workers. Indeed, they individually have a RQTH as more-than-80-per-cent EA's employees. In term of disability, the majority of Ethik Investments's employees is composed by blind or partially sighted persons. To include its disabled workers, the group seems to have developed key resources and competences.

Governance appears to be (classic but) inclusive. Indeed, groups of companies which have a blind person among their associates and for General Manager are very rare. The partnerships and managers' managerial social capital, sustain the development of co-innovations, principally in the field of events and training as we'll see after. The "Dans le Noir?" trademark, its experiential concept, and the inclusive-activities business portfolio of the group appears to be sources of synergies and even innovations. With the experience acquired through the restaurants and the event activity, a careful thought around the wellness sector conducted to the creation of a first spa in Paris and a second franchised one in Bordeaux, in 2011. For centuries, elsewhere in the world and mostly in Asia, the wellness sector has been particularly inclusive in favor of blind and partially sighted persons thanks to their natural skills in touching and handling. So, very quickly, the added value on client experience brought by blind persons' competences and situation -blindness becomes here an asset because clients who could be reluctant to undress in sight of a person in a full ability to see are more inclined to do it in front of a blind person-, is recognized by the observers -the spa is ranked second best spa of Paris by the French magazine L'Express-and by competitors as a real competitive advantage (verbatim). Training and apprenticeship of disabled employees are strategic considering the low qualification of two third of them -66% of disabled workers left school before finishing high school-. Ethik Investment focuses on this thematic in various ways. For example, the spa activity acts like a sectorial training body by assuming disable persons' training -within a certificate of professional competence in esthetics developed with the Espace Beauté Thalgo International and the access for people with a reduced visual capacity to ISIPCA's professional license in analysis and application and its professional master degree in sensory formulation and evaluation-. In the same way in other sectors, the group co-develops training and certificates with academic partners: the first master in management initially developed for blind students, and then for all disabled students was launched within Kedge Business School in 2011; the technician certificate in insurance of the École Supérieure d'Assurances was made accessible Lyon, 7-9 juin 2017 for all disabled students in 2012; idem in 2013 with IRIS school's technician certificate in IT service to organizations, and with Le CNAM's professional license degree in analysis and design of information and decision systems, and its engineering degree in information systems. The job and managerial coaching of disabled employees and services providers appears to be adapted and focused on their abilities and competences. Associated to the event activity's resources and competences it reverses positively the public's perception about employing disabled workers.

As we have just seen, the internal and external organization of Ethik Investment's activities are based on disabled workers' abilities and competences. Indeed, the organization is internally oriented to improve their competences on activities, and externally oriented to move the regard of the society through the business models' value propositions.

The value propositions of the group are addressed in a way to three stakeholders. The first kind is a goods and/or services' proposition to clients and customers. These value propositions are related to each activity or they can follow some synergies, like for example, the "spackage" which includes for two persons: a duo massage and a mixed steam room session at the wellness center, and then a head-to-head meal at the restaurant. The second kind of value propositions is (direct or indirect) an employment proposition to disabled employees and services providers.

Functions and contracts of disabled workers are classic ones. The third kind is a shared value proposition to society. However, no group revenue comes from public subsidies (as opposed to social enterprises benefiting from "employment aid" 19 ). The financial independence allows to sustain the development of innovative inclusive business models and projects. For example, since 2014, through Ethik Connection's partnership with the Fondation Malakoff Médéric Handicap, the group has also piloted a project to improve employment's access and retention for workers with autism in France and more particularly workers with Asperger autism. 20 Lyon, 7-9 juin 2017

DEFINING AND DISCUSSING THE INCLUSIVE BUSINESS MODEL BY ITS STRATEGIC INTENT

DISCUSSING THE RESULTS

In this paper we sustain that inclusive business models concern not only the developing countries and not only organizations involved against poverty. Our 'in-partnership' actionresearch led to the selection, retention, and exploration of three cases of established enterprises -Vitamine T, APF Entreprises, and Ethik Investment-which include four major inclusive business models in France: the social business model which includes predominantly and in a long-term perspective recognized disabled workers who would difficultly reach job-market expectations (i.e. the ESAT); the social business model which includes predominantly and in a long-term perspective recognized disabled workers (i.e. the EA); the social business model which temporary predominantly includes workers unemployed for a long period (i.e. the SIAE); the business model which includes, in a classic way, for half, recognized disabled workers (i.e. the disability-inclusive company). This exploration highlights distinctions and nuances between the categories ("segments"?) of people targeted as "beneficiaries" by these various kinds of enterprises. It shows that in developed countries, existing major inclusive enterprises are more focused on excluded workers' employment than directly on poverty reduction. In this way, the inclusive business models appear to be addressed to the poor people but also to other categories of disenfranchised people [START_REF] Halme | Innovation for Inclusive Business: Intrapreneurial Bricolage in Multination Corporations[END_REF] which we holistically consider to be (individually) in a situation of social exclusion or vulnerability. Indeed, poverty can be seen as a form of economic exclusion -leading in the quasi-totality of the cases to a situation of social exclusion-. Our results confirm that on the job market all those excluded workers' have a common characteristic, they are "wasted" human resources i.e. their job applications are constantly rejected because of the presumption of negative performance that recruiters have about them.

Our results, specially Ethik Investment's ones, also allow us to discuss the six key resources and competences to include wasted human resources [START_REF] Ranjatoelina | Inclure des Ressources Délaissées. Le groupe Vitamine T, un spécialiste de l'insertion[END_REF]. First, the governance of the Ethik Investment group is not hybrid but his entrepreneurial and strategic intent is inclusive. Its social innovation lies in the exclusive business character of its revenues.

It suggests to replace the "hybrid governance" by an inclusive entrepreneurial and strategic governance (maybe social), as the first key resource and competence of an inclusive business 21 Lyon, 7-9 juin 2017 model. Partnerships and leadership's "managerial social capital", the inclusive-activities portfolio, some entrepreneurial and business skills, are found in the three cases. Therefore, these three key resources and competence of inclusive business model remain unchanged.

Concerning the fifth key resource and competence, according to the results of Ethik Investment's case we understand that we should not only focus on the training of human resources initially being neglected by the market, but also on the awareness of the people and society about human resources that are being "wasted" nowadays. Finally, the sixth key resource and competence of an inclusive business model can also be amended, following our results: job coaching and individualized management based on initially-wasted-humanresources' abilities, competencies, and projections.

The SI-RCOV business model framework, elaborated and proposed in this research, extends the RCOV model [START_REF] Demil | Business Model Evolution: In Search of Dynamic Consistency[END_REF], 2015). The results reveal the methodological potential of the SI-RCOV framework to frame not only social and/or inclusive enterprises' business models, but every static or dynamic business model(s) analysis.

Those results lead us to suggest a (re)definition of what an inclusive business model is.

DEFINING WHAT AN INCLUSIVE BUSINESS MODEL IS

UNDP's definition of the inclusive business model is centered on poor people's inclusion. However, our results highlight that inclusive business models in developed countries are mostly focused on excluded workers' employment. The common points revealed by our three cases make the inclusive business models correspond to the business models based on a majority of wasted human resources. This focalization in favor of wasted human resources, can be [START_REF] Itami | Killing Two Birds with One Stone: Profit for Now and Learning for the Future[END_REF] we insist on the central role of (entrepreneurial and) strategic intent in the business model. Moreover, this centrality of strategic intent and its direction in favor of people excluded from the markets, directly refer to C.K. Prahalad's work [START_REF] Hamel | Strategic Intent. To revitalize corporate performance, we need a whole new model of strategy[END_REF][START_REF] Eisenhardt | Building Theories from Case Study Research[END_REF][START_REF] Prahalad | The Fortune at the Bottom of the Pyramid[END_REF][START_REF] Prahalad | Serving the World's Poor, Profitably[END_REF][START_REF] Prahalad | The fortune at the bottom of the pyramid: Eradicating poverty with profits[END_REF][START_REF] Prahalad | Bottom of the pyramid as a Source of Breakthrough Innovations[END_REF]. Defining theoretically the inclusive business model by its strategic intent in favor of wasted human resources also contributes to the 'extended resource-based theory' stream [START_REF] Warnier | Extending Resource-Based Theory: Considering strategic, ordinary and junk resources[END_REF][START_REF] Fréry | Competing with ordinary resources[END_REF][START_REF] Ranjatoelina | Inclure des Ressources Délaissées. Le groupe Vitamine T, un spécialiste de l'insertion[END_REF], which constitutes the first research focused on wasted resource-based business models. As we introduced it, our findings confirm the interest of this new prism -its theoretical anchorage and articulation-to renew strategic management's view upon social business models [START_REF] Yunus | Building Social Business Models: Lessons from the Grameen Experience[END_REF] and inclusive social enterprises [START_REF] Borzaga | The emergence of social enterprise[END_REF][START_REF] Nyssens | Social Enterprise. At the crossroads of market, public policies, and civil society[END_REF][START_REF] Defourny | Conceptions of Social Enterprise and Social Entrepreneurship in Europe and the United States: Convergences and Divergences[END_REF][START_REF] Gianfaldoni | Incentives, Procurement and Regulation of Work Integration Social Enterprises in France: old ideas for new firms?[END_REF]. Indeed, defining a business model by both its model of entrepreneurial and strategic intent, and its business system(s) appears particularly relevant to the exploration, the analysis and the development of business models which differentiate themselves by their social aim. In this way, this research tends to comfort the pertinence of considering within the business model prism, organizations and activities which deliberately create "not-only-economic" value [START_REF] Hart | Creating Sustainable Value[END_REF][START_REF] London | Creating mutual value: Lessons from ventures serving base of the pyramid producers[END_REF][START_REF] Porter | Creating Shared Value. How to reinvent Capitalismand unleash a wave of innovation and growth[END_REF].

IMPLICATIONS AND CONTRIBUTIONS

Regarding the inclusive business model within the 'extended resource-based theory', reveals and suggests both interesting implications and contributions. First, the use of a main strategic management theory should facilitate practitioners' appropriation equally in developing and developed countries. Indeed, the complete framework -including its theoretical definition and articulation-suggested in this research is likely to support the development of inclusive enterprises at the international level. It should also facilitate the development of strategicmanagement researchers' interest for inclusive enterprises -and especially social ones-. For instance, the 'extended resource-based theory' sheds new light on WISEs [START_REF] Borzaga | The emergence of social enterprise[END_REF][START_REF] Nyssens | Social Enterprise. At the crossroads of market, public policies, and civil society[END_REF][START_REF] Defourny | Conceptions of Social Enterprise and Social Entrepreneurship in Europe and the United States: Convergences and Divergences[END_REF][START_REF] Gianfaldoni | Incentives, Procurement and Regulation of Work Integration Social Enterprises in France: old ideas for new firms?[END_REF] models analysis [START_REF] Ranjatoelina | Inclure des Ressources Délaissées. Le groupe Vitamine T, un spécialiste de l'insertion[END_REF]. Secondly, even if the choice of the Lyon, 7-9 juin 2017 geographical investigation field could appear quite surprising, we argue that this empirical context points out some insightful implications for strategy and for society.

On the one hand, the 'extended resource-based theory' explains how an entrepreneur with an alternative strategic intent for a resource, reaches to create a performing organization.

Nevertheless, it does not evoke the imitation and/or replication of a 'generic' business model which leads to the emergence of a new sector, a new industry. Two of our three cases have been founded more than 35 years ago and move towards particularly regulated sectors and environments with strong norms -it explains why they are characteristical but non representative of their respective sectors-. As leaders of their respective sectors, these two cases should contribute to enrich the 'extended resource-based theory' (Figure 1) with a recursive phenomenon which highlights new sectors emergence -from the performing business model to a market-perceptions' actualization-i.e. corresponding to the collective response of the range of actors sharing the same strategic intent about an under-evaluated resource. Indeed, those sectors -the work-integration sector and the adapted sector-do not share the dominant perception and intent about wasted human resources on the job market. On the other hand, the very institutionalized context in France suggests an abundance of experimented initiatives -contingent certainly but-contributing, in terms of learning, to the global uprising of inclusive business models and to the reinvention of the global economic system [START_REF] Porter | Creating Shared Value. How to reinvent Capitalismand unleash a wave of innovation and growth[END_REF]. Indeed, generally inclusive rimes with universal. By analyzing this context, this research highlights three particularly inspiring enterprises for every actor aspiring to singularly do business differently.

CONCLUSION

This research focuses on a topic remaining unsufficiently observed in the literature: the business model of enterprises which deliberately predominantly include wasted human resources on the employment market. It is based on the exploration of three diversified inclusive enterprises in France -Vitamine T, APF Entreprises, and Ethik Investment-, highlighting the nuances and distinctions, and the common characteristics of their respective business models. This highlighting suggests to (re)define the inclusive business model by its strategic intent in favor of wasted human resources. Managerial and societal implications of this research are of interest to many stakeholders (e.g. institutional actors, social entrepreneurs and entrepreneurs, social Lyon, 7-9 juin 2017 economy's managers, consultants, researchers and teachers). Its theoretical contributions strengthen the extended resource-based theory. However, the exclusive investigation of cases from a developed country suggests the relevance to extend this research by exploring inclusive business models in the context of a developing country. Such an exploration will allow us to overcome the limitations of this research by consolidating our design and studying the possible determinism of context about inclusive business models' configuration.

  hand, they propose a representation of the process by which, a creative entrepreneur who identifies a new use, valorizes an under-evaluated resource on the market (Figure1).

Figure 1 :

 1 Figure 1: The extended resource-based theory

(

  2016) reference to Morrow reveals the dynamical character of perception and its dependency to cultural areas.

  and to essentialize the variety of existing inclusive enterprises in a unique definition and a unique conceptualization. Moreover, our empirical position tends to enhance the conceptual suggestion of the (extended) 'SI-RCOV framework' (Figure 2) -i.e. Strategic Intent; Resources and Competences; internal and external Organization; Value propositions-in order to frame our exploration of existing inclusive business models. 8 Lyon, 7-9 juin 2017

Figure

  Figure 2: The SI-RCOV framework

Figure 3 :

 3 Figure 3: A qualitative research desig

  portfolio, against all forms and situations of exclusion, discrimination and poverty, in France and abroad (Brussels, Belgium; Rio de Janeiro, Brazil; Bizerte, Tunisia).The singularity of our action-research partnership and the quest after exhaustivity had led us to retain three characteristical but non representative diversified enterprises -Vitamine T, APF Entreprises, and Ethik Investment-out of four established inclusive business models -the ESAT business model, the EA one, SIAE one, and classic-inclusive company business modelin France. In this perspective, we voluntarily excluded "self-inclusive" business model(s) i.e.

  17 near to Strasbourg in the Bas-Rhin French department Lyon, 7-9 juin 2017 EA and ESAT create simultaneously value propositions of three different natures, addressed to three kinds of stakeholders, at three levels. At a micro-level, the first value proposition of the EA or ESAT is an employment one to the individuals who are wasted on the employment market -it is particularly true in the ESAT where the disabled worker is considered as a beneficiary or a client-. At a meso-level, the nature of the second value proposition is consisted by products and services to clients and customers. The eight pole of skills and the two previous examples suggest the diversity, the variety of the APF Entreprises' value propositions to markets. And at a macro-level, EA and ESAT assume a general interest mission which could be seen as value proposition for the State and all the society. In this perspective, although APF Entreprises wishes to reduce its dependency to subsidies, revenues from Public services can be seen as the fair retribution of ESAT and EA' societal contribution.

  in a situation of disability. It permanently employs about 80 persons and federates an approximatively 300 consultants-contributors network, and achieved a turnover of 5 million euros in 2013. The group operates in three BtoC activities with the brand "Dans le Noir?": restaurants (present in six countries: France, United-Kingdom, United States, Spain, Russia, and Kenya), wellness centers and spas, and shops. The concept is based on taking care of customers by employees with reduced visual capacity in a (total or partial) dark environment. Ethik Connection aggregates three BtoB activities: Ethik event, event and sensitization (exported in six countries: United-Kingdom, Poland, Thailand, Saudi Arabia, Switzerland, and Spain); Ethik Management, consulting in coaching and training; and Ethik Image, consulting in strategy, communication and creation.

  explained as an inclusive strategic intent. So, to define conceptually what an inclusive business model is, our theoretical ground and the results of our multi-cases study lead us to suggest the following definition: "An Inclusive Business Model is a business model characterized by an inclusive entrepreneurial and strategic intent in favor of 'wasted' -by the traditional markets, due to their situation of poverty, exclusion, and/or vulnerability-resources as human beings. The business system(s) of such a business model realizes this differentiating inclusive intent i.e. by including these people as the predominant human resources of the value creation (employees, producers/providers, entrepreneurs) of one activity or more, developed and organized within a coherent adaptation with their abilities, competences, and projections". This definition emphasizes a holistic perspective and refers to several 22 Lyon, 7-9 juin 2017 scientific streams and concepts in strategic management. Articulating two levels -the strategic intent of the model and its realization-, it contributes to Itami and Nishino's (2010) business model definition and conception. Indeed, following

Decision process Resources-related process Level of performance Industry level

		Subjectivity	Actualisation
	-Strategic Resource	Evaluation of the	Actions on the resource
	-Ordinary Resource	resource	(business model)
	-Junk Resource
	Pricing process
			6
		Lyon, 7-9 juin 2017

1.2. THE INCLUSION OF "WASTED HUMAN RESOURCES"

Table 2 : The key resources and competences implicated in 'wasted' resource inclusion Key Resources and Competences Strategic level

 2

	1. A hybrid governance
	2. Partnerships whereby leadership's « managerial social capital » and external engagements seem to play a spreading and a non neglectable	Corporate
	legitimation role
	3. A diversified activities-portfolio of inclusive business which generate
	synergies	Business
	4. An entrepreneurial capability based on the permanent actualization
	principle of the inclusive activities-portfolio
	5. A social and professional individualized coaching in which an
	included and permanent employees' association allows a significant improvement of « wasted » human resource's 'employability'	Functional
	6. A Training body which proposes adapted training contents
	Source: Ranjatoelina & Zaoual, 2016
	Moreover, in reference to J.J. Morrow's advocacy for black American workers' inclusion in
	southern US enterprises, published in 1957 in the Harvard Business Review, Ranjatoelina and
	Zaoual (2016) suggest to replace the terms "junk resource" by "wasted resource", especially
	and obviously in the case of human resources. History shows us indeed, that the human
	resources concerned by Morrow's article, considered as negative at this time, in this space, are
	now ordinary ones. At the same time, in another space or cultural area the same resource
	shouldn't necessarily be perceived as "negative" -as Morrow shows us in its comparison
	between Southern and Northern US for example-. In this way, Ranjatoelina and Zaoual's

Table 4 : Vitamine T's business portfolio Subsidiaries Activities Capital Repartition

 4

	La Ferme des Jésuites	Gardening, maintenance of green	Vitamine T (100 %)
	Les Serres des Prés	spaces	Vitamine T (100 %)
	Inser'Croix	Pallets recycling, eco-friendly cleaning vehicles	Vitamine T (100 %)
	Soluval	Out-of-service vehicles recycling	Vitamine T (78 %) Macif (22 %)
	Envie 2e Nord	Electric, electronic, and home appliance recycling	Vitamine T (83 %) Van Gansewinkel (17 %)
	Envie Nord	Household appliances, furniture and second-hand items renovation and sale	Vitamine T (100 %)
	Janus	Temporary job placement	Vitamine T (66 %) Adecco (34 %)
	Médiapole	Social mediation	Vitamine T (100 %)
	Mobilille	Urban mobility services	Vitamine T (100 %)
	Solutis	Cleaning services	Vitamine T (100 %)
	Vitavert	Urban cleaning	Vitamine T (100 %)
	IF VT	Certified training body	Vitamine T (100 %)

within a French public-private conventionalized PhD called a PhD-CIFRE, for "Industrial Convention for a Research Formation", as a researcher-consultant

'act against exclusion foundation'

'physical disability France association'

Hauts-de-France 'regional chamber of social and solitary economy'

« Bouger les lignes ! Pour une Société Inclusive »

« Tableau de bord national. Emploi et chômage des personnes handicapées. France entière. Bilan du premier trimestre 2016 » ('National Scoreboard. Employment and unemployment of people with disability. Whole France. Results of the first 2016 quarter'). AGEFIPH Publications, N°2016-2, 2016, june 23th, 13p., available online : https://www.agefiph.fr/Actus-Publications/Publications-et-etudes

) and ordered by the Directorate-General Research


Comparing research in American urban ethnology on white/non-white encounters to French poli=cal sociology on the specificity of the "banlieues" reveals several resemblances and many differences. The laFer may stem either from methodological gaps or from the popula=ons observed, or a combina=on of both.

Where Americans focus mainly on microscopic interac=ons at street level, French scholars tend to address the same issue from the top, and they do it in a macroscopic way. Historical and cultural factors help explain why their respec=ve strategies di er in everyday life, and why academic knowledge varies from one bank of the Atlan=c to the other.

What is « urban ethnology »?

The micro study of social encounters of mobile ci=zens in urban seNngs with the eye of the cultural anthropologist?

The meso study of social problems in ci=es with the eye of a sociologist?

The macro study of urban policies and social control by poli=cal scien=sts?

The legacy of the Chicago School Field observa=on. "Neo-realist naturalism à la Zola".

A street-level view of people living at the margin: the poor, hobos, migrants, gangs, bowling teams, "freaks", ar=sts, etc. Focus on "social hybrids" from "Bohemia" and "Hobohemia" (R. Park).

The City as a social unit made of sub-units (gheFo, street corners) each with its own culture (Park, Burgess, McKenzie & Wirth, 1925).

The legacy of the Chicago School

From ecology to poli=cs: nature = disorder, culture = poli=cs.

Poli=cs is the art of dealing with the irra=onal.

Sociology is the study of crisis, poli=cs is the study of civiliza=on.

The legacy of the Chicago School

Sociology vs. Social work (1913, Albion Small): against the "do gooders" (Robert Ezrah Park).

Community studies (from the 30s to the 50s).

Community based organiza=ons (CBO) (now)?

The French Touch From Durkheimian posi=vism to Bourdieu's (and Foucault's). post-posi=vism.

From psychology to sociology.

From phenomenology to structuralism, then cri=cal studies. The pitch: What?

Interac=onnism in America / Poli=za=on in France.

Social behavior in America / Social Policy in France.

Self-organizing communi=es in the US, poli=cal movements controlled from the top in France.

Inter-ethnic and mul=cultural rela=ons in the US, transcultural rela=ons in France.

The pitch: Why?

Because objects and methods are dissimilar (race as such is not an issue in France).

Because the field is mainly assigned to sociologists in the USA and to poli=cal scien=sts in France.

Because the French State is much stronger and more redistribu=ve than the Federal administra=on in the US.

DOES METHODOLOGY MATTER? TO WHICH EXTENT THE CONTEXT MATTER?

Summary

Varieties of methods

Morally driven research in France

Bourdieu: fieldwork is not always objec=ve. It generates commitment, and difficult moral choices.

Bourdieu: dependence towards those who are observed : "Observing a community to which the researcher is estranged compels to work permanently to maintain the interpersonal link without which the survey cannot be completed".

USA: bottom up; France: Top down

Focus : US individual behavior vs. F community organizing. Indicators: US s=gmas vs. F sta=s=cs.

Case selec=on: US hazard vs. F tes=ng hypotheses.

Targets: US outsiders and denizens (Anderson) vs. F ordinary people as ci=zens.

USA: bottom up; France: Top down

The Chicago school gives depth and flesh to sta=s=cal analysis via unforeseen events that stem from any unlikely encounter.

The French Touch levels small differences, it rubs out idiosyncracies, and aggregates events into a general law.

To which extent the context matter?

Varieties of contexts

American mul=cuturalism vs French pluralism /Republicanism. Race maFers more in the US than religion does in France.

The history of slavery differs from the legacy of colonialism.

Varieties of contexts?

A young American black « has something to prove. He is a provisional status » (Elijah Anderson), "he is on proba=on" (Alice Goffman).

Same with a young Muslim in France: more oten suspected by the police than other teenagers.

  Ethnography vs. Sociology. Public affairs and Poli=cal Science vs. Poli=cal sociology. Top down or BoFom up.

Field work (USA) vs. interviews (F).

Interac=onnism + agency (USA) vs. Structuralism + ins=tu=ons (F).

Politically driven research

Chicago: figh=ng for recogni=on / Paris: figh=ng poverty.

Chicago: figh=ng segrega=on / Paris: figh=ng inequali=es.

Chicago: figh=ng policemen's inappropriate behavior / Paris: figh=ng terrorists.

Two views on the same reality?

Chicago: avoidance / Paris: engagement. Chicago: survival / Paris: struggle. Chicago: muddling through the "white space" / Paris: satura=ng or subver=ng the white space.

The American gheFo: a town in the town.

The Bri=sh clusters: islands in urban seas.

The French "quar=ers": Chinese walls + highways.

Varieties of contexts?

But: Is the "nigger moment" of acute disrespect comparable to the "délit de faciès" in France ? Yes and no.

Yes: iden=ty issue in both countries.

No: if a person speaks mainstream French she is fully French, whatever her origin is.

Community of des=ny > community of origin.

To conclude

2 genealogies, 2 levels, 2 ambi=ons.

The observa=ons made are par=ally overlapping.

American scholars are concerned with the racial issue.

French scholars are obsessed by na=onal poli=cs.


Internet as a source of new objects in PS

Applied to internet Governance

A self governed and self sustainable system through mutual consolida?on?

Crowd-sourced by the community Open community of discussions A success story leading to an Unknown Poli?cal Object (UPO) QUANGO (a quasi non governmental org) Quasi Law (and bylaws), guidelines Incomplete contract, no cons?tu?on 21/01/19

Incomplete contract

"These core values are deliberately expressed in very general terms, so that they may provide useful and relevant guidance in the broadest possible range of circumstances. Because they are not narrowly prescrip?ve, the specific way in which they apply, individually and collec?vely, to each new situa?on will necessarily depend on many factors that cannot be fully an?cipated or enumerated; and because they are statements of principle rather than prac?ce, situa?ons will inevitably arise in which perfect fidelity to all eleven core values simultaneously is not possible. The Board will exercise its judgment to determine which core values are most relevant and how they apply to the specific circumstances of the case at hand, and to determine, if necessary, an appropriate and defensible balance among compe?ng values ». (ICANN website, Governance)

The Internet Network

IGF

Move one step forward

	Cyber war Poli?cal campaigns Norm dissemina?on New diplomacy 21/01/19 Governance as an old concept in PS Governance means: one step below Government No central authority, liOle hierarchy Central and local, public and private stakeholderism 21/01/19 Benign neglect from PS LiOle interest for Internet governance Too technical? Or ethical ? Tool, rather than goal? Lack of concern for neighboring disciplines Communica?on studies Interna?onal studies Organiza?on theory GOVERNANCE OF "THE ROOT" OR "THE NETWORK". Part 2 21/01/19 Political sociology S?cks to the sociology of influence Misses the social network turn 21/01/19 International Studies Discard the autonomy of classical IOs S?ck to weak concepts such as: interna?onal regimes Regime complexes "Governance" New IOs are more challenging Meta organiza?ons Meta networks 21/01/19 International Studies Regime complexes or ins?tu?onnal complexes: "an array of par?ally overlapping and non-hierarchical ins?tu?ons governing a par?cular issue area" (Raus?la & Victor) Or: across several issue areas (Schemeil) Linkages, density; "messiness" (Marzouki) Get rid of realist accounts of IR Complexifies theories of the social networks Refine organiza?onal theory uses of 21/01/19 Abandon classical and cri?cal sociology networks 21/01/19

Classical Sociology: Networks of influence

	21/01/19 Complex sociology 21/01/19 Networks in Communication studies 21/01/19 Networks in Internet studies 21/01/19 TOWARDS AN INTERDISCIPLINARY RESEARCH ON INTERNET GOVERNANCE Part 3 21/01/19 A new theory of Governance Networked Governance (draws from Organiza?on Theory) From compe??on to symbiosis (draws from Economics and sociology) From one step behind full government to one step beyond full cooperaMon (draws from Poli?cal Science) Merger: absorp?on partnership outsourcing bridging bonding From conflict to symbiosis Autonomy conflict compe??on Coali?on: within the in-group; exclusive; temporary; specific subcontrac?ng 21/01/19 A theory of IO networks Collabora?on among units = across ?me, space, and sectors Transac?on costs (TC) and coordina?on costs (CC) are in inverse propor?on Cluster = high TC, low CC Network = Low TC, high CC 21/01/19 Internal change : Leadership, mo?va?on, exper?se, principals External change: loss of relevance, new demands, members investments & divestments Collabora?on: coordina?on, coopera?on New norms New structures Mobiliza?on of new resources, innova?on New risks & opportuni?es Overlap control or encroache-ment Niche network 1 Complex network Niche 21/01/19 From expansion to networks mandates marginaliza?on New Obsolescence or network N

InsulaMon

Coordina?on: with insiders; pooling resources and processes Collabora?on: with outsiders; project by project Coopera?on: with outsiders; across projects Symbiosis: symmetrical, reciprocal

21/01/19

Between privateness and publicness


H L Rakotoarison

F Wurtz

J Stepanek

B Delinchant

O Cugat

Integration of the Volume Segmentation Method into an Optimization Process. Application to the sizing of a Micro-Actuator for Deformable Mirrors

This work comes from the demand of the optimization of an elementary micro-actuator of a deformable mirror. First, we have created a generator which package an electromagnetic solver based on the volume segmentation method into a standard software component. An experiment and a FEM simulation are done to validate the model of elementary micro actuator. And finally, a process of optimization and Pareto methodology are used to chose the efficient coil shape between two suggested structures.

I. INTRODUCTION

Microsystems designers meet some problems when they want to manufacture prototypes of electromagnetic micro-actuators. This is caused by the cost and the time that they spend, so it is necessary to optimize the shape of the device before its manufacturing.

Electromagnetic microsystems are frequently made of micro-magnets and micro-conductors. To optimize effectively such a structure, a modeling using the volume segmentation method such as Dipole3D [START_REF] Delamare | 3D Calculation of permanent magnet interaction[END_REF] is efficient.

However, it is not evident to connect Dipole3D directly into our optimization software, because the optimizer needs a model based on a software standard.

So, an automatic model generator is build to satisfy this requirement. It allows the capitalization of our approach to other micro-actuator modeling.

After the model has been generated, a validation on a FEM simulation and on an experiment is presented.

Finally, the paper discusses the optimization process and the methodologies used to compare two suggested structures.

II. DESCRIPTION OF THE INTEGRATION OF THE MODEL IN A

OPTIMIZATION SOFTWARE

A. The modeling approach used

Dipole3D [START_REF] Delamare | 3D Calculation of permanent magnet interaction[END_REF] solves systems made of magnets and conductors by subdividing the system into elementary magnetic dipoles and elementary electric conductors, and then computing the interactions of each element by applying the Biot&Savart and magnetic moment theorems. Finally a summation of all these elementary interactions (fields, forces or torques) is made.

B. Packaging the model into a standard software component

To ensure the standardization of the models to be optimized, our laboratory strives to establish a software framework in which any form of model (analytical equations, finite element model, volume segmentation model, etc…) could be integrated in software components known as Computation OBject or COB [START_REF] Delinchant | New working possibilities to electrical software thanks to component methodologies[END_REF]: physically it is a file with a ".cob" extension.

This software component has to compute the output parameters of the model as well as the associated sensitivity. So, the COB can be illustrated by a box with inputs (Ei) and outputs (Sj) and their respective differentials (dEi, dSj).

As shown in figure 1, to standardize the model, three software layers are added to the core of Dipole3D.

In our case, the inputs of the COB match the geometric parameters of the device, the currents flowing within the conductors and the magnetization of the magnets. The outputs represent magnetic fields, forces or torques.

The architecture around the COB can be divided into two complementary software parts (Figure 2): on one side several generators, which produce the COB, and on the other side, services which use the COB such as optimizers and calculators.

Java C++

C. Sensibility calculation

The optimizer needs the differentials of the outputs because it exploits a gradient based algorithm [START_REF] Singh | Pratical Considerations in the Optimization of Induction Motor Design[END_REF]. In our case, the calculation of these differentials is done by finite differences, of which the method is evoked below:

The first step is to compute the partial derivative for each output Sj (1):

In data-processing code, this formula is valid for a value of hi which should be selected judiciously: sufficient small compared to Ei but not too small compared to the precision of the computer [START_REF] Delinchant | Reducing sensivity analysis time cost of compound model[END_REF].

The expression of the differential is (2):

III. THE AUTOMATIC MODEL GENERATOR

A. The purpose: ease of modeling

The use of Dipole3D, its integration into a COB and the computation of the differentials require a solid knowledge in programming languages. But the microsystems designer may not be a good programmer: so the automatic generator gives an easy way to model their magnetic micro-actuator with a minimum waste of time.

B. No need to code full programs…Use the generator.

The designer writes a text file which contains the description of his device, its shape, the magnetization of magnets or the current density of conductors. Descriptions are some simple keywords derived from Dipole3D: its writing is not difficult but requires respecting some rules. After defining geometric and physical properties of his device, the user only needs to click on a button of the generator to generate his model.

Figure 3 shows the internal structure of the generator.

IV. APPLICATION TO THE MODELING OF A MICRO-ACTUATOR FOR DEFORMABLE MIRROR

A. The deformable mirror

The goal of adaptive optics in astronomy is to compensate in real time degradations on the images caused by atmospheric turbulences. A deformable mirror (Figure 4) equipped with electromagnetic micro-actuators [START_REF] Cugat | Deformable Magnetic Mirror for Adaptive Optics: Technological aspects[END_REF] is a device used for this purpose.

The objective of our analysis was to find the ideal configuration of the elementary micro-actuator of this mirror making it possible to develop the maximum of force while consuming a minimum electric power, for a given dimension. Micro-magnets are stuck under the reflective membrane. Fixed micro-coils are placed respectively opposite each magnet to control the local deformation of the membrane. Each magnet/coil couple constitutes an elementary electromagnetic micro-actuator.

i n i n i i j h i j h E E E E S E h E E E S E S i ) ,... ,..., , ( ) ,.... ,..., , ( lim 2 1 2 1 0       (1) n n j i i j j j j dE E S dE E S dE E S dE E S dS                   ... ...

B. Electromagnetic micro-actuator

Our analysis (modeling and optimization) has helped designers to choose the best structure between two coils shape as shown in figure 5: the planar structure (left) and the solenoid structure (right).

C. Experimental validation and Finite Element (FLUX2D) simulation

The time necessary to optimize the model is related to objects subdivision (magnet, coil) which constitute the model. According to the desired precision, this time can increase considerably. So, before starting the optimization process, it is significant to validate the model by experimentation on a prototype and/or by simulating a model on a FEM software[8] (Figure 6).

The magnet of the prototype is made of NdFeB with 1T of magnetization, the coil contains 95 turns, and the wire diameter measures 0.1mm.

Modeling in FLUX2D and Dipole3D also takes into account the fill factor of the coil. Figure 7 gives a comparison and allows the validation of the model.

D. Model generation

Figure 8 shows the graphic interface of the generator with commands script used to model the micro-actuator, some comments (text preceding by a "//") are typed in addition to clarify the model.

The two command lines after the comment are the geometrical and physical description of the magnet.

The next command line adds a spatial translation to the magnet.

The next two command lines create the geometry of the coil and add a parameter: the current density.

The last two command lines indicate that the computation of the force is on the magnet.

E. Model specifications

The device is intended to correct images. The first significant factor is the resolution: as the surface occupied by each micro actuator is smaller, the resulting image improves.

Fig. 1 .

 1 Fig.1. The component model for sizing.

Fig. 3 .Fig. 4 .Fig. 2 .

 342 Fig.3. Internal architecture of the automatic generator.

Fig. 5 .

 5 Fig.5. Two types of elementary micro-actuators.

Fig. 8 .Fig. 7 .Fig. 6 .Fig

 876 Fig.8. The modeling command script for the automatic generator

The constraints on the input parameters (Table I) of the model are shown below. With the preceding constraints, come to be added constraints on the outputs (Table II) of the model: the force developed by each micro actuator and the heat losses by the coil which also is the objective function. F. Optimization results.

After having plugged the model into the software optimizer (CDI-Optimizer [START_REF] Delinchant | A component-based framework for the composition of simulation software modeling electrical systems[END_REF]) and configured its input and output parameters according to specifications, the optimization process was launched: an algorithm based on SQP approach was chosen [START_REF] Wurtz | A Methodology and a Tool for the Computer Aided Design with constraints of Electrical Devices[END_REF] in the software optimizer. Figure 9 shows the geometrical evolution of the two structures before and after optimizations.

G. Multi objective optimization

With the same specifications on the input parameters, each model was optimized for several output parameters (For several values of given force, the values of the Joule losses were minimized).

Hence each optimization process gives a new shape to each structure. This method is known as the Pareto border. The result demonstrates (figure 10) that for any given force, at a constrained diameter, the associated planar structure is more efficient than the solenoid structure.

V. CONCLUSIONS

The integration of the volume segmentation method (implemented in Dipole3D) into an optimization software was done to meet the demand for microsystems modeling. The automatic generator was created in the aim to offer to microsystems designers a handy tool which helps them to size their devices. It was applied to the modeling of the micro-actuator for the deformable mirror. The optimization result gives the best structure between two coils shape.


H Chetouani

B Delinchant

G Reyne

Efficient modeling approach for optimization of a system based on passive diamagnetic levitation as a platform for bio-medical applications

Keywords: Optimal design, Bio-medical systems, Microsystems, Diamagnetic levitation. I. LEVITATION IN BIOMEDICAL APPLICATIONS

Constrained optimization may use time-consuming analysis on standard methods such as the finite-element method (FEM). In order to decrease the optimization time and to enable flexible gradient based optimization, this paper reports, a semi-analytical modelling approach and optimization of two variants of a diamagnetic levitation system as contactless manipulation platform for bio-medical and biochemical applications.

The magnetic biochips are in increasing development and evolution supported by several applications in the biochemical and biomedical fields [START_REF] Winkleman | A magnetic trap for living cells suspended in a paramagnetic buffer[END_REF][START_REF] Pamme | On-chip free-flow magnetophoresis: continuous flow Separation of magnetic particles and agglomerates[END_REF][START_REF] Lee | Manipulation of biological cells using a microelectromagnet matrix[END_REF][START_REF] Watarai | Capillary magnetophoresis of human blood cells and their magnetophoretic trapping in a flow system[END_REF]. This family of microsystems includes partial or complete integrations of elementary or complex tasks processed by traditional laboratories of our scale. The automation and parallelization of these tasks [START_REF] Pamme | On-chip free-flow magnetophoresis: continuous flow Separation of magnetic particles and agglomerates[END_REF] in the small world avoids human handling which is frequently not precise and likely of errors, and reduces times and the costs necessary to achieve operations such as diagnostic, analyzes and particles sorting [START_REF] Pamme | On-chip free-flow magnetophoresis: continuous flow Separation of magnetic particles and agglomerates[END_REF][START_REF] Lee | Manipulation of biological cells using a microelectromagnet matrix[END_REF][START_REF] Watarai | Capillary magnetophoresis of human blood cells and their magnetophoretic trapping in a flow system[END_REF]. This evolution of micro-actuators based on magnetic actuation has lead to an increasing need for specific modeling methodologies especially for optimization requirements. Thus, in order to facilitate the use of gradient based optimization process [START_REF] Singh | Practical Considerations in the Optimization of Induction Motor Design[END_REF], this work deals with a realistic semi-numerical modeling approach of a system based diamagnetic levitation declined in two variants. Indeed, these systems have more and more applications, especially in biomedical field [START_REF] Chetouani | Diamagnetic levitation with permanent magnets for contactless guiding and trapping of microdroplets and particles in air and liquids[END_REF][START_REF] Chetouani | Principle and Analysis of a Two-dimensional On Chip Magnetophoresis of Bioparticles for Contamination-free Biochemical Reactors[END_REF]. Diamagnetic contactless handling of bioparticles brings amazing perspectives to biochips and avoids serious problems as adhesion, adsorption and contamination.

II. MAGNETOPHORESIS FORMULATION AND MODELING

Currently, existing modeling approaches treating diamagnetic levitation problems are numerical methods such as finite elements method or magnetic moments method [START_REF] Chadebec | A review of magnetostatic moments method[END_REF]. Theses modeling approaches are not adequate for full design studies. Therefore, in order to permit an adaptable optimization with gradient based algorithms, semianalytical modeling was chosen and then established to compute outputs and formally exact sensitivities according to the inputs parameters of design [START_REF] Delinchant | Reducing Sensitivity analysis Time-Coast of Compound Model[END_REF]. The proposed device comprises four fix magnets and a levitating diamagnetic object. In order to approach both possible diamagnetic materials: anisotropic and isotropic and both possible fluids for biological bodies: air and liquid, the models of a levitating anisotropic graphite plate in air, and a levitating isotropic latex sphere in fluid were established. The magnetic field generated by these four parallelepiped magnets was expressed using equivalent surface method [START_REF] Akoun | 3D analytical calculation of the forces exerted between two cuboidal magnets[END_REF]. In this formulation the induced induction of the diamagnetic levitating object was neglected. This induced field did not affect significantly the external field due to the low magnetic susceptibilities of the diamagnetic materials. Hereafter is reported the magnetophoretic force [START_REF] Hirota | Magneto-Archimedes Levitation and its Applications[END_REF] formulations corresponding to both proposed cases.

A. Modeling of an anisotropic diamagnetic graphite plate in air

A diamagnetic anisotropic plate in air with (2a, 2b, 2c) dimensions, having magnetic susceptibilities (x, y, z) respectively on x, y and z-axis and within a magnetic field induction expressed by its components Bx, By and Bz, experiences a magnetic force obtained from integral over whole diamagnetic plate volume [START_REF] Pamme | On-chip free-flow magnetophoresis: continuous flow Separation of magnetic particles and agglomerates[END_REF]. According to Ostrogradsky theorem (3) [START_REF] Boukallel | Levitated micro-nano force sensor using diamagnetic materials[END_REF], magnetic force components (magFx, magFy and magFz) can be simplified leading to surface integrals [START_REF] Watarai | Capillary magnetophoresis of human blood cells and their magnetophoretic trapping in a flow system[END_REF][START_REF] Singh | Practical Considerations in the Optimization of Induction Motor Design[END_REF][START_REF] Chetouani | Diamagnetic levitation with permanent magnets for contactless guiding and trapping of microdroplets and particles in air and liquids[END_REF]. This simplification allows to establish a flexible semi-numerical model based on surface integrals to compute the magnetic force components and thus to enables a faster optimization.

   v dv z y x G µ z y x magF ). , , ( 2 1 ) , , ( 0 (2)
    s v ds n f dv f . . .  (3)
                  c c b b v dZ dY Z z Y y a x G Z z Y y a x G µ dv x z y x G µ z y x magFx . . ) , , ( ) , , ( 2 1 . ) , , ( 2 1 ) , , ( 0 0 (4)
                  c c a a v dZ dX Z z b y X x G Z z b y X x G µ dv y z y x G µ z y x magFy . . ) , , ( ) , , ( 2
1 . ) , , ( 2 1 ) , , ( 0 0
(5)

                  b b a a v dY dX c z Y y X x G c z Y y X x G µ dv z z y x G µ z y x magFz . . ) , , ( ) , , ( 2
1 . ) , , ( 2 1 )
, , ( 0 0 [START_REF] Chetouani | Diamagnetic levitation with permanent magnets for contactless guiding and trapping of microdroplets and particles in air and liquids[END_REF] where 0  is the vacuum magnetic permeability.

B. Modeling of an isotropic diamagnetic latex sphere in a liquid

A diamagnetic isotropic sphere having a radius R within a susceptible liquid experiences a magnetic force according to magnetic susceptibility contrast Δχ between the liquid and the sphere material. This force is obtained with an integral over the whole sphere volume [START_REF] Delinchant | Reducing Sensitivity analysis Time-Coast of Compound Model[END_REF]. Then magnetic force components (magFx, magFy and magFz) can be simplified leading to surface integrals [START_REF] Akoun | 3D analytical calculation of the forces exerted between two cuboidal magnets[END_REF][START_REF] Hirota | Magneto-Archimedes Levitation and its Applications[END_REF][START_REF] Boukallel | Levitated micro-nano force sensor using diamagnetic materials[END_REF]. This simplification allows to establish a flexible semi-numerical model to compute magnetic force components based on surface integrals and thus a faster optimization.

x G     (7) 2 2 2 ) , ( 1 z y R z y g    , 2 2 2 ) , ( 2 z x R z x g    , 2 2 2 ) , ( 3
y x R y x g    (8)     v dv z y x G µ z y x magF ). , , ( 0 2 ) , , (  (9)
                 R R Y R Y R dY dZ Z z Y y Z Y g x G Z z Y y Z Y g x G µ z y x magFx 2 2 2 2 . . ) , ), , ( 1 ( ) , ), , ( 1 ( 2 ) , , ( 0  (10)
                 R R Z R Z R dZ dX Z z Z X g y X x G Z z Z X g y X x G µ z y x magFy 2 2 2 2 . . ) ), , ( 2 , ( ) ), , ( 2 , ( 2 ) , , ( 0  (11)
                 R R X R X R dX dY Y X g z Y y X x G Y X g z Y y X x G µ z y x magFz 2 2 2 2 . . )) , ( 3 , , ( )) , ( 3 , , ( 2 )

C. Automated modeling tool

A modeling tool [START_REF] Denis | A Generator of Software Components dedicated to the Optimization of Engineering Systems[END_REF] based on this diamagnetic computation method was developed. Designer has to describe the geometrical and physical system (size, magnetic parameters, etc) and the tool generates automatically these formulas. This tool (Fig. 1) computes forces with magnets, current conductors with several shapes (parallelepiped, sphere, cylinder, arc of cylinder, etc).

III. MODELING VALIDATION

The proposed device is composed of a diamagnetic anisotropic plate having a susceptibility χz=-4.510 -4 and χx= χy =-8.10 -5 , a density ρg=2200 kg/m 3 . It levitates above four magnets configured as shown on Fig. 2-(a). The magnetic vertical force experienced by the plate was computed semi-analytically, and then it was compared to the magnetic moment method simulation for which the induced magnetization of diamagnetic object is not neglected. The results obtained from these two modeling methods are reported on Fig. 2-( a performing modeling and that approximation (no induced induction into the diamagnetic material) is realistic.

IV. OPTIMIZATION

The optimizations performed tries to converge towards magnets structures for given levitating objects and levitation heights. Its objective is to maximise the spatial stability of the object. The stability of the levitating object is quantified by the total force gradient acting on corresponding axis. These optimizations respond to precise constrained specifications. A semi-analytical model characterizing the device was established. It enables computation of the forces exerted on the diamagnetic levitating object and theirs corresponding gradients as outputs. These outputs are required to express the stability of the levitating object according to structure geometry and physical parameters. In order to use an efficient optimization algorithm like SQP (Sequential Quadratic Programming), an automatic tool was used to generate formally exact sensitivities of the established semi-analytical model. This tool is called a generator and is part of the CADES design framework pattern shown Fig. 4, which describes how model and optimizer can interact in an iterative and reusable manner. The symbolic derivation of the model produces formal exact sensitivity (without noise like finite differences) but also quicker model. Indeed, force sensitivity depending on a diamagnetic size parameter, leads to a simple integral formula as describe in the following equations. Thus, as numerical integration take most of the model computation time, this may reduce consequently the global sizing time.

       a dx x g b x g b b a f 0 ) 0 , ( ) , ( ) , ( (13)
Using this design framework, the graphite plate and the polystyrene latex sphere devices were sized as shown in the following.

A. Diamagnetic anisotropic graphite plate in air

The device comprises a fixed part and a mobile one as shown on Fig. 5. The fix part of the device comprises four electroplated CoPt magnets [START_REF] Vieux-Rochaz | Electrodeposition of hard magnetic CoPtP material and integration into magnetic MEMS[END_REF] magnetized throughout the plane with a residual magnetization Jz=0.3 T. These magnets are identical and have as parameters magsize, magheight and gap which correspond respectively to the magnets squared base size, magnets height and distance between two adjacent magnets. The mobile part is a plate made of pyrolitic graphite which is an anisotropic material. Its magnetic susceptibilities on x,y and z axis are [χx, χy, χz] = 10 -5 [-8, -8, -45] and its density ρg=2200 kg/m 3 . This plate has as parameters: diasize (the squared base size of the plate) and diaheight (height of the plate). Both parameters were fixed respectively at 10 µm and at 0.5 µm. The objective of optimization was to converge towards a solution giving an optimal stability satisfying a fixed levitation height of 2µm. This levitation height is computed between top of magnets and bottom of diamagnetic plate at position where the total force on z axis become null. Neglecting the Archimedes force due to low density of the medium. Only two forces act vertically on the diamagnetic plate: the weight of the plate (diaweight) and the magnetic force (magFz) [START_REF] Chetouani | Diamagnetic levitation with permanent magnets for contactless guiding and trapping of microdroplets and particles in air and liquids[END_REF]. Therefore, the balance of vertical forces FtotZ can be expressed as:

ight e diaW z F mag tZ o Ft      (15)
The parameters magsize, magheight and gap were constrained as given on Table . 2. The optimization results corresponding to these constrained specifications are illustrated on Table The Pareto optimization results shown on Fig. 7 validate the obtained results of the classic optimization. This one was done in two steps. Firstly isovalues of the gradient of the force on x axis where plotted as function of the parameters gap and magsize. Secondly the curve of the parameter gap was plotted as a function of magsize with the total force on the vertical axis and its gradient constrained to be respectively null and negative to satisfy the stability criterion on vertical axis, where the force on x-axis and its gradient were free.

B. Diamagnetic latex bead in paramagnetic medium

The fix part of device is still the same used above for the diamagnetic graphite plate in air. However the mobile part is now a diamagnetic sphere made of polystyrene latex which is an isotropic material. Its susceptibility is p=-8.2.10 -6 and its density ρp=1050 kg/m 3 . The medium is a paramagnetic configured with about 0.47 M of manganese chloride tetrahydrate (MnCl2.4H2O) in pure water, having a magnetic susceptibility m=7.10 -5 and a density ρm=1000 kg/m 3 . This sphere has as parameter diasize (the radius of the sphere) fixed at 1.5 µm. The objective of optimization is to converge towards a solution giving an optimal stability satisfying a levitation height of 3 µm. The parameters magsize, magheight and gap were constrained as given on Table dist=3 µm. This position is determined from the balance of forces experienced by the sphere on vertical axis. Due to spherical geometry and the density of the medium, three forces acts verticaly: diaweight, diaArch (16) and FtotZ (17) respectively the weight of the sphere, the Archimedes force and the balance of forces. The forces curves corresponding to unstable and stable devices are shown on Fig. 9.

g diasize diaArch m   ) 8 ( 3 4 3  (16) rch A dia ight e diaW z F mag tZ o Ft        (17)

V. CONCLUSION

We report an efficient and accurate semi-analytical modeling and optimization approach of devices based on passive diamagnetic levitation. The studied devices are composed of a levitating object and fixed part of four permanent magnets dedicated for biochemical and biomedical applications. In order to establish semi-analytical modeling of the proposed device surface approach was used to compute analytically the magnetic field induction produced by the magnets. Forces components formulas experienced by the levitating objects were also simplified to surface integral expressions. These simplifications enabled faster optimizations which were thereafter performed by a SQP algorithm. The results demonstrate a solution to perform a fast and flexible optimization of devices based on diamagnetic levitation which can be generalized to other application fields. This avoids the usual approaches which are not adequate for the optimization task in this field of applications.

Fig. 1 -

 1 Fig. 1 -Interface screenshot of the tool used to generate designs computation formulas.

  b). These results show OIPE 2006 -"The 9th Workshop on Optimization and Inverse Problems in Electromagnetics" -September 13th -15th 2006, Sorrento (Italy)

Fig. 2 -

 2 Fig. 2 -(a) Device configuration, (b) Simulation results of the magnetic force Fz obtained from the semianalytical model and the magnetic moment method.

Fig. 3 -

 3 Fig. 3 -The design meshed with an tool based magnetic moments computation.FEM computation was also compared with these modeling techniques but has lead to interpretation issues. Indeed, diamagnetic forces, which are about some picoNewtons, are drowned into meshing noise. Thus to compute forces with a FEM tool, meshing noise has to be removed by this technique. Compute the force on the diamagnetic plate with χ=0. The force value result only on the noise.  Compute the force on the diamagnetic plate with real χ value, without changing the meshes.  Substract the result value with preceding value to obtain the real force (Table.1).

  1).

Fig. 4 -

 4 Fig. 4 -(a) Generators create, (b) components, (c) Services use.

OIPE 2006 -

 2006 "The 9th Workshop on Optimization and Inverse Problems in Electromagnetics" -September 13th -15th 2006, Sorrento (Italy)

  .

Fig. 5 -

 5 Fig. 5 -(a) Geometry of device with unstable plate on x axis, (b) Geometry parameters of the diamagnetic plate and the magnets, (c) Optimal design for axial stability of the diamagnetic anisotropic plate.

Fig. 6 -

 6 Fig. 6 -Forces experienced by the diamagnetic plate, (a) vertical forces according to the distance between the magnets and the plate at the case of the unstable design, (b) horizontal force and its gradient according to the x position of the plate at the case of the unstable design, (c, d) Case of the stable design.

Fig. 7 -

 7 Fig. 7 -2D cartography of stability on x axis and the optimal design localisation expressed according to the squared base size of the magnet and the gap between the magnets.

  .

  4. The optimization results corresponding to these constrained specifications are shown on Table.

5 .

 5 It illustrates the inputs parameters and the computed outputs values corresponding to two geometries. The diamagnetic sphere is unstable at the first geometry shown on Fig. 8-(a) on x axis and stable on vertical one and the levitation height is 3µm. The second one shown on Fig. 8-(c) corresponds to a solution giving an optimal horizontal stability which was obtained after optimization process. The levitation height is computed between top of magnets and bottom of diamagnetic sphere at the position where the total force on z axis become null. The levitation height is fixed at OIPE 2006 -"The 9th Workshop on Optimization and Inverse Problems in Electromagnetics" -September 13th -15th 2006, Sorrento (Italy)

Fig. 8 -

 8 Fig. 8 -(a) Geometry of device with unstable plate on x axis, (b) Optimal design for axial stability of the diamagnetic plate.

FxFig. 9 -

 9 Fig.9 -(a,b) Forces experienced by the diamagnetic plate, (a) vertical forces according to the distance between the magnets and the plate at the case of the unstable design, (b) horizontal force and its gradient according to the x position of the plate at the case of the unstable design, (c, d) Case of the stable design.

TABLE I :

 I FORCE COMPUTATION WITH FEM METHOD

	Vertical distance (µm)	Force computation with	Computation with	Resulting
		=0 (1)	=10 -5 [-8, -8, 4.5] (2)	force=(2)-(1)
	3	13.5725018E-9	13.5698702E-9	2.6316E-12

TABLE III :

 III UNSTABLE DESIGN PARAMETERS AND OPTIMIZATION RESULTS

			0	1  10 6	2  10 6	3  10 6	4  10 6	5  10 6
	Name	Designation	Unstable design	Optimal design	unity
	diaWeight	Weight of diamagnetic plate	-1.0788		-1.0788	pN
	magFZ	Vertical magnetic force	-1.0799		1.0791		pN
	FtotZ	Balance of vertical forces	1.1611E-9 (~0 N)	3.0364E-10 (~0 N) µN
	gradFx_x	Gradient of Fx along x axis	0.1808(unstable)		-1.3668 (stable)	µN/m
	gradFz_z	Gradient of Fz along z axis	-0.1916 (stable)		-1.672 (stable)	µN/m
	gap	Distance between two magnets 5		6.4430		µm
	magheight	Magnets height	2.5		10		µm
	magsize	Magnets squared base size	2.5		8.5960		µm

OIPE 2006 -"The 9th Workshop on Optimization and Inverse Problems in Electromagnetics" -September 13th -15th 2006, Sorrento (Italy)

TABLE IV :

 IV OPTIMIZATION SPECIFICATIONS

TABLE V :

 V UNSTABLE DESIGN PARAMETERS AND OPTIMIZATION RESULTS

	Name	Designation	Unstable design	Optimal design	unity
	gap	Distance between two magnets 1.4	6.0075	µm
	Magheight Magnets height	1.26552	4.7046	µm
	Magsize	Magnets squared base size	2.40428	11.0468	µm
	diaWeight Weight of sphere	0.14561	0.14561	pN
	diaArch	Archimedes force	0.13868	0.13868	pN
	magFZ	Vertical magnetic force	0.007	0.00697	pN
	FtotZ	Balance of vertical forces	0.000066 (~0 N)	0.000037 (~0 N) pN
	gradFx_x	Gradient of Fx along x axis	0.31019 (unstable)	-2.8182 (stable) nN/m
	gradFz_z	Gradient of Fz along z axis	-4.0304 (stable)	-16.684 (stable) nN/m