Marie Duru-Bellat

Social inequalities in the French education system: the joint effect of individual and contextual factors

, on topics such as gender inequalities, educational democratization in European countries, school effectiveness and school choice.

In France like in most industrialized countries, there has been an opening up of educational opportunities, during the last thirty years: thus, the proportion of a generation reaching the level of the baccalauréatthe upper secondary school leaving diploma -rose from 20% in 1966 to 40% in 1986, and was up to 68% in 19%. However, at the same time, schooling careers continue to be marked by strong social inequalities: among 20-21-year-olds (in 1996), 51% of the children of manual workers reach the level of the baccalauréat, compared with 87% of the children of top executives, teachers or lower service class members (DEP 1997). Until recently, these differences have been mostly analysed as being related to families' cultural resources, the pupils being, according to their background, more or less in phase with the contents and the values of an institution unconcerned about the differences between pupils ('indifférente aux différences', Bourdieu said). From the 1980s onwards, in connection with the growing prevalence of a less deterministic conception of social phenomena, and a more assertive one concerning the actor, more attention has been given to the context in which these social inequalities are generated, through various social processes. The context, which is first of all the school attended, but also the teachers themselves and their pedagogical practices, or the way pupils are grouped in classes, and more broadly, the organization of the system itself, which lays the framework in which actors behave. After having briefly set out the present state of social inequalities at the different levels of the system, 1 we shall analyse how contextual factors can appear finally on their own to be an important factor in the inequalities between pupils.

Inequalities in academic achievement, and in educational choices, at the successive levels of schooling

Early and cumulative inequalities in academic progression

In France, almost every child benefits from preschool education from age three (99.6% in 95-96), even if the compulsory age for schooling is six. However, preschool education remains slightly delayed among children of farmers or unskilled manual workers. That is not unimportant, because the longer the preschool education, the better one succeeds within primary school, especially at the first level (Cours Préparatoire -CP). The level of achievement at that level (CP) proves to be strongly linked with social background: among pupils having entered into the lower secondary school -collège in 1989, about 20% of the children of manual workers have repeated the CP, compared with 2% of teachers' children. Repeating a year is still quite common in France, even if research shows that it does not help pupils sufficiently in overcoming their academic weaknesses, and that repeating has even some detrimental impact upon future progress. At the end of primary education, social inequalities in knowledge (measured by standardized tests) are already quite large: when entering collège, differences of 17 points has been observed, in French, between children of manual workers and pupils of top executives (the mean score being about 66 points); the difference amounts to 18 points in mathematics (the mean score being about 63 points). 2

Unequal 'choices' in the search for difference

The social inequalities already generated when leaving the primary school widen within the lower secondary school -the collège 3 -through two distinct mechanisms. The first one concems progression: within collège, academic attainment differs according to social background; social inequalities over time are even stronger than during primary education [START_REF] Duru-Bellat | Pour une approche analytique du fonctionnement du système éducatif[END_REF]. Morever, secondary education in itself widens the inequalities in achievement observed at the beginning: pupils who are good achievers when entering collège progress more than pupils who are weak from the outset.

Furthermore, two specific processes generating inequalities are at work at the collège level: subject option choices, and (still more important) streaming mechanisms. Even if the structure of the collège has been progressively unified, there is a first choice to be made right from the first level (6ème), concerning the study of a foreign language; this choice proves to be related to social background, since, for instance, 26% of teachers' children choose to study German, compared with 8% of children of manual workers.

What is true for option choices is even more valid as far as streaming choices are concerned, especially at the end of collège; alternative routes are: entering into the upper secondary school (the lycée), to prepare for three years for the baccalauréat, be it a general or a technological one, or beginning vocational training lasting two years (brevet d'études professionnelles). As expected, these choices are related to the academic level of pupils, and the best pupils will follow, on average, the longest and the most prestigious tracks, while, on the contrary, vocational ones are perceived as relevant only for academically poor pupils. But streaming decisions differ markedly according to pupils' social background. Among pupils who have not repeated during the collège years (having not experienced important problems), 77% of top executives or teachers' children enter into the lycée, compared with 32% among manual workers' children.

Those differences are mainly the outcome of families' demands. While parents are conscious that they should give up the most demanding tracks when their child is academically too weak, this selfselection operates more or less importantly, according to the social background, especially when the child's achievement is average or slightly weak: families of low socioconomic status, who are more afraid of the risk of a failure in subsequent studies, prove to be more cautious and abandon asking for general tracks, i.e. the most prestigious ones, and fall back on a vocational route. Actually, teachers in charge of the decision-making process strive to follow families' demands; they do not modify the 'choices' of those who express strongly selective demands, thus ratifying and exacerbating the social inequalities produced by those 'choices'.

The way pupils and families choose and more broadly manage their schooling career becomes still more important in the upper secondary school. At this level, the different tracks become more specialized, and pupils' social background often proves relevant in this respect: the proportion of top executives' children (which is about 16% among the 20-24-year-olds) decreases from the tracks leading to the general baccalauréat (33%) to the technological (14%) and the vocational ones (11%). Within the general tracks, the different types are not chosen randomly: more children from high SES choose the scientific baccalauréat S than the social sciences (ES) and the humanities ones (L). This is pre-empted by options choices, made within the lycée, which are connected with each other, but not according to what would be 'pedagogically' logical: it is among pupils who have chosen to study Latin in the first year of the lycée (2nde) that the percentage of choices for a scientific second year is the highest; those pupils, having managed to enter into what is the most prestigious route, will often drop this subject which has become irrelevant. We observe too that pupils having studied Latin in the first year and having not succeeded in entering into a scientific second year (1ère), 'prefer' entering an economic one rather than a literary one, which again reveals a positional logic (since the economic baccalauréat is the 'second best' choice), rather than a pedagogical one.

Considering that in France, there is a strong link between the type of baccalauréat you obtain and which tertiary study you can follow, the choices within higher education will be marked by social inequalities: the proportion of top executive and teachers' children is 32.5% in the first level of academic university tracks, with open access, 13.5% in the two year tracks leading to a precise job at a lower executive level, and amounts to 48.5% in the special classes leading (after hard competition) to élite schools (grandes écoles). The over-representation of pupils from high SES grows with the prestige of different schools, in such proportions that those pupils make up more than 80% of the student body of schools such as Polytechnique, or the École Nationale d'Administration (Euriat and Thélot 1995).

On the whole, in tertiary education, where managing his or her own career requires from the student very sophisticated knowledge or know-how, orientation in a broad sense (including choosing another course in case of failure, choosing the best place to study, etc.) becomes the main process through which social inequalities are generated. Actually, at this level, no more social inequalities related to academic achievement are observed, which would be in addition to the schooling value one has accumulated during primary and secondary schooling.

From primary to tertiary education, a continuous process thus goes on: being behind agewise and having difficulties from the beginning of primary school, pupils from low SES enter into the secondary level and face the latter's streaming processes with an handicap as far as global levels of achievement are concerned. At the secondary level, significant social inequalities of attainment occur, at least till the first year of the upper secondary school. Nevertheless in addition, social inequalities concerning 'demand' appear each time a choice is to be made (for pupils of similar level of achievement). On the whole, social inequalities do not become blurred through time, but accumulate; and the more one goes along in the educational system, the more social inequalities of academic achievement diminish, compared with social inequalities linked to choices and orientation. In the 1980s, the social difference in the rate of access to the first form of the lycée (between children of manual workers and of top executives) was explained by three roughly equal components: inequalities in achievement within primary schooling, inequalities in achievement within collège, and orientation processes within the secondary level [START_REF] Duru-Bellat | Social inequalities in French secondary schools: from figures to theories[END_REF].

In a context of strong widening of educational opportunities, within a more and more diverse and complex system, social inequalities linked to orientation will certainly have a growing importance. This is not without ambivalent consequences upon youngsters' representations of the function of school in their own social trajectory, especially for those who, thirty years before, would have had no chance at all to enter into secondary education. Children from low SES face a progressive exclusion (or relegation towards the least prestigious tracks), which probably makes them more stigmatized than in the past: 4 they appear to have been offered some opportunity, and their schooling career appears to result solely on merit; what those youngsters 'excluded from within' feel in schools (their expérience scolaire) is often very harsh [START_REF] Dubet | A l'école. Sociologie de l'expérience scolaire[END_REF].

The schooling context does make some difference

Until the changes of the 1980s (cf. Broccolichi and van Zanten, and Derouet, 2000), the centralization prevailing in France has diverted attention away from looking at contextual effects in the generation of schooling careers. However, the latter did take place in diversified contexts, which may be not neutral as far as inequalities between pupils are concerned. In particular, collèges may differ to a large extent in the social characteristics of their pupils (for instance, the proportion of manual workers' children may vary from 10-80% according to schools).

School effects as far as progression and orientation are concerned

If French primary schools do not differ significantly in their ability to help their pupils progress, nevertheless, significant schools effects are observed both at collège and at lycée levels [START_REF] Bressoux | Les recherches sur les effets-école et les effets-maîtres[END_REF]. Schools where pupil progress is strongest implement an efficient management of time and discipline; they also have positive expectations regarding the attainment of their pupils, and achieve a good coverage of the curriculum's contents; these school characteristics, which prove to be linked with a better efficiency are more often found together in schools attended by pupils from high SES [START_REF] Grisay | L'évolution des acquis cognitifs et socio-affectifs des élèves au cours de années de collège[END_REF].

Besides, schools attended by a majority of pupils from high SES tend to be less selective as far as tracking is concerned than those which cater for a majority of low SES pupils. lt seems as if each school, consciously or not, adapts its orientation practices to its majority of 'customers'; the school tends thus to be less selective when the pupils are from middle or high social classes or more selective when the opposite appears. Thus there are contextual effects attached to every pupil in the school: for instance, pupils from low SES attending 'posh' schools get access to more prestigious tracks than when attending working class schools, which is by definition more often the case [START_REF] Cousin | Construction et évaluation de l'effet établissement: le travail des collèges[END_REF]. In fact, this results from pupils' choices: the pupils are led to adopt the attitudes and values of the group that is numerically dominant in the school: in the 'posh' collèges, the prevailing high level of educational aspirations pulls toward the top the demand of every pupil, especially those from low SES, the demands of the latter consequently prove more ambitious. Since decisions about tracking set out to follow youngsters' demands, it becomes understandable that 'posh' schools prove to be less selective [START_REF] Duru-Bellat | Pour une approche analytique du fonctionnement du système éducatif[END_REF].

The influence of teachers, their practices, and the way pupils are grouped in classrooms

Some differences emerge as much or even more often at the class level. This is particularly true as far as progress is concerned: these prove more variable from one class to another than between schools, especially at the primary level. During the first year (CP), for instance, progress is more influenced by the pupil's teacher than his or her social background [START_REF] Mingat | Expliquer la variété des acquisitions au cours préparatoire: les rôles de l'enfant, la famille et l'Ecole[END_REF]. Academically weak pupils are more prone to these teacher effects; the result is that efficient teachers distinguish themselves by their ability to make this kind of pupil progress more, the inequalities in achievement between pupils being consequently less important in their classes.

The concrete teaching practices of those teachers have seldom been studied in France. But it seems that no practice proves to be efficient in every given context. If research is unanimous in stressing the impact of the pupil's active learning time and of teachers' positive expectations, most of the relationships between practices and progress vary according to the kind of pupils studied [START_REF] Bressoux | Les recherches sur les effets-école et les effets-maîtres[END_REF]. For instance, with pupils from high SES, the most efficient teachers are very demanding, foster a high level of stimulation, and often criticize; while with pupils from low SES, it is more efficient to encourage, to try and motivate and to play clown criticisms, etc. However, some results seem more straightforward: thus a lot of practices aimed at making some differentiation in teaching do in fact widen the inequalities between pupils. This is particularly so as far as the setting up of ability groupings is concerned.

In France, a random grouping of pupils in each class is supposed to be implemented at each level. However, at least at the collège level, a large share of collèges implement some ability grouping (only about 20% do not put together pupils within classes this way). They do so, ail the more because they are attended by low SES pupils. In a context of growing competition between schools, collèges would try to keep some academically good pupils, by offering them some 'protected' classes [START_REF] Payet | Collèges de banlieue[END_REF]. Actually, at the collège level, ability grouping widens markedly differences between pupils, with better progress in high level classes and poorer ones in weak level classes, especially when these are also homogeneous [START_REF] Duru-Bellat | La constitution de classes de niveau par les collèges: les effets pervers d'une pratique à visée égalisatrice[END_REF]). As we have already mentioned, some ability grouping is achieved through the choice of a foreign language or rare subject; these choices also prove to be marked by social background; the result is that the best pupils, and pupils from the most privileged background are put together in the same classes and in the same schools (cf. [START_REF] Broccolichi | School competition and pupil flight in the urban periphery[END_REF]. Besides, the influence of the kind of class attended overlaps on to academic performances; it concerns too every day socialization, especially attitudes toward school and the image one has of oneself. At the collège level, pupils' confidence (and their parents') in their subsequent schooling career varies more according to the class they belong to than to the school attended [START_REF] Grisay | L'évolution des acquis cognitifs et socio-affectifs des élèves au cours de années de collège[END_REF].

On the whole, a substantial part of the high SES pupils' advantage in schooling rises from the fact that they have access to schools that give them better working conditions (more efficient schools, less selective as far as tracking is concerned, often receiving more resources, high level classes, etc.). 5 Conversely, it seems difficult to put in place a climate favourable to learning and fostering a positive experience of schooling when the school brings together mostly low SES children. More generally, access to a specific schooling context, and the choice of this context by actors is becoming more and more a crucial factor in the generating of social inequalities in schools.

Often underestimated, the influence of the supply of schools and of institutional and organizational factors

Finally, context also includes the way schooling careers and orientations are formally (institutionally) regulated. For instance, the way formal directives organize tracking is very important: to suggest to teachers (as it is the case in France) to follow families' demands leads to the social bias those demands incorporate into the decision. This is all the more true when official rules do not implement any selection (as is most often the case at the tertiary level), as self-selection will prevail, in tune with social bias, as already mentioned.

Besides, after the baccalauréat, youngsters' choices take place in a context characterized by a specific geographic distribution of schooling opportunities. In average towns where more and more often tertiary institutions are present, youngsters' choices (especially when they are from low SES background) tend to concentrate on the tracks offered locally. ln this respect, economic factors do intervene, as being a student is much less expensive when you can stay in your own town. Even if creating possibilities of tertiary education in average towns aims at democratizing access to this level, the fact is that it is students from low SES who prove to be the most influenced by the local opportunities; the fact that their choices are consequently distorted by supply locally leads to a real risk -from a social point of view -of a dual university.

In summary, the overall pattern of the relationships between education and jobs affects individual strategies. I n France, some diplomas are now being downgraded (as far as wages or social status are concerned); nevertheless, the comparative level of education continues to remain valuable when one is looking for a job, in a context of job shortage, resulting in a chain of depreciation of diplomas, except for the highest ones. Youngsters act quite soundly in trying to accumulate diplomas, as, if the return of one degree may prove to be devalued, it remains however, necessary, if you want to get in the front of the queue for jobs. These trends are all the more pronounced in France as general training is the dominant way to rank people and allocate them jobs within firms, a 'level of education' logic prevailing upon a logic of vocational training. The fact remains that, like monetary inflation, this relative downgrading of diplomas may widen social inequalities.

Conclusions

This short presentation of social inequalities in the French educational system shows that democratization in school is far from achieved; the fact is that, underlying macro-sociological regularities, actors, with unequal assets, strive to use the system in the way they consider to be in their own interest. Even if educational structures have on the whole evolved towards unification, actors use these structures to continuously re-implement new differentiations, aimed at positioning their children along a unique hierarchical line running, at the baccalauréat level for instance, from the scientific option clown to the technological ones. In this respect, the best route to take is the one which gives access to tertiary tracks considered to be the most promising as far as employment prospects are concerned, even if the former's academic content is not perceived as very attractive. This logic produces a lot of instrumental 'second best' choices; in this context, the notion of personal and genuine plans, so valued in official texts, does not prove very relevant and even appears as a double bind: this is because if a pupil is academically good, he or she will be persuaded, whatever his or her preferences may be, to try and enter into a scientific route, and will be firmly advised to do so, because it seems to be the 'normal' choice for good pupils.

Besides, choosing the right subject, and, more and more often, the right school, requires up to date information about how the system operates informally. In no official booklet will you find that an effective way to get a scientific baccalauréat is to choose Latin in the first year of the lycée. As Bourdieu and Passeron have said (1970), for cultural goods in general, the choice of a subject presupposes 'possession of the cultural code required for decoding the o bjects displayed'.

In other respects, we wish to stress that the development towards more autonomous schools, which is encouraged today in France, may, if no political regulation is implemented, lead to new social differences. The difference between listening to school users and being de facto submitted to their pressures is frequently blurred at the local level. The developments observed today in France lead to the same conclusion as the ones made by Ball in 1993, according to which 'choice and the market provide a way for the middle-classes to reassert their reproduction advantages in education, which had been threatened by the increasing social democratic de-differentiation of the schools'. We will focus here on inequalities linked co the pupil's social background, without dealing with the specific influences of his or her ethnie background (which is in fact very small), or with the impact of gender (positive for girls in many respects).

2.

We will use here the father's profession to characterize the child's social background but let's recall that the educational level of parents, especially the mother's is also associated wich academic achievement (Caillé and Vallet 1996) 3.

lt is only since the 1975 Educational Act (implemented in 1977) chat the French collège became truly comprehensive (on paper), the separate streams being abolished and ail the pupils being supposed to receive the same education up to the age of 15 or 16.• 4.

Before the sixties only children from high SES entered into secondary school; it was perceived as an inequality for which society was deemed responsible, but not school in itself; skill-linked inequalities between people were not considered as relevant in trying to explain the above inequalities.

5.

In tertiary education, per student expenditure is much higher in élite schools (the average unit cost is about $13 000 in the grandes écoles compared with $ 5000 in universities.


Jean-Claude Eicher

The Financing of Education: an economic issue?

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Introduction

Education has always been the subject of heated debates. After the Second World War, a sort of consensus seems to have been reached with the Universal Declaration of Human Rights voted by the General Assembly of the United Nations in 1948. As a result of this recognition of education as a basic human right and because economic research seemed to have proved that education was a highly profitable investment for society as well as for the individual, there was a worldwide explosion in school enrolments. From a little over 240 million pupils in primary schools in 1960, the figure reached 541 million 20 years later. In higher education, the growth was even more spectacular, from 11.7 to 51 million students. Although the growth rate has somewhat slowed down in the last 20 years, it has remained great at the primary level in developing countries, where the number of pupils increased from less than 450 million in 1980 to over 570 million in 1996. But the developed countries were experiencing a decrease due to the decline in the birth rate. Yet higher education enrolments kept growing everywhere, from 51 million students to over 84 million. This could but raise many problems. In developing countries, it generally meant opening thousands of schools and hiring thousands of new teachers and creating institutions of higher learning from scratch. In developed countries, where all children already received basic education in 1960, reforms mainly affected the upper secondary system and higher education, which now enrol a majority of each age group.

Recognising that education is a basic human right implied that it should be free, at least at the lower levels. This principle was more or less respected in most countries, which induced a tremendous increase in the public budgets devoted to education. A financial crisis was forecast in the mid-1960s [START_REF] Coombs | The World Educational Crisis. A Systems Analysis[END_REF]. The financing of higher education soon became a major issue and the financial burden on public budgets in many developing countries was often considered unbearable as from the mid-l 970s when the effects of the world economic crisis became difficult to ignore. In any case, it became clear that the increase in the public effort in favour of education, which was visible almost everywhere in the 1960s (where the percentage of Gross Domestic Product (GDP) spent publicly on schools increased from 3.47 to 4.86 in developed countries and from 2.55 to 3.63 in developing countries), could not be sustained for very long. The fact that social demand kept increasing was bound to create tensions and give rise to speculations about new sources of financing.

At first, no major changes were observed, but public resources became scarcer. Public resources in proportion to the GDP tended to stabilise in the late 1970s and in the 1980s in developed countries and a growing number of developing countries stabilised or

The Financing of Education: an economic issue? decreased their effort in the 1980s. Research on the actual spending shows that resources allocated to schools have, in most cases, decreased much more sharply than these macro indices show, especially in Africa. The slight improvement that was seen in the 1990s in the poorest countries is not sufficient to enable them to reconcile an increase in enrolment in primary education and acceptable quality. In many developed countries, public expenditure per tertiary level student has tended to decrease since the mid-1970s.

But if changes in the sources of funds are visible in most cases, one observes that they are the result of the financial squeeze on public budgets and, until very recently and in a minority of cases, are not the result of a coherent and systematic reflection on optimal financing. Why is that? We shall attempt to answer this question after giving an overview of the financial situation of the education sector and its evolution in the world by studying the shortcomings of the analytical approach of this problem by economists. Then, we shall focus on the main areas of discussions which have emerged recently.

An Overview of the Financial Situation

The adoption of the principle of the 'right to education' by all the countries that signed the Universal Declaration of Human Rights was generally expressed as a right to free basic education. We shall therefore consider basic education and the higher levels of schooling separately.

Basic education is generally compulsory, whether this is rigidly enforced (as in all developed countries) or not. Its financial basis seems to be clear-cut: the public authorities shoulder the whole burden, as it is provided free to the households. But, in fact, there is always a cost to the latter for at least three reasons:

First, the principle applies to public schools but not always or fully to private schools which may, in some cases, enrol a large share of the student population.

In developed countries, the private sector is generally limited or non-existent at primary level. In Europe, only Belgium and the Netherlands enrol a majority of pupils in private schools which are fully subsidised by the State. The same is true in France and Denmark, where that proportion is between 10% and 20%. Only Spain, the U.K. and Greece have a significant sector of non-subsidised private schools where tuition fees are fairly high. But it does not exceed 13% of enrolment in Spain, 6% in the U.K. and 4% in Greece. In the US, the private sector enrols a little less than 10% of the primary school pupils in schools where tuition fees amount on average to around $1,700. The proportion is lower at the secondary level (6%) but the fee is higher ($3,650). In Canada, the respective figures are 4% and 6%. In Japan, there are almost no private schools at the primary level and less than 3% at the lower secondary level.

The situation is different and very heterogeneous in developing countries, as Table 1 shows. As most of these private schools receive little or no public subsidies, one can see that in some countries, and especially at the secondary level, basic education is costly for a significant number of households. 10.

Second, in most countries, certain costs are borne by parents or have been shifted to them in recent years. In Africa, for instance, textbooks and uniforms (often compulsory) in many cases represent a heavy financial burden. Only the salaries of teachers are generally paid by the State.

Third, some costs have to be borne by the family if a child is attending school. Transport, for instance, is rarely free. In some countries like Japan and the Republic of Korea, private lessons are important, especially at the secondary level. On the whole, in developed countries, although most of the private sector is usually heavily subsidised, the financial burden of compulsory education has not increased in the last 40 years because of a decrease in enrolments due to the declining fertility. But in many developing countries it has increased both for the public authorities and for the households and more for the latter for the reasons evoked above.

At the post-compulsory level, the situation is different. There has been a great, often spectacular rise in enrolments in most countries of the developed and developing world. The private sector is usually much larger than at the lower levels. A majority of pupils are enrolled in it in upper secondary education in some countries like Bostwana and Zimbabwe, El Salvador and Lebanon and between one-third and one half in many others.

In higher education, the sources of financing are more diversified. In the l 980s, there were four different patterns:

-In the USSR and countries which had adopted the same political régime, the State paid all expenses and controlled the supply. Higher education was free. Students paid no fee and room and board were free.

-In Japan and several other Asian countries (the Republic of Korea, the Philippines, and to a lesser extent Indonesia and Thailand) and in Brazil, the system was mainly private. Between 70% and 80% of the students attended private institutions which received most of their income from tuition and fees and (marginally) from research subsidies from private firms.

Public institutions also charged tuition and fees which, although much lower than in the private sector, were quite sizeable. Other countries have since followed the same route, the most visible example being Chile.

-In the US and Canada, there is great diversification. The private sector enrols a minority of the students (around 25% in the US) but charges high fees. Tuition is nevertheless fairly expensive in public universities ($3,750 vs $13,700 in private universities in the early 1990s). But a significant proportion (39 % in 1993) of students are enrolled in two-year institutions, mostly public, where tuition and fees are low ($1,250 on average) and student aid high. One may therefore say that the type of financing ranges from almost 100% public to 75% private and the amount spent per student from $5,700 to $30,500.

-In Europe (and in many developing countries which were colonised by European countries in the past) the situation at first seemed far from uniform. But, from the financial point of view, there was great uniformity until recently: students paid no tuition fee or a token one ; close to 100% of the resources of the universities came from public authorities; aids to students were widespread and helped the most needy to support themselves while studying.

In recent years, the Soviet model has disappeared, the Japanese model has slightly changed towards an increase in State participation to the financing of the private sector (at least in Japan and Korea) and the American model has shown a slight retrenchment in public subsidies and a rather sharp increase in tuition fees at the research universities. The European model has become more homogeneous as far as State control of universities is concerned, but shows divergent evolutions in tuition fees. Today, in a majority of countries, tuition and fees have substantially increased. Three groups may be observed:

• Countries which still charge no fees. They are a clear minority : Denmark, Norway, Sweden, Germany, Austria and Greece.

• Countries where they are low and have been kept so for the last 25 years in spite of aborted efforts by the government to raise them: today, France is the last country in this situation, with a basic fee of around $150.

• Countries where fees are substantial (between $400 and $4,000): Belgium, Ireland, Italy, the Netherlands, Portugal, Spain, Switzerland and the UK.

Looking at this evolution, five conclusions can be drawn:

• There is a clear trend towards higher fees. This is seen in the fact that most increases are recent (in the l 990s in Italy, Portugal, U.K.), that heated discussions preceded and accompanied the raise in most cases, and that in two of the no fee countries at least (Denmark and Germany), the question is raised.

• This encountered strong resistance on the part of student organisations and political parties on the left of the spectrum; that resistance was strong enough in some cases to defeat several attempts (in France) or to bring a partial revision of the initial decision (in Ireland and Portugal).

• Rather high fees do not always mean high costs to the students. For instance, in the Netherlands the fees are largely compensated by public subsidies.

• The fees are generally in the $500 to $1,000 range, which is far below those in American (or Korean) universities.

• But, although the issue of student fees is coming to the fore in different forms, the situation is far from stabilised and an alignment of all countries on the substantial fees group is not yet on the official agenda.

Why such an array of financial solutions, especially in higher education? Why have countries with comparable political institutions made very different choices? Part of the answer lies in the incapacity of economists to offer a clear 'optimal' solution.

The 'Classical' Discussion on Financing and its Shortcomings

When the Human Capital theory was developed 40 years ago it was radically opposed by Marxist economists on the ground that the appropriation of capital by a few leads to the exploitation of man by man, so that pretending that, through education, man is investing in himself and therefore expecting profits is tantamount to saying that he is exploiting himself through the appropriation of those profits. This rather abstract controversy obscured the fact that the approach of Human Capital theorists and of Soviet economists to education was very similar and was based almost exclusively on considerations of efficiency. Bath groups started with the hypothesis that education is an investment in man, in other words, that it mobilises scarce resources today in the hope that the productive capacity of the recipient will improve in the future.

The Marxist approach, developed by Soviet economists like Strumilin in the 1920s, was quite coherent [START_REF] Strumilin | The economic significance of Nation Education, i n : UNESCO[END_REF]. It was based on the assumption that education improves the skills of the worker and therefore contributes to an increase 'in the productivity of the nation' (Strumilin, 1969, p. 432). It went on to try to measure these differences in productivity and then compare them with the cost of training in order to calculate the equivalent of what would be the rates of return in market economics and to determine the optimal development of the school system. The problem of equity was not analysed but was supposed to be solved by the organisation of a Socialist society: salaries were not linked to individual productivity, only social rates of return were pertinent. Society as a whole, represented by the State, paid for the investment in education and reaped the benefits. People were educated according to their intellectual capacities. It was therefore assumed that equality of opportunities prevailed. But in actual practice the system never worked quite this way.

The Human Capital approach initiated by T. Schultz in the late 1950s [START_REF] Schultz | Investment in man: an economist's view[END_REF] and developed by G. Becker [START_REF] Becker | Human Capital. A theoritical and empirical analysis, with special reference ta education[END_REF] was also based on the assumption that education should be considered as an investment and went on to propose measurement of its rate of return in order to determine its optimal level. But it mainly considered the point of view of the individual and concentrated on demand. It was only later that Human Capital theorists and other neo-classical economists developed considerations on the financing of education. Starting from the 'orthodox' assumption that the market system, as long as it works properly, leads to an optimal allocation of resources, these authors encouraged a mixed system of public and private contributions. The main arguments have often been presented [START_REF] Eicher | Rethinking the finance of post-compulsory education[END_REF]. We shall only summarise them here.

Private financing by the students (or their family) is mainly justified by the straightforward Human Capital argument of profitability: education enables students to earn more after graduation. They should therefore finance the initial investment. But other arguments are also advanced: on the demand side, the 'token user charge' argument states that what is provided free is often consumed wastefully. If students have to participate in the cost they will behave more rationally, choose more wisely their field of study and try to graduate as quickly as possible. The 'participation' argument says that students who pay tuition are entitled to participate in the definition of the content and organisation of their curriculum which may therefore be more adapted to their needs than when it is built only by academics who are primarily interested in their own welfare.

On the supply side, it is argued that tuition fees represent a source of independent income for the institution and increase its autonomy and its capacity to use resources in an optimal way.

Other private sources of funds are also advocated, drawing on the same profitability argument: if firms are going to benefit from the higher productivity of the graduates, they should participate in the financing. The same may be said of philanthropists who derive satisfactions from the development of education.

But it is also observed that there is no fully competitive market for education which militates in favour of public financing. Public financing of education is recommended by advocates of the market system on two main grounds.

On the one hand, imperfect information. The students are unable not only to evaluate with any precision the quality of their training, and more precisely its market value, but also to know how much they will earn until they retire from active life. This amount depends not only on the present market value of their degree, but also on future competition in the labour market and on general economic conditions. There is also the question of the imperfect information of lenders on the credit-worth of students, which may mean a high risk premium on loans. This lack of accurate information is bound to lead most students to be cautious and to undervalue their private benefits. This means they will underinvest in education unless public subsidies push the price down.

On the other hand, education is typically a good which has spill-over effects. The family, the local community and society as a whole all benefit from this progress in knowledge, but individual student-investors do not take these positive external effects into account when they make their choice. This is a second cause of under-investment and another reason why public subsidies are required to reach the allocative optimum.

Finally, one may add another argument in favour of public financing if one considers the State as an autonomous decision-maker which attempts to maximise its utility. If the income tax is progressive, graduates, who earn more than non-graduates, will pay more. The State may therefore consider it worthwhile to spend on education now in order to get more tax revenues later.

The sum of these arguments leads to conclude in favour of a mix between private and public financing. Market imperfections make the pure market solution, i.e. pure private financing, sub-optimal. But it is to be noted that none of the arguments in favour of public financing leads to a conclusion in favour of free education. This economic approach therefore brings the beginning of a solution to the problem of the financing of education. But it does not provide a clear-cut solution in any concrete situation.

First, only the general principle is clear: each constituency should contribute to the cost of education in proportion to the benefits it expects from it. Unfortunately, most of these benefits are difficult or impossible to measure. The monetary profits represented by higher incomes have to be valued today, but will be spread over time. Those who obtain the same degree at the same time will not have the same income. Even if it were possible to measure each future individual income stream, would it be considered as acceptable to base each individual present contribution to the cost of schooling on these differences?

Many of the benefits are non-monetary and non-economic: a better social status, a more interesting job... as well as the present satisfaction derived from student life.

One thing at least is clear. The sum of the various benefits accruing to the individual graduate is great. The 'European model' of financing higher education where students' contribution to the cost of their studies is very low does not seem to be an optimal solution from the point of view of resource allocation.

Second, this economic analysis only looks at the efficiency dimension of the problem. But the economist, much as he would like to remain in the positive dimension of his field of research, cannot avoid the normative aspects. After all, the aim of economic activity is to increase social welfare and social welfare is not independent of the welfare of each person.

'A society is a co-operative venture for the mutual advantage of its members' [START_REF] Barr | The Economies of the Welfare State[END_REF]. In order to survive, its members must have some common values. The satisfaction of recognised 'basic needs' is a fundamental principle of organisation.

In modern societies, education is recognised as one of those basic needs. Optimal financing should therefore not only be that which brings about an optimal allocation of resources (the efficiency principle), but also that which ensures the satisfaction of that basic need for everybody. If the optimal financial scheme defined only along efficiency lines supposes a private contribution which is beyond the contributive capacity of a fraction of the population, equity is not ensured. This is the other reason why financial settings vary so much from one country to the next: the solution proposed by neoclassical economists was not considered acceptable.

But great progress has been made in recent years in the approach by economists to the problem of social justice. It has led to focus on new issues which are worth discussing.

Main Issues under Discussion

In the field of financing non-market activities, the issues are many. Of course, there is still the central question: who should pay and for what? But there is also that of the definition of the cost to be borne and shared: cost of supplying the service as it has for a long time more or less implicitly been assumed, or cost to the recipient? Supply side or demand side analysis?

There is also the myriad of questions linked to public financing: should the public authorities supply education themselves, the institutions (the 'schools') being bureaucratic units without any autonomy, or should they subsidise autonomous actors? Which actors should be subsidised: the suppliers or the beneficiaries? How should they be subsidised: should institutions be given lump sums they can use as they like, or should the money be affected to a precise function? Should the subsidy to the recipients be given to the recipients or to those considered responsible for their well-being? And last but not least of this incomplete list of questions: should the subsidy given to the student be refundable or not, in other words, should it be a loan or a grant; and if a loan, should the refund be linked to future income or not [START_REF] Eicher | Rethinking the finance of post-compulsory education[END_REF]? Let us say a few words on each of these issues as an introduction to some of the main debates of the day.

Who Should Pay for What?

We reminded the reader earlier that the neo-classical economic analysis centred on efficiency led to conclude that mixed public and private financing was preferable to either polar solution. But besides the fact that it was unable to recommend a precise mix in each actual case study, it implicitly neglected considerations of social justice.

If the economist acknowledges that in any society a fundamental principle of organisation is that agreed-upon basic needs must be satisfied and that education is considered as one of these basic needs in modern nations, he has to admit that, in order for this need to be satisfied, education must be free. But this is not the final and universal answer to the question of the financing of education. As Nicholas Barr quite aptly reminds us 'the importance of Education in people's lives should not obscure its economic dimension. Resources devoted to education cannot be used for other purposes ... ; if we spent the whole of national income on education, there would be no food or health care' (Barr, 1993, p. 337).

In the other words, there is the crucial question of the extent of the right to satisfy this basic need. One may assume that basic education fills this basic need and that it was made compulsory for that purpose. This means that basic education should be totally free, which is not always the case, but that post-compulsory education has no reason to be so.

This distinction is not always well understood, as witnessed by the discussions in the preliminary phases of the UNESCO World Conference on Higher Education of 1998. In the synthesis on Management and Financing prepared by Malcolm Slibeck [START_REF] Slibeck | The Management and Financing of Higher Education[END_REF], the latter cites the main arguments put forward against the levying of tuition fees. Among these, there is that of the benefits to society as a whole, which in no case may be used to advocate full public financing, but only to argue that fees should not cover the whole cost; the bold assertion of many studies that the existence of fees reduces access (which is contradicted by the spectacular development of higher education in Japan, Korea and other Asian countries); the surprising statement that 'it is not reasonable to have fees in periods of economic recession' (should the State spend more when it has lower tax revenues?); another extreme assertion is that in developing countries most families are unable to pay the fees; and, finally, another unproved statement, that fees are not a necessary condition for better efficiency.

Fortunately, the general conclusion and the introduction by Jacques Delors are more nuanced and admit that 'it will be impossible to undefinitely postpone the participation of the student to the cost of his (or her) studies' [START_REF] Delors | L' Education -Un trésor est caché dedans[END_REF]. But the emergence of mass higher education in developed countries means that many teenagers from less privileged groups who, in the past, did not acceed to the university level because they followed short professionnal streams in secondary schools, now enrol in higher education institutions. They usually cannot afford to pay substantial tuition fees and to support themselves without taking at least a part-time job. The equal opportunity principle, if applied to this group, means that either they should be partially or totally exempted of fees, or that they should be allowed to make deferred payments. The basic question is not: should they pay fees, but when should they pay them? Low fees or no fees at all does not seem to be the optimal solution, either from the efficiency or from the equity point of view, and the traditional attitude in favour of free education, which still prevails in Europe, does not seem warranted, even when many youngsters from low-income groups start to have access to higher education.

Another important question is that of the limitations of the supply side approach. Cost analysis and cost measurements usually study what could be called the production side. What is measured is the resources that are mobilised in order to offer the training. But schooling is an activity which takes a long time, much longer than to buy most goods and services. This means that it cannot, as a rule, be acquired during one's 'free' time and prevents the trainee from having a full-time wage-earning occupation. Beyond the period when schooling is compulsory, it engenders forgone earnings. In other words, students are prevented from earning an income that is sufficient to caver their needs while studying. For them, the cost of education comprises the cost of living (or the part of it which they cannot caver by working part-time) plus the portion of the supply cost they are asked to finance through fees. It is quite different from total supply cost.

In order to ensure equality of opportunity, students should therefore be helped financially to support this 'demand cost'. Help may come from the family, which raises the issue of the status of the student: should he or she be considered autonomous and at what age?

But the family itself may be unable to help the student, in which case the eventual public subsidy should concern not only tuition and fees but also the cost of living.

The question of who should provide the service is not a financial question except if it can be shown that it is provided more cheaply by autonomous agencies than by bureaucratic departments.

Nor does the issue of which actor should be subsidised have a direct financial dimension.

What is important from the financial point of view is to decide whether it is more costeffective to subsidise the schools or the students. Once this decision has been taken, further questions are raised which all have a financial dimension.

Subsidies given to institutions as lump sums are likely to be less costly to administer than targeted ones. From the financial point of view, the first solution allows for more money to be distributed. Subsidies distributed to the students usually require more detailed enquiries before a choice of beneficiairies is made than subsidies to parents, such as tax rebates. They are therefore more costly to administer (but probably more equitable).

This choice raises the question of the status of the children vis-à-vis their parents. In some countries, they are considered independent when they can vote. This is the case in Scandinavian countries where the financial situation of the parents is not taken into account when deciding whether students should receive public aid or not. As it is more and more frequent nowadays that children still live at their parent's home long after they reach their political majority, it may be considered as inequitable to give the same subsidy to those who remain dependent as to those who have to fare for themselves. But it avoids having to rely on the student's declaration.

A very important financial problem is that of the type of subsidy the student should get, or more precisely that of the choice between a grant and a loan. The case in favour of loans is now well documented (Eicher & Chevaillier, 1993, pp. 491-495). Loans do not deter the enrolment of the poor, as is often stated, because the main inequality between students of rich and poor families is not that the latter cannot pay but that they cannot pay now. Their degree will allow them to earn higher incomes than non-graduates and it is not a priori shocking to have them use part of this increase to repay the loan. Three other main arguments in favour of loans may also be cited: the student who has to borrow is likely to be more rational about his choice of field of study and more 'serious' about studying than the student who does not, especially when tuition fees are very low; loans allow 'rich' students not to rely exclusively on the goodwill of their parents; having to contract a loan may deter the less gifted and the less motivated students from enrolling, thereby making human capital accumulation more costeffective. But purely commercial loans are likely to deter the poor (who have to borrow) and to create inequalities between those who will and those who will not have to repay a loan.

On the other hand, when loans have (in principle) to be repaid, a loan system will be less costly for the State than an aid system based on grants and would contribute to a better balance between public and private financing in countries where the initial participation of students to the cost of their studies is low.

Systems of income-contingent loans have been designed to conciliate efficiency and social justice. But they present two potential drawbacks: adverse selection if the amount repaid is much smaller for those who earn little than for those with high incomes, in which case those who expect to obtain a high socio-economic standing after graduation opt out of the scheme; moral hazard if a sizeable proportion of the borrowers decides to drop out or opt for low-paid jobs. These drawbacks can be avoided or at least mitigated if only the level of each periodical repayment varies with income but not the potential total amount to be repaid.

It can be shown that, considering that a proportion of borrowers will have no income at all and therefore will not repay anything and that there is always a certain level of default, such a scheme must be subsidised in order to function at all. But, in any case it is less costly for the State than a grant scheme, notwithstanding its other potential advantages described above.

Today, these issues are more fully and systematically explored by economists, instead of being only dealt with in purely technical terms by the initiators of such schemes.

One last point. The building of a true European Union is hardly compatible with the existence of highly different financing schemes for post-compulsory education, and especially higher education, in the different European countries. Greater student mobility, which is strongly encouraged, would be impeded by these different arrangements. It is therefore to be hoped that this issue, which has emerged recently as a major one, will be tackled quickly and efficiently.

TABLE I .

 I Proportion of Pupils Enrolled in Private Schools (Number of countries in each category for which data are available)

		Less than 20% in	Between 20% and 33%	Above 33%
		private schools
	Africa
	Primary	24	6	2
	Secondary	4	11	13
	Latin America
	Primary	18	4	1
	Secondary	1	9	6
	Asia
	Primary	16	3	3
	Secondary	15	7	4
	Source: World Report on Education, UNESCO 1998 -Table

The Financing of Education: an economic issue?


Fernand G J Gounaris

Michel Renard

Higgs boson form factor effects in t t production by W -W + and ZZ fusion

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Mickaël Paris

Yassine Haddab

Philippe Lutz

Patrick Rougeot

published or not. The documents may come     Practical characterisation of the friction force for the positioning and orientation of Micro-Components.

Practical Characterisation of the Friction Force for the Positioning and Orientation of Micro-Components

Mickaël Paris and Yassine Haddab and Philippe Lutz and Patrick Rougeot

Abstract-This paper deals with the description of a method for the measurement of friction force between a very small object (80 to 300 µm) and a support. The goal is to design a feeder based on controlled mechanical vibrations in order to drive microcomponents by breaking the friction force. The contact model is based on the Hertz theory and the Greenwood-Williamson multi-asperity model. The amplitude of the static friction force is measured in a clean environment with an AFM (Atomic Force Microscope) whose cantilever is placed in the vertical position. Using this setup and the modeling, we have estimated the interfacial shear stress between the microcomponent and the support.

I. INTRODUCTION

In order to perform micro-assembly tasks, micro-assembly systems must be able to carry out three main functions: handling, joining and feeding. In the microfactory concept, feeding systems are taking a great importance to move and drive the components between and inside the assembly cells. To obtain a good efficiency, the feeding system have to be modular (at the architectural and control level) and must allow automatic control of the position and the orientation of the micro-objects.

In the literature some microsystems like conveyors and feeders based on different approaches are presented. Some of them use various fields in order to move an object or a pallet. In [START_REF] Fukuta | Pneumatic Two-Dimensional Conveyance System for autonomous Distributed MEMS[END_REF] a pneumatic conveyance is used, in [START_REF] Nakazawa | Electromagnetic Micro-Parts Conveyer with Coil-Diode Modules[END_REF] and [START_REF] Iizuka | A Micro X-Y-theta Conveyor by Superconducting Magnetic Levitation[END_REF] magnetic conveyors are developed, and in [START_REF] Moesner | Contactless Manipulation of Microparts by Electric Field Traps[END_REF] an electric field is used to control the displacement step. The concept of ciliary micromotion is also developed in [START_REF] Suh | CMOS Integrated Ciliary Actuato Array as a General-Purpose Micromanipulation Tool for Small Objects[END_REF]; the ciliary micro-actuators cooperate in order to move the microcomponents. Ultrasonic field is also used like [START_REF] Böhringer | Parallele microassembly with Electrostatic Force Field[END_REF] and [START_REF] Haake | Particle positionning by a two-or threedimensional ultrasound field excited by surface waves[END_REF].

One approach is to use mechanical vibration, implemented notably in the vibrating bowls [START_REF] Böhringer | Parallele microassembly with Electrostatic Force Field[END_REF] or step feeders where the vibrations drive a component to a particular place. However, these systems are often dedicated to particular microcomponents with sizes > 1 mm 3 .

In [START_REF] Böhringer | Parallele microassembly with Electrostatic Force Field[END_REF], a table is moved along a vertical direction by a piezoelectric actuator, and it allows only to break the friction and surface forces. However, the positioning of the parts is obtained by the electrostatic fields produced by four electrodes.

Our objective is to design a feeder based on controlled mechanical vibrations and well adapted for very small size components by breaking the adhesion forces, very present at the small scale (< 500µm), and drive them at the right All authors are with FEMTO-ST Institute, UMR CNRS 6174 -UFC / ENSMM / UTBM, Automatic Control and Micro-Mechatronic Systems Department, 24 Rue Alain Savary, 25000 Besançon, France mickael.paris@ens2m.fr position with a very good level of precision. We propose a planar system where there is no prestressing action on the micro-component and the step is induced by using inertial force.

The displacement of the moving plate along the horizontal direction is realized by a piezo-electric stack actuator Fig. 1. It enables to get enough dynamics to break the adhesion forces and the friction forces. The result is a displacement of Fig. 1. Feeder by inertial force the micro-object in the opposite direction and so, the inertial force acting on the micro-object is defined by

∑ - → F = m. - → a
where F, is the tangential or inertial force, m the microobject's mass and a the acceleration of the plate. Moreover, understanding the interactions between the surfaces of the micro-objects and the feeder is critical to control the motion. So, the plate's acceleration will be adapted for an automatic control. Friction and surface forces depend on the roughness of both surfaces. This roughness influences the contact between them. The study of roughness parameters and the contact between two flat surfaces will allow to evaluate the friction and the interfacial strengths.

II. STATE OF THE ART ON CONTACT

The static friction was first estimated by Leonardo da Vinci, Charles Augustine Coulomb, and Guillaume Amontons. The first results are known under the name of Laws of Amontons-Coulomb:

1) The force of friction is directly proportional to the applied load.

2) The force of friction is independent of the nominal area of contact. It is in 1950 that David Tabor and Frank P. Bowden showed that the friction force F f depends on the real area ("A r ") of contact as F f = τA r , where τ is the friction stress which is independent of the contact surface. The friction depends on three factors: the real area, the strength of interfacial bonds, and the deformation processes involved when these interfacial bonds are broken during sliding. This first model has been completed by Greenwood and Williamson [8] in order to take into account all asperities in contact between the two surfaces (Fig. 2). Each surface is characterized by the Fig. 2. Two rough surfaces in contact geometry of its summits, which is considered as spherical, and all summits have the same radius R i Furthermore, the height of these asperities varies randomly according to a law φ i (z).

These two surfaces are represented by an equivalent rough surface and a perfect smooth rigid surface in contact separated by a distance d (Fig. 3). The equivalent rough surface is characterised by the shape of asperities and the height distribution. All asperity summits have the same radius R,

1 R = 1 R 1 + 1 R 2 , (1)
where R 1 and R 2 are the mean radius of asperities of the two surfaces in contact, respectively, and their heights vary randomly following a Gaussian probability density function φ (z):

φ (z) = 1 √ 2πσ exp -0.5 z -µ σ 2 , ( 2
)
where σ is the standard deviation of asperity heights:

σ = σ 2 1 + σ 2 2 , (3)
σ 1 and σ 2 are the standard deviation of height distribution of asperities for the two surfaces, and µ the mean height asperities of the rough equivalent surface.

The GW model considers the cumulative effect of the actions of individual local asperities, in other words, the effect of each individual asperity in contact do not affect the behavior of the nearby asperities. When an asperity is in contact, depending on its height, it is then more or less flattened and according to Hertz theory the compliance is:

δ = z -d.
Chang et al. [START_REF] Chang | An elastic-plastic model for the contat rough surfaces[END_REF] extended the elastic GW model into the elastic-plastic contact regime (the CEB model). In [START_REF]Adhesion model for metallic rough surfaces[END_REF], the effect of adhesion was included by using the DMT model [START_REF] Derjaguin | Effect of contact deformation on the adhesion of particles[END_REF] for contacting asperities and the Lennard-Jones potential between non-contacting asperities. Finally a model for calculating the coefficient of friction was given in [START_REF] Chang | Static friction coefficient model for metallic rough surfaces[END_REF]. Fuller and Tabor [START_REF] Fuller | The effect of surface roughness of the adhesion of elastic solids[END_REF] developed a theoretical model which use the JKR [START_REF] Jonhson | Surface energy and the contact of elastic solids[END_REF] model of adhesion with a Gaussian distribution of asperity heights. Adams and Müftü model [START_REF] Adams | A scale-dependent model for multiasperity model for contact and friction[END_REF], [START_REF]Height dependent radii of curvatures in a contact and friction model[END_REF] includes Fig. 3. GW model of contact mechanics the effects of adhesion, and the height-dependent radius of curvature using the Maugis model and extends the Hurtado and Kim single asperity friction model [START_REF] Hurtado | Scale effects in friction of singleasperity contacts. i. from concurrent slip to single-dislocation-assisted slip[END_REF] to a multiasperity friction model.

III. CONTACT MODEL

For two real surfaces separated by a distance d (defined from the average height of the asperities) the number of contacting asperities n is :

n = N ∞ d φ (z)dz (4)
where N = ηA n , is the number of all asperities, η the density of asperities per unit area, A n the nominal contact area, z the height coordinate measured from the average height of asperities. The real area is defined by:

A r = N ∞ d A(δ )φ (z)dz (5)
A(δ ) being the area of a single asperity in contact and P(δ ) the corresponding asperity load. So the total load is :

P r = N ∞ d P(δ )φ (z)dz (6)
The total shear force F r acting on the real surface, is determined by integrating the force acting on each single asperity:

F r = N ∞ d A(δ )τφ (z)dz, ( 7
)
where τ is the interfacial shear stress. As we can see, F r depends on the area of a single asperity in contact A(δ ), consequently, it depends on the choice of the model of contact.

The real surface and A(δ ) depend on the load and the surface forces. These forces induce an additional surface dS on each asperity and we consider in this first work that their effects as negligible on. Thus only the load is taken into account and the contact model is based on the Hertz theory.

So P(δ ) and A(δ ) for a single asperity in contact is expressed by:

P(δ ) = 4 3 E * R 1 2 δ 3 2 = 4 3 E * R 1 2 (z -d) 3 2 , ( 8
)
where E * is the effective elastic modulus, and

A(δ ) = πa 2 δ = πδ R = π(z -d)R, ( 9
)
where a δ is the contact radius. If we combine ( 6) and ( 8) we can evaluate the separation distance d (Fig. 9) since the total load is the weight of the micro-object.

P r = 4 3 NE * R 1 2 ∞ d (z -d) 3 2 φ (z)dz (10)
N and R are evaluated from the scanning of the surfaces. In order to find numerically the value of d we use a function P r (d) defined piecewise on two intervals; on [µ, z max [, it is defined by [START_REF]Adhesion model for metallic rough surfaces[END_REF]; on [z max , ∞[, it is the constant 0. z max represents the highest asperity height of the equivalent rough surface. Physically, d exist only if two surfaces are in contact, then d cannot be bigger than z max .

P r (d) =    4 3 NE * R 1 2 z max d (z -d) 3 2 φ (z)dz if d ∈ [µ, z max [, 0 otherwise.
Since we can find d, we are able to find the real contact area between the two surfaces, by using the equations ( 5) and ( 9):

A r = NπR ∞ d (z -d)φ (z)dz (11)

IV. FORCES MEASUREMENT

To analyse the validity of the micro-force modeling, experimental force measurements are necessary. This part deals with the presentation of the micro-force measurement system. The interactions between the micro-objects and the surface are measured by a specifically developed system called AMIS-2 (AFM based MIcromanipulation System, second version).

A. Surfaces in contact

Two kinds of objects are used: micro-objects and supports. Both of them are cut in a silicon wafer. In the experiments the micro-objects are put on the support, and we study the interactions between these two objects. Two kinds of supports have been built: flat supports and supports with grooves allowing to reduce the surface by half, see Fig. 4. Let p be the period and h the step height. The nominal area between the micro-object and the support is decreased from 100% to 50%. Each micro-object is a cuboid, and the Table(I) shows their different characteristics (density of silicon : 2330kg/m 3 ). We are able to vary two parameters: the contact area between the micro-object and the support and the weight of the micro-objects.

B. AMIS-2 station and experimental procedures

A view of AMIS-2 is given Fig. 5. This system is based on an Atomic Force Microscope and three linear micropositioning stages. These stages are used to fit the support under the AFM's cantilever and to align the micro-object with the latter. The AFM is installed in a non-conventional position. The objective is here to place the cantilever in vertical position to measure its curvature when the object is in contact. This is why, inside AMIS-2, the AFM is perpendicularly placed with regard to its "normal" position as during the scanning of a surface Fig. 6.

Different kinds of rectangular cantilevers are used to adapt the resolution according to the size of the objects and the range of the photodiode. Indeed, given that the surface of objects varies from 90000 µm 2 to 6400 µm 2 , it is necessary to adapt the stiffness of the cantilever. The table II resumes the different characteristics of the used cantilevers. In order to decrease the influences of the environmental conditions, we work under a class 100 vertical laminar flow workstation, and we maintain the temperature at 25°C.

Our set-up is used to obtain experimental force curves based on the real-time measurement of the AFM cantilever bending. A force curve is a quasi-static trajectory which correspond to an "approach and depart" cycle between the directions, the support is moved along the x direction. As soon as the object touches the cantilever, we observe the normal force which acts on the cantilever, until a maximal value. After that, we observe the sliding of the object on the support. The objective is to find the maximum value of the static friction, for different objects and different supports (i.e. roughness parameters: d, R, σ , µ, N). Before performing the evaluation of the static friction force, we perform a scan of the surface topography with the AFM (Fig. 8) in order to evaluate the roughness parameters of the GW equivalent surface.

C. Characteristics of the equivalent surface

We define the total number of asperities for the equivalent surface, as the sum of the number of asperities for each surface. When a point resulting from the scanning is higher than its eight nearest neighbours, it is considered as an asperity summit. Thus, the mean height of the asperities for the first surface, µ 1 , is calculated by :

µ 1 = 1 M M-1 ∑ i=0 z i , ( 12
)
where M is the number of asperities from the sample scanning and z i their respective height. µ 2 is calculated with the same method. So µ for the equivalent surface is the average of µ 1 and µ 2 . The standard deviation σ defined by (3), is obtained by estimating the root mean square (RMS) parameter S q of each surface and is defined by

S q = 1 M M-1 ∑ i=0 [z i -µ] 2 . ( 13
)
Equation ( 3) can be rewritten as:

σ = S 2 q 1 + S 2 q 2 . ( 14
)
The mean radius of asperities for each surface is obtained from a roughness profile. Each asperity is approximated by a curve fit and the mean radius is the average of all radius. As all the parameters of equation ( 2) and ( 10) are known, it is possible to calculate the separation distance d by resolving the equation ( 10) when P r (d) is equaled to the weight of the micro-object. Figure 9 shows the evolution of the distance d versus the load of a 300 × 300 micro-object put on a flat support and support with grooves. For a given load, the distance d decreases when the contact surface decreases. In fact, the number n of asperities in contact decreases, and the partial load which is supported by each of them is greater. Determining d allows us to evaluate the real area. The distance d is nearly constant for any micro-object placed on the flat support (d = 34.638 nm). When the micro-objects are placed on the supports with grooves, we observe that d = 34.600 nm. In fact, their weights are so weak that they can't change significantly the separation distance. Table III resumes the obtained results. We notice a constant ratio between the true areas whatever the dimensions of the microobjects are.

V. EXPERIMENTAL RESULTS

A. Force measurement

The micro-objects are initially placed on a flat support and the Fig. 10 illustrates the force curve measured with the AFM for a 300 × 300 micro-object. In this example we notice a maximum value of friction force F r = 0.91 µN. When the micro-object is placed on the surface with grooves Fig. 11, the maximum value of the friction force decreases and in our example, F r = 0.708 µN. We observe a diminution of the friction force amplitude when the real area decreases. In this case, the ratio between the friction force amplitudes is 0.74. This value is close to the ratio between the real areas. These first results comply the Tabor's theory between the friction force and the real area. The interfacial shear stress τ can be considered as constant at this scale. From this result we can evaluate the shear stress.

Based on the evaluation of the friction force for a 300 × 300 micro-objects the mean value of the interfacial shear stress is 18.75 (GPa) (see table(VI)). Other experiments have been performed using micro-objects with various sizes. Table(V) presents the results. We notice that the shear factor is between 16.81 < τ < 25.33 (GPa). The obtained result is 22.18 ±3.15GPa, that is equivalent to an uncertainty of 14.2%.

B. Application on the feeding system

First experiments on the feeding system have shown the validity of using a vibrating system (Fig. 1) for feeding very small components. The piezoelectric stack is supplied by a sawtooth voltage of 100 Hz and 200 V pp . The obtained

VI. CONCLUSIONS AND FUTURE WORKS

A. Conclusions

In this work, we have presented a method to determine the friction force for a flat micro-object in contact with a flat support. This force will be used to control an inertial force feeding system. The model of contact is based on the Hertz theory and the Greenwood-Williamson multi-asperity contact theory. This first approach has permitted to evaluate the separation distance d between the surface of the micro-object and the support. Furthermore, for all the micro-objects the real contact area ratio with the flat support and the support with grooves is constant. Finally, the interfacial shear stress have been evaluated experimentally, and the results give a value of 16.81 < τ < 25.33 (GPa).

The experimental set up has allowed to find the maximum friction force required to move a micro-object.

B. Future Works

The evaluation of τ and d will allow to elaborate controllers for the designed feeding system. To improve our approach, we will include the effect of the adhesion forces inside the contact model by using a model based on the DMT, JKR or Maugis's theory. Moreover, experiments with other types of materials and supports will be performed.

Fig. 4 .

 4 Fig. 4. Representation of the supports and the objects used.

Fig. 5 .Fig. 7 .

 57 Fig. 5. AMIS-2 station

Fig. 8 .

 8 Fig. 8. Topography of silicon surface obtained using an AFM.

Fig. 9 .

 9 Fig. 9. Load of 300 × 300 micro-object vs separation distance d for a flat support and a support with grooves.

Fig. 10 .

 10 Fig. 10. Friction force curve for a 300 × 300 micro-object on the flat support.

Fig. 11 .

 11 Fig. 11. Friction force curve for a 300 × 300 micro-object on support with grooves

  micro-objects Real area 10 -17 (m 2 ) Mean F r 10 -6 (N) Mean τ (GPa) Real area 10 -17 (m 2 ) Mean F r 10 -6 (N) Mean τ (GPa) cuboid of 500 × 500 µm 2 , is about 3.3 µm/step. Figure12illustrates the presents results.

Fig. 12 .

 12 Fig. 12. Vibrating experiment.

TABLE II CHARACTERISTIC

 II OF RECTANGULAR CANTILEVERS. THICKNESS, WIDTH AND LENGTH ARE THE NOMINAL VALUES. THE RESONANCE FREQUENCY IS FOUND EXPERIMENTALLY BY THE AFM. THE STIFFNESS IS DETERMINED FROM ITS UNLOADED RESONANT FREQUENCY.

	Cantilevers	Nanosensors	Ultrasharp
		TL-FM	NSC35/AIBS
	Thickness (µm)	3	2
	Width (µm)	28	35
	Length (µm)	225	130
	Stiffness (N/m)	2.08	1.25
	Resonance Frequency (kHz)	70,42	105

TABLE IV SUMMARY

 IV OF FRICTION FORCES MEASURES FOR A 300 × 300 MICRO-OBJECT PLACED ON FLAT SUPPORT AND ON A SUPPORT WITH GROOVES.

	Friction forces	F r (µN)	F r (µN)	Ratio
		on flat support	on support with grooves
		0.9759	0.7078
		0.9174	0.6962
	Mean	0.94	0.70	0.74

TABLE V EVALUATION

 V OF THE INTERFACIAL SHEAR STRESS τ FOR MICRO-OBJECTS PLACED ON A FLAT SUPPORT.

	micro-objects	300	200	100	80
	Real area 10 -17 (m 2 )	4.97	2.21	0.552 0.353
	Mean F r 10 -6 (N)	0.94	0.37	0.17	0.08
	τ (GPa)	19.03 16.81 25.33 22.91

TABLE VI EVALUATION

 VI OF THE INTERFACIAL SHEAR STRESS τ FOR A 300 × 300 MICRO-OBJECT

VII. ACKNOWLEDGMENTS

This project is partially supported by the EUPASS project (Evolvable Ultra-Precision Assembly Systems: http://eupass.org).