Alexis Ferrand
email: alexis.ferrand@univ-lille1.

Session "Exchanges in personal networks" Types of Regulations of Exchanges

Properties of the contents of ties and of the their sociometric arrangments are maintained by specific regulation processes. The paper discusses -and illustrates with data -the idea that several types of regulation of exchanges in networks can be distinguished as combinations of tree dimensions: interpersonal agreement / collective categorical norms / local norms in a networks.

TYPES OF REGULATION OF EXCHANGES

INTRODUCTION

The more general and classical definitions of social capital recognize two dimensions: -a structured network of ties, -a set of resources which flows through the ties. For example, P.Bourdieu 's definition emphases the dimension of resources (Le capital social. Notes provisoires. Actes de la recherche en sciences sociales, 1980, 31 : 2-3) : «The volume of social capital own by a specific agent depends on the range of the network of ties he is actually able to mobilize and on the volume of economic, cultural, symbolic capital owns by everyone linked to him. » The capital of alters, their resources are defined as elements of Ego's capital. To be used as capital by Egos, resources have to flow from alters to ego who does something with them in the line of his interests, or resources have to flow from alters to others persons in a way which interests ego. In both cases there is a circulation of resources which change of ownership.

James Coleman emphasizes more the structure of the network (Social capital in the creation of human capital. American Journal of Sociology, 1988, Vol 94, p.95-120) : «social capital constitutes a particular kind of resource available to an actor.../ Social capital is defined by its function. It is not a single entity but a variety of different entities, with two elements in common: they all consist of some aspect of social structures, and they facilitate certain actions ... /.. (p.98).. Unlike other forms of capital, social capital inheres in the structure of relations between actors and among actors. It is not lodged either in the actors themselves or in physical implements of production. (p.98) » Later in the paper, Coleman came to define one of the more important effect of the structure. He writes: « If A does something for B and trusts B to reciprocate in the future, this establishes an expectation in A and an obligation on the part of B. This obligation can be conceived as a credit slip held by A for performance by B../.. (p.102) » This form of social capital depends on two elements: trustworthiness of the social environment, which means that obligations will be repaid, and the actual extent of obligations held. But trustworthiness finally is said to depend on the closure of the relational structure (that means on the possibilities for actors to sanction a deviant behavior). In that respect structure is important as channel through which resources flow, but also as condition for social control.

In both definitions resources flow. And Coleman goes further in defining conditions of social control. But we don't know what kind of norm that control is supposed to impose. The background of both definitions implies something like a norm of reciprocity. But nothing is said to define how balance can be obtained between resources given and resources received. A kind of reciprocity must exist, but there is no principle to define how to reach that reciprocity. A norm imposes to maintain reciprocity, to reach a certain balance through exchanges, but the evaluation of content is not defined by a norm. It is an old question, a classical difficulty for exchange theory.

The basic idea of that presentation is that even if we find interesting results about the effects of social capital we will define a poor theory unless we are able to understand how evaluation of resources are performed in networks. We can imagine that a part of researches on social capital will have the same output as those on social support: a lot of empirical results gathered around few narrow common propositions and a lot of contradictory small pieces of theory. The idea is that reality is complex. Even if epistemology recommends parsimony in the definition of models trying to approximate empirical data, we have to preserve the theoretical possibility of complexity. An expression of that complexity is that several types of regulations are simultaneously operating in a given social exchange, sometimes in harmony, sometimes with tensions. I will understand regulation in that presentation as principles which define what resources can be exchanged in each kind of tie, given the other existing ties. It is a narrow definition, but nevertheless it raises a lot of problems.

TYPES OF REGULATION

Structural, categorical, personal order: C.Mitchell

Let me go back to a pioneer book published twenty five years ago. In the introduction of « Network analysis, Studies in human interaction » Clyde Mitchell has defined three ways of understanding and explaining social behavior. He has suggested the conceptual separation of three types or orders of social relationships which can be significant in the analysis of the behavior of people in town. These types are: a. « the structural order by means of which the behavior of people is interpreted in terms of actions appropriate to the position they occupy in an ordered set of positions, such as in a factory, a family, a mine, a voluntary association,... « Here the behavior is interpreted in terms status and roles defined by and inside a specific institution. b. « the categorical order by means of which the behavior of people in unstructured situations may be interpreted in terms of social stereotypes such as class, race, ethnicity » c. « the personal order by means of which the behavior of people in either structured or unstructured situations may be interpreted in terms of the personal links individuals have with a set of people and the links these people have in turn among themselves and with others such as the social networks of the families in Bott's study. « That third order is described later in the text by Mitchell as the order of one or several networks of interpersonal relations. We can understand the personal order as a kind of regulation of behavior due to embeddedness of relations in networks of interpersonal ties. AND it can be opposed to categorical and structural orders which are grounded on normative principles, specific (as status role) or general (as stereotypes).

Mitchell has given recommendations about the way of using that typology. He wrote: « These three orders of social relationships, however, should not be looked upon as three different types of actual behavior, but rather as three different ways of making abstractions from the same actual behavior so as to achieve different types of understanding and explanation. By this argument, therefore, there can be no opposition of structural and personal links but only different ways of subsuming the data into explanatory frameworks. (p.20) » I retain the idea that a relational reality can be analyzed through different explanatory frames because that relational reality combines, mixes the different types of order. In other words, it is possible to imagine that a given reality is regulated by a combination of various processes interacting. Then the line of research is to define the various types of regulations, and to identify how they interact and in what proportion in a given network of relations.

Trust: P.Blau

The regulation of exchanges by trust is often quoted. Mitchell's typology of orders can be complemented by a discussion about the emergence of trust in dyadic relations as it has been defined by Peter Blau in his classic « Power and exchange in social life ». Even if P.Blau, in a Simelian perspective, emphasizes the triadic nature of exchanges, when he analyses the emergence of trust, he makes the point that trust can be a property of the relation between two individuals, of a dyad, regardless their relational environment. Three arguments support this idea, -First, trust emerges from common experiences of partners. The kind of behavior and exchanges possible and successful in time t are the basis for positive anticipations regarding an increasing rate of successful exchanges at t+l. This process of trust formation tends to allow an isolation of the dyad from its social context. As an extreme case, it can exist in a social vacuum, without any kind of social control.

-Secondly trust is due to investments which cannot be recovered in case of rupture. The story of the tie and time spent to maintain it are like funds held as guarantee. Ego can trust alter if he knows how much alter will loose in case of rupture. And there is no intervention of social control here.

-Third trust can exist when a small number of trustworthy relations exist for each partner. Knowing they have only few alternatives, they are encouraged to make use, and by the fact to maintain, existing ones.

THREE TYPES OF REGULATION

Then we can give the global picture of three types of regulation by combining previous definitions.

Regulation by dyadic trust

Anticipations of partners are mainly oriented by interpersonal agreement. They are guaranteed by previous experiences and by the amount of investments impossible to recover in case of rupture. Actors are also constrained by the very small number of alternatives available. Relational control has no importance and in some cases exchanges are totally hidden to others relations of partners.

Local regulation by the network of interpersonal relations

Anticipations of partners are grounded on shared norms and on the knowledge that the network is able to be informed of a fault and to sanction it. The network provides alternatives. Example are exchanges of help between brothers..

Global categorical regulation

Anticipations of partners are grounded on general norms or stereotypes. Sanctions are imposed by specialized agent or anonymous people as public. Examples are that specific sub set of Goffman 's interactions in public when they occur among people without personal information.

Articulation between regulations

Now, if agree with that simple typology of kinds of regulations, we have to address the question of their operating mode. We can say that these regulations are supposed to work more or less together. They are interdependent. Each can exert a part of control dependent on the part played by others. To precise that interdependence, we can say that the sum of their various intervention is a constant. Or, in other words, if we want to weight the intervention of each regulation to analyze particular interaction or exchange, then the sum of weights should be one in all cases, but the proportion of each type will change from case to case.

We can portray that in the classical triangle where the coordinates of a point always sum at one. That graphic representation stresses the interdependency of regulations. Down left, one can put a point which portrays an anonymous economic transaction with a shopkeeper, mainly under global control. But moving the point toward the right, we still portray the anonymous control of the law but also the emerging control of a network of customers able to make the local reputation of the shopkeeper By moving up the point we can introduce more specific agreements between the shopkeeper and a specific customer. If we look in others directions, at the top we find the more private, close, elective, particularistic, interactions. As example there will be some special kind of friendships or particular interpersonal interactions with kinsman but independent of the other kin relations. Down right we will find relations embedded in some form of social circle, as a club, a voluntary group, some kind of religious local community, or in a subnetwork build up in a neighborhood or among professionals.

Regultation by dyadic trust

Role relationships, closeness, embeddedness, and types of regulations

Now some precisions can be given about the meaning of regulation in contrast with others concepts.

Regulation and embeddedness

Regulation and embeddedness are two concepts interdependent: embeddedness describes, indicates, the level of sociometric dependency of a relation on others relations in a given network. Embeddedness is the major structural dimension of regulation. But regulation is more than embeddedness. It implies also contents, norms, patterns of behavior, symbolic meanings, used as shared frames of references to bargain and to exert control.

Closeness

The subjective feeling of closeness of a relationship can indicate the dominance of the type of regulation based either on dyadic trust or on the embeddedness of the tie in a densely knit subnetwork of close friends and acquaintances. There is no a priori univocal relation between closeness and one type of regulation.

Roles relationships

Seemingly, it is clear that when we ask people to label their personal relationships with role flags as 'friend', 'neighbor', 'co-worker'.... these categories capture interesting features of the reality. Mainly they indicate the more frequent social context in which actors interact. Some context imply more often categorical regulation: we can imagine that relations between coworkers are more generally driven by a categorical regulation, when friendship ties should be more often driven by an interpersonal network regulation. These global tendencies can be captured by empirical surveys. But, again, there is no univocal conceptual relation between roles relationships and kind of regulation: one can be more or less committed with a specific neighbor, at an extreme such relation can be more trustful than with a close member of the family.

DYADIC REGULATION AND DIVERSITY VS CATEGORICAL REGULATION AND HOMOGENEITY

From that global hypothesis about interdependence between the three types of regulations, more precise hypothesis can be deduced. I want to discuss and illustrate briefly one of them.

That hypothesis is about the effect of kinds of regulation on the diversity of contents of exchanges.

We can assume that the more categorical the regulation is, the more homogeneous the social prescriptions and the social controls are, the less varied should be the combinations of exchanges in a given kind of tie. If a categorical regulation is operating, the classical functionalist idea that the social pattern is represented in the data by the more frequent kind of combination of exchange is pertinent: if neighbor watch more often on the cat than on the grandmother it is because he has to do so. On the contrary, the dyadic regulation allows actors to bargain a large range of combinations of exchanges. Then, by hypothesis, there are no dominant pattern, and a larger number of different combinations of exchanges.

The gap between homogeneity and variety is empirically obvious if we want to look at it.

Data

Let's give an example. From a national survey, (INSEE Modes de Vie 1988-1989) I have extracted relations of exchanges of helps during the last twelve months in a working class sub sample.

-Informations are asked about exchanges between households and not individuals.

-Relations between household are described from the point of view of any of the spouses.

-Four categories of role relationships are used as proxy indicators of types of regulation.

-Answers are categorized in 10 types of exchanges (reciprocal or not) possible in each relation. 1) Cares of children .2) Cares, shopping, housekeeping, helps for transport. 3) Administrative help. 4) Needlework, to can food. 5) To care garden or pets. 6) Help for maintenance of house or car, for moving 7) Help for important house works. 8) Help for school work. 9) To borrow money. 10) To borrow various items, others helps

From multiplexity to variety

Multiplexity

A basic property of exchange relations is their level of multiplexity. And we see in the tab below the classical result: kinship relations allow a larger number of types of exchanges (2.6), when relations with neighbors or colleagues are more specialized (1.6). That is an empirical trend which can be interpreted as the effect of global normative references as well as of structural constraints. In all categories of relations, the coefficient of variation of multiplexity is quite similar: standard deviation range from sixty to seventy percent of the mean. In all categories of relations actors have the same tendencies to make use of the bounded liberty to specialize more or less their exchanges. Only a limited range of level of multiplexity is actualized in interactions and exchanges.

Diversity of arrangements

Now we can examine another property which is the diversity of the combinations of various types of exchanges. Given the mean number of types of exchanges in relations, we exclude the very multiplex ties as special cases and retain relations which comprise from 1 to a maximum of 3 types of exchanges chosen among the10 cited above. Then the range of multiplexity among the categories of relations is narrowed to [1.4 -1.8]. Also we can control the size of the sample by comparing sub sample of 500 relations of each category.

Then 820 different arrangements of exchanges are formally possible. That is the diversity offered by the questionnaire to define contents of relations. But observed diversity is, of course, much more limited: it ranges from 58 to 82 (ten times less than the formal possibilities). It is a first indicator of the diversity allowed to actors by the kind of regulation of the ties. People do combine types of exchanges in a more or less restricted way. The diversity in parents/child relations is twice as big as that of collateral relations.

That is interesting because they are both elements of the family institution and embedded in the same kinship network able to control them. Also the length of these two categories of relations by definition is about of same order: you know yours parents since as long as your brothers. Possibility to invest is similar. Nevertheless, we are obliged to say that parent-child relations are much more diverse than collateral, and that they are more often regulated by dyadic bargaining able to find a huge variety of agreements on combinations of kind of helps given and kind of helps received. But we see also that friendly relations are less diverse than collateral, and colleague or neighbor relations less diverse than friendly relations.

CONCLUSION

For that paper, it is not useful to discuss the reasons of existence of theses various level of diversity.

The first issue is to accept that they reveal a social fact. Diversity is not a kind of empirical difficulty or a statistical aberration that we have to manage with clever procedures of data analysis, segmentation, classification, and so on... These various level of diversity are the phenomenal expression of different dominant types of regulation of exchanges in relations. Some relations are mainly governed by homogenous categorical norms which impose a limited number of possibilities when other relations are predominantly shaped by norms specific to a network, and others are regulated by more open bargaining between actors which produce a large number of possible arrangements.

At the theoretical level as well as at the methodological level these differences in regulations involve differences in the way to analyze and interpret the building of relations.

If you examine the arrangements below and the number of relations which are concerned, it is clear that, on the left, exists something like a social regularity, and on the right nothing like a social regularity. In the same population and the same categories of relations, two types of regulation produce facts described by these data1 . The kind of rules which impose homogeneity are not of the same nature as rules which are used as references in more open dyadic bargaining : on one hand we can do as if the high frequency of a behavior indicate the content of an unconditional norm, on the other hand we have to uncover conditional rules of bargaining. The form of the analysis is not the same, even when the data are collected in the same way and belong to the same data set.

5th European Conference on Network Analysis -Sitges -1998

  It is not only the total number of arrangements which is important, as a proof of an average « liberty » of actors, but also the concentration of relations in a limited number of patterns, others relation being more subject to dyadic regulation. If we count the number of different combinations needed to gather 75% of a category of relations, we see for example -that 75% of parents/child relations are spread over 40 different combinations, -when 75% of collateral relations are distributed over 22 different combinations.

	Roles relationships as	Nb Tot of relations	MULTIPLEXITY	DIVERSITY OF ARRANGEMENTS
	weak indicators of		Mean number of types	Total number of	Nb of different
	types of regulations		of exchanges by	different	arrangements to
			relation	arrangements	define 75% of the
					relations
	Parents/Child	500	1.8	82	40
	Collateral	500	1.6	72	22
	Friends	500	1.4	60	14
	Neigb. Colleagues	500	1.4	58	11

  Number of relations for more frequent arrangements of types of exchanges (left col), and for more rare arrangements of types of exchanges (right col)

	Arrangements	Number of	Arrangements	Number of
	of types of	relations %	of types of	relations %
	exchanges			exchanges
	0100000000	133	26.6	0101000000	1	0.2
	0000010000	55	11.0	0110010000	1	0.2
	0000100000	50	10.0	1000010000	1	0.2
	0000000001	42	8.4	1000010001	1	0.2
	1000000000	38	7.6	1000110000	1	0.2
	0010000000	15	3.0	1001000000	1	0.2
	1100000000	15	3.0	1001100000	1	0.2

5th European Conference on Network Analysis -Sitges -1998Types of regulations of exchanges A.Ferrand

5th European Conference on Network Analysis -Sitges -1998

Arrangments are the patterns of answers given to 5th European Conference on Network Analysis -Sitges -1998 Types of regulations of exchanges A.Ferrand


Dominique Fratantonio
email: dominique.fratantonio@insa-toulouse.fr

Stefan Stefanov
email: stefanov@imbm.bas.bg

Marcos Rojas-Cardenas
email: marcos.rojas@insa-toulouse.fr

Christine Barrot

Stéphane Colin
email: colin@insa-toulouse.fr

µFLU-NEGF18-149 PHOTOLUMINESCENT MODELS IN DIRECT SIMULATIONS MONTE CARLO FOR MOLECULAR TAGGING TECHNIQUES

Keywords: Molecular tagging, photoluminescence, Direct Simulation Monte Carlo

Molecular tagging techniques are promising tools for providing local measurements of pressure, temperature and velocity fields in rarefied gas flows. These techniques are based on the optical collection of photons emitted by a molecular tracer, such as acetone or diacetyl vapor, when excited by UV light. The measurement of the gas properties of interest is carried out by exploiting the intensity, the lifetime and/or the spatial displacement of the emitting tracer. A key point for the success of these techniques resides on the ability of accurately extracting the information from the distribution of the emitted light. In this work, a simple statistical model for describing the photoluminescence process is proposed and implemented in the framework of the Direct Simulation Monte Carlo method. New experimental data on acetone and diacetyl emission are compared to the numerical simulations.

EXTENDED ABSTRACT Introduction

The subject of rarefied gas flows is of central interest in the field of microfluidics. Especially in the last decades, the development of microfabrication techniques increased the number of practical applications and pushed the interest of the scientific community in further analysing the gas behaviour at the micro-scale. Microdevices that deal with micro-gas flows already exist, such as Knudsen pumps [START_REF] An | A Si-micromachined 162-stage two-part Knudsen pump for on-chip vacuum[END_REF], micro-actuators for aeronautical and space applications [START_REF] Cattafesta | Actuators for active flow control[END_REF] and micro heat exchangers [START_REF] Gerken | Heat transfer enhancement with gas-to-gas micro heat exchangers[END_REF].

By shrinking the dimensions of the system, the degree of rarefaction increases as a consequence of a reduction of the number of intermolecular collisions. When the mean free path , namely the average distance travelled by a molecule between two consecutive collisions, is comparable or higher than the characteristic dimension of the system , thermodynamic non-equilibrium phenomena appear, thus heat and mass transfers in the system cannot be modelled by using the classical continuum assumption. Since many micro-devices are constituted by elements that deal with gas-wall interactions, such as micro-channels, understanding how the interaction between gas molecules and solid surface changes the macroscopic properties of the flow as the level of rarefaction increases is of fundamental importance. Indeed, local thermodynamic disequilibria at the wall produce a velocity slip and a temperature jump [START_REF] Colin | Gas microflows in the slip flow regime: a critical review on convective heat transfer[END_REF]. Theoretical models for describing the effect of local thermodynamic non-equilibrium have been developed since more than one century [START_REF] Maxwell | On stresses in rarefied gases arising from inequalities of temperature[END_REF]. However, these mathematical models need to be validated and adjusted by means of experimental data. Indeed, most of the experimental studies available in literature related to rarefied gas flows in micro-channels provide measurement of global quantities, such as mass flow rates, inlet and outlet pressure and temperature. Therefore, the effect of the local thermodynamic disequilibrium is only indirectly evaluated [START_REF] Pitakarnnop | A novel experimental setup for gas microflows[END_REF][START_REF] Silva | Experimental analysis of velocity slip at the wall for gas flows of nitrogen, R134a, and R600a through a metallic microtube[END_REF]. To the best of our knowledge, there are no direct measurements of velocity profiles in confined rarefied gas flows.

In this context, the molecular tagging technique is a promising tool for answering to this urgent need of local experimental data on confined rarefied gas flows. It is a low-intrusive, optical technique based on the exploitation of a molecular tracer that is able to emit light in the visible spectrum when excited by a UV laser source. Common molecular tracers employed are acetone and diacetyl vapor [START_REF] Hadj Mohand | Molecular tagging velocimetry by direct phosphorescence in gas microflows: correction of Taylor dispersion[END_REF][START_REF] Hiller | Velocity visualization in gas flows using laser induced phosphorescence of biacetyl[END_REF]. By following the displacement of the tagged tracer molecules, the molecular tagging velocimetry (MTV) could provide direct measurement of the slip velocity at the wall, as well as the overall velocity profile in micro-channels. The molecular tagging thermometry (MTT) can instead provide local information on the gas temperature distribution and on temperature jump at the wall by measuring the intensity and the duration of the light emitted by the tracer. The MTV has already been applied to liquid flows and non-rarefied gas flows in channels [START_REF] Maynes | Velocity profile characterization in sub-millimeter diameter tubes using molecular tagging velocimetry[END_REF][START_REF] Samouda | Micro molecular tagging velocimetry for analysis of gas flows in mini and micro systems[END_REF] while the MTT has seen applications in liquid flows and gas flows in combustion chambers [START_REF] Thomson | Spatially resolved temperature measurements in a liquid using laser induced phosphorescence[END_REF][START_REF] Luong | Toluene laser-induced fluorescence for in-cylinder temperature imaging in internal combustion engines[END_REF]. No applications on rarefied gas flows in confined systems exist at this moment, to the extent of our knowledge. However, recent experimental studies provided evidences on the feasibility of the application of the MTV and MTT to gas flows in rarefied conditions [START_REF] Yeachana | Preliminary investigations on temperature dependency of acetone vapor luminescence for molecular tagging thermometry[END_REF][START_REF] Fratantonio | Molecular taggin velocimetry for confined rarefied gas flows: phosphorescence emission at low pressure[END_REF].

A key point for the success of these techniques resides on the accurate reconstruction of the velocity and temperature distribution of the gas from the light emission of tracer. Strictly speaking, the MTV and MTT provide information about the intensity, the lifetime and the spatial distribution of the tracer emission, but does not provide a direct measurement of the fluid dynamic and thermodynamic properties of the gas flow under analysis. For instance, the molecular tagging velocimetry (MTV) requires an advection-diffusion modelling of the tracer displacement for reconstructing the velocity field from the tracer displacement field [START_REF] Frezzotti | Role of diffusion on molecular tagging velocimetry technique for rarefied gas flow analysis[END_REF]. However, this methodology of post-processing the data needs an accurate estimation of the diffusion coefficient and the intramolecular processes that occur in the tracer molecules can affect the diffusion mechanisms, e.g., through possible variations of temperature or even molecular dissociation produced by the photon excitation. For the molecular tagging thermometry (MTT), the gas temperature measurement is based on the relationship between the tracer temperature and the intensity or the lifetime of the tracer emission. However, the photoluminescence process is characterized by intramolecular transitions that can bias the tracer temperature from the gas temperature and could possibly modify the gas temperature itself in a significant manner. For these reasons, designing a mathematical model that takes into account for the most important intramolecular processes is necessary to exploit the experimental data on the tracer emission for reconstructing the gas properties of interest.

In this work, new experimental data on acetone and diacetyl emission are presented and a novel implementation of photoluminescence models in the framework of the Direct Simulation Monte Carlo (DSMC) method is proposed. DSMC simulations are carried out for a mixture of gas and tracer molecules.

The intermolecular collisions and the intramolecular transitions are both simulated for better understanding how these two phenomena interact and affect the pressure and temperature distribution of the gas-tracer mixture, the molecular diffusion of the tracer, and the spatial and temporal evolution of the tracer emission as well. Various events characterize the photoluminescence phenomenon. Starting from the photon absorption, the molecular excitation produces a change in the electronic state as well as an activation of rotational and vibrational modes. Following the excitation, many events can occur: intramolecular transitions, e.g., vibrational relaxations and intersystem crossing transitions, non-radiative de-excitations, e.g., molecular quenching, and radiative de-excitations, such as fluorescence and phosphorescence emissions [START_REF] Rohatgi-Mukherjee | Fundamentals of photochemistry[END_REF]. A mathematical representation that describes all the intramolecular processes is a difficult task. Therefore, a first basic representation that takes into account for only the excitation and the radiative emission events is here proposed. Later, the complexity of the model will be gradually increased with the aim to numerically reproduce the experimental data.

Proceedings of the 5th European Conference on Microfluidics -µFlu18 3 rd European Conference on Non-Equilibrium Gas Flows -NEGF18

February 28-March 2, 2018 -Strasbourg, France 3

The laser excitation process occurs in a time interval of the order of a few nanoseconds. Therefore, the photon absorption happens practically instantly when compared to the de-excitation relaxation time and to the fluid dynamic characteristic times, such as heat transfers and molecular diffusion. In the DSMC representation, each model particle corresponds to a group of molecules. Following the photon absorption, only a percentage of molecules belonging to a particle are excited.

The modelling of the radiative de-excitation event is based on experimental observations. In literature, experimental studies demonstrated that the luminescence time evolution given by acetone and diacetyl molecules fits an exponential or bi-exponential function [START_REF] Almy | Lifetime of fluorescence in diacetyl and acetone[END_REF][START_REF] Jian-Bang | Principles of flow field diagnostics by laser induced biacetyl phosphorescence[END_REF]. The experimental data presented in this work confirm this fact. From these observations, the emission rate of photons provided by one model particle is hypothesized to be proportional to the number of excited molecules contained in it, with the constant of proportionality corresponding to the emission rate constant [START_REF] Thurber | Pressure and composition dependences of acetone laserinduced fluorescence with excitation at 248, 266, and 308 nm[END_REF]. Starting from this hypothesis, a probability density function (PDF) that defines the number of occurrence of radiative deexcitations is associated to each model particle of the DSMC simulation. In order to reproduce the exponential decay of the excited molecule population that is experimentally observed, a Poisson probability distribution is chosen:

! , (1)
where is the average number of occurrence in a time interval Δ , such that Δ Δ . The acceptance-rejection method [START_REF] Bird | Molecular gas dynamics and the direct simulation monte carlo of gas flows[END_REF] is then applied to generate the random variable . As a result of this choice, the numerical simulation provides an exponential evolution of the light emission with a characteristic time equals to 1/ . Figure 1 provides an example of experimental result and DSMC simulation of the luminescence emission of diacetyl excited by a laser beam. The comparison reveals that the experimental data are characterized by an higher dispersion of light with respect to the DSMC result. This is supposed to be due to noise produced by background light emission of diacetyl molecules absorbed by the walls of the experimental cell. This source of noise is currently not modelled in the DSMC simulation, and it will be considered in future developments.

Figure 1 :

 1 Figure 1: (a) experimental data and (b) DSMC simulation on the light emission of diacetyl vapor at pressure 1000 Pa and 50 µs after the laser beam excitation.

Acknowledgements

This research obtained financial support from the European Community's Seventh Framework Program (FP7/2007-2013) under grant agreement no 215504, and from the Fédération de Recherche Fermat, FR 3089. The second author, S.S. acknowledges the partial support of the Bulgarian NSF under Grant No. DN 02/7-2016.

Proceedings of the 5th European Conference on Microfluidics -µFlu18 3 rd European Conference on Non-Equilibrium Gas Flows -NEGF18

February 28-March 2, 2018 -Strasbourg, France


Yichang Wang
email: yichang.wang@insa-toulouse.fr

Yanfeng Gao
email: yanfeng.gao@insa-toulouse.fr

Pascale Magaud
email: pascale.magaud@unilim.fr

Lucien Baldas
email: lucien.baldas@insa-toulouse.fr

Christine Lafforgue
email: christine.lafforgue@insa-toulouse.fr

Stéphane Colin
email: stephane.colin@insa-toulouse.fr

µFLU-NEGF18-126 INERTIAL MIGRATION OF NEUTRALLY BUOYANT PARTICLES IN SQUARE CHANNELS AT HIGH REYNOLDS NUMBERS

Keywords: suspensions, inertial focusing, particle-laden flows, high Reynolds numbers

 revealed experimentally the presence of eight equilibrium positions in millimetric square channels for Reynolds numbers higher than 250. The aim of the present work is to extend these results obtained at millimeter scale to the micrometer scale. To this end, in situ visualization of particles flowing in square micro-channels at Reynolds numbers ranging from 5 to 300 have been conducted and analyzed.

Introduction

The inertial migration of neutrally buoyant particles was firstly quantitatively highlighted by Segre and Silberberg in the 1960s. Millimetric particles, flowing in a millimeter-scale straight cylindrical tube, were observed to migrate at moderate Reynolds numbers across the streamlines and to focus on an annulus with a radius of ~ 0.6 times the tube radius [START_REF] Segre | Radial particle displacements in Poiseuille flow of suspensions[END_REF]. However, at this diameter, long channels of several meters were needed for the particles to reach their final equilibrium positions. A few decades later, thanks to the advances in microfabrication techniques, micro-scale channels were used. Since then, the inertial migration phenomenon in microchannel has gained considerable attention due to a wide variety of applications such as separation, concentration, counting, detecting, sorting or mixing of particles in suspension.

Experimental studies with square microchannels have shown a similar migration phenomenon. Di Carlo et al. [START_REF] Di Carlo | Continuous inertial focusing, ordering, and separation of particles in microchannels[END_REF] in 2007 observed that neutrally buoyant particles flowing at moderate Reynolds numbers focus only on four equilibrium positions located near each channel wall along their symmetry planes. These results were confirmed by numerical simulations [START_REF] Di Carlo | Particle segregation and dynamics in confined flows[END_REF][START_REF] Abbas | Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers[END_REF]. Square channels are thus particularly advantageous due to their easy manufacturing process and the reduced numbers of focusing positions. However, several experimental and numerical studies have recently concluded that, depending on the flow conditions, the number of equilibrium positions could vary and they could be located in different zones. Abbas et al. [START_REF] Abbas | Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers[END_REF] highlighted that in square micro-channels, particles concentrate in the channel centerline at low flow inertia (typically Reynolds number Re < 1). At the same time, Miura et al. [START_REF] Miura | Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels[END_REF] have obtained experimentally eight equilibrium positions in square millimetric channels for Reynolds numbers higher than 250. These eight equilibrium positions, located at the centers of the channel faces and at the corners were also confirmed numerically by Nakagawa et al. [START_REF] Nakagawa | Inertial migration of a spherical particle in laminar square channel flows from low to high Reynolds numbers[END_REF] in 2015.

Considering the variety of applications of particle inertial migration in microfluidics, it seems important to perfectly identify the different equilibrium positions for a wide range of Reynolds numbers and to clearly evaluate the efficiency of the inertial focusing in these flow conditions. The aim of this work is then to check the validity of Miura et al. results at the micrometer scale.

In the present paper, experiments with neutrally buoyant spherical particles flowing in square microchannels are conducted at Reynolds numbers ranging from 5.6 to 280. A so-called "focusing degree" is introduced to quantify the development of the inertial focusing. Influence of the particle to channel size ratio on the focusing degree are presented. Finally, a possible distribution of the particles in the cross-section for Reynolds numbers higher than 250 is proposed.

Experimental method

The spherical particles used for this study are made of polystyrene (Microparticles GmbH®) with diameters d p = 5.3 and 8.44 µm and a density ρ = 1050 kg m -3 . The fluid density is matched to the particle one by using a mixture of 23 % glycerol and 77 % deionized water with a particles volume fraction Φ = 0.1 % for the 8.44 µm particles and Φ = 0.025 % for the 5.3 µm particles, ensuring the same number of particles in a given volume for both cases. The suspension flows in square borosilicate micro-channels (Vitrocom) with 80 × 80 μm 2 inner section and 10 cm length. The flow rates generated by a syringe pump (PDH 4400, Harward Apparatus), range from 667 nL/s to 33 µL/s corresponding to Re from 5.6 to 280 (Re = UH/ν where U is the mean flow velocity, H the channel height and ν the kinematic viscosity of the mixture). Particle positions in the channel are in situ observed thanks to an Olympus microscope (BX 51) and images are recorded in several places along the channel length by a high-speed camera (Photron Fastcam SA3) focusing at the midplane of the channel. At least 2000 images are captured to yield satisfactory results. The setup and the image processing have been detailed in previous works [START_REF] Abbas | Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers[END_REF][START_REF] Gao | Self-ordered particle trains in inertial microchannel flows[END_REF].

Results and discussion

Fig. 1 displays the overall particle distributions for different Re. These distributions are obtained by superposing in the same image the centers of particles identified in the 2000 acquired images. For Reynolds number less than 150, the total migration is not complete at a distance from channel inlet z/H = 1000. The particles distributions visualized in the images thus represent the development of the inertial migration. Indeed, in Fig. 1, at Re = 14, particles are still randomly distributed over the image, indicating a relatively uniform distribution in the cross-section. As the Reynolds number increases from 14 to 112, particles are seen to concentrate in lines located near the channel walls and on the centerline of the picture, corresponding to the four well known equilibrium positions. This result confirms that a shorter streamwise length is required for focalization when the Reynolds number is increased [START_REF] Abbas | Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers[END_REF]. For Reynolds numbers higher than 150, the migration is fully-developed at z/H = 1000. At Re = 280, the middle band which corresponds to the top and the bottom focusing zones is larger as seen in Fig. 1, suggesting that the particles are no longer concentrated in the four equilibrium positions but are distributed more widely at the periphery of the channel cross-section. This decrease in the focalization efficiency might be due to the particle migration towards new additional equilibrium positions near the channel corners, as observed by Miura et al. [START_REF] Miura | Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels[END_REF] in square millimetric channel for Re higher than 250. Since at moderate Re in square channels, particles are known to focus at four equilibrium positions near the centers of the channel faces, a parameter , termed "focusing degree" and defined as the percentage of particles focused at the four equilibrium positions in comparison with the total number of particles in the microchannel has been introduced [START_REF] Gao | Self-ordered particle trains in inertial microchannel flows[END_REF]. Fig. 2 illustrates the focusing degree  for various Re at a distance from channel inlet z/H = 1000 and for two different particle to channel size ratios. For d p /H = 0.11 (particles of diameter d p = 8.44 µm),  increases with increasing Re, reaches a maximum at Re ~ 150 and then decreases. This confirms that at a fixed distance from channel inlet, the focalization is first enhanced with increasing Reynolds number up to a maximum when the focalization becomes fully-developed. The decrease of  observed for higher Re could be due to the arising of other equilibrium positions near the channel corners [START_REF] Miura | Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels[END_REF].

For d p /H = 0.066, the evolution is similar. However, the maximum percentage of focused particles is lower and is reached at a higher Reynolds number. This result confirms that a higher streamwise length is required for the focalization of smaller particles [START_REF] Abbas | Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers[END_REF]. In addition, it seems that a higher level of focalization is reached for larger particles. To confirm the existence of the eight equilibrium positions previously observed by Miura, several other experiments have been conducted for Reynolds numbers higher than ~ 250. As shown in Fig. 3 (Left), additional focusing lines appear, suggesting the cross sectional distribution presented in Fig. 3 (Right). Further experiments have however to be done to confirm this trend, for example by using the projection experimental method described in [START_REF] Lafforgue-Baldas | Study of Microfocusing Potentialities to Improve Bioparticle Separation Processes: Towards an Experimental Approach[END_REF] which allows to obtain an image distribution of the particles in the cross section at the outlet of the channel.

Conclusion

The inertial migration towards the well-known four equilibrium positions of neutrally buoyant particles flowing in square micro-channels could be used to separate, concentrate or detect particles from a mixture. The performance of these devices depends on the efficiency of the inertial migration. We show in this work that at a fixed distance from channel inlet a specific Reynolds number exists for which the focalization is optimal, i.e., for which the rate of particles located on the four equilibrium positions is the highest. Under this value, the migration is not fully-developed and over this value, new additional equilibrium positions arise. This "optimal" Reynolds number depends on the particle to channel size ratio. The determination of this "optimal" Reynolds number is essential for the design of new separation devices.

Figure 1 :

 1 Figure 1: Overall particle distributions observed from channel midplane for different Re at a distance z/H = 1000 from channel inlet and for particles of diameter d p = 8.44 µm.

Figure 2 :

 2 Figure 2: Focusing degree  at z/H = 1000 from channel inlet with respect to Re, for different particle to channel size ratios d p /H.

Figure 3 :

 3 Figure 3: Left: Overall particle distributions observed from channel midplane for Re = 280 at a distance z/H = 1000 from channel inlet and for particles with diameter d p = 8.44 µm in a bidisperse suspension. Right: Deduced particle distributions across the channel cross-section.

Acknowledgements

The authors acknowledge FERMaT research federation for its support.


Dan Penny
email: dan.penny@sydney.edu.au

Tegan Hall

Damian Evans

Martin Polkinghorne

Jeremy A Sabloff

Geoarchaeological evidence from Angkor, Cambodia, reveals a gradual decline rather than a catastrophic 15th-century collapse

come

Geoarchaeological evidence from Angkor, Cambodia, reveals a gradual decline rather than a catastrophic 15th-century collapse

Alternative models exist for the movement of large urban populations following the 15th-century CE abandonment of Angkor, Cambodia. One model emphasizes an urban diaspora following the implosion of state control in the capital related, in part, to hydroclimatic variability. An alternative model suggests a more complex picture and a gradual rather than catastrophic demographic movement. No decisive empirical data exist to distinguish between these two competing models. Here we show that the intensity of land use within the economic and administrative core of the city began to decline more than one century before the Ayutthayan invasion that conventionally marks the end of the Angkor Period. Using paleobotanical and stratigraphic data derived from radiometrically dated sediment cores extracted from the 12th-century walled city of Angkor Thom, we show that indicia for burning, forest disturbance, and soil erosion all decline as early as the first decades of the 14th century CE, and that the moat of Angkor Thom was no longer being maintained by the end of the 14th century. These data indicate a protracted decline in occupation within the economic and administrative core of the city, rather than an abrupt demographic collapse, suggesting the focus of power began to shift to urban centers outside of the capital during the 14th century.

Angkor | collapse | Cambodia | archaeology T he demise of Angkor (Fig. 1) remains poorly understood.

The paucity of epigraphic evidence and monumental construction after the 13th/14th century CE means that many accounts of this period are vague and speculative. One narrative identifies the sack of Angkor by Thai forces from Ayutthaya in 1431 CE as the coup de grâce-"definitive, complete, and irremediable" (ref. 1, p. 258)-preceded by a protracted decline in state power and influence from the 14th century CE. Although Ayutthayan forces are believed to have occupied Angkor for a period between 12 y and 15 y, historical sources are both equivocal and contradictory regarding these events [START_REF] Vickery | Cambodia after Angkor. The chronicular evidences for the fourteenth to the sixteenth centuries[END_REF]. Cambodian narratives on collapse transformed over many hundreds of years and are largely institutional and community constructions that emerged between the 16th and 19th centuries [START_REF] Mikaelian | Le passé entre mémoire d'Angkor et déni de La _ nvaek: La conscience de l'histoire dans le royaume khmer du XVII e siècle[END_REF][START_REF] Thompson | Mémoires du Cambodge[END_REF]. Moreover, there is little reflection on the mechanics of demographic change despite known continuity of residential occupation and substantial building works into the 16th century CE [START_REF] Castillo | Life goes on: Archaeobotanical investigations of diet and ritual at Angkor Thom, Cambodia (14th-15th centuries CE)[END_REF][START_REF] Leroy | First direct dating for the construction and modification of the Baphuon temple mountain in Angkor, Cambodia[END_REF][START_REF] Polkinghorne | One Buddha can hide another[END_REF][START_REF] Pottier | Embryons et tortues: Des dépôts de fondation découverts au perron nord de la terrasse des Éléphants[END_REF][START_REF] Thompson | The ancestral cult in transition: Reflections on spatial organization of Cambodia's early Theravada Complex[END_REF].

Numerous hypotheses have been proposed to account for Angkor's decline. Groslier [START_REF] Groslier | La cité hydraulique angkorienne: Exploitation ou surexploitation du sol?[END_REF] suggested the capital collapsed because of the deterioration of the irrigation system and systemic environmental degradation associated with extensive forest clearance [START_REF] Penny | The demise of Angkor: Systemic vulnerability of urban infrastructure to climatic variations[END_REF][START_REF] Fletcher | The water management network of Angkor, Cambodia[END_REF]. Others have emphasized the supposed economic and social distress caused by the Jayavarman VII's "building orgy" (ref. 1, p. 258), and the torpor associated with the rise of Therav ada Buddhism (ref. 13, p. 497; ref. 14, p. 224). Still others claim the growing lure of maritime trade in the Mekong Delta may have eroded the power base of Angkor [START_REF] Vickery | Cambodia after Angkor. The chronicular evidences for the fourteenth to the sixteenth centuries[END_REF], or that climate change [START_REF] Yasuda | Climate deterioration and Angkor's demise[END_REF][START_REF] Day | Paleoenvironmental history of the West Baray, Angkor (Cambodia)[END_REF][START_REF] Buckley | Climate as a contributing factor in the demise of Angkor, Cambodia[END_REF][START_REF] Lieberman | The impact of climate on Southeast Asia, circa 950-1820: New findings[END_REF] or epidemic disease [START_REF] Reed | The curse of Angkor[END_REF][START_REF] Verdrager | Angkor. Le mystère de la ville morte et Anophèles dirus[END_REF] may have contributed. All of these explanations are problematic, however, and none have proven decisive [START_REF] Coe | Angkor and the Khmer Civilization[END_REF].

Lucero et al. [START_REF] Lucero | From 'collapse' to urban diaspora: The transformation of low-density, dispersed agrarian urbanism[END_REF] argue that the Khmer elite, like those in other tropical low-density cities had, by the 16th century, relocated to small and burgeoning entrepôts on the fringes of the ancient agrarian kingdom. In their view, "the low density dispersed urban landscape faded away and the urban world recreated itself in a more compact form in new locations and regions along the peripheries. This movement across the landscape we term urban diaspora, when people abandon not only the urban centers but much of the metropolitan heartland and move to peripheral areas where different kinds of networks and economic and political foci emerge" (ref. 22, p. 1139-1140). Evans [START_REF] Evans | Airborne laser scanning as a method for exploring long-term socioecological dynamics in Cambodia[END_REF] takes a contrary view, arguing that the demise of Angkor as the locus of power "may not, in fact, have involved the physical 'movement' of anything much at all, let alone radical demographic shifts" (ref. 23, p. 9). Rather, he suggests continuity and fluidity of power between royal houses, and a slow rather than catastrophic decline in urban population.

Whether the supposed "urban diaspora" associated with the demise of Angkor presaged or followed the administrative and commercial demise of the city is a matter of speculation, as is the speed with which that process occurred. This is a potentially decisive issue in revealing the process by which large low-density cities like Angkor ultimately fail, and one that can be addressed empirically. This paper will provide a radiometrically dated record of land use from an area of central Angkor that was a focal point for administrative and commercial activities from the early 10th century onward. Using these data, there are two competing models we seek to evaluate: first, a relatively abrupt (decadal scale) exodus of people from the core area precipitated by

Significance

Contrasting models exist to explain the movement of urban populations following the 15th-century demise of Angkor. Here we present geoarchaeological data from the urban core of Angkor that indicate a protracted decline in land use intensity during the 14th century rather than an abrupt demographic collapse. These results argue against traditional explanations for the demise of Angkor, which emphasize the role of interventionist foreign powers in forcing collapse, and imply a more complex and protracted transformation. discrete periods of hydroclimatic change and social upheaval in the 14th and 15th centuries, caused by the dependence of the elite on the inflow of surplus agricultural yield from the countryside, and, alternatively, a more gradual (centennial scale) decline in the elite, non-rice-producing population that may be asynchronous with periods of hydroclimatic instability, and which may point to the primacy of exogenous forces and a slower, more complex transformation in the Cambodian state.

Here we interrogate land use-sensitive proxies measured from drill cores of sediment accumulated within the encircling moat of the 12th-century citadel of Angkor Thom. Variations in land use over time, inferred from these proxies, reflect patterns of occupation and abandonment and can be absolutely dated. Centered on the area surrounding the southern gate to Angkor Thom, this area has been a site of occupation for millennia and sits at the center of Angkor's administrative and political operations (see SI Appendix for more detail).

Result

Summary stratigraphic data are plotted against depth in Fig. 2 and are described in SI Appendix. Volume magnetic susceptibility, expressed as a dimensionless ratio value in the international system of units (SI), is low and variable in all cores (ranging from an average of 2.97 ± 3.26 × 10 -6 SI for core AT/01/06/B, to 5.39 ± 4.16 × 10 -6 SI for core AT/01/06/A), reflecting the diamagnetic properties of the primarily siliciclastic or biogenic sediment. Sequence slotting demonstrated strong correlation between the four cores based on their magnetic susceptibility profiles (Delta is 0.15 between AT/01/06/B and AT/01/06/A, and 0.25 between AT/01/06/ B and AT/01/04/B; Rp = 0.999, Rs = 0.974). This indicates that all cores are representative of the stratigraphy at the core site, allowing an analytical focus on one core only. Core AT/01/04/B (70 cm in length) was chosen for this purpose.

Results of radiocarbon analyses are presented in SI Appendix, Table S1. The Hohenheim wood standard (OZI296) returned an age of 2,210 ± 40 14 C y B.P., closely coherent with its radiocarbon age 2,215 ± 5 14 C y B.P., and its weighted average consensus age of 2,232 ± 5 y B.P. Accordingly, contamination of the samples during the extensive pretreatment procedure can be disregarded.

OZI295, taken toward the base of unit 1 (61 cm to 62 cm depth), returned a calibrated age in the first century CE, suggesting that this mottled sandy clay is the substrate into which the moat of Angkor Tom would be cut, or is reworked from same. OZI294 and OZH173 bracket the abrupt boundary between units 2 and 3 (44 cm depth) and return ages of the late 11th and late 12th centuries, respectively, in good agreement with the epigraphic age for the enclosure [START_REF] Coedès | Études cambodgiennes[END_REF]. The change in color, magnetic susceptibility, organic carbon, mineral bulk density, and mineral influx at this boundary (Fig. 2) reflects the establishment of reducing conditions and better preservation and/or greater input of biomass to the sediment. This pattern is consistent with the excavation of temple moats and groundwater fed reservoirs at Angkor [START_REF] Penny | The use of AMS 14 C dating to explore issues of occupation and demise at the medieval city of Angkor, Cambodia[END_REF]. OZH173, taken from the base of unit 3 and thus representing the earliest organic sedimentation with the newly excavated moat, was deposited between 1051 CE and 1264 CE (weighted mean probability of 1197 CE; SI Appendix, Table S1). This coincides closely with the coronation of Jayavarman VII (reign 1182/3 CE to 1220 CE) suggesting, as Coedès (ref. [START_REF] Coedès | Études cambodgiennes[END_REF], p. 89) and Jacques (ref. 26, p. 45) argue, that the building of the Angkor Thom enclosure wall, and the excavation of its moat, was undertaken early in Jayavarman's reign. This is, however, earlier than the date proposed by Gaucher ( 27) for Jayavarman's final remodeling of the moat, and closer in age to the deepening of the moat in Gaucher's (28) "phase 2" period between the 11th century and the end of 12th century.

There are a number of age inversions in the middle of the sequence, and the probability distributions of three of these ages (OZI293, OZI291, and OZH171) are effectively ignored (or "bypassed"; ref. [START_REF] Blaauw | Flexible paleoclimate age-depth models using an autoregressive gamma process[END_REF] in the calculation of the chronological model (SI Appendix, Fig. S1).

Forty-eight pollen and spore samples were analyzed, producing a dataset with 194 variables (taxa). Seventy-seven palynomorph types were unidentified, representing, on average, 1.55% of each sample. The number of individual palynomorphs ranged from a minimum of 19 (53 cm to 54 cm depth) to a maximum of 2,285 (0 cm to 1 cm depth), with a mean of 310 individuals per sample. A total of 14,997 individuals were recorded. A description of the palynological and microcharcoal data is given in SI Appendix. Taxa are expressed as absolute abundances against depth in SI Appendix, Fig. S2, and as variance around the long-term mean, grouped into broad habitat classes, in Fig. 3. Stratigraphically constrained classification identified five sample groups (0 to 16, 17 to 26, 27, 28 to 44, and 48 to 54 cm depth; SI Appendix, Fig. S3).

Principal Component Analysis (PCA) indicates that the first two principal components account for 53% and 30%, respectively, of the variance in the data set (SI Appendix, Fig. S4A). Scree plot, in comparison with a broken stick model (SI Appendix, Fig. S4B), suggests that only the first two components are significant. Variable loading scores indicate that charcoal concentrations (0.72) and arboreal (trees and shrubs) pollen concentrations (0.58) most strongly influence the distribution of sample scores along the second component axis, while pollen from local sources, reflecting the occupation of the moat by swamp vegetation, most strongly influences the distribution of sample scores along the first component axis (herbs, aquatics, and ferns have loading scores of 0.51, 0.57, and 0.52, respectively).

Disturbance and Land Use

The findings described in Result indicate that the moat of Angkor Thom was excavated between the end of the 11th century and the end of the 12th, and indicate a modeled age of 1125 CE. From that time, the surrounding dryland vegetation was characterized by a changing admixture of dry forest and cultivated plants, with no clear dominant taxon. The herbaceous and aquatic assemblage is dominated by grasses and sedges and a relatively limited representation of typical herbaceous swamp (Chenopodiaceae/Amaranthaceae group, which is here dominated by Alternanthera pollen, as well as Ludwigia and Persicaria) and obligate aquatic taxa (Ceratophyllum leaf spines). Regular, probably low-intensity burning is clearly important, with sedimentary charcoal being highly variable around the long-term mean from the early 12th to the late 14th centuries. It is not surprising, then, that indicators of disturbance (possibly Urticaceae/Moraceae but particularly Macaranga) are important in the dryland pollen fallout during this period, and particularly so from the 1270s CE (25 cm depth).

Sedimentation within the moat was dominated by siliciclastic materials from its excavation until the last decades of the 14th century, when organic sediment derived from encroaching swamp vegetation began to dominate. Mineral influx values remained high and variable until the mid/late 13th century. The rate at which mineral sediment accumulated in the moat can be taken as a proxy for the rate of supply, there being no authigenic minerals present in the sediment. The pathways for supply of mineral sediment to the moat include erosion of the surrounding banks (although the banks and causeways are encased in laterite and sandstone steps), deposition of fines from within the city itself through drainage into the southwest corner of the encircling wall, and windblown sediment, primarily from the proximal areas kept free of vegetation due to continual use (such as roadways and market areas, for example), but also small amounts of dust fallout from regional sources. Increased supply of mineral material to depositional sinks around Angkor Thom reflects disturbance and use, either through construction, vegetation removal (directly or through burning), or agriculture.

The relationship between the rate of supply (controlled by land use) and the rate of mineral accumulation in the moat is potentially compromised by the development of local aquatic vegetation which can "isolate" the sediment from mineral input by trapping mineral sediment at the moat margins or on floating vegetation mats. This potentially confounding influence is most likely in the upper 14 cm of the core (stratigraphic unit 5, a modeled age of 1340 CE), and particularly in the upper 6 cm of the core (ca. 1420 CE) where the presence of fibrous peat and an average organic content above 68% by weight (Fig. 2) indicates unequivocally the presence of a floating mat of swamp vegetation at the core site. Mineral influx and organic carbon values are, however, not significantly correlated down core (r 2 = 0.21), nor are inorganic and organic influx values (r 2 = 0.146). If the development of floating vegetation were trapping mineral sediment, then one would expect a strong negative relationship between these variables. This suggests that change in mineral flux to the core site is indeed controlled by the rate of supply and is not influenced by mineral sediment being trapped by local swamp vegetation.

Decomposition of the data by PCA reveals that the second principal component scores (PC2) most strongly reflect variation in burning and dryland vegetation in central Angkor. The plot of these scores against time can, therefore, be used as a proxy for land use intensity from the 12th century (Fig. 3). PC2 scores decline sharply and consistently from the early 14th century (1316 CE or 17 cm depth). During that time period, mineral influx (reflecting soil disturbance) and PC2 scores (reflecting, primarily, fire frequency and vegetation disturbance) are very strongly correlated (r 2 = 0.88; n = 9), but the fact that the correlation between these two variables is much weaker for all samples (r 2 = 0.27; n = 38) suggests a strong and consistent response to changes in land use in central Angkor from the early 14th century. Below 17 cm depth (a modeled age of 1316 CE), the PC1 and PC2 scores are strongly correlated (R 2 = 0.87). Above 17 cm depth, the two axes scores become weakly anticorrelated (R 2 = 0.13), reflecting the increasing importance of swamp vegetation in influencing PC1, which appears to be quite independent of changes in land use intensity suggested by PC2. In fact, it is not until 11 cm depth (ca. 1374 CE) that significant changes in PC1 scores are apparent. This, in turn, suggests that occupation of the moat of Angkor Thom by floating swamp vegetation occurred more than half a century after the first indications for a decline in land use intensity in the dryland pollen and charcoal data. Regardless, it is clear that proxy indicators for fire and dryland vegetation changing in concert with proxies for soil disturbance and occupation from the early 14th century indicate a clear and consistent decrease from that time.

Decline Versus Collapse

Here we present sedimentological and palynological data from central Angkor that reflect changes in land use intensity over time. Prima facie, these data imply that land use intensity in the administrative and commercial core of Angkor declined progressively from the first decades of the 14th century, rather than catastrophically as a result of a demographic "collapse" associated with the Ayutthayan occupation of Angkor one century later. The last known inscription associated with the consecration of a monument of Angkor is dated to 1295 CE, at the Ma _ ngal artha temple within Angkor Thom, and the data presented here suggest that land use began to attenuate around the south gate of Angkor Thom only two decades later. By the end of the 14th century, the southern moat of Angkor Thom was overgrown with vegetation, and management, by implication, had ceased. The hypothesized fragmentation of Angkor's water management network [START_REF] Penny | The demise of Angkor: Systemic vulnerability of urban infrastructure to climatic variations[END_REF] and the climatic variability that likely triggered that fragmentation [START_REF] Buckley | Climate as a contributing factor in the demise of Angkor, Cambodia[END_REF] occurred in this changing administrative and political context. Evidence for a gradual decline in the vibrancy of Angkor's administrative core is consistent with an emerging consensus that multiple factors coalesced to encourage the Cambodian elite to relocate closer to the Mekong and Tonle Sap River [START_REF] Polkinghorne | Reconfiguring kingdoms: The end of Angkor and the emergence of early modern period Cambodia. Angkor: Exploring Cambodia's Sacred City[END_REF]. Not least among these factors was the burgeoning territorial ambitions of neighboring states, better access to profitable maritime trade networks closer to the South China Sea, and an increasingly unwieldy and restrictive urban fabric at Angkor. Our data support the interpretation offered by Evans (23) that the demise of Angkor was characterized by a "gradual demographic decline" (ref. 23, p. 172) rather than the sudden mass movement of large urban populations envisaged by Briggs (1), or the "disappearance" of the residential population implied by Lucero et al. [START_REF] Lucero | From 'collapse' to urban diaspora: The transformation of low-density, dispersed agrarian urbanism[END_REF]. An additional complexity here is that a decline in land use in the urban core presupposes an analogous decline in land use in the much larger agricultural landscape. However, Groslier [START_REF] Groslier | For a geographic history of Cambodia[END_REF] argued against this, suggesting that pre-Angkor period patterns of agricultural land use reasserted themselves after the demise of Angkor's administration, suggesting a deep resilience in the low-density, productive landscape.

Comparative data from secondary cities within Angkor's settlement network [START_REF] Hall | Iron and fire: Geoarchaeological history of a Khmer peripheral centre during the decline of the Angkorian Empire, Cambodia[END_REF][START_REF] Hall | Re-evaluating the occupation history of Koh Ker, Cambodia, during the Angkor period: A palaeo-ecological approach[END_REF][START_REF] Penny | The environmental impact of Cambodia's ancient city of Mahendraparvata (Phnom Kulen)[END_REF] suggest that measurable change in land use intensity was highly asynchronous, akin to complex patterns of collapse and persistence across the Maya territories [START_REF] Bazy | Multiple waves of political disintegration in the Classic Maya collapse: New insights from the excavation of Group D, Ceibal, Guatemala[END_REF]. This While the breakdown of Angkor's hydraulic network, most likely associated with climate variability in the mid-14th and early 15th centuries, represents the end of Angkor as a viable settlement, our data indicate that it was presaged by a protracted demographic decline. This raises the likelihood that the urban elite did not leave Angkor because the infrastructure failed, as has been suggested, but that the infrastructure failed (or was not maintained and repaired) because the urban elites had already left. The absence of Angkor's ruling elite by the end of the 14th century casts a different light over the Ayutthayan occupation of the city from 1431 CE, and over Cambodian narratives that emphasize loss at the hands of interventionist neighboring states.

Materials and Methods

A core site was established ∼390 m west of the southern axial causeway of Angkor Thom, immediately north of the 10th-century brick temple Prasat Bei (Fig. 4), and ∼45 m north of the southern embankment of the moat (13°25′36.95″N, 103°51′24.24″E). A description of the area and its history is provided in SI Appendix. This sampling location places the cores south of the smaller 9th-to 11th-century moat identified by Gaucher [START_REF] Gaucher | Considérations nouvelles sur la fondation d'Angkor Thom. Angkor, naissance d'un mythe[END_REF][START_REF] Gaucher | L'Enceinte d'Angkor Thom: Archéologie d'une forme, chronologie d'une ville. Deux décennies de coopération archéologique franco-cambodgienne a Angkor[END_REF], but within the moat following its final renovation by Jayavarman VII in the 12th century. A coring platform was used to deploy a rope-operated percussion corer [START_REF] Chambers | A rod-less piston corer for lake sediments: An improved, rope-operated percussion corer[END_REF]. Core samples were retained in 60-mm diameter PVC liners. It was necessary to remove the upper ∼20 cm of matted herbaceous vegetation to permit penetration of the core barrel. Four cores were taken from the site (AT/01/04/A, AT/01/04/B, AT/01/06/A, and AT/01/06/B), from adjacent locations (∼1 m apart along an E-W axis).

Volume magnetic susceptibility (κ) was measured on all cores in the field using a Bartington MS2 Meter with a 72-mm diameter MS2C core-scanning loop sensor to determine whether correlation between cores could be made and, therefore, whether a representative sample had been obtained [START_REF] Dearing | Magnetic susceptibility. Environmental Magnetism: A Practical Guide[END_REF]. Correlation between replicate cores was established using a sequence slotting technique [START_REF] Thompson | Sequence slotting for stratigraphic correlation between cores: Theory and practice[END_REF] based on volume magnetic susceptibility data from each core. Calculations were performed with CPLSlot 2.4b [START_REF] Thompson | Core correlation. Tracking Environmental Change Using Lake Sediments[END_REF]. Core liners were split longitudinally in the laboratory. All cores were described [START_REF] Schnurrenberger | Classification of lacustrine sediments based on sedimentary components[END_REF] and color recorded [START_REF] Color | Munsell Soil Color Charts (Gretag Macbeth[END_REF]. The core was subsampled at contiguous 1-cm intervals for loss on ignition (ref. [START_REF] Dean | Determination of carbonate and organic matter in calcareous sediments and sedimentary rocks by loss on ignition; comparison with other methods[END_REF]; LOI 550 × 4 h following ref. [START_REF] Heiri | Loss on ignition as a method for estimating organic and carbonate content in sediments: Reproducibility and comparability of results[END_REF], and palynological analysis [START_REF] Van Der Kaars | A late quaternary palaeoecological record from the Banda Sea, Indonesia: Patterns of vegetation, climate and biomass burning in Indonesia and northern Australia[END_REF]. Pollen and spores were counted at 400 to 1,000 magnification using a Zeiss Axioskop microscope. Taxonomy was based primarily on reference material collected from vouchered plant specimens (National Herbarium of The Netherlands), and nomenclature followed ref. [START_REF] Punt | Glossary of Pollen and Spore Terminology[END_REF]. Charcoal particles within the pollen preparations (therefore 200-to 7-μm fraction) were counted, and their absolute abundance was calculated [START_REF] Stockmarr | Tablets with spores used in absolute pollen analysis[END_REF]. The absolute abundance of pollen grains and spores was calculated in the same manner.

Nine subsamples (×5.48 g wet weight) were taken from core AT/01/04/B for accelerator mass spectrometry radiocarbon dating, using pollen as the target fraction. Pollen was extracted from these samples following ref. [START_REF] Brown | Radiocarbon dating of pollen by accelerator mass spectroscopy[END_REF], with the exception that the samples were initially sieved at 63 μm rather than 180 μm, and no other sieving was conducted. A radiocarbon standard (0.367 g dry weight of Hohenheim oak; FIRI code H; consensus value 2,232 ± 5 y B.P.; ref. [START_REF] Boaretto | Summary findings of the fourth international radiocarbon intercomparison (FIRI) (1998-2001)[END_REF]) was pretreated with the sediment samples and dated so as to identify any laboratorybased contamination. Radiocarbon ages were calibrated using Calib 7.10 (IntCal13; ref. [START_REF] Reimer | IntCal13 and Marine13 radiocarbon age calibration curves 0-50,000 years cal BP[END_REF], and a chronological model was developed, using Bacon 2.2 [START_REF] Blaauw | Flexible paleoclimate age-depth models using an autoregressive gamma process[END_REF].

Stratigraphically constrained cluster analysis was used to identify points of significant change in the data and was performed with an incremental sumof-squares method (53) on the squared Euclidian distances of absolute pollen abundances using the Rioja package (54) in R 3.3.1 [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF]. Comparison of residual variance in the data with a "broken stick" model is used to determine the number of "significant" group boundaries within the pollen sequence [START_REF] Bennett | Determination of the number of zones in a biostratigraphical sequence[END_REF]. PCA was used to decompose absolute pollen and charcoal data into four components. All variables were normalized using division by their SD. All calculations were performed using PAST Software v. 3.13 [START_REF] Hammer | PAST-palaeontological statistics, ver. 1.89[END_REF].

Fig. 1 .

 1 Fig. 1. Location map of Angkor, and the location of sites mentioned in the text.

Fig. 2 .

 2 Fig. 2. Stratigraphic and sedimentological data for core AT/01/04/B, plotted against depth. Stratigraphic units are identified based on changes in color and texture.

3 ∑ 3 ∑Fig. 3 .

 333 Fig.3. Summary stratigraphic, microbotanical, and numerical results, plotted around the long-term mean value for each variable, against modeled age and depth.

Fig. 4 .

 4 Fig. 4. Lidar-based topographic map of central Angkor, showing the location of the core site in relation to features described in the text and the topographic evidence for intensive occupation both within and surrounding the moat and enclosure wall of Angkor Thom.

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ACKNOWLEDGMENTS. We acknowledge the support and collaboration of the Authority for the Protection and Management of Angkor and the Region of Siem Reap (APSARA National Authority), Cambodia. This work was funded by the Australian Research Council's Discovery Projects Scheme Grant DP170102574, Discovery Early Career Researcher Award DE150100756, the European Research Council under the European Union's Horizon 2020 research and innovation programme Grant Agreement 639828, and the Australian Nuclear Science and Technology Organization Award AINGRA05134.


Daniel Mariuta

Lucien Baldas

Jürgen J Brander

Katja Haas-Santo

Stéphane Le Calvé

Stéphane Colin

Pascale Magaud

Christine Barrot-Lattes

µFLU-NEGF18-147 RECENT DEVELOPMENTS IN MINIATURIZED OPTICAL SYSTEMS FOR CONTINUOUS FLUORESCENCE DETECTION IN LIQUID FLOWS

Keywords: Fluorescence, miniaturization, in-time detection, high sensitivity, integration strategies, commercialization

Miniaturization of continuous fluorescence detection is a challenging task due to the multiple and sensitive parameters intervening in the process. By analyzing fluorescence sensing architectures proposed during the last two years, this work has the goal to identify some trends in the process of fluorescence miniaturization for in-time liquid detection. A lack of postulated strategies regarding the miniaturization process was observed and this review tries to answer partially to this need. The identified integration strategies excel in fulfilling partially the desired functions of a fully autonomous miniaturized detector and further research is needed in order to develop sensing micro-system being capable to step outside of the lab world.

Introduction

Today, miniaturized devices follow a straightforward path, and they have come closer and closer to a goal which has been desired for a long time: commercialization of devices with reduced geometrical dimensions and small reagent consumption, being able to perform ultra-high precision analysis to replace the bulky and expensive devices used up to now in many fields such as medicine, biology, chemistry and environmental monitoring. The success in the process of analysis miniaturization will be a historical achievement which will come with a multitude of advantages for the humankind. The costs of analysis which now are expensive from financial, time and logistical point of view would dramatically decrease.

One of the possible analysis methods for these devices is based on fluorescence detection. There are some recent attempts to develop on-chip detection systems, whose contributions and successes maintain the hope that in the near future these devices will cross the border of commercialization. A possible reason for not having yet merchandisable on-chip fluorescence sensing platforms is the lack of postulated modular integration strategies of fluorescence measurement chain in order to further be mastered and improved iteratively. Within the present work, the novel fluorescence sensing platforms from the last two years have been analyzed for identifying some current on-chip integration strategies of the fluorescence measurement components used for developing ultra-portable, compact and very sensitive detection devices. An ideal integration strategy has to provide automatic, low cost, multiple analysis, fast response time and compact on-chip sensing platform.

Literature review

1. Printed board circuits (PBC) used as mechanical and electrical support for light emitting sources and/or photon detectors represents a strategy permitting a high degree of modularity and a parallel layering distribution of the detector device functions. This strategy was used for fluorescence sensing platforms proposed by Babikian et al. [START_REF] Babikian | A Digital Signal Processing-Assisted Microfluidic PCB for On-Chip Fluorescence Detection[END_REF] and Shin et al., [START_REF] Shin | A portable fluorescent sensing system using multiple LEDs[END_REF]. Moreover, both proposed heterogeneous integration strategies/architectures have the potential to be broadly applicable for multiple analysis. The on-chip fluorescence detection device proposed by Babikian et al. [START_REF] Babikian | A Digital Signal Processing-Assisted Microfluidic PCB for On-Chip Fluorescence Detection[END_REF] integrates optical, electronic, electro-mechanical, and fluidic components on the same chip (figure 1, left). Four well established technologies (printed circuit board, microelectronics, isotachophoresis and digital signal processing) were integrated in order to provide a device with the form factor of a credit card. This device avoids using bulky high-quality components and filters, being classified as a lensless fluorescence detection system. The detection sensitivity reached is 10 nM for measuring the concentration of a fluorescein within a microchannel of 500µm×100µm. In the cited work it was demonstrated that PCB can support heterogeneous and 3-D integration within a microfluidic chip which is also important from a manufacturing point of view. Shin et al. [START_REF] Shin | A portable fluorescent sensing system using multiple LEDs[END_REF] developed a portable fluorescent sensor platform which employs multiple excitation sources (figure 1, right). The light sources, having different wavelengths, are turned on or off sequentially to stimulate different fluorescent molecules developing in this way a portable multi-analytes fluorescent system for multiple target detection. The light emitting diodes are controlled by an integrated electronic circuit and a microcontroller on board and detection is ensured by a highly sensitive silicon photomultiplier. The disposability of the microfluidic part is a very important feature of this device. 2. Ngernsutivorakul et al. [START_REF] Ngernsutivorakul | Design and microfabrication of a miniature fiber optic probe with integrated lenses and mirrors for Raman and fluorescence measurements[END_REF] proposed a strategy which integrates lenses, filtering networks and optical fibers into an PDMS probe (figure 2). This strategy might enable a new route which coupled with the progress registered in the field of microfabrication could replace the complex and critical alignment of bulky and expensive optical components, which were drastically limiting the miniaturization process. Polydimethylsiloxane (PDMS) was used to create 0.5 mm thick and 1 mm wide compact probes into which pre-aligned mirrors, lenses and two fiber optic guides are incorporated. The incorporation of the filters at the tip of the probe would diminish the background noise and improve the sensitivity. This probe is connected with the chip in order to facilitate the excitation in the detection chamber and collection of the fluorescence as well. Further improvements are possible according to the authors by using more compact light sources and detectors. The efficiency was tested for different capillary dimensions and for different applications and the limit of detection was found being comparable with the other micro devices using integrated optics and optical fibers (100 nM).

3. Organic layers used as light sources and photon detectors is not a new strategy in the miniaturization process of fluorescence detection, but some recent works (Shu et al. [START_REF] Shu | Highly sensitive on-chip fluorescence sensor with integrated fully solution processed organic light sources and detectors[END_REF], Jahns et al. [START_REF] Jahns | Organic optoelectronics for lab-on-chip fluorescence detection[END_REF]) reported considerable achievements. Shu et al. [START_REF] Shu | Highly sensitive on-chip fluorescence sensor with integrated fully solution processed organic light sources and detectors[END_REF] introduced and tested for the first time a fluorescence light detector combining both an organic electrochemical cell (OLEC) and an organic photodiode (OPD) Reprinted from [START_REF] Ngernsutivorakul | Design and microfabrication of a miniature fiber optic probe with integrated lenses and mirrors for Raman and fluorescence measurements[END_REF] within one microchip (figure 3). Organic electronics introduce some unbeatable advantages such as direct onchip integration, easy emission and detection wavelength tuning and compatibility with flexible substrates. The proposed sensor is able to measure fluorescein concentrations lower than 1 µM. Furthermore, fully solution processing and vacuum free fabrication procedures used for fabrication of the OLEC and OPD, easy tuning of the excitation light color enable another promising integration strategy for low-cost, disposable, point of care applications [START_REF] Shu | Highly sensitive on-chip fluorescence sensor with integrated fully solution processed organic light sources and detectors[END_REF]. 4. Guduru et al. [START_REF] Guduru | Highly integrated lab-on-a-chip for fluorescence detection[END_REF] proposed an on-chip configuration which integrates in the same glass substrate the microfluidic network, the excitation source, the filtering and the light collection elements (figure 4). The strategy proposed by the authors involves the implementation of one dimensional photonic crystal layer working similarly as a Bragg mirror for a selective selection of the wavelengths and the fluorescence collection is performed by a Binary Fresnel Lens (BFL) which is placed on top of the photonic crystal. For the proposed configuration, the photonic crystal, which has the role of a filter, was fabricated on top of the layer containing the microchannel network. The measurement efficiency was not very high due to defects in the silica film, non-total transparency of the ablated regions and irregularities in the Fresnel zones. The authors mentioned that the optical quality of the photonic crystal could be improved using thermal treatment after the deposition process. Higher manufacturing precision would increase the device efficiency.

Conclusion

During the last years, a considerable effort has been conducted in order to propose viable solutions for multiple target, low cost and sensitive on-chip fluorescence detection. It has been found a lack of reviews in the literature to summarize and point out the new achievements regarding the light emitting sources, waveguides, focusing optics, miniaturized photon detectors and strategies to couple all these into a cheap, easy to use, compact micro-detection system.

Printed board circuits allow development of a modular architecture and the potential for a very compact, reproducible, easy to use multi target analyzers. Further research should be focused on developing methods to efficiently couple the excitation/emission light transfer in order to maximize the signal to noise ratio and avoid direct illumination of the photon detector. The strategy proposing the integration of the filtering, lenses and optical fiber into a micro fabricated PDMS probes has the advantage of drastically miniaturizing the optical elements of the measurement process, but is not suitable for multiple target analysis. Organic layers used as light sources and photon detectors is the most promising integration strategy from the point of view of automatization, compactness, low cost fabrication and ease of use. Long term functionality of the organic layers has to be further improved to maximize the potential for a real autonomous and merchandisable sensing platform. The forth strategy identified within this review, proposes a layering filtration method based on a 1-D photonic crystal and an efficiently fluorescence collection using binary Fresnel lenses, all integrated within two thin layers on a chip. This strategy could be improved in order to increase the ease of use. For example, avoiding the use of optical fiber for excitation light transfer is one of the possibilities, considering the complexity of light alignment issues in this case.

Figure 1 :

 1 Figure 1: Left -Cross-sectional diagram of the microfluidic PCB system, reprinted from [1]. Right -Parallel layeringintegration strategy proposed in[START_REF] Shin | A portable fluorescent sensing system using multiple LEDs[END_REF]

Figure 2 :

 2 Figure 2: a. Top view of the probe positioned on a PDMS chip, b. Image on the probe on the PDMS chip, c. Front view of the probe on a chip d. Side-view of the probe on a chip and the experimental set-up for fluorescence detection.Reprinted from[START_REF] Ngernsutivorakul | Design and microfabrication of a miniature fiber optic probe with integrated lenses and mirrors for Raman and fluorescence measurements[END_REF]

Figure 3 :

 3 Figure 3: a. fully solution processed OPD; b. first linear polarization filter oriented at 0 degree; c. glass microfluidic chip; d. second linear polarization filter oriented at 90 degree; e. fully solution processed blue OLEC. Reprinted from [4].

Figure 4 :

 4 Figure 4: Microfluidic chip with the Fresnel lens, composed of a fluidic channel, an excitation fiber perpendicular to it and a filtering and collection part on the top surface. Reprinted from[START_REF] Guduru | Highly integrated lab-on-a-chip for fluorescence detection[END_REF]

Acknowledgements

This project has received funding from the European Union's Framework Programme for Research and Innovation Horizon 2020 (2014-2020) under the Marie Sklodowska-Curie Grant Agreement No. 643095.